Abstract: Life, as a parasite, evolved a mind/brain over 3,000 million years by creating a new space using multicellular organisms and a Mathematics of the Mind that is an improvement on the measurement/entanglement of a probability space to enhance its survival/success rate. Three fundamental quests of the dimensions of a probability space define our universe, the conservation of energy, the creation of space creates energy and the speed of all photons is constant in vacuo and these explain the strange effects of the theory of relativity. General mathematics is open-ended and supplies answers of context as well as concept to all disciplines of knowledge by expanding the existing mathematics that is based on a counting space and the four axioms of the mind/brain. Given that all mathematics are ‘hand-maidens’, general mathematics extends the range to include all disciplines and examples are given of solutions of long-standing enigmas. In particular, Plato’s political system is used as an example of context to show how general mathematics can solve the world’s problems, if we so desire, and further, allows us to move Survival of the Fittest into a higher level of Survival of the Best using the concept of the ‘Second Coming’.

 

Preamble: a great deal of this theory will appear simple because we are already using it in a top-down fashion, but I will present it bottom-up and new interpretations of concepts of science that have been used for centuries will appear, as will logical solutions to enigmas that have eluded science. The extent and ease with which a theory integrates with us is a measure of the soundness of the theory with respect to us as well as predictions based on that theory. Also, the expansion/questing of a class/organization of derivations that we know as mathematics from the counting space (a+b) has been expanded and developed over thousands of years, but the recent additions of the Mandelbrot set z2+c, the Julia set and the Fatou set have produced unusual patterns, but taken together, they suggest a new branch of mathematics/organization that uses four axioms (forward-planning, questing, relevance and elegance) to link the mind/brain into the mathematics/organization. In particular, this sequence culminates in questing a measuring space (a+b)=1 and space-time that, I believe, generates a universe in a probability space. and is the way that our universe naturally evolved and as Life evolved, forward planning, for the predator/prey relationship and sexual attraction formed the basis of evolution through Survival of the Fittest.

 

What, to my mind, is general mathematics? It is the method of solving every possible problem that can ever exist, now or in the future, and it does this by using the dimensions of a probability space and that ties it into the thinking of Life that has evolved as a parasite within the universe. Simply put, general mathematics is the mathematics of concepts and the four axioms of Life that we, as parasites, have built on the measurement/entanglement of our probability universe. Mathematics is woefully deficient because it neglects context and concentrates on concepts, which is not surprising because we invented mathematics to do what we wanted/needed, and that was count sheep etc. Mathematics is a special case of general mathematics and need not change, but the addition of context and entanglement means that social problems can be addressed and the methods given, should/could solve the world’s problems as well as to redefine our evolution.

 

For completeness, general mathematics is necessarily simple and is composed of two parts, the mathematics of concepts that presents the concepts and the contexts between them because the fifth dimension says that concept and context are orthogonal/independent and so, both parts must be considered, as in Cartesian coordinates. The four axioms I will now call ‘search axioms’ because there must be forward-planning to initiate the search, questing is (total) searching, relevance is comparing the search elements and elegance is the selection.

 

The elegance of this derivation is obvious in its simplicity, but, I do wish to point out that it took me years to derive the mathematics of concepts, only to find it obvious within the fifth dimension and it took months to derive the four search axioms through Life, the space and the fifth dimension, only to find that they are obvious from common sense, when you know what to look for. This, I believe, shows that common sense is derived from the ‘shards’/pieces of the fundamental organization behind the universe.

 

Firstly, does mathematics exist? Secondly, there is the ‘mathematics’ of the physical space that we call the universe, and thirdly there is the mathematics of ourselves and the other members of Life that are parasitic. There can be no doubt that Life is a parasite because it evolved to use the host (universe) for its own ends, and further, we contain numerous parasites within us, some symbiotic, for example, mitochondria, and some not, and ‘your body contains about 23,000 human genes, in contrast to over 1 million bacterial genes.’ (Super Genes, Deepak Chopra and Rudolph E. Tanzi, p 76). Fourthly, there is the mathematics that we have not yet discovered.

 

I believe that our universe is a probability of existence space and a probability space has the dimensions of x, y, z, time passing and (a+b+c …)=1 for measurement of energy/probability at points a, b, c … and further, in chapter 84, Godel’s Incompleteness theorems were discussed in the context of the constant speed of light and that the usual definition of mathematics makes mathematics necessarily incomplete. Hence, firstly, I suggest that the general mathematics should have no separate existence, apart from convenience, and should be incorporated into each and every discipline because, it will be shown that mathematics is a special case of the mathematics of concepts that is applicable and appropriate to everything because it is written in the fifth dimension, (a+b)=1, for simplicity, where a and b are measurement/observers.

 

Secondly, mathematics has taken a counting space (a+b) that grew from the need to count livestock etc. and the four axioms that link the mind/brain to the counting space to make a (not very good) approximation to the measuring space (a+b)=1 that is the fifth dimension of a probability space. The reality of the universe is an all-encompassing entanglement that goes with the necessity of continual measurement of energy, but the biocomputer of evolution over 3,000 million years has built on the physical ‘bones’ of entanglement, and this innovation, I call the Mathematics of the Mind.

 

Concerning the four axioms, quoted above, from chapter 81: ‘The Math Book, (by Clifford A. Pickover, p 284) gives the five Peano Axioms as a basis of arithmetic, and certain things appeared to be missing, such as the mind/brain to determine elegance of content, forward planning (dimension 6), the measurement of each numeral (questing) and the relationship between numerals (relevance)’.

 

Further, ‘If we unfold (a+b)=1 in a probability space, as above, including Life, we get:

concept/forward-planning/quest/relevance/beauty/context.

 

If we unfold (a+b)=1 in a probability space, as above, excluding Life, we get:

measurement/quest/relevance/entanglement.’

 

Notice that forward-planning is a dimension specific to Life and necessary for the predator/prey basis of iteration and the four axioms are immediately obvious in the above.

 

It took me years to derive the Mathematics of the Mind because it was so subtle in its effect, so much so that I often wondered if there was a discernable effect. I say this because it is the questing that is important and that produces a universe and more quests evolve as the search widens or contracts within (a +/and b)=1. Notice that questing is an all-encompassing term that includes the effects of quantum mechanics, business, relationships, mathematics etc. This notion of questing and relevance is fundamental to a probability space and underlies the mathematics of concepts where everything is related/entangled. Contracting to (a+b) leads to the Golden ratio and concepts of beauty/elegance.

 

Thirdly, in a probability space, (a+b)=1 is not a mathematics, it is measurement/entanglement that quests every point so that the total sum is unity and always remains unity and it is also not a logic, though it is similar, and it will be seen below that it is an organization. This state of affairs requires that every point be quested continually and all the points be adjusted so that the total remains unity, and in the case of our universe, this is the law of conservation of energy (when set to zero). The energy of the Big-Bang/Big-Whoosh is zero, but splits/quests into a positive (all energy except gravity) and a negative (gravity) portion to create the expanding universe that makes a place in which Life can live.

 

Contrast this simple organization of energy to the common notion that the Big Bang creates all the energy instantly and the momentum creates the expanding universe and it is obvious that there are no organizational constraints limiting it, and so the current theory is logically wrong when we ask the question ‘how big?’. The Big Whoosh is organizationally sensible/accountable and contains the current concept of inflation, not as some mysterious happening, but as the basic property of the expansion-of-space/creation-of-energy. It will be shown below that energy to space ratio is constant for all time, so, increased space creates energy in two forms, energy (positive) and potential (negative) that we call gravity. This is an important point that seems to have been missed, that gravity is a potential energy wanting/enabling us to fall to the centre of the earth. Presumably the acceleration due to gravity, as a concept, was more useful than the energy context, but, I believe that some of Newton’s work is overly simplistic and is due for a revamp.

 

The complete picture is given, if we, from chapter 81, ‘unfold (a+b)=1, where unfolding is following the questing [of quantum mechanics, evolution, business etc.]. The fifth dimension (a+b)=1, in this simple form produces four absolutes/solutions (ignoring, for the moment, the fact that the speed of light is an absolute and must be constant):

(a) measurement/entanglement that are local physical and independent/orthogonal (a+b)=1 [classical local action and reaction of matter that provides expansion of the universe, reflection, diffraction of light and water waves],

(b) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b)=1 [conservation of (zero) energy across the universe, gravity, creation of space/mass/energy/time through the Lorentz contraction],

(c) measurement/entanglement that are local physical and independent/orthogonal, (a+b) [local/personal appreciation], and

(d) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b) [universal/reality-wide appreciation]’

 

‘Note that (a) and (b) are the physical structure of the universe [described in many earlier chapters] and (c) and (d) were derived in chapter 78 resulting from the ratio of an interval [Golden ratio] that has been reported to produce a feeling that is used, I believe, by Life to compare contentment/elegance/beauty in both a personal and a reality-wide comparison that is behind the important sexual selection as a major driver in evolution.’

 

‘For completeness, I want to foreshadow another quest that is the “orderliness” of (a+b)=1 that embodies a general mathematic/organization that lies behind logic/mathematics. In a similar way that proverbs are a higher level of thought, everyday logic is, I believe, the reverse, and is our view of, or the mental “breakdown” of organization.’

 

Concepts are distinct, but context requires different viewpoints, so, the above, to put it simply, I believe, shows that (a+b)=1 is a mathematic leading to an organization that we see as part of our reality as ‘shards’/parts of the organization that we need to live within and we call that ‘everyday’ logic. However, (a+b)=1 contains measurement/entanglement that quests to produce a universe naturally, that expands through inflation (continually, but at different rates) and there are two steps missing, part A, questing the dimensions and part B, Life’s parasitization of the universe, as was discussed above. The concept of the universe occurring ‘naturally’ brings to mind a conservative field, which it is, and all processes work in reverse if time passing is made negative and the universe shrinks and disappears because inflation works backward. Contrast the simplicity of the Big Whoosh with the current theory of the Big Bang and the sudden appearance of huge amounts of energy/momentum.

 

Part A, from chapter 84, ‘”the Lorentz contraction is a means of preventing chaos occurring, in a physical and logical sense, because, as the speed of a non-zero mass particle approaches the speed of light, the dimensions change proportionately so that it never reaches that speed. The dimensions are fundamental to the space that they describe and from chapter 83, ‘if we quest the dimensions, we find three constant relationships: energy to time for all space, energy to space for all time and space to time for all energies because all of the dimensions change by the Lorentz contraction. The first appears to suggest conservation of energy over time, the second that space has a set energy and that the creation of space creates energy, as is commonly thought, and could be the mechanism that forces matter/galaxies with its negative potential energy to move outwards as space is created. The third relationship shows that all (free) energy, in the form of photons must have a constant speed, relative to the measurer, and this is the Michelson-Morley result (for all motions).’ These relationships are necessary quests in a measurement space and the second relationship, that space has a set energy and that the creation of space creates energy suggests a reason for dark energy to exist.” ‘Dark energy is everywhere – a property of space itself – whereas dark matter occurs in blobs in the vicinity of galaxies.’ (Star – Craving Mad, Fred Watson, p 256)

 

Part B, Life is important because we are telling the story and in a measuring space, we evolved an ability to tune into the physical world as a parasite must do and use the properties of the space for our own end, for example, a sense of smell was probably one of the first senses and provides a direction to hunt/eat, and the two hemispheres of the brain attest to this. Later, the Cambrian enabled, I believe, multicellular organisms to evolve larger brains coupled with the efficient lensed eyes and planning for predator and prey situations to create a new type of space using concept/context. Given that 3,000 million years of evolution (iterations) based on a multitude of attempts, the resultant evolution of the brain should be based on the best possible method of operation.  This is indeed the case and the best possible method is general mathematics that is composed of the mathematics of concepts and the four axioms.

 

Now, I originally called the questing of (a+b)=1 to be the Mathematics of the Mind that uses concepts and context to answer the (heritable) question of ‘is that a lion?’ as well as the equally important ‘is it far enough away to ignore?’. The physical (a+b)=1 is measurement/entanglement locally and (a and b)=1 is universe wide, but Life has changed a and b to be concept/context in a local reality. In other words, Life has taken the physical (a+b)=1 and changed it into something completely different! It appears that the organization/relation (a+b)=1 is the important part, not so much a and b, and that is as we would expect in a probability space, and this leads to the mathematics of concepts/context, including concepts and contexts that we cannot (at present) comprehend.

 

Fourthly, this answers the question of the future of a general mathematics, in that anything that is evolved/invented can be handled because general mathematics is written in the dimensions and Life can quest the relationship (a+b)=1 in all its permutations as is mentioned above. Concepts that are alien to us are common in nature, such as echo-location in bats, electromagnetic senses in sharks and platypuses, ultraviolet sight in bees and probably a lot more if we looked for them.

 

Specific examples for ourselves are (a+b) gives the Golden ratio (chapter 78), (a and b)=1 gives gravity (discussed above), (a+b)=1 gives diffraction (chapter 77), Plato’s political system (chapter 67) etc. The enigma of the Michelson-Morley experiment, where the measurement of the speed of light is the same for all observers indicates that a probability space is appropriate and it was this particular enigma that prompted this search/endeavour.

 

Another example, from chapter 84 is the reason ‘that particles, light etc. unfailingly travel in a straight line, given no entanglement, is that, if they did not, they would cause a logical singularity in the conservation of energy equation (a and b)=1 because it would have multiple solutions. In other words, a particle does not travel in a straight line because of momentum, but because momentum/energy is accountable in a measuring space, and it can be restated, again, that travel in a straight line is not only a physical property, but also a logical property.’

 

It would be nice to simplify motion to fit Newton’s laws of motion, but there is an entanglement across the universe that is an intimate part of a probability space and cannot be ‘glossed’ over, and only a universe-wide function, such as the conservation of energy should be used to show that realistically, a particle is acted-upon/entangled with every energy source in the universe. This is the elegant simplicity of the context of the complex and by all means use the simple (concept) but you must also satisfy the complex (context).

 

I would like to offer a further example that simplicity is the over-riding criterion, but sometimes a decision complicates simplicity. From above, ‘the Lorentz contraction is a means of preventing chaos occurring, in a physical and logical sense, because, as the speed of a non-zero mass particle approaches the speed of light, the dimensions change proportionately so that it never reaches that speed.’ I have often wondered why all of the effects, energy/mass, length and time passing, change by the same amount? Following the line of thought, above, it seems logical to me that it is simpler to change all of the dimensions by the same amount and it is more complicated to decide on one particular dimension to change. It would then seem that Occam’s razor is a fundamental/over-riding criteria that is a quest of the requirement of zero energy and it means that the postulate of the law of conservation of energy is simply a realization of the splitting of nothing into positive and negative energy and it is accountable only in a lowest state.

 

Whilst on this subject, the dimensions can be written as energy, x, y, z and time passing, or as (a+b)=1, x, y, z and time passing, because everything is energy from the Big-Bang/Big-Whoosh and only ‘exists’ if it is measured by an observer/iteration. Thus the dimensions are:

 

energy is equivalent to (a+b)=1, x, y, z and time passing

 

and each of these is related through the Lorentz contraction and this explains why energy, length, time and the relationship of measurement/observer all vary together to keep the total energy at zero. This answers another enigma, why length, time and mass change as the speed of light is approached by a particle with rest-mass. Everything is energy and all states of energy are equivalent, including mass, so E=mc2 is an equivalence relationship not an equation and all types of energy are states of energy. A small digression that contributes to understanding this might be appropriate.

 

‘Bookkeeping now has the potential to make or break the planet. Because accounting reduces everything to its monetary value, it has allowed us to value least that apparently free source of life itself: the planet…. “But there may be one last hope for life on earth: accountants.”’ (Double Entry: How the Merchants of Venice Created Modern Finance, Jane Gleeson-White) The four axioms include double entry bookkeeping because they were derived from the dimensions and show the accounting of energy, and a system must be used that accounts for the positive and the negative that must be the same because of (a+b+c …)=0, where a, b, c, … are energies, and hence the principle of least action for the total of energy must always be the same and that requires a minimum.

 

In other words, everything is energy and every portion of energy has the same attraction of gravity because of the book-keeping. This is not an observation that should be treated lightly because, it is not logic, as we tend to call it, it is the basic organization behind the questing of the universe. This ‘book-keeping’ is the ‘power’, I believe, behind the natural formation of universes in probability spaces and is a double entry of gravity/energy and energy/energy and that accounting is the reason why the principle of least action appears to be a physical law.

 

From chapter 84, ‘the principle of least action … says, essentially, that things happen in a way that requires least effort. So, a beam of light will travel in a straight line because that is the shortest path between two points…. Quantum theory, which describes how things work on a subatomic scale, seems to be the one area where the principle of least action does not apply. Quantum objects can be in two states at once, and can take multiple paths when travelling from one place to another. Richard Feynman went so far as to suggest that a quantum particle will simultaneously take every possible path when making a journey.’ (30 Second Theories, editor Paul Parsons, p16).

 

‘The above paragraph describes the development of physics from Newton’s first law of motion to quantum mechanics, and by implication, everything in between is also flawed, based on postulates that are unprovable. How do you prove that a particle travels in a straight line when entanglement is universe-wide and simplifications need to be treated through the mathematics of concepts? However, this is a simplification that follows from Newton’s simple laws of motion, and diffraction proves that light does not travel in a straight line, but is acted upon by the short-range entanglement (a+b)=1,see chapter 77.’

 

Similarly, from chapter 84 ‘”quantum mechanics may be an exception to the principle of least action” cannot be true because the questing in a measurement space leads to the universe going about its measurement business of assessing every possibility, as it has to in a measuring space, so that the law of conservation of energy remains at zero. Feynman’s approach is just this, a statement of the property of a measurement space and Feynman’s approach works because that is how a probability space works.’

 

‘”There is a delightful story of Eddington being congratulated by a colleague for being one of only three people in the world who understood relativity. When Eddington paused, and his colleague commented that there was really no need to be so modest about it, the Cambridge astronomer replied that, no, he was just trying to think who the third person might be.” (Star – Craving Mad, Fred Watson, p 202) As one that has suffered under the paradoxes of modern-day physics, I hope that I have erased them and made physics more understandable.’  I have included this story because it shows that looking top-down, using a mathematics based on counting sheep can lead to difficulties. The universe is simple, where six dimensions quest Life and a universe and every explanation is simple from the bottom-up.

 

It has been said that ‘mathematics is the hand-maiden to the sciences’, but, it could be that mathematics is hampering the sciences, and even worse, mathematics has done little for the social sciences. This general mathematics brings context onto an equal footing with concept and fits with the mathematics of concepts that is needed to manipulate the concepts found in the social sciences. The basic problem that the world is facing is entanglement/context between parties/population/groups from around the world and the sharing of common resources.

 

General mathematics will provide an answer, but we have to set out the problem and a quick and easy description of the use of the mathematics of concepts from chapter 75 is ‘if we take the Cartesian system of the X-Y plane, we can say that some point is composed of two independent variables (x, y), and the mathematics of concepts can be handled similarly, bearing in mind that an iteration or mind/brain initiates a measurement and we are dealing with world O and world P. A little foreshadowing will make it easier to understand, that world P is a probability space and only has iteration, whereas Life has made world O into a “determinate”/non-entanglement world because of the necessity of creating a reality as part of questing/Survival-of-the-Fittest.’

 

Further, ‘taking the easy case of world P, questing is: X-Y axes with the concepts to be examined spread equally spaced along the X axis, and a curve/^ is drawn between each concept and every other concept with a height ^ equal to its probability and the sum of all the “heights” is 1. This comes straight from the entanglement/measurement of the probabilities in a probability space. To move it into world O in order to automate or use a mind/brain, move the concepts and the ^ to make a “normal” curve and read off the best concepts and their context. If this looks simple, ask yourself “why should it be complicated?”, when the universe requires only 5 dimensions and life six dimensions.’

 

Notice that this use of the mathematics of concepts assumes/needs, just as mathematics does, the use of the four axioms: elegance, forward-planning, questing and relevance as the basis of context/organization that is used by the mind in assigning the ‘numbers’/importance to the context. Notice also, that the context has to be numericalized and that shows that context is crucial to decisions and yet, that is precisely the part that we tend to ignore/under-use in day-to-day decisions.

 

I want to repeat the previous paragraph because it is crucial to the uptake and use of a mathematics of concept/context because we can all list the world’s problems, such as over-population, over-fishing, mass extinction, pollution and so on for any number of concepts. The solution lies in the context because the context shows/points-out those people that have their own agenda and how that agenda is often not in the general interest. This is the Problem of the Commons (concept) where every person extracts as much as possible/practical from the (free) common without safeguarding/husbanding its resources. The solution (context) is in the knowledge of who is misusing the common and doing something about it.

 

Even worse are the political parties that try to manipulate the (so called) democratic vote to their own ends and a quick description of Plato’s political system (chapter 67) shows that there are three orthogonalities/independent groups that move the motivation/setting-of-policy from the politicians to the universities and leave the politicians to ‘strut the stage’. The universities are the repositories of knowledge/expertise and the voters make the choices with the media transmitting the choices whilst the politicians have the important job of ‘oiling’/contexting/bringing-together everyone. Notice that the democracy of Plato’s time was not a compulsory vote and only interested parties voted. This is important because a compulsory vote skews the result unless everyone is an informed voter. This very important point of every voter being informed dictates that universities provide a set of unbiased informed choices for voters to choose from, and they are noticeably absent from current elections. This is a case-in-point of universities using a formal general mathematics, that all agree on, to provide guidance to voters.

 

From chapter 67,  ‘because this is so new/different/important, I thought that I would put in an example to show how effective this method can be in guiding/controlling governments through the reporting of government policies by the universities through the media to the voters with virtue as the aim. Most of the countries use the capitalist system with some degree of democracy because it is (probably) considered the most “efficient”, but using Plato’s idea of involving the universities as “policy generators”, turns a two-way into a three-way organization, and the “flip” might happen (virtually) “over-night”. Countries could easily incorporate Plato’s idea because it is simple to install, (practically) costless and much more efficient and “steals a march” on any country not using it.’ In a ‘nutshell’, these are three concepts (voters, politicians and universities) with the media providing/transmitting the context between the three groups and politicians’ careers are not wasted/curtailed pursuing necessary, but unpopular views.

 

I would like to offer a final example from the book, Super Genes, Deepak Chopra and Rudolph E. Tanzi, that presents the Super Genes that consist of a combination of genome, epigenetics and the microbiome that is the bacterial flora living on, and in the body. ‘Human beings could be the first creatures in the history of life on Earth to self-direct where their evolution is going. If so, the super genome becomes the key to everyone’s future …. To get there, however, three major changes would need to be established in our understanding of evolution, and each of them would topple a pillar of Darwinian theory.’

 

‘First, evolution must be driven by more than random chance.

Second, evolution has to drastically speed up, able to bring changes not in hundreds of thousands and millions of years, but in a single generation.

Third, evolution must be self-organizing and thus mindful, allowing for the influence of choice making, learning, and experience. These are serious challenges to the status quo. Ordinarily the argument would take place within the small circle of professional evolutionists. But the goal is so important to everyone’s life that we want to bring you into the privileged circle.’ (p 253) Notice the author’s use of the italic for ‘mindful’ and self-organizing suggests that a plan must be in the collective minds of the population and where does that plan come from? I suggest general mathematics and in particular, the organization that is Plato’s politics.

 

This quotation is the concept of what is needed for the future, viewed from the point of view of genetics. Genome, epigenetics and microbiome could contribute, but the concept calls for a context, and genome, epigenetics and microbiome are basically physical and not logical. The means of effecting these three conditions is to abandon iteration (Survival of the Fittest) and use general mathematics to supply context and use, what I call, the Survival of the Best that is a means of using context to change society to fit into the mould that is required by the experts/universities to make the changes to society. This requires general mathematics, and more specifically, the mathematics of concepts and the four axioms of the mind/brain. As with Plato’s politics above, context can only be applied by the informed, but, unlike Plato’s ideas of philosopher’s governing the state, the voting public would still make the choices.

 

Controlling our evolution is now possible with general mathematics because it is an organizational ‘overlay’ that will produce answers to social problems and even more than that, it is necessary if we are to become symbiotic with our environment. There are many ways to influence our evolution, but there is only one unique organizational bottom-up method that guarantees a result if it is put in place and forms a rallying call of ‘virtue as the aim’ that everyone can get behind, according to Plato, with the added advantage that transgressors become quickly apparent.

 

The major religions through the ages have resulted from the life and times of individuals, Buddha, Confucius, Jesus etc., but here is a unique opportunity, using the unique general mathematics to democratically determine in which direction our evolution should proceed, address the problems of over-production, over-population etc. and even form one religion (chapter 37). As mathematics is to general mathematics, as iteration is to the mind/brain, as Survival of the Fittest is to Survival of the Best so a number of religions are to a democratically designed religion. There is a ‘quantum leap’ from one to the other and we are now able to take advantage of it, if we choose.

 

From chapter 37, “The first surprise, and it was a surprise to me when I realized it, that having said that we need a single religion by amalgamating the common bits of the existing religions, it appears that we already have a global religion, and it is already functioning and in place. Furthermore, this religion uses the operator of reality in the required form of ‘get on with your neighbour’ with the added bonus of ‘otherwise we will make it our business to see that you do’”. The answer is, of course the government/judiciary/police system that all countries use.

 

The proverbs say, ‘if it looks like a duck and it quacks like a duck, it probably is a duck’, and this sounds like the Second Coming! After all, can we expect someone to fix our population problems, fix our over-consumption problems etc? Surely it is more logical that we be given the opportunity to fix them ourselves, as in the accounts of Sodom and Gomorrah. ‘In Abrahamic religions, Sodom and Gomorrah have become synonymous with impenitent sin, and their fall with a proverbial manifestation of divine retribution.’ (Wikipedia) We have a choice, through general mathematics, so, do we take it? One is tempted to say ‘Hail, the child is born!’ because general mathematics is the bottom-up gateway to allowing us to democratically determine our planet’s evolution. ‘Heady Stuff!’, are we ready for it? Can we wait much longer with global warming in the ‘wings’?

 

People understand that burning fossil fuels leads to the concept of global warming, but ‘there is a far greater disaster facing the West than the worst possible scenarios for climate change. Western civilization is in a decline which has been in motion since the late nineteenth century, and has accelerated greatly since the 1960s. This is the same decline as occurred in countless other civilizations, from Sumer to ancient China and from India to Rome, the end point of which is complete social and economic collapse.’ (Biohistory, Decline and Fall of the West, Jim Penman, p 232) Can we afford mistakes that might possibly arise without the universities’ know-how and participation? Universities contain ‘god-like’ wisdom if we can tap the special/specific talents of the academic specialists through the actions of generalists. That is, only generalist academics can data-mine the universities that Plato’s politics needs to present to the voters and politicians as a set of options and explanations.

 

Conclusion: How important is general mathematics? We can gain some idea by comparing that firstly, both mathematics (counting space (a+b)) and general mathematics (measuring space (a+b)=1) need the mind/brain and the four axioms, and secondly, a quest to an individual’s feelings (Golden ratio (a+b)) that Life uses to denote beauty/elegance (mathematics) can be contrasted to the importance of the formation of the universe through (a+b)=1 (general mathematics). Clearly, there is hugely more scope opened up using general mathematics compared to mathematics.

 

Another example of estimating the importance of general mathematics is through communication. ‘In or around 1450, Johannes Gutenberg, a goldsmith, discovered after years of experiment how to make movable type to be used in a printing press. A single press could now produce 3,600 pages a day compared with just a few by hand copying…. The World Wide Web was first used in a sceptical CERN in Switzerland to organize the internal telephone directory although its founder, Tim Berners-Lee, the modern Gutenberg, always had far grander ambitions for it’. (The Second Curve, Charles Handy, p 34) The relation between books and the readers, and website and browser is concept/context and general mathematics provides the formal recognition/comparison in assessing their value to the reader. We use this process naturally, but nonetheless it is general mathematics, written in the dimensions, needing the four axioms and often the concept and the context (especially) is miss-used, leading to a lack of balance.

 

Further, a normal mathematical proof is that you prove a concept, but general mathematics is different because it contains context and this paper, mathematically speaking, is different because it move into disparate areas, but connected because everything is connected/entangled, literally. Perhaps it reads like a story, because stories contain concepts and context, and that being so, mathematics, as it stands, is obviously incomplete (Godel’s Incompleteness Theorems).

 

I believe that general mathematics is the organization that naturally quests the dimensions and includes Life and is the iteration of measurement/entanglement space plus the mathematics of concepts that evolved with the mind/brain plus the creation of a higher level of entanglement. Also, I have always considered that the mathematics of concepts must provide a prediction (relevance) and I predict that there are no enigmas that cannot be solved using this general mathematics. I have answered a number of enigmas, above, to my satisfaction, but there is the problem of global warming, population control etc. These problems come under the heading that we should be better parasites and not kill our host and ourselves by our actions and our ultimate aim, I believe, is to become symbionts, and that can be done, I believe, by using Plato’s politics and Survival of the Best. These problems have been with us for a very long time and have been itemised as a wish that God would fix them eventually.

 

For 2,000 years there has been the hope that a ‘Second Coming’ will make the Earth a paradise. ‘The world to come, age to come, or heaven on Earth are eschatological phrases reflecting the belief that the current world or current age is flawed or cursed and will be replaced in the future by a better world or age or paradise.’ (Wikipedia, World to come) I cannot help wondering whether any god will/would give everyone paradise, or make them earn it?

 

This is a reasoned/scientific paper that offers a means of attaining Survival of the Best and achieving an unflawed earthly existence that could be taken to mean a symbiotic relationship with our environment. Should we wait for divine intervention or organize ourselves using basic scientific principles?

 

There is only one open-ended general mathematics in a probability space and using this, it is likely to be an opportunity to ‘put everything right’ for ourselves and for our environment. Plato’s politics provides the expertise and the social organizational structure to allow us to change society with society’s blessing and full understanding and participation. A call-to-arms with ‘virtue’ as the aim, might be appropriate and ‘carry the day’!

 

Finally, this paper presents a unique usable solution that handles concept and context between groups of people, animals, food sources etc. and presents the idea of working together to become symbiotic, a ‘Second Coming’, academic knowledge of history and Survival of the Best as an aim for the future. These are aims that bring us together, and to contrast, ‘modelling how humans behave is tricky. Revealing patterns is possible, but crisply modelling behaviour at an individual level is mind-bogglingly difficult. As for forecasting chains of events, this is almost impossible.’ (Digital vs Human, Richard Watson, p 234) This shows that we have ‘lost’ our (common) way and if we can state desirable/necessary aims, that are achievable, as above, I believe, through Plato’s political system, we do not need to forecast important chains of events, because that is the universities’ decision/recommendation/consensus for the voters.

 

References: all quotations are fully referenced in the body and earlier chapters can be found on    darrylpenney.com    if required.

 

Chapter 84: Occam’s Razor, Principle of Least Action, Why a Particle Travels in a Straight Line, Why Science is Flawed, a Mathematical Giggle and the Derivation of Everything. .

Chapter 83: The Big Whoosh, Godel’s Incompleteness Theorems, Perpetual Motion Machines, the Axioms that Define the Mind, Bell’s Inequality, Limitations on Quantum Computing.

 

Chapter 81: Parasites in Probability Space, General Mathematics, Logic, Measurement, Organization, the Four Axioms of Measurement that Link the Mind/brain to Mathematics and the Dimensions of a Probability Space, Life as a Possible Sixth Dimension, the Why of Godel’s Incompleteness Theorems and the Goal of Explaining Everything by a Single, Elegant, Unified Equation is Attained.

 

Chapter 78: Love, Beauty, Ecstasy, the Golden Ratio and the Reason that Sexual Selection Works.

 

Chapter 77: Diffraction, Why Matter is Solid and Bounces, Unfolding the Two Types of Entanglement and an Upgrade to Newton’s Laws of Motion.

 

Chapter 75: The Nature of Life and Logic, Newton Laws of Motion, Reflection and Diffraction.

 

Chapter 67: Unfolding Democracy, the Fifth Dimension and Waking Plato to Save our World.

 

Chapter 37: ‘Hark, the Herald Angels Sing’.

 

by Darryl Penney

 

Abstract: Occam’s razor has remained a proverb for seven hundred years because, I believe that it is a ‘reflection’ in the physical world of a logical process that we call the conservation of energy. The conservation of energy cannot be explained by mathematics because mathematics is only a special case of a general mathematics that is composed of the mathematics of concepts that can be seen in the dimensions of a probability space and the four axioms that place Life within the universe as a parasite. The principle of least action is similarly flawed by considering inappropriate units/properties and using energy and the relation that energy is equivalent to (a+b)=1 for measurement/observers a and b shows the simplicity that is the universe. The problems that the world is facing have occurred because Life is hurting both itself and the environment that is its host, and the use of a general mathematics, in particular the context, needs to be used because our methods to date, using concepts, have not been sufficiently successful. Godel’s Incompleteness Theorems are used to show that mathematics is incomplete because (of the limited speed of light and) it is defined to be incomplete and correcting this, through the dimensions, means that the mathematics of concepts would be integral to all science/philosophy/politics etc. The Derivation of Everything is not a theory because there is no alternative and is derived from space-time, energy is equivalent to (a+b)=1 and the four axioms linking the mind/brain of Life to its environment, including any parasites that might evolve.

 

Many times I have wondered about Occam’s razor, as have many other people over the last seven hundred years and yet ‘even today, controversy surrounds attempts to turn Ockham’s Razor into a rigorous mathematical rule’ (30 Second Theories, editor Paul Parsons, p142). I would like to quote further because the reference is concise yet sufficiently complete for my purpose and also contains the ‘tone’ that is common in top-down thinking.

 

‘There’s something about a nice, neat explanation that commands respect. And there is a reason for that. According to the 14^th-centuary English logician named William of Ockham: elegant explanations are more likely to be right than convoluted and messy ones. He recommended making the least number of assumptions needed to do the job when devising explanations – or, as later authors put it, taking a metaphorical razor to them, paring them down to the bare minimum. The underlying motivation is that nature prefers simplicity to complexity.’ (p 142)

 

I shall start with the problem that lies within the previous sentence, and that problem is that language is inexact and changes with time, so, we have to use both concept and context, and to record those contexts because they change with time. Measurement by a mind/brain consists of two independent/orthogonal parts, a concept and a number of contexts, where the concept is usually constant, but the context changes gradually with respect to everything around it. This relevance/relativity is fundamental because there is only three fixed absolutes, and that is, from the dimensions, the speed of light in a vacuum, conservation of energy and the energy of space.

 

Also, the physical world has no motivation except energy gradients, whereas Life uses life and death to fuel a complex organic computer and so, nature does not ‘prefer simplicity to complexity’, it uses both as needed, but there is, by necessity, an underlying simplicity, because, bottom-up, everything is derivable from (a +/and b)=1. Occam’s razor is a world (our) O simple solution to the mathematics of concepts and is a ‘guide’ that is generally correct and is thus a proverb. Notice that the word ‘proverb’ means standing on behalf of a verb and is context. This previous sentence is in reference to world O, but not to the physical world P, because Life is a parasite that has evolved within the physical world for its own ends.

 

‘Even today, controversy surrounds attempts to turn Ockham’s Razor into a rigorous mathematical rule’ (p 142) and perhaps this derivation will change that endeavour because we do not realize its context because firstly, mathematics uses four axioms that link our mind/brain into mathematics, and mathematics is a special case of the mathematics of concepts, secondly, our universe is a probability space that is defined by energy is equivalent to (a+b)=1 for measurement/observers a and b, and thirdly, the organization of the universe lies above the mathematics of concepts and ‘logic’, and I believe that ‘logic’ is the ‘shards’ of our view of this organization. Expanding these three concepts, below.

 

Firstly, ‘from chapter 83, let me call mathematics (a+b) and that also has a solution, if we realize it (questing), called the golden ratio, and, I believe that allows us to ‘feel’ elegance/beauty etc. of solutions, scenery, physical beauty etc. Now (a+b) is a counting space, so, I can call it ‘mathematics’ because mathematics started as a counting space, but our mind/brain has always ‘stood outside’ of this counting space and made (a+b) into a mathematical measuring space. I will quote from chapter 81: ‘The Math Book, (by Clifford A. Pickover, p 284) gives the five Peano Axioms as a basis of arithmetic, and certain things appeared to be missing, such as the mind/brain to determine elegance of content, forward planning (dimension 6), the measurement of each numeral (questing) and the relationship between numerals (relevance)’.

 

Secondly, If we, from chapter 81, ‘unfold (a+b)=1, where unfolding is following the questing [of quantum mechanics, evolution, business etc.]. The fifth dimension (a+b)=1, in this simple form produces four absolutes/solutions (ignoring, for the moment, the fact that the speed of light is an absolute and must be constant):

(a) measurement/entanglement that are local physical and independent/orthogonal (a+b)=1 [classical local action and reaction of matter that provides expansion of the universe, reflection, diffraction of light and water waves],

(b) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b)=1 [conservation of (zero) energy across the universe, gravity, creation of space/mass/energy/time through the Lorentz contraction],

(c) measurement/entanglement that are local physical and independent/orthogonal, (a+b) [local/personal appreciation], and

(d) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b) [universal/reality-wide appreciation]’

 

‘Note that (a) and (b) are the physical structure of the universe [described in many earlier chapters] and (c) and (d) were derived in chapter 78 resulting from the ratio of an interval [Golden ratio] that has been reported to produce a feeling that is used, I believe, by Life to compare contentment/elegance/beauty in both a personal and a reality-wide comparison that is behind the important sexual selection as a major driver in evolution.’

 

Thirdly, again from chapter 81, ‘for completeness, I want to foreshadow another quest that is the “orderliness” of (a+b)=1 that embodies a general mathematic/organization that lies behind logic/mathematics. In a similar way that proverbs are a higher level of thought, everyday logic is, I believe, the reverse, and is our view of, or the mental “breakdown” of organization.’

 

Occam’s razor is a case in point, in that what we see as a proverb is a mere ‘reflection’ of one of the most fundamental laws of our universe and that is the law of conservation of energy. We understand the concept that energy is conserved and changes from one form to another without loss, but the context is that something has to calculate the energy at every point in the universe and it has to do so instantaneously! This is within the ability of a probability space, with space-time and what I call the fifth dimension (a+b)=1, where a and b are measurement/observers.

 

From chapter 83, ‘the universe is a perpetual motion machine that contains no (total) energy, but we can extract energy for our own use, and this requires the universe to expand, and further, the universe will continue to expand forever, or, until the Big Blink occurs.’ This is the general organization referred to above and logic is similar to the reflections of another world, as discussed by Plato. In other words, the beauty of the bottom-up universe from (a+b)=1 and (a and b)=1 comes top-down to us as logic and Occam’s razor and these “shards” are what we can make/understand of the organization of the universe.

 

‘So let us look at the question of perpetual motion machines and the local entanglement of (a+b)=1 generates local interaction between matter leading to friction/diffraction and this friction rules out macroscopic perpetual motion machines. However, (a and b)=1 represent a communication/entanglement that extends universe-wide and operates with infinite speed to prevent logical singularities through the conservation of energy, to prevent speeds faster than the speed of light in a vacuum, to prevent chaos occurring etc.’ The fact that perpetual motion machines exist goes some way towards explaining the many attempts to produce a working model over historical times.

 

The above paragraph shows that the logical (a and b)=1 generate perpetual motion and the local counterpart (a+b)=1 generates local interaction, or to put it more simply, the former generates gravity (a logical universe-wide entanglement), whereas the latter generate a similar, but different physical local entanglement that we see as friction, diffraction and ‘bounciness’. Occam’s razor is a product of the logical that we try to use in the physical world, and that is, in my opinion, the basic reason that it has not been amenable to mathematical analysis for the last seven hundred years. In other words, it has not been amenable to mathematical analysis because mathematics does not contain context because that is supplied by the mind/brain. I used perpetual motion machines to ‘picture’ organization and I often use the word ‘logical’ because it gives the impression that a process is logical when I should be using entanglement/communication and so I will quote the following ‘description’ of logic:

 

‘I found in chapter 75, ‘in a “nutshell”:

(1) We are the selection out of the multiverse because we are here.

(2) The one ‘dimensional’ use of the properties of world P that are properties of the space and could be called logical [as a machine is logical], but most important is Occams’ razor because simplicity is paramount.

(3) The two ‘dimensional’ use of worlds O and P by Life, and concept/context can perhaps be replaced by concept/quest/relevance/entanglement, where the concept evolved through forward-planning by the mind/brain and measurement by the eyes etc.

(4) Formal logic.

(5) Proverbs are a ‘higher’ logic/thinking that uses the mathematics of concepts to provide quick responses.

(6) The solution of (a +/and b)=1 is an absolute [Michelson-Morley] that the speed of light is a constant and all other measurements must have an assigned absolute [Plato’s problem] except for (7).

(7) The solution of the interval (a +/and b) is an absolute [Golden ratio] that makes beauty/appreciation/enjoyment logical/repeatable/relatable.’

 

‘This ‘recipe’ of logic appears at odds with the usual consideration that mathematics and logic ‘go together like a horse and carriage’ as shown by the attempt to derive mathematics from logic, above. The dimensions, I believe, show that our universe is based on mathematics and ‘logic’ from (a +/and b)=1, because mathematics and ‘logic’ go together [independence of +/and], but the actuality is, both for the physical world P space, measurement/entanglement (universe-wide) and for the world O space, concept/context (within a reality) that neither entanglement nor context is logic, but are communication.’

 

In other words, this is what happens to ‘logic’ when it does not exist in the physical world, but seems to exist because it’s the way that we think. In our (necessarily) limited reality, Life needs to confabulate images of predators as soon as possible with limited information to provide a heritable quick response, and logic is the contextual equivalent of concepts that enables a fast response. It is a waste of limited resources to react to a lion (concept) that is too far away to attack (context).

 

Occam’s razor is ‘logically’ exact/appropriate as shown by the conservation of energy in a logical/communicational sense in the physical world P, whereas in world O, Occam’s razor is an inexact proverb that is a guide only. Expanding this sentence, in world O, we can accomplish something in many different ways, with differing efficiency and the choice is ours, guided by Occam’s razor that the simplest method is usually the ‘best’. In the physical world, Occam’s razor is a strict fundamental ‘law’ that contains a singularity, that if broken/attained, leads to chaos because it is a restatement of the physics of a probability space.

 

So, I believe that Occam’s razor is a strict-law/property-of-our-space in the physical worlds O and P (measurement/entanglement), but is a proverb in word O (concept/context). Further, ‘all too often, however, spotting the “simpler” explanation is easier said than done: for example, is Einstein’s law of gravity really simpler than Newton’s?’ (p 142) The seeking of a ‘simpler’ explanation is not, I believe, the goal, it is to seek the ‘best fit’ explanation, and I will outline, what is, I believe, the role of gravity.

 

Gravity has a concept that it is a value of attractiveness between all types of energy, such as photons and mass, and this can be proven in the same way as why energy travels in a straight line, and the ‘value’ of gravity is one that works because we are here [out of the multiverse]. Gravity, as a context, is one half (a and b)=1 of the basic ‘bookkeeping’ of a probability space (a +/and b)=1 and the ‘local’ equivalent is (a+b)=1 from the basic equivalence relation energy is equivalent to (a +/and b)=1. Notice that the words that we use are historical and energy can be positive/negative, whilst the right hand side is measurement/entanglement, both universe-wide and locally.

 

Thus, gravity is energy, not a force, and taken to be negative and all other energies are positive, but the total must remain zero. I will stress/use energy because the basic equivalence contains energy, measurement and observer and the use of other units must be (effectively) synonyms/states, such as matter, momentum, frequency etc. I repeat that I am considering gravity to be an energy, not a force, though it obviously can cause a force, and is one half of the energy of the Big-Bang/Big-Whoosh and the only way to balance the energies of everything is to create space, which is gravity/energy to balance the energy/energy.

 

The Lorentz contraction is a means of preventing chaos occurring, in a physical and logical sense, because, as the speed of a non-zero mass particle approaches the speed of light, the dimensions change proportionately so that it never reaches that speed. The dimensions are fundamental to the space that they describe and from chapter 83, ‘if we quest the dimensions, we find three constant relationships: energy to time for all space, energy to space for all time and space to time for all energies because all of the dimensions change by the Lorentz contraction. The first appears to suggest conservation of energy over time, the second that space has a set energy and that the creation of space creates energy, as is commonly thought, and could be the mechanism that forces matter with its negative potential energy to move outwards as space is created. The third relationship shows that all (free) energy, in the form of photons must have a constant speed, relative to the measurer, and this is the Michelson-Morley result (for all motions).’ These relationships are necessary quests in a measurement space and the second relationship, that space has a set energy and that the creation of space creates energy suggests a reason for dark energy to exist.

 

I want to revisit the sentence, from above, ‘in the physical world, Occam’s razor is a strict fundamental “law” that contains a singularity that if broken leads to chaos because it is a restatement of the physics of a probability space (a+b)=1’ because it shows why modern physics is fundamentally flawed. The following quotation ‘as theories go, the principle of least action is just common sense: natural motion always takes the easiest and shortest route’ (p 16) is a top-down postulate that shows that common sense is our view of the ‘shards’ of an over-arching organization that is the universe defined by the dimensions.

 

‘The principle of least action … says, essentially, that things happen in a way that requires least effort. So, a beam of light will travel in a straight line because that is the shortest path between two points…. Quantum theory, which describes how things work on a subatomic scale, seems to be the one area where the principle of least action does not apply. Quantum objects can be in two states at once, and can take multiple paths when travelling from one place to another. Richard Feynman went so far as to suggest that a quantum particle will simultaneously take every possible path when making a journey.’ (p 16)

 

The above paragraph describes the development of physics from Newton’s first law of motion to quantum mechanics, and by implication, everything in between is also flawed, based on postulates that are unprovable. How do you prove that a particle travels in a straight line when entanglement is universe-wide and simplifications need to be treated through the mathematics of concepts? However, this is a simplification that follows from Newton’s simple laws of motion, and diffraction proves that light does not travel in a straight line, but is acted upon by the short-range entanglement (a+b)=1,see chapter 77.

 

Simplifying physics is a worthwhile aim, but using simplified incorrect laws such as Newton’s laws of motion only confuses the issue. Newton worked on diffraction and must have seen the bending of light in diffraction, but was unable to find a simple solution. There is a simple answer, and that is the short-range entanglement (a+b)=1, and, as it is the counterpart of gravity (a and b)=1, simplifying physics should come from the bottom-up use of the dimensions. There is elegance in the simple context of wide-ranging solutions as well as simple concepts and solutions, bearing in mind that many of the simple equations reflect states of energy, such as frequency/energy, mass/energy etc. We have to accept that (literally) everything is positive and negative energy and that the total is zero.

 

If it is accepted that energy is equivalent to (a +/and b)=1, then it becomes easy to prove that, given no other influences, which is unrealistic, a particle/photon travels in a straight line. Physics has agreed that there is a physical universe but has ignored the logical side and we have many unsolved problems, such as the Michelson-Morley experiment, diffraction, gravity, ‘bounciness’ etc. and these are readily solvable using this fifth dimension.

 

The reason that particles, light etc. unfailingly travel in a straight line, given no entanglement, is that, if they did not, they would cause a logical singularity in the conservation of energy equation (a and b)=1 because it would have multiple solutions. In other words, a particle does not travel in a straight line because of momentum, but because momentum/energy is accountable in a measuring space, and it can be restated, again, that travel in a straight line is not only a physical property, but also a logical property, as above. Chapter 75 uses the local entanglement of (a+b)=1 to show simply why diffraction occurs and the form of the resultant wavefront. Huygens describes the effect, but the underlying principle has evaded researchers because the answer is logical/entanglement.

 

Descartes thought that velocity was universally conserved and Newton believed in ‘action at a distance’ and both were somewhat correct because momentum is a combination of matter/mass energy and a kinetic component (velocity), so both velocity and momentum are a compound form of energy. Likewise, ‘action at a distance’ occurs through energy gradients (concept) and the entanglement (context) to produce it. Whilst all these units are correct in world O, world P uses energy and that simplifies things. In fact, I believe that the Big-Bang/Big-Whoosh is the splitting of nothing into positive and negative energy (questing), so there is nothing in the universe that is not energy.

 

Similarly, ‘quantum mechanics may be an exception to the principle of least action’ cannot be true because the questing in a measurement space leads to the universe going about its measurement business of assessing every possibility, as it has to in a measuring space, so that the law of conservation of energy remains at zero. Feynman’s approach is just this, a statement of the property of a measurement space and Feynman’s approach works because that is how a probability space works.

 

Conclusion: there is no use wasting words, I believe that the above shows that physics needs the logical half that it has ignored, mathematics needs the general mathematics that combines the mathematics of concepts and the interaction of the mind/brain and society in general has to appreciate the context of their concepts to solve the many problems that face us and the environment today. This ‘trinity’, I believe, as in the Bible, is historical, for ease of understanding/discussion and it is apparent that the bottom-up use of the mathematics of concepts brings everything together. Literally everything (energy and concepts) is entangled and can only be considered in parts in a limited way and according to the mathematics of concepts.

 

In particular, in chapter 83, is was shown that the concept of Godel’s Incompleteness Theorems showed that communication at the limiting speed of light would impose problems with communication of information in the context of a general mathematics. Similarly, if we say that energy is equivalent to (a+b)=1, the four axioms of the mind/brain, space x, y, z and time passing, we define a general physics/everything that is simple, easily understood, generates the universe and our place in it and already realizes the limits imposed by relativity. It could be called a ‘pocket’/concise Theory of Everything.

 

However, the orthogonal concept/context shows that, as above, simplicity has two faces, simplicity of concept and simplicity of an infinite/universe-wide context. So, a Theory of Everything requires two faces, be simple and quest itself into everything and

 

energy is equivalent to (a+b)=1, the four axioms of the mind/brain, space x, y, z and time passing in a probability space

 

 does just that. I believe that I have proven beyond doubt that our universe is a probability space and the derivations from chapter 81:

 

‘If we unfold (a+b)=1 in a probability space, as above, including Life, we get:

concept/forward-planning/quest/relevance/beauty/context.

 

If we unfold (a+b)=1 in a probability space, as above, excluding Life, we get:

measurement/quest/relevance/entanglement.’

 

These are derivations from the dimensions, a probability space and from Life and are not a theory, so, I believe that I can call this the Derivation of Everything because it unfolds itself into a universe complete with parasites. In other words, a theory is one of a number of alternative possibilities and in this case, a probability space encompasses all possibilities within itself, from certainty of existence (1) to certainty of non-existence (0) and is the most general, all encompassing description of a reality that is possible. If we, and the universe are to have a reality, it must be continuous, complete and have the correct dimensions and a probability space is just that.

 

I continue to use Godel’s Incompleteness Theorems as a concept on which to hang context (I have no wish to know anything else about it, which is a good thing as I would probably not understand it) and I now find another context/concept/meaning of the theorems and that is, mathematics is incomplete because, as above, firstly, the speed of light for communication, and secondly, mathematics does not, by definition, use all of the dimensions. In other words, we have defined mathematics to be incomplete and are shocked to find that it is incomplete! What a giggle! This is an example of the problems that come from top-down and I am using it to show also, that everything must be entangled/complete.

 

Surely the time has come to include the use of the mathematics of concepts that is apparent in/from the dimensions of a probability space and applies to every facet of our universe. It will not detract from mathematics, only increase the special case of mathematics into a general mathematics because the same mind/brain is being used, but the ‘floor’ is changed from (a+b) to (a+b)=1, that is, from a counting-space to the mathematics of concepts and will be discussed later.

 

References: all quotations are fully referenced in the body and earlier chapters can be found on    darrylpenney.com    if required.

by Darryl Penney

 

Abstract: The Big Bang theory has fundamental flaws and a better representation is the Big Whoosh (Modified Steady State) model that incorporates inflation as a natural result of the dimensions of our universe. Perpetual motion machines are commonplace and we actually live inside one that we call the universe and this realization suggests that a Steady-State/Big-Whoosh model is more appropriate than a Big Bang. Four axioms show why a counting space (a+b) is turned into a mathematics by the mind/brain and a more appropriate mathematical space (a+b) =1 provides a degree of completeness and this equation is evident in the dimensions of a probability space and is the fifth dimension that has been sought for a 100 years and answers Bell’s Inequality. The mind/brain evolved as a parasite within the universe and communicates with the universe through the four axioms that are necessary to any calculation and shows why the mathematics of concepts is the natural mathematics and shows the difficulty of imposing the axioms on the physical, as in quantum computing, because the axioms are the way of measuring the physical. Completeness is possible in logic/entanglement (a and b)=1, but the constant speed of (free) energy/light that is a product of the dimensions shows that we can never know everything (a+b)=1, where a and b are measurement/observers.

 

In chapter 81, I derived a simple equation that defines our universe and consequently, I find that my bottom-up view contrasts with the top-down view that is currently used throughout science. Enigmas and strange (to me, now) explanations abound and yet are tolerated by the scientific community, and as an example, neither the Big Bang nor the Steady State expansion of the universe can be reconciled with inflation, but the Big Whoosh contains inflation as a natural effect and it is an ongoing natural phenomenon. The Big Whoosh is closer to the outmoded Steady State model because the observed expansion of the galaxies is not from residual momentum of the Big Bang, but is a result of the dimensions being linked through the Lorentz contraction and the (apparent) expansion of matter comes from the expansion of space (and matter) to maintain the conservation of energy.

 

Looking bottom-up by assuming that our universe is a probability space changes the perspective, and whilst it might seem presumptuous of me to suggest changes in long held views, such as the Big Bang, above, my justification is the description of the universe from a simple equation/equivalence derived in chapter 81, reproduced below, as well as the apparent/assumed correctness of derivations. There is necessarily a time delay with peer review, but everything seems to fit so well that I will continue to look at some of science’s self-confessed ‘limits of science’ (Beyond Reason: Eight Great Problems that Reveal the Limits of Science, A. K Dewdney, cover) through the view that I now hold.

 

I believe that we need to explain the (apparent) enigma of Godel’s Incompleteness theorems as a matter of urgency. ‘It would never be possible to create a fully complete system of mathematics where everything from the lowest axioms to the highest, most complex proofs could be shown to be unequivocally true (The book of Numbers, Peter J. Bentley, p 101) ‘Turing managed to prove that it was not possible to show universally (for any given examples) that a logical or arithmetic statement was true or not. This was yet another nail in the coffin of “perfect mathematics”’ (p 102). This (apparent) enigma obviously caused a ‘stir’ in the mathematics community, as it should, but all that these quotations are saying is that mathematics is not complete, and I also, believe that mathematics is not complete because it is a special limited case of a complete mathematics, that I call the mathematics of concepts that can be seen in the dimensions of a probability space.

 

This use of a special case mathematics derived top-down is an example of a wider problem that is basic to science etc., and that problem is, I believe, (1) that the mind is separate to the problem, and

(2) that no definition is given of the space in which we live, so it is small wonder that Godel’s Incompleteness theorems are sending warning signals. Mathematics has been called the ‘handmaiden of the sciences’, but it is not serving science well because it is flawed. ‘Quantum physics and relativity theory are practically all mathematics – with an interpretive framework grounded in observations. In contrast, biology has relatively little mathematics in it, but a host of observational data that ecologists and biologists are still trying to make sense of.’ (Beyond Reason: Eight Great Problems that Reveal the Limits of Science, A. K Dewdney, p 6) This quotation is saying that mathematics cannot handle ‘a host of observational data that ecologists and biologists are still trying to make sense of’ and I believe that that is because mathematics is a limited case of the mathematics of concepts and concepts are needed in the ‘softer’ sciences.

 

Firstly, the reason that quantum physics and relativity theory are practically all mathematics is because (special case) mathematics is being used and, to a hammer, all problems look like nails. The mathematics of concepts provides the mathematics for quantum physics and relativity as well as concepts for biology etc., if it were used, and it is obvious that incompleteness disappears because the mathematics of concepts is a quest of the dimensions and the dimensions ensure completeness. Unfortunately, the dimensions themselves produce a singularity that confounds this statement, below. Secondly, quantum physics and relativity are important because they are special cases of scientific progress of the space that we live in and they are also used continually in the form of questing and relevance in everyday life because questing is looking at all possibilities and relevance is judging their relevance. The scope of questing and relevance do not seem to be appreciated, but they occur every time that we measure by looking, feeling, buying, selling etc. and are basic to a measuring space, such as a probability space. These few concepts are so basic and far-reaching that a simple mathematical statement unfolds itself into a universe!

 

As a simple example, let me call mathematics (a+b) and that also has a solution, if we realize it (questing), called the golden ratio, and, I believe that allows us to ‘feel’ elegance/beauty etc. of solutions/beauty etc. Now (a+b) is a counting space, so, I can call it ‘mathematics’ because mathematics started as a counting space, but our mind/brain has always ‘stood outside’ of this counting space and made (a+b) into a mathematical measuring space. I will quote from chapter 81: ’The Math Book, by Clifford A. Pickover, p 284) gives the five Peano Axioms as a basis of arithmetic, and certain things appeared to be missing, such as the mind/brain to determine elegance of content, forward planning (dimension 6), the measurement of each numeral (questing) and the relationship between numerals (relevance), so keeping these four quantities: elegance, forward-planning, questing and relevance in mind, I will return to them via the dimensions and the properties of a probability space.’

 

It seems that our mind/brain is doing a lot of the important work in mathematics and that allows us to consider (a+b) as a measuring space, but, as both mathematics and the mind/brain are contained in our universe/space, they must be linked through the dimensions. So, if mathematics is a special case, let’s define a more comprehensive mathematics by (a+b)=1 and a more comprehensive physics/mathematics from space (x, y, z), time passing and (a+b)=1. It is obvious that this is a simplification of a probability space but it will be found to contain enough dimensions, of the right type, to generate everything that we need to create our universe.

 

This statement is a huge ‘ask’/request from the basics of a probability space, but if the content of the probability space is called energy, then

 

Energy is equivalent to (a+b)=1,

 

and we know that equivalence statements are simple because the left and right sides are the same thing and are states of each other. A moment’s reflection will show this to be correct because the Big-Bang/Big-Whoosh is energy in a probability space, but a probability space is a measuring space defined by (a+b)=1 and a measuring space must contain questing and relevance of energy. When life evolved, it supplied a mind/brain and a use for elegance/beauty and used questing and ‘logic’ that are fundamental mechanisms behind a probability space.

 

If we, from chapter 81, ‘unfold (a+b)=1, where unfolding is following the questing [of quantum mechanics, evolution, business etc.]. The fifth dimension (a+b)=1, in this simple form produces four absolutes/solutions (ignoring, for the moment, the fact that the speed of light is an absolute and must be constant):

(a) measurement/entanglement that are local physical and independent/orthogonal (a+b)=1 [classical local action and reaction of matter that provides expansion of the universe, reflection, diffraction of light and water waves],

(b) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b)=1 [conservation of (zero) energy across the universe, gravity, creation of space/mass/energy/time through the Lorentz contraction],

(c) measurement/entanglement that are local physical and independent/orthogonal, (a+b) [local/personal appreciation], and

(d) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b) [universal/reality-wide appreciation]’

 

‘Note that (a) and (b) are the physical structure of the universe [described in many earlier chapters] and (c) and (d) were derived in chapter 78 resulting from the ratio of an interval [Golden ratio] that has been reported to produce a feeling that is used, I believe, by Life to compare contentment/elegance/beauty in both a personal and a reality-wide comparison that is behind the important sexual selection as a major driver in evolution.’

 

‘For completeness, I want to foreshadow another quest that is the “orderliness” of (a+b)=1 that embodies a general mathematic/organization that lies behind logic/mathematics. In a similar way that proverbs are a higher level of thought, everyday logic is, I believe, the reverse, and is the mental “breakdown” of organization.’ In other words, if we do not understand the big picture, logic is the bits that we can understand.

 

Life is a parasite that has evolved to use our universe through evolution and especially necessary is a new dimension that Life has evolved that I call forward-planning, also, I need to explain the multiple orthogonality of (a+b)=1 that is obvious when pointed out, and yet is crucial to the organization of our world and society. The mathematics of concepts is the orthogonality of a, b and a+b, for the world of Life (O) (as concept and context) as is measurement and entanglement in the physical world (P), as well as the physical and logical relationship within the measurement (+/and).

 

Descartes used orthogonality in the Cartesian coordinates (x, y, z) to simplify the definition of the physical attributes of a particle and we can do the same thing with the physical (a+b)=1 and the logical (a and b)=1 parts of the fifth dimension. Questing is simplifying to find and examine every possibility of the dimensions for relevance in the calculation of energy and that is the Big Whoosh. Energy splits into positive and negative (questing) and the energy affects all of the dimensions equally through the Lorentz contraction and the universe expands through inflation and Steady State.

 

Mathematics, as used, is concept/context with the mind/brain supplying the four axioms above and these four axioms are also necessary for the mathematics of concepts, so, whilst there is nothing wrong with mathematics, it does need a complete makeover to be complete and align with Godel’s theorems. I make this statement with confidence, for the moment (see below), not knowing Godel’theorems, but because I am using the dimensions and are confident that the six dimensions are enough.

 

Whilst the following has been derived simply above, from chapter 81, ‘the right hand side of the relationship is a simplification of “everything” from the dimensions that expands to cover the universe in a probability space because of the inbuilt questing. The left hand side is (literally) ‘everything’ from the Big-Bang/Big-Whoosh and the relationship is our old friend:

 

energy is equivalent to (a+b)=1, where energy is everything and a and b are measurement/observers in a probability space.’

 

This relationship is (almost) obvious when you know what it is, and the mathematics of concepts likewise, and yet it took me a long time to understand, and this simplicity and completeness explains why I am proceeding with derivations under faith alone, as above. ‘As science advances, more patterns and regularities are revealed in nature. These advances cut down the number of disconnected facts worth remembering’. (30 Second Theories, forward Martin Rees, editor Paul Parsons)

 

‘If we unfold (a+b)=1 in a probability space, as above, including Life, we get:

concept/forward-planning/quest/relevance/beauty/context.

 

(a+b)=1 in a probability space, as above, excluding Life, we get:

measurement/quest/relevance/entanglement.’

 

‘If the mathematics of concepts can be seen in the dimensions, so it must be universally applicable and true. Can we afford to neglect it, especially as it “unlocks” processes that we have not yet explored, applies to all disciplines and is “natural” to a probability space, unlike mathematics that is obviously flawed/foreign, but useful in world (our) O?’

 

The above derivation was prompted by Godel’s Incompleteness Theorems in this instance, but the mathematics of concepts took years to develop and could then be recognized in the dimensions of a probability space. To my mind, this fact proves usefulness/legitimacy. The ability to describe situations in a better way inspires confidence, so let us look at the question of perpetual motion machines and the local entanglement of (a+b)=1 generates local interaction between matter leading to friction/diffraction and this friction rules out macroscopic perpetual motion machines. However, (a and b)=1 represent a communication/entanglement that extends universe-wide and operates with infinite speed to prevent logical singularities through the conservation of energy, prevent speeds faster than the speed of light in a vacuum, prevent chaos occurring etc.

 

A probability space is a measurement space and the energy at every point is summed and must remain at zero. Thus (a and b)=1 combines every atom/point across the universe in an entanglement and every atom is a frictionless logic machine that absorbs photons and expels photons, combines chemically, gravitationally, changes speed etc. without friction, but driven by energy profiles so atoms (physically and logically) are perpetual motion machines. Notice that gravitation energy is negative and all the other energies are positive so that the total energy is always zero and this leads us into, as parasites, a truly amazing perpetual motion machine.

 

Given that the dimensions (space, time and mass-energy/(a+b)=1)) increase equally by the Lorentz contraction, as photons move into new space, where the basic equivalence relation ‘mass/energy is equivalent to (a+b)=1’, quoted above, is the general mathematic/organization, this, I believe is the reason that the galaxies are expanding as a Big-Whoosh, and not a Big Bang, and the rate of expansion depends on the energy produced, which should be constant, ignoring inflation that occurred because space was so small, since the speed of light is constant and creating new space constantly. This means that the total energy is zero, but energy is being created in a useable form and we use it continually by living in the warmth of local gravitational accumulations of energy, and so, perpetual motion machines exist both logically and physically and are used by us for energy. So, in other words, the universe is a perpetual motion machine that contains no (total) energy, but we can extract energy for our own use, and this requires the universe to expand, and further, the universe will continue to expand forever, or, until the Big Blink occurs.

 

It is interesting that ‘the recognition that c [the speed of light] is not constant after all has gained ground in the past decade.’ (p 57) If we quest the dimensions, we find three constant relationships: energy to time for all space, energy to space for all time and space to time for all energies because all of the dimensions change by the Lorentz contraction. The first appears to suggest conservation of energy over time, the second that space has a set energy and that the creation of space creates energy, as is commonly thought, and could be the mechanism that forces matter with its negative potential energy to move outwards as space is created. The third relationship shows that all (free) energy, in the form of photons must have a constant speed, relative to the measurer, and this is the Michelson-Morley result (for all motions).

 

As an example of unfolding and also showing the ever-presence of chaos, the two Heisenberg uncertainty relationships [energy-time and energy-space] contain inequalities that suggest that finite sized particles/something lie behind the problems of measurement. ‘Heisenberg’s uncertainty principle is expressed by a formula that relates our ability to measure a particle’s momentum to our ability to measure its position. If we denote our uncertainty about position by delta(x) and our uncertainty about momentum by delta(p), the principle is readily formulated:

delta(x).delta(p)>=h.     where h is Plank’s constant.’ (p 67)

 

Also, from chapter 73, ‘remember that a probability of existence space has an infinitely small chance of existing [at 1] and likewise, has an infinitely small chance of not existing [at 0], and forms a “twilight zone”’, and whatever we are, we are logic because logic only comes from iteration or a mind/brain.’ Notice that the simplest case, as we would expect, is a probability of existence and not a definite existence and that is in line with the idea presented above that the definite is a special case and the indefinite is the general case. Of course, there is nothing to say that our universe does not exist, but I believe that a probability space is necessary because it has enough dimensions to allow Life to develop.

 

The paragraph above seems to make a little more sense of the enormity of the number of galaxies, the size and age of our universe etc. when it is considered as existing in a possibility of existence space. Further, the presence of singularities, both physical and logical, suggest that only a ‘limited’ number of universes survive without chaos occurring, and, of course, ours is one of that number, but singularities abound within the universe and, in particular, could be responsible for evolution, see below. In other words, singularities are considered unusual, but like questing and relevance, I believe that singularities are all around us, from black holes to death, and they are a necessary part of life and recycling nutrients.

 

Another example that shows that entanglement is not local but fits with the over-arching entanglement of a probability space is ‘the violation of Bell’s inequality was observed a number of times, in experiments with electron-positron pairs, with protons, with photons and even with qubits. So there is no doubt: whatever it is, Nature is not local.’ (Quantum Mechanics, Dr Alexandre Zagoskin, p 335) ‘The effects of nonlocality extend well beyond the reach of laboratory apparatus. Every fundamental particle in out bodies has interacted with untold billions of fundamental particles everywhere else in the universe, and all are to some degree entangled with each other.’ (Beyond Reason, A. K Dewdney, p 79) Surely it is not a large step to considering that entanglement is a property of a space such as a probability space and (literally) everything is entangled as in a probability space.

 

‘Entangled states make the spooky action at a distance a reality’. (Quantum Mechanics, Dr Alexandre Zagoskin, p 322) is a quotation that, I believe, needs more explanation because the entanglement and spooky action at a distance are similar, yet distinctly different, and that sameness and difference should be noted by comparing the top-down quotation with bottom-up explanation. From above:

(a) measurement/entanglement that are local physical and independent/orthogonal (a+b)=1 [classical local action and reaction of matter that provides expansion of the universe, reflection, diffraction of light and water waves],

(b) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b)=1 [conservation of (zero) energy across the universe, gravity, creation of space/mass/energy/time through the Lorentz contraction],

 

and, measurement/quest/relevance/entanglement.

 

Entanglement is orthogonal to measurement and is part of a measurement in physical (non-Life) probability space, both physically and logically [(a+b)=1 and (a and b)=1], whereas spooky action at a distance is an energy gradient of gravity (negative energy, positive attraction to energy and infinite logical propagation speed), whereas electromagnetic photons are positive energy and speed of light propagation etc. The word ‘reality’, as I use it has a definite meaning and is entanglement, without Life, but deterministic and contextual with Life, but I think that the use in the quotation may have been used in the sense of ‘true’. It is crucial that Life be considered as there are four axioms linking Life with the physical environment in which it is parasitic and any discussion of life requires the intervention of Life.

 

I have mentioned before, citing Newton’s laws of motion that science is not ‘house-keeping’ and upgrading science as I believe should be done, and the paragraph above is a case in point. Indeed, this whole chapter is on the same subject and I can only urge that science do as mathematics did in trying to add a bottom-up base to science. The linking of the four new axioms to mathematics (and everything) and the mind/brain as well as the use of a probability space leaves the problem of updating science and mathematics, I believe, to an urgent ‘in-house revitalization’ that is now possible.

 

‘Despite significant progress since the turn of the century, the very possibility of quantum computing on a practically useful scale remains a matter of serious controversy’ (p 99) This debate is enhanced by the fact that the four axioms, above, need to be an intimate part of the decision making process and quantum computing is, like mathematics, a special case of the mathematics of concepts. The mind/brain is/has-been separate to mathematics for simplicity and the picture becomes more obscure with quantum computing because something has to provide those four axioms in the determination. They are measurements of a mind/brain and external to the physical. However, I can say that due to the dimensions, the addition of the mind/brain, through the four axioms will work with the mathematics of concepts, and that is our primary concern in our current mass extinction.

 

To expand the above paragraph, our mind/brain has ‘meshed’ with the physical entanglement through measurement of the senses even though the mathematics of concepts is part of the dimensions, we still need the four axioms to access information. The same is true for the special cases of mathematics, quantum computing etc., so how does the mind/brain set the boundary conditions, through the four axioms to define the question and thus the answer. As above, mathematics uses the counting space (a+b) and adds the four axioms via the mind/brain, so, can quantum computing that is part of the physical world (P) contain boundary conditions that are part of our world (O)?

 

I believe that the recognition of the need for context from the mathematics of concepts is a ‘quantum leap’ that will literally open up a new dimension in mathematics and show how the mind/brain should be used. It is also a good opportunity to stress the potential of the mind/brain in solving the world’s problems by producing genius and ‘good’ citizens, as opposed to criminals etc. that are a necessary part of managing future populations.

 

Another chapter from Beyond Reason (p 85) is ‘The Edge of Chaos: Unpredictable Systems’ and this carries on from the paragraph above if we ask ‘what is the opposite of chaos?’. Usually our language has a distinct opposite to a word and in more complicated scenarios, a number of opposites and that leads into measuring contexts between them in the mathematics of concepts and the need for a mind/brain to choose. Let me suggest, for simplicity, that the opposite of Unpredictable Systems could be the mind/brain and, as mentioned previously, the mind creates a new space out of the physical, and multicellular Life is an organization of all the cells in the body. It took a large part of evolutionary time to produce single-celled organisms and they are necessarily small because of the strength of the cell wall, and, not surprisingly, the organization of the multi-cellular organism ‘mirrors’ that of the cell.

 

The multi-celled organism evolved a new space, a larger size that allowed efficiency in senses, principally a new method of sight, increased mind/brain and teeth/bones for predator/prey interaction that the better sight enabled. All life is in constant danger of chaos because predators and scavengers must return the remains of life to the common environment for reuse. Continental drift recycles the continents themselves, suns exhaust their fuel and galaxies collide, but the increase in space creates more energy for the universe’s perpetual motion.

 

Conclusion: the above is a look at what might be considered some of the subjects that are ‘Beyond Reason’ according to top down thinking and I have tried to show how logical is the universe when defined by the dimensions of a probability space and the forward thinking of the Life/parasites that evolved in that space. New definitions must be given to contexts within the mathematics of concepts by words such as quest, relevance, chaos etc. that underlie the workings of the universe and especially the basic equivalence energy is equivalent to (a+b)=1.

 

The test of a good theory is to extrapolate, as has been done above, and a simple example comes to mind that sums up the above. Einstein said “Not only is the universe stranger than we think, it is stranger than we can think”. (p 83) This ‘strangeness’ represents top-down thinking, whereas, I am promoting bottom-up thinking that basically says that the universe is simple when you choose to build on the dimensions of a probability space.

 

Secondly, ‘stranger than we can think’ is ‘obscure’ and represents the problem that leads us into the need to use the mathematics of concepts and the orthogonality of +/and. The mathematics of concepts ‘splits’ ‘can’ into its concepts and contexts and into physical and logical (+/and), and we find that ‘can’/logical/concept has infinite speed of communication and satisfies ‘can’/logical/concept of the conservation of energy, Godel’s theorems of completeness etc.

 

However, ‘can’/physical/concept has finite speed of communication in the speed of light and restricts ‘can’/physical/context and shows that a singularity exists (speed of light) that we cannot overcome and so, we cannot know everything that is happening. This last sentence was probably in Einstein’s mind through his work on relativity. In other words, we can know everything logically, but not physically because the speed of light is constant. However, ‘can’ can be taken as the ability to understand the workings of the universe, and, is that beyond our comprehension? I don’t believe that it is because our mind/brain is based on the mathematics of concepts that is the driver for determining the universe [(a+b)=1].

 

Thus, Godel’s theorems need the rider that logic is complete because it is infinitely fast, but communication/context must always be incomplete because the speed of light is a constant. Notice that the addition to both Einstein’s quotation and Godel’s theorems is the same and shows how a definitive base and bottom-up questing shows commonality.

 

References: all quotations are fully referenced in the body and earlier chapters can be found on    darrylpenney.com    if required.

 

by Darryl Penney

 

Abstract: I believe that our universe is a probability space and the dimensions and properties of that space define us and everything around us and in particular mathematics is supposed/defined to be bottom-up, and I believe that it both is, and is not, and needs four new axioms to link mathematics and the properties of our universe to the act of measurement by Life. These four axioms fit/lock-together all of science and mathematics into a complete workable whole/organization with respect to Life, and that fit is so complete that, I believe, it proves, beyond doubt, that our universe is a probability space. The fit is so complete through evolution that Life should be considered a parasite that has evolved in our probability space and so, Life should also be acknowledged as another dimension. Mathematics is a special case of the mathematics of concepts that is defined by the dimensions, operated by the properties of our space and is the basis of our mind/brain. General mathematics is the over-arching organization of the universe that can now be linked to the dimensions and the mind/brain by the four axioms and our use of this organization has produced, I believe, two ‘short cuts’, proverbs to enhance our thinking, and logic to incorporate the organization around us into usable/useful additions to our reality. An explanation of two apparent enigmas is given, the Michelson-Morley experiment and Godel’s Incompleteness theorems and a simple, elegant relationship that underlies and describes everything is: energy is equivalent to (a+b)=1, where energy is everything and a and b are measurement/observers in a probability space.

 

 

I have been concerned by the use of top-down assumptions by science that have led to errors/inadequacies and have recently completed chapter 76: ‘When Philosophy meets Mathematical Physics’ that finds that these three disciplines have much in common when viewed from the bottom-up. Also, I am aware that mathematics prides itself in being bottom-up by using basic axioms, and indeed, mathematics is a special case of the mathematics of concepts that is apparent in the dimensions, but Life is a parasite that lives embedded and contained within the physical structure of the universe and has imposed its presence in a way that complicates the physical universe and an additional four axioms are needed to link mathematics to our mind/brain.

 

The mind/brain’s of the observer has always ‘stood outside’ and separate to science and mathematics, but, as the dimensions define everything, they must include, science, mathematics etc. and the mind/brain, so, there must be a link between the two and that link is to be found in measurement. Measurement has always been poorly understood [Michelson-Morley], I believe, because it has been inaccessible from top-down, and this is shown by the problems that started with quantum mechanics over a hundred years ago. However, from bottom-up, the relationship is apparent and it will be seen that mathematics is a special case of the mathematics of concepts that can be derived from the dimensions and those dimensions underlie the functioning of the physical world and (both) mathematics need the four axioms to define their place in the space/universe relative to Life.

 

I have read that a number of observers have wondered whether the observer in an experiment on quantum mechanics influences the result and the answer is yes for two reasons, firstly, questing returns the answer that is sought and that is a basic property of a probability space. Secondly, the observer is part of the measurement process because, as below:

concept(measurement)/Life/questing/relevance/elegance/context(entanglement).

 

Life uses forward-planning to ask the question and ‘future time’ does not exist in a mathematical probability space, so Life has created a new type of space that is a deterministic reality. Entanglement is used universe-wide [gravity, conservation of energy etc.] and locally [action and reaction, reflection etc.], but life uses a reality that uses a determinate space, see below.

 

The Math Book, by Clifford A. Pickover, p 284) gives the five Peano Axioms as a basis of arithmetic, and certain things appeared to be missing, such as the mind/brain to determine elegance of content, forward planning (dimension 6), the measurement of each numeral (questing) and the relationship between numerals (relevance), so keeping these four quantities: elegance, forward-planning, questing and relevance in mind, I will return to them via the dimensions and the properties of a probability space.

 

In chapter 76, I wondered if philosophy was logical and again, here, I wonder whether our interpretation of mathematics is based on something real and basic. So, I will derive THE General Mathematics in a Probability Space. I used ‘THE’ because there is only one basic/standard ’version’, based on the dimensions and its use depends on the properties of a probability space/universe. In the next chapter A General Mathematics will be derived using other (present and future) attributes of the mind/brain, but forward-planning is too important/necessary, and, I believe, that it is an integral and necessary part of every evolution.

 

In fact, it could be said that Life is a dimension of our probability space because we are necessary for the description of our space, and everything in that space must derive from the dimensions because that is the requirement of a dimension. Thus, if we evolved in one probability space, the possibility exists that Life could exist in all/any probability spaces and that dimension should be included in a mathematical probability space. In other words, if Life is a dimension of a probability space (through forward-planning) then the derivation of the general mathematics/organization, as shown below, contains

 

concept(measurement)/Life/questing/relevance/elegance/context(entanglement)

 

When I first derived the mathematics of concepts, before I saw it in the fifth dimension, I used an operator that I called the Logic of the Half-truth that contained ‘truth’ explicitly and dealing with singularities [Lorentz contraction] in the dimensions [mass/energy, time and length], it is apparent that  ‘truth’ ‘contains’ consistency and consistency is required if we are not to have logical/physical singularities occurring. Consistency is basic to the mathematics of concepts and shows itself as arriving at the same answer from different directions and that is why I want to show the four axioms top-down and bottom-up.

 

In other words, THE general mathematics does and does not include us, but we are the ‘storytellers’ and are part of the ‘story’ and, at this point I need to include forward-planning because forward-planning is intrinsic to any concept of competition. The concept of ‘the’ and ‘a’ is a distinction that is carried through our space/universe because the definite is the special case and the indefinite is the general case [questing versus quantum mechanics].

 

We live in a probability space because it is a simple space [Occam’s razor and simplicity is paramount] and it is one space that answers the enigma of the Michelson-Morley experiment. For decades I have wondered about this enigma, that a physical thing, such as the speed of light, is the same to different people moving at different speeds, but this ability to see/experience the same as other organisms, is fundamental to our reality. Logically, and that will be discussed below, if we did not see the same things, a predator would remove those that could not see/feel/experience the predator and that is logic/logical because I am using my mind/brain. The answer to the question of ‘what is logic?’ will become clearer, below, in the act of measuring, and the act of measuring is at the ‘heart’ of a probability space.

 

The Michelson-Morley experiment was an enigma to me and it would be remiss of me not to share the answer, and that answer is, I believe, that we live in a probability space and a probability space provides the answer. The five dimensions of length (x, y, z), time passing and energy/(a+b)=1 quest to three cases of (two of) Heisenberg uncertainty [energy/time and energy/ position] and, for all energies, the speed (length to time) of free energy (photons) is constant to every measurement because the dimensions are all equally scaled by the Lorentz transformation (see chapter 72). To repeat, the speed of photons is constant to every measurement, means that any observer sees the speed of light as a constant no matter how they are moving and thus, the enigma is a property of a probability space!

 

The creation of space, time and energy provides the impetus to the expansion of the universe, and that is necessary for us to exist, and this formation of space, time and energy mimics the effects of a Big Bang, and provides another example of the ‘traps’ of top-down thinking. I had better explain that the outward movement of the galaxies suggests residual momentum from a Big Bang, but, I believe, that the expansion of the galaxies is necessary to provide the increased (potential gravitational) energy necessary to balance the increase in space, that is created by the movement of photons, because length, time and energy change as one [all by the Lorentz transformation]. Top-down is fraught with traps!

 

So, the dimensions of a mathematical probability space are length [x, y, z], time-passing and (a+b+c …)=1 where a, b, c…. are the probabilities at each point, and if I simplify that to: length [x, y, z], time passing  and (a+b)=1, for measurement/observers a and b, for simplicity, that is (apart somewhat from forward-planning) THE general mathematics of a physical probability space. Q.E.D.

 

However, to ‘operate’ the mathematic (concept), we need an operator (context) that can access the measurement of the space and we evolved to do just that, as part of Survival of the Fittest because that is the function of a successful parasite! The effect of this expression encompasses everything, but the mind/brain of Life links into this expression as well and complicates the story because the story includes us. Hence, again:

 

concept(measurement)/Life/questing/relevance/elegance/context(entanglement).

 

From chapter 79, the following quotation is from the book, The Story of Measurement by Andrew Robinson, ‘the Nobel laureate Eugene Wigner, gave a celebrated lecture with the title, “The unreasonable effectiveness of mathematics in the natural sciences”…. The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it.’ (p 45) As the British physicist James Jeans (1877-1946) once put it: ‘The universe appears to have been designed by a pure mathematician.’ (Is God a Mathematician, Mario Livio, p 1) and ‘Einstein once wondered: “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?”’ (p 1)

 

The above quotations show that many mathematicians believe that our universe is mathematical in nature and to mathematicians it does look mathematical. This is the problem that, to a hammer, all problems look like nails, or like quantum mechanics (or everything), what you measure (quest) is what you get. It will be shown that the universe is mathematical, but we have made mathematics a quest (like quantum mechanics) out of the physical mathematics of concepts and, as we will see, the over-arching reality is organization as distinct from, but including, mathematics and logic.

 

The simple general mathematical expression of the fifth dimension is (a+b)=1 and is basic to the probability space. ‘In the sixth century A D the term quadrivium was coined by Boethius to designate the four mathematical sciences dealing with numbers and magnitude: astronomy, geometry, arithmetic, and music. (p 102) ‘What was important to the Pythagoreans was the arithmetical relationship between the pitches … the arithmetic mean ½(a+b) … the harmonic mean 2ab/(a+b) … the geometric mean (square root ab). These numerical relationships were thought to provide a key to the structure of the entire universe. Indeed, the same ratios were thought to be found in the distances between the planets, and it was taught by the later Pythagoreans that the planets, or the spheres that carried them around a central fire, also produced sounds – the famous harmony of the spheres.’ (Let Newton be!, p 106, edited by John Fauvel)

 

Thus the basic idea behind a mathematical space is not new, but the ancient Greeks had the wrong expression, which is not surprising as the equation, not to mention a probability space were not well understood. However, in spirit/’hammer’, there are similarities to the derivation above, but I have to explain that it took me years to derive what I called the Mathematics of the Mind, re-named it the mathematics of concepts and, in the interests of settling the top-down/bottom-up problem, it is part of THE ‘General Mathematics in a Probability Space’. The intricate nature of this mathematics with respect to us will be discussed in the next chapter.

 

I believe that our mind/brain functions and deals with concepts and context using general-mathematics/mathematics-of-concepts by the use of ‘lobes’ in the brain to ‘concentrate’ concepts physically, see chapters 8 to 12, and that evolution [development of logic] is a bio-computer that we can use as a forward planning tool in reverse. In other words, our mind/brain evolved to use the most efficient method of handling concepts because of the iteration [questing] of Survival of the Fittest.

 

I find an easy way to think of the dimensions is as a theatre [x, y, z], time passing and everything that can happen, including the universe, is defined by (a+b)=1. This is surprising simple, and it is simple [Occam’s razor] and as well, it contains the properties of the space [questing and relevance] and another dimension [6], that is forward planning that (possibly) belongs in our world O and not in the physical/probability world P, due to the units that we use, that evolved for the predator/prey situation in which we evolved. The world O units, for simplicity, contain time interval and distance in order to calculate safe distances to coexist with predators [through speed of attack] and so inter-twined is the predator/prey situation, as the driver of Survival of the Fittest, that it can be used as a bio-computer.

 

So, let us unfold (a+b)=1, where unfolding is following the questing [of quantum mechanics, evolution, business etc.]. The fifth dimension (a+b)=1, in this simple form produces four absolutes/solutions (ignoring the fact that the speed of light is an absolute and must be constant):

(a) measurement/entanglement that are local physical and independent/orthogonal (a+b)=1 [classical local action and reaction of matter that provides expansion of the universe, reflection, diffraction of light and water waves],

(b) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b)=1 [conservation of (zero) energy across the universe, gravity, creation of space/mass/energy/time through the Lorentz contraction],

(c) measurement/entanglement that are local physical and independent/orthogonal, (a+b) [local/personal appreciation], and

(d) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b) [universal/reality-wide appreciation]

 

Note that (a) and (b) are the physical structure of the universe [described in many earlier chapters] and (c) and (d) were derived in chapter 78 resulting from the ratio of an interval [Golden ratio] that has been reported to produce a feeling that is used, I believe, by Life to compare contentment/elegance/beauty in both a personal and a reality-wide comparison that is behind the important sexual selection as a major driver in evolution.

 

For completeness, I want to foreshadow another quest that is the ‘orderliness’ of (a+b)=1 that embodies a general mathematic/organization that lies behind logic/mathematics. In a similar way that proverbs are a higher level of thought, everyday logic is, I believe, the reverse, and is the mental ‘breakdown’ of organization. For example, we have built up from the dimensions that potential gravity gradients are necessary for existence and this means that an object falls to the ground and at the same time, it is (everyday) logic/experience that something will fall to the ground without going through the calculations or thinking about it. We could say that proverbs and logic ‘simplify’ our lives.

 

From chapter 76: we derived:

‘concept/forward-planning/quest/relevance/beauty/context

for Life in world O, bearing in mind that Life lives in a deterministic reality that must be complete and continuous and the physical world P, that is totally entangled becomes:

 

measurement/quest/relevance/entanglement’.

 

These two expressions are the result of adding the mathematics of concepts, the properties of a probability space and then the effect of Life and is a more informative form of the general mathematics/organization.

 

As promised above, we meet the four axioms (forward-planning/quest/relevance/beauty) associated with the independent/orthogonal concept/context and I believe that they are intimately connected to the relationship between the mind/brain, that instigates the measurement and that being measured. I must stress something that is not obvious until pointed out, concept and context, also measurement and entanglement are both necessary and they are orthogonal and independent.

 

From above, for comparison, ‘certain things appeared to be missing, such as the mind/brain to determine elegance of content, forward planning (dimension 6), the measurement of each numeral (questing) and the relationship between numerals (relevance)’. The sequence of events actually happened as described, and having derived the above relationship bottom-up, it suddenly struck me that it was the ‘missing link’ to linking mathematics, science and every measurement, by a mind/brain, to the dimensions and a probability space. In other words, the four axioms link Life to a physical probability space world P and make an interconnected whole of everything and brings two new mathematics that work for every discipline and are specific to managing our relationship between people, Life and the physical world. In other words, it is what we need to become good little parasites, if we so choose!

 

A quick and easy description of the use of the mathematics of concepts from chapter 75 is ‘if we take the Cartesian system of the X-Y plane, we can say that some point is composed of two independent variables (x, y), and the mathematics of concepts can be handled similarly, bearing in mind that an iteration or mind/brain initiates a measurement and we are dealing with world O and world P. A little foreshadowing will make it easier to understand, that world P is a probability space and only has iteration, whereas Life has made world O into a “determinate”/non-entanglement world because of the necessity of creating a reality as part of questing/Survival-of-the-Fittest.’

 

Further, ‘taking the easy case of world P, questing is: X-Y axes with the concepts to be examined spread equally spaced along the X axis, and a curve/^ is drawn between each concept and every other concept with a height ^ equal to its probability and the sum of all the ‘heights’ is 1. This comes straight from the entanglement/measurement of the probabilities in a probability space. To move it into world O in order to automate or use a mind/brain, move the concepts and the ^ to make a ‘normal’ curve and read off the best concepts and their context. If this looks simple, ask yourself ‘why should it be complicated?’, when the universe requires only 5 dimensions and life six dimensions.’

 

Notice that this use of the mathematics of concepts assumes/needs, just as mathematics does, the use of the four axioms: elegance, forward-planning, questing and relevance as the basis of context/organization that is used by the mind in assigning the ‘numbers’/importance to the context. Notice also, that the context has to be numericalized and that shows that context is crucial to decisions and yet, that is precisely the part that we tend to ignore/under-use in day-to-day decisions. This seems to be an opportune opportunity to wonder if, or point out, that the lack of numericalization and appreciation of the importance of context may have led to the world’s current problems.

 

The problem with measurement appears to be a lack of definition of a relationship between the measurer and that being measured and that was the original problem in quantum mechanics that has not been fully answered for over a hundred years. The original question of whether a photon was a wave or particle can be seen as questing and you get the result that you seek, whereas, there are actually four factors (elegance, forward-planning, questing and relevance) that are involved in the measurement process and the full measurement process is necessary to use the mathematics of concepts in a useful way. A complete set of factors is only obtained by using bottom-up derivations and not an incomplete set that may come from top-down, and, using incomplete knowledge as if it were complete could lead to the problems that we see in the world around us.

 

There remains the question of where logic fits into this, after all ‘British philosophers and mathematicians Bertrand Russell and Alfred North Whitehead collaborated for eight years to produce their landmark work Principia Mathematica (three volumes, nearly 2,000 pages, 1910-1913), which aimed to demonstrate that mathematics can be stated using concepts of logic such as class and membership in a class.’ (The Maths Book, Clifford A. Pickover, p 324) However, I suggest (not having read the book, nor do I intend doing so, looking at a sample page) that the same quantities (forward-planning, questing, elegance and relevance) have to be taken into account in the Principia Mathematica and also, I wonder about the fundamentality of logic versus mathematics and that is resolved, I believe, below.

 

I found in chapter 75, ‘in a “nutshell”:

(1) We are the selection out of the multiverse because we are here.

(2) The one ‘dimensional’ use of the properties of world P that are properties of the space and could be called logical [as a machine is logical], but most important is Occams’ razor because simplicity is paramount.

(3) The two ‘dimensional’ use of worlds O and P by Life, and concept/context can perhaps be replaced by concept/quest/relevance/entanglement, where the concept evolved through forward-planning by the mind/brain and measurement by the eyes etc.

(4) Formal logic.

(5) Proverbs are a ‘higher’ logic/thinking that uses the mathematics of concepts to provide quick responses.

(6) The solution of (a +/and b)=1 is an absolute [Michelson-Morley] that the speed of light is a constant and all other measurements must have an assigned absolute [Plato’s problem] except for (7).

(7) The solution of the interval (a +/and b) is an absolute [Golden ratio] that makes beauty/appreciation/enjoyment logical/repeatable/relatable.’

 

This ‘recipe’ of logic appears at odds with the usual consideration that mathematics and logic ‘go together like a horse and carriage’ as shown by the attempt to derive mathematics from logic, above. The dimensions, I believe, show that our universe is based on mathematics and ‘logic’ from (a +/and b)=1, because mathematics and ‘logic’ go together [independence of +/and], but the actuality is, both for the physical world P space, measurement/entanglement (universe-wide) and for the world O space, concept/context (within a reality) that neither entanglement nor context is logic, but are communication. So, to draw further attention to entanglement/context being communication as part of the mathematics of concepts, where is logic? Is logic what we see when we look at organization? Is logic/communication a proverb in reverse that helps us understand how ‘bits’ fit together organizationally? Is communication the basis of organization, or is organization a ‘string’ of logical ‘bits’ joined together through communication?

 

Working bottom-up shows a different way of looking at concepts from top-down that employs guesswork and I am going to suggest that logic must evolve from mathematics and involves an iteration or mind/brain. Iteration is mathematical and is defined mathematically, whereas logic requires choice and both are found in iteration (to a certain extent) and iteration has produced Life through Survival of the Fittest. In other words, iteration [Survival of the Fittest] has been the driver of evolution at the same time that Life has developed logical process in their mind/brain as part of being able to compete in the iteration.

 

So, we are back to iteration in world P and the mind/brain uses logic in world O, where world O contains world P and that explains the diversity of the things that we call ‘logical’. Also, from chapter 73, ‘remember that a probability of existence space has an infinitely small chance of existing [at 1] and likewise, has an infinitely small chance of not existing [at 0], and forms a “twilight zone”’, and whatever we are, we are logic because logic only comes from iteration or a mind/brain.’ Notice that the simplest case, as we would expect, is a probability of existence and not a definite existence and that is in line with the idea presented above that the definite is a special case and the indefinite is the general case. Of course, there is nothing to say that our universe does not exist, but I believe that a probability space has the dimensions needed to allow Life to develop.

 

The senses [touch, hearing, sight etc.] that we evolved, only evolved because they worked and they worked because they interacted with the physical world [as measurement/entanglement] and this was an iteration because of the vast number of generations that contributed to evolution. I believe that we developed logic as part of the forward-planning that is required in a predator/prey situation, but we have used memory to build that logic on previous experience [locked in by fear/emotion]. We have gone further by using our evolution/history to solve problems [proverbs] and guide our way, as I point out with Newton’s laws of motion and the understanding of ‘the so called thesis of the Unity of the Virtues’, as derived in chapter 76.

 

From above: concept/forward-planning/quest/relevance/beauty/context is a solution/derivation to space-time and (a+b)=1, which is a general mathematics and each term involves measurement and communication (‘logic’) in a probability space. A simple comparison of concept and context has been given, above, and each value that is summed to unity is ‘judged’ (forward-planning, questing, relevance, elegance) and this judgement is logic of all types, but judgement/choice requires a mind/brain to ‘compare’. All our bodily parts/structures are progressively changed/improved without going back [I called this the Rule of Life], and whilst this is logical, it maintains a reality because animals’ brains have a sub-format [hindbrain] and reality is vital to survival. Perhaps it is clearer to say that we have created logic in the mind/brain to survive, but we use iteration as a basis of the immune system.

 

Mind/brains are built up progressively [the cortex enlarges] as animals evolved, and, unlike a computer, thoughts/data are curtailed/approximated and produce [somewhat randomly, in the lobes] new thoughts to be considered/compared (chapters 8 to 12). A good example of evolution is why we have two hemispheres to our brains (chapter 12) and the search, by Life, to overcome this historical problem is shown by: ‘anterior commissure, a collection of nerve cells that connects the brain’s two hemispheres. It is smaller and appeared earlier in evolution than the corpus callosum’ (The Brain Encyclopedia, Carol Turkington, p 26).

 

The four axioms show that we are not controlling ourselves and our world as well as we could because of a lack of understanding of organization (see chapter 73), and, in fact, we have caused an extinction-event to rival the Cambrian and the general-mathematics may hopefully be able to use forward planning etc. to bring ourselves under control before it is too late.

 

A simple example of the use of the general mathematics/organization might be appropriate to explain the ‘why?’ of the (apparent) enigma of Godel’s Incompleteness theorems. ‘It would never be possible to create a fully complete system of mathematics where everything from the lowest axioms to the highest, most complex proofs could be shown to be unequivocally true (The book of Numbers, Peter J. Bentley, p 101) ‘Turing managed to prove that it was not possible to show universally (for any given examples) that a logical or arithmetic statement was true or not. This was yet another nail in the coffin of “perfect mathematics”’ (p 102). This (apparent) enigma obviously caused a ‘stir’ in the mathematics community and, as I know little of the subject, my ‘penny’s worth’ may or may not contribute to the understanding behind Godel’s theorems, but it does add-another-factor to the idea that our universe is a probability space because it does produce a reason, and further, it shows that the explanation is organizational more than mathematical or logical and shows the ‘position’ of general mathematics/organization ‘above’ mathematics and logic as outlined above.

 

All of the general mathematics/organization is applicable to Godel’s theorems, as expected, but the properties of the space, ‘relevance’ and ‘questing’ seem particularly pertinent to the following, that the Theory of

Relativity is physical, the constant speed of light (energy) is logical and physical, Godel’s theorems would appear to be logical. Logical relativity is a property of the space and infinitely fast like the conservation of energy, and in the same way can invoke chaos throughout the universe if a logical singularity occurs.

 

This says to me, that a special exact case (mathematics is defined to be exact) cannot encompass, in the limit, a mathematics of concepts that is exact only in the limit and Godel’s theorems are a statement of this logical singularity. Thus, we can use mathematics, but is there a limit, like the Lorentz contraction that will stop every point in a probability space being set to a value that makes the sum not equal to unity and thus produce a logical singularity. If measurement is at the ‘heart’ of a probability space, then the sheer number of ‘factors’/points may be adequate safeguard, or, out of the multiverse, it has not yet happened.

 

Another simple example, using the above, might be useful in changing the traditional mindset. Einstein’s equation E=mc2 is world O and says as much about the units as it does about the relationship between E and m. In world P, E is equivalent to m, after all, they are both states of energy. I suggest that simple equations are often states, for example, energy = Planck’s constant times frequency, where mass and frequency, in world P are (basically) the same thing and the result of quests. This problem of the particle/wave nature of the electromagnetic spectrum confounded science, and further, the word ‘electromagnetic’ delves even further into questing.

 

There is nothing wrong with exploring our universe, but the problem of description is to ‘lump’, not ‘split’, and to look for ‘basics’. ‘The goal of explaining everything by a single, elegant, unified equation is still pursued by physicists today’ (p 214) is unobtainable for the same reason as given above. However, if we look in world P, we might find a relationship of a sort that is valid in that world.

 

The goal in the quotation is concept driven and neglects context. Small and simple (concept) might be elegant, but so is infinite and logical (context) and I have already quoted this ‘relationship’, above, as the basis of measurement [concept/context]. The right hand side of the ‘relationship is a simplification of ‘everything’ from the dimensions that expands to cover the universe in a probability space because of the inbuilt questing. The left hand side is (literally) ‘everything’ from the Big-Bang/Big-Whoosh and the relationship is our old friend:

 

energy is equivalent to (a+b)=1, where energy is everything and a and b are measurement/observers in a probability space.

 

If we unfold (a+b)=1 in a probability space, as above, including Life, we get:

concept/forward-planning/quest/relevance/beauty/context.

 

If we unfold (a+b)=1 in a probability space, as above, excluding Life, we get:

measurement/quest/relevance/entanglement.

 

If the mathematics of concepts can be seen in the dimensions, so it must be universally applicable and true. Can we afford to neglect it, especially as it ‘unlocks’ processes that we have not yet explored, applies to all disciplines and is ‘natural’ to a probability space, unlike mathematics that is obviously flawed/foreign, but useful in world O?

 

Conclusion: The general mathematics/organization describes the organization of everything because it is based on the dimensions through the (physical world P) mathematics of concepts that contains the special case of mathematics (our world O) by indicating the four axioms of measurement that link Life with its surroundings and shows the basic bottom-up decision making process in applying context to concepts using a mind/brain.

 

The question of logic was, I believe, laid to rest as a context of the concept of the general mathematics/organization in the form of two ‘opposites’, proverbs being the consolidation of the mathematics of concepts to improve the mind/brain’s performance in evolution, and logic as a means of understanding/using ‘bits’/parts of the general organization of the universe to improve our reality as another means of increasing our performance in evolution.

 

I have been bemoaning the top-down methods used by philosophy, science and even (somewhat differently), mathematics and I feel that I have shown that we do live in a probability space and that a probability space generates enough dimensions and properties to show that bottom-up can be used to organizationally align science etc. to adjust the imbalance that is creating the world’s problems.

 

‘It took another three hundred and fifty years for the Catholic Church to admit that “mistakes had been made in the case of Galileo” in a statement made by Pope John Paul II in 1992’ (p 165). The world’s problems cannot wait for hundreds of years for a general acceptance of the fact that we live in a probability universe, but science, by using bottom-up, can attack/solve the problems immediately by using the mathematics of concepts together with the four axioms [Einstein’s, and Academia’s acceptance of the Michelson-Morley experiment is a case in point]. That said, the mathematics derived here is the mathematics of every discipline including science. It is a general method of analysing everything to completeness and knowing that it is correct, within certain limitations.

 

The above has shown how Life is superimposed on the physical, through the two sets of relationships, firstly, the physical environment, and secondly, for life using that environment, and that shows that our presence is that of either a parasite or welcome-addition/symbiont. A parasite should not kill or injure its host and if it does, it is poorly adapted and should change/adjust its methods of survival. We are treating our environment poorly [over-population, mass extinction, global warming etc.], and, I believe, that we now have the organizational/mathematical/logical/social skills to rectify the problem and become welcome-additions/symbionts and reap the benefits that develop from symbiosis with our world and all that it holds.

 

References: all quotations are fully referenced in the body and earlier chapters can be found on    darrylpenney.com    if required.

 

 

By Darryl Penney

 

Abstract: the golden ratio has intrigued scholars from all ‘walks of life’ and many books have been written on the subject over hundreds of years because of a ‘feeling’ about a ratio that a number of people say is important, and the reason is, I believe, that the ratio is a quest/solution to the fifth dimension. I also believe that this feeling of ‘something’ that has been ascribed as being of beauty/completeness/satisfaction is probably a resonance with the measurement/entanglement/ecstasy of the ‘fabric’ of the whole universe as well as locally. It seems that this effect is defined physically/measurably simply by a ratio, but logically as a feeling and the possibilities of beauty/completeness/satisfaction have been explored/quested by Life and used to that end simply because it can be used. In other words, it is possible that Life has taken a ‘resonance’ of our universe [absolute] and has ascribed to it the concept of beauty/completeness/satisfaction, defining an absolute for one of the large number of concepts that Plato had problems defining, such as justice, for which an absolute must be assigned. Beauty/completeness/satisfaction can be incorporated into our reality because the ‘resonance’ is common to all members and so can be used as a selection ‘tool’ and ‘the primary focus’ of Darwin’s major work Descent of Man, ‘two-thirds of the text was devoted to sexual selection’, but does not say how or why it exists.

 

The following quotation is from the book, The Story of Measurement by Andrew Robinson (p 42) and sums well the extreme feelings that the golden ratio has invoked for hundreds if not thousands of years and sets the scene for, I believe, an explanation of why those feelings have been generated. The vagueness of the feelings that such a simple ratio can invoke is, I believe, a window into the workings of the universe and how Life has made use of what might be only an un-needed off-shoot of the fifth dimension and shows the measurement/entanglement of a ratio (measurement) and a feeling (entanglement). Notice that there is a local effect (a+b) and a universe-wide effect (a and b) of measurement/entanglement in a similar way to local measurement/entanglement of the ‘bounciness of matter’ (a+b)=1 and universe-wide measurement/entanglement of gravity (a and b)=1 [chapter 77].

 

But first, a digression is necessary , ‘the Nobel laureate Eugene Wigner, gave a celebrated lecture with the title, “The unreasonable effectiveness of mathematics in the natural sciences”…. The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it.’ (p 45) I need to say that there is a rational explanation and that is that mathematics ‘works’ because mathematical/logical relationships are the fifth dimension and quests of a mathematical relationship (a+b)=1 are the basis of our universe. Further, it will be shown that one of the quests may or may not be necessary to the functioning of the universe, but Life, I believe, has used it to enrich our lives and provide a means of sexual selection.

 

‘It is often claimed that the face in Leonardo’s Mona Lisa reveals the proportions of the golden ratio. That is, if you draw a rectangle around her face, the ratio of the rectangle’s height to its width is close to 1.618:1 (just over 8:5) Leonardo never noted that the ratio was in his mind, but it is a fact that he was a close friend of Luca Pacioli, who published a three-volume treatise on the ratio, Divina Proportione. Pacioli particularly believed that the ratio’s ‘divine proportion’ was to be found in the human face.’

 

‘The ratio has been alleged in many other contexts, such as the Greek Parthenon, the two-column type area of Gutenberg’s Bible, the spirals of the chambered nautilus shell, and even the proportions of modern credit cards. It has fascinated mathematicians from Euclid (who first defined it in writing) to Kepler and Roger Penrose. ‘”Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal.  In fact, it is probably fair to say that the golden ratio has inspired thinkers of all disciplines like no other number in the history of mathematics”, writes Mario Livio in the Golden Ratio. But there is no proof that any of these apparent incidences are intentional.’

 

‘Mathematically, the golden ratio, now known as phi – after Phidias, the Greek sculptor said to have used it in the Parthenon – is best defined in terms of the division of a line into a larger part a and a smaller part b. The golden ratio is the ratio when the whole line is to the larger part as the larger part is to the smaller part. To be more precise: phi = (a+b)/a=a/b. It equals (1+ square root 5)/2, an irrational number approximately equal to 1.618.’

 

In a probability space the physical dimensions are space-time and  (a+b)=1 as an illustration, for measurements/observers a and b and this fifth dimension can be unfolded to see the component parts that the probability space quests in the manner of quantum mechanics. Questing is continual and means that measurements remain indeterminate, as they must, until a measurement is required by an iteration or mind/brain and that measurement is current only at that time of measurement.

 

Firstly, (a+b)=1 can be unfolded to show (1) from the equation, measurement/observer a and b, (2) from the equation, entanglement (a+b), (3) the logical part of measurement/observer a and b, so there is an independent/orthogonal logical duality to measurement, (4) there is the logical part of entanglement (a and b), and there is only one solution/absolute (5/6) to this equation and that is that the speed of electromagnetic radiation is a constant/absolute. Note that this solution has a physical side and a logical side that occurs because the dimensions [space-time, energy] produce the space to time relation for all energies, and the other two combinations produce the Heisenberg uncertainty relations energy-space and energy-time. The physical side is quested and returns a particle, wave, magnetic or electrical effect as sought, and it is an interesting point that the electromagnetic effect is taken to mean that the electric and magnetic fields are orthogonal. The lack of a solution other than for the speed of light leads to Plato’s problem (7/8) of no absolutes unless assigned for justice, beauty etc.

 

Secondly, an illustration of the (logical) questing that is carried out infinitely fast [product of the space] compared to the constant slow speed of light, relativisation of the dimensions allows the law of conservation of energy to maintain the energy at zero [negative potential, the others energies positive]. However, the questing that is the ‘organizational power’ behind quantum mechanics quests every possibility and we have yet to consider another possibility, and that is (9/10) (a+b).

 

(a+b) is very similar to the interval of the golden ratio and bearing in mind that (a+b) represents measurement and logic as independent/orthogonal entities in the physical world, they will necessarily appear as concept/context to our mind/brain. (a+b) contains a possibility that must be quested, so let’s do it, as above, that it is an interval, and an interval has a solution and that solution is the golden ratio. To expand, (a+b) would contain a duality/orthogonality of measurement and logic, both of which are essential to appreciation of music, paintings, scenery etc. and, as we have seen, logic is a ‘rag bag’ of entanglement/logics of space/machine as well as world O.

 

It could be that (a+b)/a=a/b represents the experience of the measurement operation to the thing being measured equates to the relation of the measurement to the observer, but this might be reading too much into the fifth dimension and it might just be a piece of luck that brightens our world. On the other hand, it does seem to make sense to a (logical) degree, but that does lead into the question of the difference between logic and mathematics. ‘In the Principia, Russell and Whitehead defended the view that mathematics was basically an elaboration of the laws of logic, with no clear demarcation between them.’ (Is God a Mathematician?, Mario Livio, p 189) The derivation below shows, bottom-up, a foreshadowing that the universe is based on mathematics, but we, Life and the bio-computer of evolution derive logic, but that will have to wait for the future.

 

The Golden ratio may not be necessary to the functioning of the universe and is a mechanical logic quested at the same time as the necessary parts and we have made use of it in world O. In fact, as an example, there may be no absolute for justice, beauty etc. (Plato’s problem), but we still need a reality of administration from, say, no punishment to capital punishment that has a consensus in concept and context etc., or, another example, the reality of beauty giving a ratio/measurement (golden ratio) as well as consensus of agreement because consensus is necessary in a reality if it is to be useful.

 

Thirdly, notice that a and b have been considered as measurement/entanglement in the physical universe and can be written as (a+b+c …)=1, but the mental field of the mind/brain leads to concept/context because our mind/brain evolved a new and different field that is determinate, not universe-wide because our reality must be definite and defined if we don’t want to end as something’s dinner. Our mind/brain uses (11/12) the mathematics of concepts that is immediately apparent from (a+b)=1. In other words, Life is bound by the dimensions of the universe, but Life has created its own universe that is the ‘struggle of life’ bounded by its own reality and we have, by necessity, changed our outlook into the Newtonian mode.

 

In the physical universe, everything goes to completion, but Life has ‘built’ on this by using the units of survival [flight distance] – speed of attack and distance to escape or catch the prey and this requires a measurement by the eye (usually) that coalesces (necessarily) into what we want to see. In other words, a force is an impulse that is halted and requires a mind/brain to determine how much force is to be applied.  Newtonian physics is built on forces, ‘as we now know, his faith in forces was justified to such an extent that it is widely regarded as Newton’s most important scientific innovation.’ (Let Newton be!, John Henry, p 59, edited by John Fauvel)

 

Further, ‘a slightly naughty thought can come to one’s mind here. Is it due to the nature of physics that the mathematical tools started by Newton are so essential for many parts of physics through the centuries? Or is our selection of worked-on parts of physics still largely Newtonian? (p 244) This quotation requires/legitimises the search for enigmas, such as the golden ratio, constant speed of light, logic of gravity etc. that are hidden by Newtonian physics because the logic is subsumed into the concept of force.

 

To digress, the above is a derivation/explanation that I am comfortable with, but how does it jibe with history over thousands of years? Surprisingly, what I am saying is not much different to the ideas of antiquity to Newton’s day. ‘In the sixth century A D the term quadrivium was coined by Boethius to designate the four mathematical sciences dealing with numbers and magnitude: astronomy, geometry, arithmetic, and music. (p 102) ‘What was important to the Pythagoreans was the arithmetical relationship between the pitches … the arithmetic mean ½(a+b) … the harmonic mean 2ab/(a+b) … the geometric mean square root (ab). These numerical relationships were thought to provide a key to the structure of the entire universe. Indeed, the same ratios were thought to be found in the distances between the planets, and it was taught by the later Pythagoreans that the planets, or the spheres that carried them around a central fire, also produced sounds – the famous harmony of the spheres.’ (p 106)

 

Is the contraction/illustration (a+b)=1 and (a+b) very much different to the above? Also, (a+b)=1 is a simplification that is intimately-linked/derivable-from the dimensions that underlie the structure of the universe in a similar way as was believed, above. The continuity of reality is apparent because 0 [certainty of non-existence] and 1 [certainty of existence] are infinitely unlikely, but still exist and we have no way of knowing whether we exist, do not exist or exist in some ‘twilight zone’. For those people that are more comfortable with existence, there is the possibility of existence, but we need the dimensions of a probability space to exist. On the other hand, Life can exist here, and through evolution, determines a logic of possibilities that is open to us through studying fossils and history and that makes us agents of logic.

 

To return to (11/12) the mathematics of concepts, this is immediately apparent from the dimensions (a+b+c+d etc.)=1, where I have used ‘etc.’ to indicate that it is our choice to limit the number of terms because this is the basis of the evolved mind/brain and not universe-wide entanglement. Notice that both measurement and logic are available and we use both in decision-making because as we increase the number of concepts and contexts, the accuracy of our decision should increase. This decision-making is five dimensions, but the predator/prey situation requires (13) forward-planning and a future time, and that could be a sixth dimension that Life uses and is a fundamental part of staying alive. Contrast this to: future-time as required by Life, Newtonian-time is a fixed time interval, Einstein-time varies with relative speed according to the Lorentz transformation, the universe-time is continually changing as part of relativisation and time in a mathematical probability space is time-passing.

 

I will repeat a quotation from chapter 77, ‘it seems that … knowledge cannot spring from experience alone but only from a comparison of the inventions of the intellect with the facts of observation’, wrote Einstein, (The Story of Measurement, Andrew Robinson, p 10) because the golden ratio has caused such questing from scholars for a long time. There is an explanation, as above, that the fundamentals of the universe ‘speak’ to us and that happens much more than is often appreciated. Our world O contains/subsumes world (physical) P and we often don’t realize/appreciate the basis of measurement behind sight, hearing etc., entanglement behind society etc. and ecstasy behind pleasure/appreciation as well as the combinations. In other words, the fifth dimension (world P) is measurement/entanglement/ecstasy, but whilst the effect is there in world P, the interpretation is world O, concept/context/pleasure and the sixth dimension [forward-planning] is purely world O.

 

Further, quantum mechanics and relativity do not affect us, usually, but we don’t recognise that the questing, behind quantum mechanics is the familiar evolution, business and organizational practices. Relativity and relevance have a basis in love, family life, reality as well as evolution and business etc. The physical world intrudes in small ways, but usually our reality, having evolved over 3,000 million years disguises them because our mind/brain has built a determinate space on the entanglement space of the universe. The physical manifestations are there in the diffraction of water waves, the Michelson-Morley experiment, our seeing is measuring, our forward-planning produced the Newtonian units of speed, force and distance that we use for hunting etc.

 

Questing, I believe, involves all possibilities that necessarily remain indeterminate until measured at some instant in some way and using Einstein’s quotation and looking at the description of the golden ratio, the golden ratio is a unique solution and an absolute of beauty/love etc., but it is entwined with the other two to make combinations even though independent/orthogonal. This links in with the mathematics of concepts and shows that the proverb ‘handsome is, as handsome does’ (a simple solution of the mathematics of concepts) needs the new attractor, that is, the golden ratio (an absolute) to make it more useful and accurate, especially to make a reality [consensus] for sexual selection.

 

Given that the female half of the population aspire to beauty by painting their faces, hanging jewellery from their ears, walking on high heels etc. and the other half would like to possess that ‘beauty’, it can be seen that beauty in all its forms from music, art, bush-walking etc. form a large part of our lives. The relationships can take many forms, such as harmonics, but absolutes are unique solutions, such as the constancy of the speed of electromagnetic radiation, instantaneous entanglement across the universe for the conservation of energy, gravity and other ‘nuts and bolts’, and now we can assign the appreciation of a concept of beauty/correctness/satisfaction to world O.

 

Over the years, I have gained the impression that sexual selection was a small part of evolution and it came as a surprise that the ‘primary focus’ of Darwin’s major work Descent of Man, ‘two-thirds of the text was devoted to sexual selection. Darwin believed that the more attractive an individual animal is to potential mates, the more likely he or she is to be successful in the “struggle for reproduction”.’ (Evolution in the Antipodes: Charles Darwin and Australia, Tom Frame, p 38)

 

As mentioned above, and I am sure that Darwin would have agreed that colour in fish, birds etc. play a large part in sexual selection, as well as the beauty of the pelt, ratio of limb size are all sexual signals and we should not be surprised by the fact that the Golden ratio, as an absolute, is so all-pervasive. It is well known that ladies wear long hair, to be identifiably feminine, and as a measure of their personal health. My dancing partner spends an inordinate amount of time worrying about her hair, its length, thickness, condition etc. However, it must be recognised that sexual selection is more than a (Newtonian) concept because it also generates a local logic/feeling [context, within the self, (a+b)] but also a resonance with the universe [context, across the reality, (a and b)] both measurably and is a concept that can be used logically and practically as a ‘target’ for evolution.

 

Conclusion: Every space and what is in it must be a product of the dimensions of that space and the test is simply to derive everything from the dimensions and if anything cannot be explained, we need to add another dimension to cater for it. I am, at present, content that the five physical (and the sixth in world O) are adequate to generate our universe. I have always wondered how science could use/accept logic, beauty etc. as part of the four space-time dimensions, and I believe that the above, using five dimensions is far more believable [also it was/has been expected/anticipated since the 1920s].

 

‘Bohr argued that we needed to go back to the drawing board to understand the quantum world and could not use concepts that were familiar in everyday life’ (50 physics ideas, Joanne Baker). The irony is, and I believe that I have shown it above, that the everyday world is the same as the quantum and the relative world when viewed in the correct way through the fifth dimension. The ‘roots’ are questing and relevance and they pervade literally everything, such as organization, evolution, family etc. and they are concept, context and satisfaction and underlie the questable-part of the fifth dimension.

 

Finally, placing the above within an over-arching unity, I believe that every ‘transaction’, in the mode of quantum mechanics to derive a determinate answer requires answering each of:

 

measurement/forward-planning/quest/relevance/beauty/entanglement

 

References: all quotations are fully referenced in the body and earlier chapters can be found on   darrylpenney.com  if required.

By Darryl Penney

 

Abstract: Life has taken the physics of our universe and used it for our own convenience to create a reality that can support us, as well as evolving a mind/brain that uses a sixth dimension that allows us to forward-plan. We take this for granted, and so find difficulty with relativity and quantum mechanics, even though they are in everyday use, but we don’t understand the context, whereas diffraction is an everyday occurrence that shows the physics of the universe intruding into the world that we have created and shows that Newton’s laws of motion are too simplistic and their outdatedness shows that science has broken its cardinal rule of continually re-building science, as it should in the light of the derivation presented here, and a modernized version of Newton’s laws is attempted. The probabilistic nature of the universe lies behind entanglement and produces diffraction, reflection and makes matter ‘solid’ so that it bounces and creates space and energy so that matter can form solar systems etc. and allow us a place to evolve and shows the difference between local (physical) and universe-wide (logical) entanglement. The solution to Huygens principle appears to be a simple local entanglement between photons and the aperture and indicates that the intensity of the diffraction decreases closest to the aperture.

 

 

‘Dutch physicist Christiaan Huygens devised a practical way for predicting the progression of waves … each point on the circular wave can be thought of as a new source of circular waves … by repeating the principle many times the evolution of the wave can be tracked’ [Huygens’ principle]. (50 physics ideas, Joanne Baker, p 60) ‘A linear wave remains straight as it propagates because the circular wavelets it produces along its length add together to form a new linear wave front ahead of the first. If you watch sets of parallel linear ocean waves as they pass through a small opening in a harbour wall, however, they distort into arcs once they pass through the gap … called diffraction. (p 61)

 

‘One unrealistic prediction of Huygens’ principle is that if all these new wavelets are sources of wave energy then they should generate a reverse wave as well as a forward wave. So why does a wave propagate only forwards? Huygens did not have an answer and simply assumed that wave energy propagates outwards and backwards motion is ignored. Therefore Huygens principle is really only a useful tool for predicting the evolution of waves rather than a fully explanatory law.’ (p 63)

 

The idea that the phenomonen of diffraction is not well understood is reinforced by the following quotation. ‘The Huygens–Fresnel principle provides a good basis for understanding and predicting the wave propagation of light. However, there are limitations to the principle and differing views as to whether it is an accurate representation of reality or whether “Huygens’ principle actually does give the right answer but for the wrong reasons”.’ (Huygens-Fresnel principle, History, Wikipedia)

The sentence: “Huygens’ principle actually does give the right answer but for the wrong reasons” suggests that Newtonian physics is not correct and it will be shown to be conceptually based and is deficient in context, where both concept and context are independent and form a duality. Additionly, Newtonian physics mixes our world O concepts/context without adequate regard to the physical world P measurement/entanglement and that leads to difficulties with relativity, quantum mechanics etc. as well as, as we shall see, diffraction. These difficulties have arisen, I believe, firstly, because top-down methods are being used instead of bottom-up methods derived from the dimensions and secondly, that Newtonian physics is being used.

 

‘Where Newton’s laws do not hold is for things moving close to the speed of light or with very small masses. It is in these extremes that Einstein’s relativity and the science of quantum mechanics takes over. (50 physics ideas, Joanne Baker, p 11) This is not quite true because diffraction is an enigma to physics and has remained so for over 300 years and needs a re-think, and secondly, everything is based on five dimensions that smoothly intertwine and I will show that relativity and quantum mechanics are all around us and do not suddenly ‘take over’.

 

In chapter 75, it was shown that Newton’s laws of motion are too simplistic and need to be amended to ‘a body remains at rest, or in uniform motion unless acted on by a measurement and/or entanglement’. This is still not the general case but it does contain the independence/duality of the fifth dimension [(a+b)=1 for measurement/observers a and b, as an illustration] and is expressed only in physical world P units. The present law is adequate in world (our) O units of force, velocity and time interval that are part of Life’s reality, but form only a simple picture, and the other laws will be considered below.

 

Secondly, relevance and questing underlie relativity and quantum mechanics and act throughout the universe and we use them all the time in relationships, business and everyday life. Physics has difficulty with relativity and quantum mechanics and they came to prominence due to (seemingly) bizarre happenings that can be simply explained when it is accepted that we live in a probability of existence universe. Literally everything is based on relevance [entanglement] and questing [continual measurement] because they are a requirement of a probability space.

 

I have used the following quotation before to try to justify a change in the ‘view’ of science to include the fifth dimension explicitly, as compared to the ‘dipping’ method usually used, in other words, I am using ‘bottom-up’ versus the traditional ‘top-down’ approach. ‘It is not always appreciated that, 60 years ago, the makers of modern quantum theory were totally steeped, immersed, educated, brainwashed, if you like – in the mathematical methods of Lagrange and Hamilton; these ideas had grown out of, and were the natural evolution of, Newton’s dynamical ideas.’ (Let Newton be!, edited by John Fauvel, p 244) Further, ‘as we now know, his faith in forces was justified to such an extent that it is widely regarded as Newton’s most important scientific innovation.’ (p 128) ‘A slightly naughty thought can come to one’s mind here. Is it due to the nature of physics that the mathematical tools started by Newton are so essential for many parts of physics through the centuries? Or is our selection of worked-on parts of physics still largely Newtonian? (p 244)

 

It might be easiest to foreshadow the derivation by repeating an example from chapter 75, ‘A prediction/example might clarify the overall picture because statistical mechanics takes a concept, such as photons leaving a point source and assumes that enough photons are leaving randomly, so that there is an even distribution. I am saying that an independent/orthogonal entanglement ensures that there is an even distribution (context) and further, in more complicated cases, such as diffraction, a specific simple sequence occurs that becomes an enigma and unexplainable according to our present grasp of the laws of physics.’

 

I have to say that I believe that our universe is a probability of existence space with the dimensions of space-time and a fifth dimension (a +/and b)=1, as an indication, where a and b are measurement/observers and it can be seen that ‘+’ describes a measurement/entanglement duality and that this duality is necessarily independent/orthogonal. Further, the ‘and’ describes a measurement/entanglement logical duality and that this duality is necessarily independent/orthogonal also. [these independent/orthogonalities are examples of the questing of (a+b)=1, and it is obvious that there must be independence/orthogonality if there is to be questing.] I mention this because science recognises the measurement, but not the entanglement and this is shown in statistical mechanics and Newton’s laws, above. These assumptions are unnecessary if logic/entanglement is recognised and produces much ‘richer’ results, as we will see. It is interesting that entanglement of particles is now recognised (top-down), but not the overall entanglement of a probability space.

 

Diffraction is an enigma, as are aspects of relativity and quantum mechanics only because the method of viewing them needs a better description, and that description is provided through the dimensions of a probability space [space-time and (a+b)=1]. ‘Light travels in straight lines; waves do not; they bend around corners, as has been observed for sound and water waves; therefore, light cannot consist in (ether) waves…. Obviously Newton reported only experiences of a general kind – just the kind of everyday experience which was typical of Aristotle’s style of science. In the debate on the nature of light, Newton used no controlled experiments, such as he had performed to support his colour theory.’ (p 96) ‘Interestingly enough, it was Newton himself who supplied the main line of argument against Huygens’ theory, when he claimed that it was unable to explain the rectilinear propagation of light.’ (p 98)

 

From chapter 75, ‘consider a beam of light passing through a small hole [comparable to the wavelength] and Newton’s laws of motion says that the beam passes through as it entered because no force acts on it, however, I am saying that entanglement provides a logical reason for the photon to change direction without a force. [Newton’s law is a simplification with little context as will become apparent]. The beam is diffracted and spreads out according to Huygens’ principle, where Huygen’s ‘wavelets’, generated at each instant are, I believe, probabilities and the photon changes direction in accordance with the logic/entanglement to make a new total semicircular wavefront.’

 

‘To simplify, a photon has a measurement/entanglement duality, a constant speed/energy (concept), but direction is a context, and in the same way that a vector has force and direction, the photon has energy/speed and a direction and obeys Newton’s law ‘unless acted upon by a force or entanglement’ [my addition]. Force is a world O concept and in world P we have to use energy/logic, or more accurately, energy-measurement/entanglement. Whilst my derivation is more complicated, it predicts and explains independent/orthogonal outcomes, and as an example, ‘one unrealistic prediction of Huygens’ principle is that if all these new wavelets are sources of wave energy then they should generate a reverse wave as well as a forward wave. So why does a wave propagate only forwards? Huygens did not have an answer’. (50 physics ideas, Joanne Baker, p63)’

 

‘If the wavelets are considered probability fronts, the probability of the photon reversing is zero given the simple thought experiment and that solves that problem. If we bring the real world into the picture by introducing a dust mote, the probability front increases behind because of the entanglement of photon and dust mote as they approach and at some point the probability becomes unity and reflection occurs as a logical effect. Notice that if the photon energy is sufficient, the probabilities

include the photoelectric effect or absorption and it can be seen that the iteration/questing inherent in the mathematics of concepts is becoming apparent. This interpretation makes more sense/logic than photons ‘bouncing off’, which is nonsensical as it is an entanglement, as shown below’

 

From chapter 73, ‘remember that a probability of existence space has an infinitely small chance of existing [at 1] and likewise, has an infinitely small chance of not existing [at 0], and forms a “twilight zone”’, and whatever we are, we are logic because logic only comes from iteration or a mind/brain.’ Further, the Theory of Everything suggests the evolution of consciousness starts at the Big Bang/Whoosh and proceeds through energy, particles, bacteria, multicelled organisms to us etc., but within that space, there exists measurement/entanglement [later with life evolving concepts/context]. Given that Newton was dipping into both worlds O and P [a mind/brain is required to measure a force], the three laws of motion are predominately concept/context and don’t consider world P sufficiently and that is why the laws break down when relativisation and quantum mechanics are involved, because logic is involved explicitly.’

 

This is the fundamental logic, I believe, that sits behind our probability space, that there is a higher probability that the simplest ‘path’ be taken than other ‘paths’ [Occam’s razor] and a higher formal recognition of this is relativisation [(a+b+c …)=1]. Relativisation is the mechanism behind the Law of Conservation of Energy and could allow particles to change direction through measurement/entanglement that is continually being adjusted (physically and logically) to prevent a physical or logical singularity that would, presumably, throw the universe into chaos.

 

Photons have a constant speed [ratio of the dimensions] but their energies are continually relatified [Pound-Rebka] and Newton’s first law, that a photon remains in a state of uniform motion is clearly correct, but its energy is continually changing at any time because relativisation is continuous across the universe to keep the conservation of energy at zero. Consequently, a particle’s kinetic energy and speed change continually. Secondly, any extra energy given to the photon does not change its speed. Thirdly, direction does have an entanglement component and Huygens’ principle is the workably correct means that has a ‘logical’ explanation as would be expected in a probability space.  Fourthly, a basic universe-wide factor should be used, and the conservation of energy is just that.

 

This leads to two implications, firstly, ‘from his study of the manner in which pulses and waves in material media spread out after passing through gaps, Newton argued that since light travels straight on through such gaps, its nature cannot be understood using wave theory alone.’ (Let Newton be!, edited by John Fauvel, p 57) Secondly, if I can repeat that ‘a slightly naughty thought can come to one’s mind here. Is it due to the nature of physics that the mathematical tools started by Newton are so essential for many parts of physics through the centuries? Or is our selection of worked-on parts of physics still largely Newtonian? (p 244) The previous paragraph is a good example of this quotation, and shows that using Newton’s forces has stifled basic physics for 300 years and I am confident that a bottom-up approach is the correct way to go because it is based on the dimensions.

 

A small digression that shows how ‘tenuous’/unscientific the top-down method can be, is shown by the three laws of motion put forward by Descartes. ‘In order to avoid such notions of occult powers of motion, much of Descartes’ Principles of philosophy was devoted to an explanation of how or why matter moves, and what keeps it in motion.’ (p 133) and the three laws given were very close to those of Newton, but, ‘Descartes insisted that the amount of motion in the universe is constant. (p 134) ‘Newton … did not deny the occult nature of his active principles’ (p 135) That these ideas have flowed through physics for 300 years shows, and I believe, that the ‘selection of worked-on parts of physics [is] still largely Newtonian’!

 

It might sound strange that Descartes should say that the speed or amount of motion is constant, but in the physical world, momentum is energy and Newton used energy as force times distance, but time is a dimension, as space is, and symmetry says that force times time is an energy (impulse), and conservation of energy is what Descartes was, in effect, saying. Thus, Newton seems to have ‘swept the board/decks’ and is still influencing science to this day, but, it must be remembered that it is only an approximation.

 

A point should be made, and I keep repeating it because it is so important, about top-down and bottom-up, that Descartes looked for a universal ‘base’ in that speed is conserved. This is the bottom-up approach and he made a valiant attempt to do this, but Newton looked in a ‘non-base’ description of motion and that was accepted. I am proposing a return to the ‘base’ idea of conservation of energy and that the total energy in the universe is zero at all times and that is a statement of relativisation. Remember that relativisation is a concept (two observers see the speed of light to be the same) and context ((a+b+c …)=1) and leads into relativity, quantum mechanics etc.

 

I am going to ‘treat’ myself to a little philosophy that ‘begs’ to be said, that I have always believed that science ‘re-built its house’ as theories ‘improved’ and I am dismayed at the use of Newton’s laws of motion being used without question for 300 years and have to point out that, I believe that the lack of context, of science, has led to the social problems that the world faces. I have said it before, that the mathematics of concepts must be used and this is a prime example.

 

Light emanating from a source is intimately connected to the photons and atoms around it, logically through entanglement (a and b), and not, as assumed by Newton’s laws of motion, free ‘spirits’ dependent on their momentum. The probability space is the over-arching space (chapter 74) that must maintain the conservation of energy and relativises all the dimensions to achieve this and photons are infinitely variable [energy-wise] and able to accomplish this [Pound-Rebka]. So, how do I explain the reason for diffraction?  The simplest reason is that a single photon has entanglement with the mass of matter that consists of the aperture and that affects the edges of the beam and ‘pulls’ it around.

 

Very simply, the body of the aperture is 0 degrees (the face can not move) plus the closest photon is 90 degrees at the first instant and the average from simple entanglement is 45 degrees. At the next instant, 0+45 averages to 22.5 degrees and in the limit is 0 degrees and a half-circle wavefront results. Similarly, for the next photon that is further away from the edge of the aperture (45+90)/2=67.5 degrees). I am only saying that there is local entanglement of the simplest kind and yet that produces the unusual effect that is inexplicable without acknowledging entanglement of photons and aperture.

 

The effect is unusual as the photons in the centre are progressively ‘peeled open’ like a flower as time passes. The wavefront is semicircular because the speed of light is constant, but the intensity of the light would diminish as the angle decreases, and this appears to be the case from photographs. We have to expect simplicity to be the reigning order in a probability space, and I am confident that simple entanglement is sufficient reason for the effect.

 

It is now apparent that the problem with Huygens principle, as mentioned above, is that it supplies no reason for light to bend in the bizarre way that it does and whilst entanglement supplies that reason, the probability wavelets show where the photon should be. I have to admit to being surprised in the degree of entanglement between light and aperture and the magnitude of the effect and further that nothing came of it with so much study, but again, it needs bottom-up to see it. Also, it is interesting that Newton made sense, to a certain degree, of gravity/entanglement [(a and b)=1] and its effect on the planets, but failed to recognise the effect of local entanglement [(a+b)=1] displayed in diffraction that he also studied.

 

A photon moves because it logically has to move [ratio of dimensions] and its energy level (concept) is determined logically by relativisation, but context is provided by entanglement and we know that Huygens principle ‘works’, so, ‘it seems that … knowledge cannot spring from experience alone but only from a comparison of the inventions of the intellect with the facts of observation’, wrote Einstein. (The Story of Measurement, Andrew Robinson, p 10) Science has progressed at a rapid rate over the last 300 years, but the thought that our universe is a probability space opens new vistas, and I have presented a few here.

 

On the question of water waves, do the effects of logic, bearing in mind that there are a number of ‘types’ of logic and I’m only using the mechanical world P logic, influence water to cause diffraction? We use logic, the common-sense logic, that we have built on measurement/entanglement continually throughout the day [World O contains world P] and as we are using these fundamental properties, so why shouldn’t water waves react with fundamental properties as well?

 

In other words, world P contains measurement/entanglement, but our mind/brain builds on this physics to create a space that is not everywhere entangled, but is indeterminate because our reality demands that our living space be continuous, otherwise magic or an un-sensed something will eat us. This could be a lion that we need to see or a bacterium that we need to fight. We live in a world that is a combination of world O and world P and there is no reason that a world P phenomenon should not be present macroscopically as well as microscopically.

 

Having set up the above explanation, it seems a pity not to extend these thoughts and Rutherford’s Gold Foil Experiment (physics.tutorvista.com) presents ‘on the basis of these observations Rutherford made the following conclusions:

• Since most of the alpha particles passed straight through the gold foil without any deflection, most of the space within the atoms is empty.
• Since some of the alpha particles (which are big in size) were deflected by large angles or bounced backwards, they must have approached some positively charged region responsible for the deflection. This positively charged region is now called the nucleus.
• As very few alpha particles undergone the deflection, it was concluded that the volume occupied by the central region ( nucleus ) is very small.
• Since alpha particles which are relatively denser, were deflected by the central volume of charge, it shows that almost the complete mass of the atom must be within the central volume.’

Rutherford’s experiment makes an enigma of reflection! If most of the huge (relatively) alpha particles pass through, why do we get an apparently perfect reflection from a mirror? The answer, from above, is, I believe, due to entanglement of the photons and/with the mirror, and we are told that an electrical conductor is a ‘sea’ of electrons, but that is a concept, and the context is that they are linked together and perhaps explains electric and magnetic fields that are the same, but orthogonal. Notice that I have ignored them, because I have not needed them.

 

As a wavefront of photons approaches a mirror at right angles, Huygens’ wavefronts at each instant form a plane parallel to the mirror and the entanglement would increase the reverse probability until, at some point, the wavefront reverses and all photons are affected and the image is returned. Notice that I am suggesting a combined effect, not an individual ‘bouncing’ that, according to Rutherford’s experiment does not happen. There must be a probability effect standing in front of the reflecting surface and this can be seen in the case of internal reflection.

 

If two pieces of glass with parallel edges are pushed together, a light ray will pass from one to another, and as the separation is increased a smaller proportion of the wave is transmitted (evanescent wave) and a larger proportion is internally reflected. This is usually considered to be a quantum mechanical effect, similar to the tunnel effect, but it seems more plausible, considering its macroscopic size, to consider it a contextual effect [I am introducing this because they are perhaps the same effect by different names]. The justification is that probabilities exist in a probability space, whereas a wave equation is an added complication with the same effect as context. It could be said that context/entanglement provides the ‘spring’ in the concept/measurement of a collision, especially as entanglement is the means of ensuring conservation of energy. Furthermore, conservation-of-energy/relativisation is instantaneously ‘calculated’ by the space and probabilities are constantly involved. Note that the two ‘types’ of entanglement are becoming apparent, one local (physical) and one universe-wide (logical).

 

This imposes ‘rigidity’ to collisions of matter, and that is necessary considering the ease with which an alpha particle passes through gold leaf. ‘What gives matter its rigidity? Atoms are mostly empty space, so why can’t you squeeze them like a sponge or push materials through each other like cheese through a grater? The question of why matter inhabits space is one of the most profound in physics. If it were not true we could fall into the centre of the earth or sink through floors, and buildings would squash under their own weight.’ (50 physics ideas, Joanne Baker, p 120)

 

This requires the multiverse [that we are able to survive in this universe] and the fact that we need a rigidity to give a collision, otherwise everything would stick together and prevent the universe expanding as it does. Gravitational attraction provides the negative energy to balance the positive energy/matter that the universe is composed of, and the magnitude of the ‘rigidity’ of matter has to ‘work’ for us to be here. In other words, this ‘bounciness’ of matter is necessary to enable space and energy [split] to be created so that there is enough volume for ‘stickiness’/gravity to form solar systems so that we can evolve.

 

I would like to restate the paragraph above to reinforce the question: ‘why matter inhabits space is one of the most profound in physics’, and the reason is that there has to be enough ‘bounce’ to form the negative energy and thus space, but there has to be enough gravity to form solar systems. Further, Newton’s third law that ‘action and reaction is equal and opposite’ is the measurement/entanglement of (a+b)=1, whereas universe-wide effects are logical measurement/entanglement from (a and b)=1. Both (a+b)=1 and (a and b)=1 are properties of a probability space and are continually quested, but the entanglement is different and one affects local relativity whilst the other is universe-wide.

 

Repeating the following quotation: ‘a slightly naughty thought can come to one’s mind here. Is it due to the nature of physics that the mathematical tools started by Newton are so essential for many parts of physics through the centuries? Or is our selection of worked-on parts of physics still largely Newtonian? ’ (Let Newton be!, edited by John Fauvel, p 244) The answer can now be given by restating Newton’s laws of motion in a modern form by using concepts from previous chapters.

 

But first, Newton’s ‘solution of the problem of motion in the solar system was so complete, so total, so precise, so stunning, that it was taken for generations as the model of what any decent theory should be like, not just in physics, but in all fields of human endeavour. It took a long time before one began to understand – and the understanding is not yet universal – that his genius selected an area where such perfection of solution was possible. This is a rarity in science. It is not universal. … I regard this as profoundly misleading. In my view, most of science is not like the Newtonian solar system, but much more like weather forecasting.’ (p 245)

 

The answer to the question: ‘is our selection of worked-on parts of physics still largely Newtonian?’ is, from the preceding paragraph must be a resounding ‘yes’ for two reasons, firstly, as above, that experiments could be described ‘exactly’, but secondly, that mathematics, used to describe the experiment is ‘exact’. In preceding chapters, an explanation of the general mathematics of concepts can be seen in the dimensions of a probability space, and shows that mathematics is a special case. In other words, the mathematics needed to describe the vast majority of weather-type problems is only now available in the mathematics of concepts.

 

Thirdly, in chapter 73, in the abstract, I mentioned ‘The quantum/evolution – logic/gravity description of the universe produces a range of conditions/understanding that can be applied to every organization/society, and science, as practiced today, struck it lucky in a top-down approach that “proves the rule” and its success shows how effective the application of the science of organization/management can be to solving the world’s problems and re-establishing a meaningful evolution through Plato’s politics.’ However, as mentioned above, Newton’s laws of motion have remained untouched for over 300 years and, in the light of the above, a re-thinking and re-writing might be in order, and the concept/attractor that science continually ‘re-builds’ its ‘house’ need to be reinstated and I suggest the following.

 

1 A particle remains at rest or in uniform motion unless acted upon by an energy gradient, except that it will be continually relativised, and in the case of a photon, the speed is always constant and an absolute, and only the energy is relativised.

 

It is a property of a probability space that ‘free’ energy must move at the speed of light, unless energetic enough to form a particle as is indicated by the space-time and fifth dimension/energy. The interval of time is a world (our) O invention that was needed for survival in a predator/prey situation, and that takes speed and acceleration out of world (physical/probability) P.

 

2 The modulus of energy, if greater than zero, can be transmitted to, or form, other types of energy without loss, at any distance via a change in the dimensions (space, time and energy/mass) equally through the Lorentz contraction acting between two frames of reference to prevent a singularity.

 

Gravitational potential/energy is negative, all other energies are positive and the sum is zero (conservation of energy), but energy contains an orthogonal measurement/entanglement and this entanglement/relativisation is instantaneous and universe wide (a and b)=1, whereas positive energies are restricted to at, or below, the speed of light (a+b)=1.  This is a logical requirement [Lorentz contraction] that affects the dimensions equally and if exceeded, produces chaos everywhere.

 

A Newtonian force is a combination of concept and measurement that down-plays entanglement and in Newton’s day ‘the only allowable notion of force, therefore, was force of impact; all other concepts of force, such as attraction and repulsion, were regarded by these natural philosophers as occult.’ (p 127) Also, Einstein used ‘spooky action at a distance’ for these same forces, yet a probability space contains the mechanism in relativisation to explain this.

 

3 Locally, momentum is conserved and local entanglement (a+b)=1 allows action and reaction to be equal and opposite and that is necessary to generate space so that matter can condense as solar systems etc., but energy is conserved (at zero) universe-wide (measurement) and adjusted continually and instantly (entanglement, (a and b)=1).

 

Decartes thought that momentum was conserved universally and that non-occult forces are the physical world of collisions and was incorrect in the first instance and correct in the second, but Newton combined world O and P in a local scenario that has taken 300 years to understand/unravel. The use of force subsumes context/entanglement and combines world O and P, which is acceptable when the separation is understood.

 

Conclusion: I think that is apparent that the difficulties with relativity, quantum mechanics, diffraction, mathematics, organizations, over-population etc. become solvable when the dimensions are used to generate measurement/entanglement, the mathematics of concepts, concepts/context, no absolutes except light speed [and the Golden ratio], Plato’s democracy etc. The use of general methods that always work make possible solutions that always work, and that is what the world needs, but we need to recognize that the mathematics of concepts is basic and that its use, especially the recording of context ‘shows up’/targets inconsistencies in the argument of two sides and leads to ‘agreement by derision’ as is used in politics today. The above is in bold because it is so important and I was going to leave it at that, but, I have weakened and have to say that there is no other way to effectively argue/compare concepts, and that is why the world is in a mess.

 

References: all quotations are fully referenced in the body and earlier chapters can be found on    darrylpenney.com    if required.

by Darryl Penney

 

Abstract: much of philosophy today would be intelligible to the ancient Greeks and this lack of change lies, I believe, in the abandonment of the mathematics of concepts within the rise of mathematics. A return to the mathematics of concepts, the recognition of the fifth dimension and the properties of a probability space allow a bottom-up base of concept and context that allows philosophy to be unfolded and de-cluttered. Two other derivations are necessary, logic and organization, again as concept and context and examples are given of the necessity of re-writing Newton’s laws of motion and the classic problem of the Unity of the Virtues.

 

I have said before that the subject of Philosophy is a ‘closed book’ to me and I have often wondered why that is so, and one explanation could be that we are not supposed to find answers. ‘Bertrand Russell in The Problems of Philosophy: Thus, to sum up our discussion of the value of philosophy; Philosophy is to be studied, not for the sake of any definitive answers to its questions, since no definitive answers can, as a rule, be known to be true, but rather for the sake of the questions themselves; because these questions enlarge our conception of what is possible, enrich our intellectual imagination and diminish the dogmatic assurance which closes the mind against speculation’ (Is God a Mathematician?, Mario Livio, p 252)

 

On the other hand, it occurred to me that perhaps philosophy may not be as logical as it suggests/claims! After all, I found that what we call logic often exists as a ‘chimera’ where what appears to be logic is a mathematical entity and the following two paragraphs (from chapter 75) indicate that the universe is based on mathematics and not logic, and further, that we are the means of turning mathematics into logic.

 

‘An example of questing the fifth dimension [(a+b)=1] comes to mind because the total energy of the Big-Bang/Big-Whoosh is zero at all times, and yet, from chapter 72: “One requirement any law of nature must satisfy is that it dictates that the energy of an isolated body surrounded by empty space is positive, which means that one has to do work to assemble the body. That’s because if the energy of an isolated body were negative, it could be created in a state of motion so that its negative energy was exactly balanced by the positive energy due to its motion…. Empty space would therefore be unstable.” (The Grand Design, Stephen Hawking and Leonard Mlodinow, p 179). This is logical, but is it really logic or mathematics, which is a special case of the mathematics of concepts that is apparent from the dimensions?’ On the other hand, is it the context of a concept that requires a mind/brain?

 

‘In a simple planetary system, the total energy equation zero = (p+q) where p and q are kinetic energy and potential energy and mirrors the fifth dimension in context [measuring each other continuously and instantaneously] to the concept of “Newton’s inverse square law of gravity explained in one equation the orbits of all the planets as described in the three laws of Johannes Kepler.” (50 physics ideas, Joanne Baker, p 17) Notice that I mentioned concept and context, but Newton used world O thinking of the force of attraction between the planets and this invokes a determination and subsumes the logic/context.’

 

So, logic, from chapter 75, ‘in a ‘nutshell’:

 

(1) We are the selection out of the multiverse because we are here.

(2) The one ‘dimensional’ use of the properties of world P that are properties of the space and could be called logical [as a machine is logical], but most important is Occams’ razor because simplicity is paramount.

(3) The two ‘dimensional’ use of worlds O and P by Life, and concept/context can perhaps be replaced by concept/quest/relevance/entanglement, where the concept evolved through forward-planning by the mind/brain and measurement by the eyes etc.

(4) Formal logic.

(5) Proverbs are a ‘higher’ logic/thinking that uses the mathematics of concepts to provide quick responses.

(6) The solution of (a +/and b)=1 is an absolute [Michelson-Morley] that the speed of light is a constant and all other measurements must have an assigned absolute [Plato’s problem] except for (7).

(7) The solution of the interval (a +/and b) is an absolute [Golden ratio] that makes beauty/appreciation/enjoyment logical/repeatable/relatable.’

From (3) above (and chapter 78):

 concept/forward-planning/quest/relevance/beauty/context

for Life in world O, bearing in mind that Life lives in a deterministic reality that must be complete and continuous and the physical world P, that is totally entangled, becomes:

 

measurement/quest/relevance/entanglement

 

and for “something” to be “logical”, it must contain answers to all six conditions because it is a restatement of the dimensions, absolutes and the properties of the probability space. This is a concept because it is limited in scope and contains concept/forward-planning/beauty (bearing in mind that forward-planning is a construction by the mind/brain of Life) and context is quest/relevance/context. This context was discussed in chapter 73, ‘given that relativisation (A), the mathematics of concepts (B) and setting out the concepts/attractors and setting the context (C), the use of an absolute (D) [forward-planning] chosen by the universities (E) [the ‘best’ absolute] are derived above.’

‘Further, (F) is experimentation/trials/measurement etc., as suggested by Francis Bacon to bring about a ‘scientific method’ that has proved spectacularly successful in science/technology and this could be considered a ‘break-through’ because most ‘science’ was derived by ‘thought’ for thousands of years. However, the duality of concept/context and measurement/entanglement means that theorists (H) should be included and it is apparent that a mathematics of concepts has been set up [(A) to (H) in total] where more factors produce a better organization, but what is the purpose of an organization? An organization is set up [forward-planned] for a number of reasons, but basically it is to satisfy a need and/or to evolve (I), and I should stress that these eight points are (possibly) the most important of many more that may need to be considered.’

 

It should be noted from (6) and (7) that major solutions/absolutes exist from the entanglement simplification (a+b)=1 that show that the speed of light is constant and that a measure of beauty, in the form of a ratio is available to Life. In particular, I believe that Life uses the Golden ratio as part of its reality and the form of reality (completeness and continuity) requires/ensures that the criterion of beauty is a reality having completeness and continuity across the reality (chapter78).

 

The dimensions, when used bottom-up are a powerful tool that links the speed of light with our reality [Michelson-Morley] and shows the intertwining of the physical and our worlds. In fact, everything in the universe can be derived from five dimensions if we live in a probability universe, and I believe that I have proved that to my satisfaction, the key to tackling the problems of society and of the world become solvable and the key is in chapter 67 that describes a modern means of attaining Plato’s political aspirations and the basis to that is organization, above.

 

‘Plato hankered, in his search for real knowledge, after the kind of certainty which the truths of mathematics have, but because he was after things and not truths, the things had to be necessarily existing things. Looked at in this light, even the road to Larissa does not really qualify (it might be washed away, as roads in Greece sometimes are).’ (Greek Philosophers, R. M. Hare, p 142) Mathematics did not exist in Plato’s time and certainty does not exist except in constructs such as mathematics,  similarly, uncertainty always exists in the mathematics of concepts unless we change the field to a reality because Life is uncomfortable with uncertainty, but questing is basic to a probability space and requires uncertainty until a measurement is made.

 

This quotation should be sufficient to establish my points, but is Plato relevant today? ‘Philosophy, as it is studied in the West today, is an invention of the ancient Greeks. So too, to a great extent, are science and mathematics. But today’s science and mathematics so far transcend the achievement of the Greeks that no modern scientist is likely to study Euclid or Hippocrates or Archimedes for other than purely antiquarian reasons. Modern philosophers, by contrast, continue to discuss problems which were first raised some two thousand five hundred years ago, and they often do so in terms which their Greek predecessors would have found fully intelligible.’ (p v)

 

So, Plato needed mathematics, which did not exist in his day, and great strides have been made since, using mathematics/science/technology over the last 2,500 years, but not, it appears, in philosophy. Philosophy needs the mathematics of concepts, that contains mathematics as a special case, and this is immediately apparent from the fifth dimension (a+b)=1. Science has forged ahead using mathematics, but more importantly it used the organizational context above that provided the impetus. This fact of organizational context can be shown simply by looking at the simplicity/inapplicability of Newton’s laws of motion.

 

From chapter 73, ‘the comparison of the rules of organization, above, with the basis of science, below, shows that the success of science was organizationally lucky/fortuitous, because, from above, many of our organizations are inadequate, such as the process of law, the making of laws by public servants, the food offered by shops, the fishing industry [a commons] etc. are deficient, but science was a ‘stroke’ of luck because acceptance (A) of a theory is required by scientists in general and that theory requires the mathematics of concepts (B) [to compare theories] and invites additions and checking (C) of the result (D) by those with a long-time career (E) in the subject and this often requires experimentation (F) and theorists (G) to fit it all together, and finally, the overall idea of science is to ‘push’ the boundaries (H) of what we know. It is hard to resist a giggle that science has been using the fifth dimension, top-down without acknowledging its existence!’

 

However, a small digression that shows how ‘tenuous’/unscientific the top-down method can be, is shown by the three laws of motion put forward by Descartes. “In order to avoid such notions of occult powers of motion, much of Descartes’ Principles of philosophy was devoted to an explanation of how or why matter moves, and what keeps it in motion.” (Let Newton be!, p 133, edited by John Fauvel) and the three laws given were very close to those of Newton, but, “Descartes insisted that the amount of motion in the universe is constant.” (p 134) “Newton … did not deny the occult nature of his active principles” (p 135) “A slightly naughty thought can come to one’s mind here. Is it due to the nature of physics that the mathematical tools started by Newton are so essential for many parts of physics through the centuries? Or is our selection of worked-on parts of physics still largely Newtonian?” (p 244) That these ideas have flowed through physics for 300 years shows, I believe, that the ‘selection of worked-on parts of physics is still largely Newtonian’!

 

A point should be made, and I keep repeating it because it is so important, about top-down and bottom-up, that Descartes looked for a universal ‘base’ because he believed that speed was conserved. This is the bottom-up approach and he made a valiant attempt to do this, but Newton looked in a ‘non-base’ description of motion and that was accepted. I am proposing a return to the ‘base’ idea of conservation of energy and that the total energy in the universe is zero at all times and that is a statement of relativisation. Remember that relativisation is a concept (two observers measure the speed of light to be the same, and that is an enigma except in a probability space) and context ((a+b+c …)=1).

 

However, as I will have to foreshadow to some extent, Newton’s laws of motion have remained untouched for over 300 years and, in the light of the above, a re-thinking and re-writing might be in order, and the concept/attractor that science continually ‘re-builds’ its ‘house’ need to be reinstated and re-applied, and I suggest the following from chapter 77.

 

‘1 A particle remains at rest or in uniform motion unless acted upon by an energy gradient, except that it will be continually relativised, and in the case of a photon, the speed is always constant and an absolute, and only the energy is relativised.’

 

‘It is a property of a probability space that ‘free’ energy moves at the speed of light, unless energetic enough to form a particle as is indicated by the space-time and fifth dimension/energy. The interval of time is a world (our) O invention that was needed for survival in a predator/prey situation, and that takes speed and acceleration out of world (physical/probability) P.’

 

‘2 The modulus of energy, if greater than zero, can be transmitted to, or form, other types of energy without loss, at any distance via a change in the dimensions (space, time and energy/mass) equally through the Lorentz contraction acting between two frames of reference to prevent a singularity.’

 

‘Gravitational potential/energy is negative, all other energies are positive and the sum is zero (conservation of energy), but energy contains an orthogonal measurement/entanglement and this entanglement/relativisation is instantaneous and universe wide (a and b)=1, whereas positive energies are restricted to at, or below, the speed of light (a+b)=1.  This is a logical requirement [Lorentz contraction] that affects the dimensions equally and if exceeded, produces chaos everywhere.’

 

‘A Newtonian force is a combination of concept and measurement that down-plays entanglement and in Newton’s day ‘the only allowable notion of force, therefore, was force of impact; all other concepts of force, such as attraction and repulsion, were regarded by these natural philosophers as occult.’ (p 127) Also, Einstein used ‘spooky action at a distance’ for these same forces, yet a probability space contains the mechanism in relativisation to explain this.’

 

‘3 Locally, momentum is conserved and local entanglement (a+b)=1 allows action and reaction to be equal and opposite and that is necessary to generate space so that matter can condense as solar systems etc., but energy is conserved (at zero) universe-wide (measurement) and adjusted continually and instantly (entanglement, (a and b)=1).’

 

‘Decartes thought that momentum was conserved universally and that non-occult forces are the physical world of collisions and was incorrect in the first instance and correct in the second, but Newton combined world O and P in a local scenario that has taken 300 years to understand/unravel. The use of force subsumes context/entanglement and combines world O and P, which is acceptable when the separation is understood.’

 

First, it is useful to give a quick and easy description of the use of the mathematics of concepts from chapter 75.

 

‘If we take the Cartesian system of the X-Y plane, we can say that some point is composed of two independent variables (x, y), and the mathematics of concepts can be handled similarly, bearing in mind that an iteration or mind/brain initiates a measurement and we are dealing with world O and world P. A little foreshadowing will make it easier to understand, that world P is a probability space and only has iteration, whereas Life has made world O into a “determinate”/non-entanglement world because of the necessity of creating a reality as part of questing/Survival-of-the-Fittest.’

 

‘So, taking the easy case of world P, questing is: X-Y axes with the concepts to be examined spread equally spaced along the X axis, and a curve/^ is drawn between each concept and every other concept with a height ^ equal to its probability and the sum of all the ‘heights’ is 1. This comes straight from the entanglement/measurement of the probabilities in a probability space. To move it into world O in order to automate or use a mind/brain, move the concepts and the ^ to make a ‘normal’ curve and read off the best concepts and their context. If this looks simple, ask yourself ‘why should it be complicated?’, when the universe requires only 5 dimensions and life six dimensions.’

 

There is one further point, and that is that the decision that has been made is a concept and whilst the context has be taken into account, the context must be recorded and be re-evaluated periodically to maintain relevance. This is, of course, questing and relevance that are part of a probability space and we need measurement and entanglement as well, and for (our) world O [concept/forward-planning/quest/relevance/beauty/context] that is a combination of concept and context. Further, I believe that this is ‘elegant infinite’, which is the context to mathematics’ ‘elegant simple’, that is a concept.

 

I gave the example of Newton’s laws and another example [that illustrates relevance over time] might be ‘the doctrine that virtue is knowledge is the key to understanding the so called thesis of the Unity of the Virtues, maintained by Socrates in Protagoras. In that dialogue Protagorus assumes a broadly traditional picture of the virtues as a set of attributes distinct from one another, as, for example, the different bodily senses are distinct.’ (Greek Philosophers, R. M. Hare, p 64) ‘The theory that virtue is knowledge is, as we have seen, flawed, in that one of its central propositions, that virtue is always in the agent’s interest, is nowhere adequately supported in the Socratic dialogues. It also has a deeper flaw in that it is incoherent.’ (p 66)

 

All life obeys questing, which is another name for Survival of the Fittest and as part of this, relevance is required and relevance is reality. We have to sense predators and live among them, but keeping a forward-plan if the predator gets too close and we need continuity and completeness, otherwise, magic/predators sneak in without us sensing them. The larger animals protect their offspring by teaching them and helping them until they ‘know the ropes’.

 

The Greek philosophers advocated a mentor, but the Bible was more formal by using, I believe, the mathematics of concepts to divide God into three parts to, I believe, make understanding easier, and I believe that over the last 2000 years the Church ‘lost’ the Holy Spirit. I derived three Laws of Life and they ‘mirror’ the Trinity. God the Father is creation, the Holy Spirit is the wider environment and God, the Son is family and other close relationships, see Chapter 1.

 

From bottom-up, questing and relevance through the untold generations make up an iteration/computer and what we see is what is logical/has-evolved given the conditions on the planet, we have done the best that we can and teaching offspring works, because we do it. ‘Socrates suggests that, on the contrary, the names of individual virtues, courage, self-control, etc., are all “names of one and the same thing” (329c-d)’ (p 65) This is true if time is taken into account because as we go back in time, these successful traits lead to success in the tribe even without names, just observation and as time passes, these attributes are progressively named. ‘Socrates suggests that, on the contrary, the names of the individual virtues, courage, self-control, etc., are all “names of one and the same thing” (329c-d)’ (p 65) is top-down thinking, and translated into bottom-up becomes ‘names of one successful concept of survival (emulation/knowledge through teaching) that has the context of those names (virtue, courage, self-control, etc.) as a means of attaining breeding success’. [using forward-planning in reverse]

 

‘The incoherence emerges when we ask “what is virtue knowledge of?” The answer indicated by Meno and Protagoras is that virtue is knowledge of the agent’s good, in that, given the standing motivation to achieve one’s good, knowledge of what that good is will be necessary if one is to pursue it reliably, and sufficient to guarantee that the pursuit is successful.’ (p 66) This suggests that knowledge of virtue (concept) is necessary and to pursue it (context) with the motivation being Survival of the Fittest and especially the family etc.

 

The dimension of time-passing culturally ‘splits off’ the virtues and are similar to the accumulation of the senses (feeling, smell, sight etc.) because it is part of reality and questing has, through evolution, determined relevance otherwise they would not exist at this time. These virtues have been with us for 3,000 million years when bacteria swapped DNA. The answer to “what is virtue knowledge of?” is answered by the parents to the best of their ability to enhance their investment by ‘on the job’ teaching as well as family input, and over time the adult becomes the agent of a group and it appears that doing the best for each person, as decided by the person, is the best that we can hope for.

 

From chapter 78, ‘The Nobel laureate Eugene Wigner, gave a celebrated lecture with the title, “The unreasonable effectiveness of mathematics in the natural sciences”…. The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it.’ (The Story of Measurement, Andrew Robinson, p 45) I need to say that there is a rational explanation that mathematics ‘works’ because mathematical/logical relationships are the fifth dimension and quests of a mathematical relationship (a+b)=1 are the basis of our universe and this will be explored later.’ (chapter 81)

 

Conclusion: the title: ‘When Philosophy Meets Mathematical Physics’ is, I believe, appropriate and is an opportunity to reorganize both philosophy and science from the bottom-up. As to why I cannot understand philosophy, I present the following quotation, again, but now I believe that it has been turned ‘on its head’.

 

‘Bertrand Russell in The Problems of Philosophy: Thus, to sum up our discussion of the value of philosophy; Philosophy is to be studied, not for the sake of any definitive answers to its questions, since no definitive answers can, as a rule, be known to be true, but rather for the sake of the questions themselves; because these questions enlarge our conception of what is possible, enrich our intellectual imagination and diminish the dogmatic assurance which closes the mind against speculation’ (Is God a Mathematician?, Mario Livio, p 252)

 

Thus, I do not know whether to apologise to philosophers that in my ignorance I have turned their mental exercise into a confrontation with the mathematical physicists, or giggle that they will have to work (or fight) together to straighten thing out. As an indication, Plato’s political system (chapter 67) needs to be implemented as soon as possible.

 

References: all quotations are fully referenced in the body and earlier chapters can be found on    darrylpenney.com    if required.

Abstract: our mind/brain uses logic continually, but it is a mixture, and I have derived it and place it in context so that we can understand it better and use it properly. Life has evolved a common-sense logic that is a product of its reality and necessary for its continuance and growth, but there are higher levels of logic such as the Golden ratio that is an absolute that we use to underpin an appreciation of beauty/balance/enjoyment etc. with which we can all relate, as is necessary in a reality. Examples are given of the logic of the ’physical’ universe arising out of the fifth dimension and the formation of Everything and its methods applied to relativity, quantum mechanics, inflation, diffraction and reflection of photons etc. as well as indicating a problem with Newton’s laws of motion, and a breakdown in the fundamental basis of science.

I have often wondered about the logic of common sense, why we have it and how frequently we use it. In fact we use it all the time and often without thinking about it, in a similar way to our use of our gamma nervous system that evolved to continually counter-balance our movements. I hasten to add that formal logic is not being considered because, like mathematics, it is constricting and I will rely on the following quotation:

 

‘If a man will begin with certainties, he shall end in doubts, but if he will be content to begin with doubts, he shall end in certainties.’ Francis Bacon, 1606 (Feral Future, Tim Low, p xiii)

 

By this, I believe that mathematics and formal logic are based (as much as possible) on a definitive simplicity that cannot lead to the larger picture [evidenced by the constraint of Newton on physics for 300 years], and indeed, that simplicity [concept] is part of the problem because there is, by necessity, another simplicity [context] and they are not related, and can be shown [(a+b)=1] to be independent/orthogonal. If we are content with doubts [mathematics of concepts], indeterminism [questing], relativity [relevance], logic [common-sense], entanglement, concepts/context etc., we find, I believe, a different type of elegance to the elegance of mathematics/logic and one that fills in the ‘difficulties’ of physics that we have all encountered, and these difficulties start at the very bottom, with existence.

 

Let’s start with the statement, ‘if mathematics corresponds to the mathematics of concepts, how does formal logic correspond to logic’? This suggests a symmetry and the first step is to quest for the answer and when we have an answer that satisfies us, it becomes determinate to us, and we can do this because that is how our probability space maintains itself and we are part of fields within that space. If that sounds familiar, it is because we live within ‘layers’ of a few basic fields that are based on concepts that have been difficult to understand, such as quantum mechanics, relativity and the fifth dimension (a+b)=1, and yet are simple. In other words, questing the equation (a+b)=1, along with space-time, derives the universe and everything in it, including Life and leads from defined simplicity to simplifying the infinite in the statement, above. [Notice that (a+b)=1 is actually (a+b+c …)=1 and is not simple and the quotation is, I believe, apt]

 

From chapter 73, ‘remember that a probability of existence space has an infinitely small chance of existing [at 1] and likewise, has an infinitely small chance of not existing [at 0], and forms a “twilight zone”’, and whatever we are, we are logic because logic only comes from iteration or a mind/brain. However, the Theory of Everything was used to ascribe consciousness to all things animate and inanimate and so consciousness is another word for logic, and it will be shown later that logic/consciousness is physical in the form of measurement/entanglement that grades through evolution, to the ‘metaphysical’ as concept/context.’

 

As Descartes said, ‘I think, therefore I am’ and that might be the first and simplest attractor in the mathematics of concepts that we are using to examine the statement, above. The mathematics of concepts is ‘natural’ and predates mathematics, and I believe, was responsible for the Trinity of the Bible, so, it is old, forgotten and unfortunately necessary to our civilization because it holds the ‘key’ to the working of everything, and it can be identified in the dimensions of a probability space [space-time and (a+b)=1 for measurement/observers a and b, as an illustration]. Another necessary/important piece of information is that our mind/brain took 3,000 million years to evolve and it evolved using the simplest and most logical principles and that is the mathematics of concepts. The proof of this sentence is simply that conceptually, efficiency is always sought and contextually, otherwise you will be eaten sooner.

 

To repeat, mathematics is a special case of the mathematics of concepts and mathematics is our invention [world (our) O] and the mathematics of concepts is immediately apparent in the dimensions of our probability of existence universe P and is the general basic mathematical relationship that underlies everything. Entanglement is immediately obvious and the ‘+/and’ signifies that the entanglement is both measurement and logic because questing is a necessary property of a probability space and every possibility will be quested/examined [as in quantum mechanics, Life].

 

A requirement of questing is that every possibility must be quested/examined and that statement logically requires that the result be indeterminate until a measurement is made. This determination by measurement makes quantum mechanics seem ‘strange’ but ‘balancing’ has to be done at an infinite speed [a function of the space and to prevent logical singularities] and the measurement [a, b] is accompanied by the entanglement that is both physical (a+b)=1 and logical (a and b)=1 and provides relativisation [(a+b+c …)=1, duality].

 

Relativisation needs to be defined and it is composed of two parts, firstly a concept where two observes moving relative to each other measure the speed of light to be the same, which is an enigma, and secondly, as a context that the sum of energy at every point in the universe is zero, which also strains belief. Relativisation comes about because there is one solution/absolute to the equation (a+b)=1, and that is, that the speed of every photon is constant for all free energy. A photon is an energy concept/measurement of potential [Pound-Rebka] and an energy context/kinetic-energy/logic that requires motion and this is the ‘static’ mode of ‘free’ energy. The ‘dynamic’ mode is the creation of energy [separation into negative potential and positive other energies] creates space and time through the dimensions and produces, in extreme cases, inflation [of the Big Bang].

 

An example of questing the fifth dimension [(a+b)=1] comes to mind because the total energy of the Big-Bang/Big-Whoosh is zero at all times, and yet, from chapter 72: ‘One requirement any law of nature must satisfy is that it dictates that the energy of an isolated body surrounded by empty space is positive, which means that one has to do work to assemble the body. That’s because if the energy of an isolated body were negative, it could be created in a state of motion so that its negative energy was exactly balanced by the positive energy due to its motion…. Empty space would therefore be unstable.’ (The Grand Design, Stephen Hawking and Leonard Mlodinow, p 179). This is logical, but is it really logic or mathematics, which is mathematics of concepts that is apparent from the dimensions?

 

In a simple planetary system, the total energy equation zero = (p+q) where p and q are kinetic energy and potential energy and mirrors the fifth dimension in context [measuring each other continuously and instantaneously] to the concept of ‘Newton’s inverse square law of gravity explained in one equation the orbits of all the planets as described in the three laws of Johannes Kepler’. (50 physics ideas, Joanne Baker, p 17) Notice that I mentioned concept and context, but Newton used world O thinking of the force of attraction between the planets and this invokes a determination and subsumes the logic/context.

 

Further, both positive and negative energy exits because, the equation (a+b)=1 must contain both [questing, simplicity] and from chapter 72:

 

‘Concept/measurement: 0 = kinetic (energy)+ gravity (energy) + mass + dark matter + dark energy + photon energy + chemical etc. acting at the speed of photons in vacuo as a maximum.

 

Context/logic: 0 = kinetic + gravity (logic) + mass + dark matter + dark energy + photon energy + chemical etc. acting at an infinite speed.

 

where gravity is always negative and all the other energies are positive. It is a commonly held idea that ‘all objects in the universe may exert a tiny gravitational pull that might subtly affect our movement’ (p 6) and they cannot do that unless gravity [logic] is propagated instantaneously.

 

Notice that different states of energy have different properties (as would be expected), and in particular, that the speed of logic/gravity is instantaneous as it must be in a probability space to prevent logical singularities and further, that the context/logic equation needs an infinite speed of gravity to keep track of the other contexts to satisfy (a+b)=1. In other words, the dimension (a+b+c…..)=1 cannot be simplified (logically) because any omission could cause a singularity as can be seen from the mathematics of concepts and Feynman’s formulations. In other words, the logic of gravity ‘flashes’ around keeping track of the logic components of all the states of energy and relativises them.’

 

The above example answered the question for me that positive and negative energies exist, from the dimensions, and not from supposition [Ockam’s razor, a simple solution of the mathematics of concepts] and further that logic is just as important as the mass/energy in the universe. Another example is that I mentioned a singularity field in chapter 74 and one has to acknowledge that our universe is logically capable of protecting itself against logical singularities, see below. I will foreshadow that the simple concept/word of logic will change below because logic is different in the physical world [P] and the mental world [O].

 

From chapter 72, ‘I believe that the Big Bang or perhaps more accurately, a Big Whoosh, was a runaway creation or splitting of nothing into a positive part and a negative part of (only) the energy concepts over a very small period of time and I will quote, and compare to ‘the universe begins to expand at an exponential rate. Indeed, the universe continued to expand exponentially as long as the inflation field was the dominant source of energy density. This phase of inflation began when the universe was about 10x-36 seconds old. This energy eventually decays away (by design) and inflation ends by about 10x-35 seconds. This enormous kinetic energy turns into heat, and we are now again in the conventional hot Big Bang phase, initially dominated by radiation and relativistic particles.’ (The Infinite Cosmos, Joseph Silk, p 116) This quotation, according to the above, is a little strange, as there is no ‘inflation field’, only creation of space/time in a perfectly natural way by the creation of energy (balanced by potential energy) and this depends on the rate of creation of energy and ‘exponential’ is not an apt term. Inflation could be thought of as a ‘normal curve’ and slowed when energy creation slowed, but it is a natural process whenever energy is created (not transferred).’

 

From chapter 72, ‘an interesting point is that it is commonly considered that the galaxies are moving outward due to the momentum imparted by the Big-Bang/Big-Whoosh, but an alternative explanation is more ‘definitive’, and by that I mean that the outward momentum tells us little and leads to questions, such as ‘is the universe speeding up, remaining constant or slowing down its rate of expansion?’. However, if we use the above, that the dimensions show that the speed of light is constant and that there are no restrictions placed on the energy of the photons, then as the original photons, from the Big-Bang/Big-Whoosh spread out, and are still doing so at considerably lower energy [cosmological red-shift], they are creating space at a constant rate/speed. This increase in space forces the galaxies to move outward to preserve the Law of Conservation of Energy, and is not the residual momentum imparted by the Big Bang, as it is commonly considered to be. In other words, space increases to hold energy and that forces the other dimensions (and energy) to increase by the same amount [Lorentz factor] and as the speed of electromagnetic waves is constant, the expansion of the galaxies should be constant.

 

To explain Newton’s view from chapter 74 ‘as we now know, his faith in forces was justified to such an extent that it is widely regarded as Newton’s most important scientific innovation.’ (Let Newton be!, edited by John Fauvel, p 128) ‘A slightly naughty thought can come to one’s mind here. Is it due to the nature of physics that the mathematical tools started by Newton are so essential for many parts of physics through the centuries? Or is our selection of worked-on parts of physics still largely Newtonian? (p 244) The question posed in the last two sentences was answered at the end of chapter 74, and again here, that ‘physics is still largely Newtonian’ because it does not use the fifth dimension in its entirety, but ‘dips’ into it when convenient/necessary.

 

Logic is just as important as the physical, and, as they are independent/orthogonal, both explanations/proofs should be given. Logic and measurement are independent and it is meaningless to say that either is more important or assign percentages (with any exactitude). If we take the Cartesian system of the X-Y plane, we can say that some point is composed of two independent variables (x, y), and the mathematics of concepts can be handled similarly, bearing in mind that an iteration or mind/brain initiates a measurement and we are dealing with world O and world P. A little foreshadowing will make it easier to understand, that world P is a probability space and only has iteration, whereas Life has made world O into a ‘determinate’/non-entanglement world because of the necessity of creating a reality as part of questing/Survival-of-the-Fittest.

 

So, taking the easy case of world P, questing is: X-Y axes with the concepts to be examined spread equally spaced along the X axis, and a curve/^ is drawn between each concept and every other concept with a height ^ equal to its probability and the sum of all the ‘heights’ is 1. This comes straight from the entanglement/measurement of the probabilities in a probability space. To move it into world O in order to automate or use a mind/brain, move the concepts and the ^ to make a ‘normal’ curve and read off the best concepts and their context. If this looks simple, ask yourself ‘why should it be complicated?’, when the universe requires only 5 dimensions and life six dimensions.

 

A small digression in that the two ‘toughest’ problems in physics are generally considered to be quantum mechanics [questing, entanglement,  measuring ‘sticks’] and relativity [relevance, entanglement, measuring ‘sticks’] and yet they are simple properties immediately apparent from the dimensions of a probability space, as can also be seen the general mathematics of concepts. Common-sense logic is much more complicated because we have taken the ‘logic’ that must exist for us to be here and used it along with the mathematics of concepts, questing and relevance to produce Life with a mind/brain that changes the field in which it lives and leaves us with the interaction of worlds O and P.

 

Bear in mind that the above [normal form, solution] is a ‘snapshot’ and must be recorded with the decision to give relevance/relativity so that as time passes, and circumstances change, it is easy to rearrange the attractors and context, add different attractors and update or challenge the decision. This is crucial and can be seen from chapter 73, ‘thus, given that relativisation (1), the mathematics of concepts (2) and setting out the concepts/attractors and setting the context (3), the use of an absolute (4) [forward-planning] chosen by the universities (5) [the ‘best’ absolute] are derived above’.

 

‘Further, (6) is experimentation/trials/measurement etc., as suggested by Francis Bacon to bring about a ‘scientific method’ that has proved spectacularly successful in science/technology and this could be considered a ‘break-through’ because most ‘science’ was derived by ‘thought’ for thousands of years. However, the duality of concept/context and measurement/logic means that theorists (7) should be included and it is apparent that a mathematics of concepts has been set up [(1) to (7) in total] where more factors produce a better organization, but what is the purpose of an organization? An organization is set up for a number of reasons, but basically it is to satisfy a need and/or to evolve (8), and I should stress that these eight points are (possibly) the most important of many more that may need to be considered.’

 

Again, in chapter 73, I point out that science fortuitously/luckily uses this organizational derivation, but most organizations do not use as many attractors and their performance is so inadequate as to have caused, I believe, an Extinction event. These themes keep appearing because they are attractors that are relevant and cannot be ignored as they (somewhat) have been ignored using the Newtonian system. As a specific example, Newton’s laws of motion have not been challenged in 300 years, and I believe that they need rewriting, as I have done, but will have to wait till a later date. To foreshadow, with a simple example, a photon keeps the same speed irrespective of the energy in contradiction of the first law.

 

World O is our world and not important in the universe [400 billion galaxies], but it is to us, although in 10,000 years we have brought it to its ‘knees’ and I doubt that many would deny that, but it can be turned around, I believe, when we have the correct tools [as shown above]. Mathematics is a special case of the mathematics of concepts and chapter 74 showed how a Unified Field Theory needed a new general mathematics to describe it, and as well as a new mathematics, we need a new logic because the logic that science uses is ‘catch as catch can’ instead of a legitimate theory, that is consistent  (50/50) with concepts/measurement. Two simple examples are unassailable. Firstly, in Einstein’s Special Theory of Relativity, an assumption/postulate is made of relativisation [constancy of the speed of light, Michelson-Morley] of the speed of light to two different observers, and secondly, Feynman’s History.

 

From chapter 72, another example is the Feynman method of the solution of the double/single slit experiment with light and a rational explanation based on the dimensions of our universe. ‘In the 1940s Richard Feynman had a startling insight regarding the difference between the quantum and Newtonian worlds…. The pattern we find when we fire molecules with both slits open is not the sum of the patterns we find when we run the experiment twice, once with just one slit open, and once with only the other open. Instead, when both slits are open we find a series of light and dark bands, the latter being regions in which no particle lands.’ (The Grand Design, Stephen Hawking and Leonard Mlodinow, p 74)

 

‘Feynman realized … that particles take every possible path connecting those points. This, Feynman asserted, is what makes quantum physics different from Newtonian physics. The situation at both slits matters because, rather than following a single definite path, particles take every path, and they take them all simultaneously…. Feynman formulated a mathematical expression – the Feynman sum over histories – that reflects this idea and reproduces all the laws of quantum physics. In Feyman’s theory the mathematics and physical picture are different from that of the original formulation of quantum physics, but the predictions are the same.’ (p 75)

 

“In the double slit experiment Feynman’s ideas mean the particles take paths that go through only one slit or only the other; paths that thread through the first slit, back out through the second slit, and then through the first again; paths that visit the restaurant that serves that great curried shrimp ….. It might sound nutty, but for the purposes of most fundamental physics done today … Feynman’s formulation has proved more useful than the original one.’  (p 75)

 

‘Looking at the fifth dimension CEM (mathematics of concepts/entanglement/measurement it is literally obvious that Feynman’s formulation was correct because entanglement (context) links every point, measurement (concept) is available for every point and provides the probability that is necessary in a probability space all instantaneously. Feynman’s formulation is a mathematics of concepts that links probabilities and entanglement of energy together and in doing so, was necessarily correct, even if he didn’t know why. The simplicity, above, of quantum mechanical probabilities is, to my mind a proof that our universe must be a probability space.’

 

The above, on the Feynman example quotes ‘Feynman asserted, is what makes quantum physics different from Newtonian physics’ and this is incorrect because Feynman is, inadvertently, using world P and Newton used world O thinking and the difference is that world O necessarily contains measurement/concepts measured/determined by a mind/brain because force has to be determined.

 

In other words, neither Feynman nor Newton mentions logic and logic is 50% of the scene and is independent/orthogonal and is hidden in the above, but definitely still there. Newton thought that the force was between the centres of the masses, and so it is, if thought of in the simple terms considered [world O thinking], but if we use the Feynman example, gravity must be calculated over every possibility and that is the logic of entanglement. Again, in other words, world P is a measurement/entanglement and in world O, it is concept/context. Bearing this in mind, a quotation from chapter 74 should make it clearer.

 

‘A Unified Field Theory, to unify everything cannot be simple [because it has to include everything], but it is simple when the mathematics of concepts is used, because the mathematics of concepts is immediately apparent from the fifth dimension and the dimensions embrace everything. The existing theory contains four fields ranging from sub-atomic to universe-wide, so this extension of the theory is simply filling in the ‘bits’ in between. The ability of the mathematics of concepts to include mathematics and physics is ‘complex elegant’ [but the ‘opposite/different to ‘simple elegant’ because the concept is simple, but the context is infinite] and allows the areas of interest to be prioritised in a way that mathematics cannot do [without a mind/brain selecting them with some context in mind, which is, of course, the mathematics of concepts].

 

Newton’s treatment of gravity was elegant in its simplicity [forces act through the centres, proportional to the masses and inversely proportional to the square of the separation] and it is small wonder that it was applauded, lauded and became the ‘hallmark’ of good science and science has used the same basic methods ever since. The conservation of energy/matter requires that the energy of gravity balance all of the other energies. Conservative fields, such as gravitation require inversely proportionality to the square of the separation. ‘In physics, an inverse-square law is any physical law stating that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cause for this can be understood as geometric dilution corresponding to point-source radiation into three-dimensional space.’ (Wikipedia, Inverse-square law) It will be shown at a later date that ‘geometric dilution’ is an entanglement phenomonen.

 

The force acting through the centres is a simplification that mirrors the difference between Newton’s simplified experiment and Feynman’s approach to quantum probabilities that is in line with a probability space where every possibility has to be considered. The logical part of gravity is a relativisation that is an integral part of a probability space and requires questing throughout the space at an infinite speed. Thus the conservation of energy requires questing the logical part of gravity at every point in the universe.

 

However, a thought experiment, simplifies the situation by deleting context, and that can be serious because a measurement is a snapshot in context and similar to a photograph album with no dates or explanations attached to the pictures, so as time passes they lose relevance unless annotated. Another problem is that Newton, Einstein and Feynman thought in world O terms, but their theories relied on postulates that are expressible only in world P. The latter two are direct ‘steals’, but Newton took the ‘action to completion’ [impulse equals change in momentum] and applied a measurement [by a mind/brain] to gain the concept of force [incomplete action] instead of energy.

 

Further, the existing [unified field] theory/thoughts uses logic that assumes that a ‘particle’ affects the ‘object of interest’, presumably because there has to be something (logically) to effect the change. We ‘know’ that there has to be something, so we use the logic of the fifth dimension intuitively, but there is another field, and it is measurement with a ‘particle of logic’ subsumed within the fifth dimension. In other words, this extension of context fills out the theory and gets rid of assumptions and replaces them with the dimensions, and unifies everything.

 

The one thing that the greatest minds through out history have done is to reach into the fifth dimension for ideas as can be seen in chapter 70. ‘On a personal note, philosophy is a ‘closed book’ to me, but I can still “unfold” it by treating philosophers as concepts and applying the mathematics of concepts to them and this is made possible by the excellent analyses in the book ‘The Great Philosophers: the lives and ideas of history’s greatest thinkers’ by Stephen Law. ‘Unfolding’ is the investigation of the context and concepts and fitting the concepts (philosophers) into an array and mapping their contexts onto a fixed/unchanging basis that no one can dispute, and that is the dimensions of our (probability of existence) universe.’

 

A ‘guess’ is a strong word to apply to the greatest thinkers, but they got away with delving into logic for a good reason, and that is that ‘logic’ is a world O concept/context that is heritable and derived from our success at survival over 3,000 million years and we all have the same common sense because that is the ‘herd mentality’/reality. We all have to have a reality to exist and we must see the same things and react to them in the same way otherwise something will ‘track us down’ [sixth dimension] and eat us.

 

A second type of logic lies within world P that produces an anti-singularity field that is complex and works well, such as relativisation to preserve the logic that no particle (with rest mass) can exceed the speed of light in a vacuum. It could be that our universe, out of the multiverse contains the appropriate values that make relativisation work.  In other words, the ‘twilight zone’ scenario, above, necessitates a questing within the probabilities that reflect, I believe, differing values of the physical constants, except the speed of light that must be an absolute [together with the Golden ratio because we have entered mathematics].

 

These two types of logic are not difficult to understand because the second is automatic (world P) and in the first, our mind/brain evolved to link into the probability space for measurement, as we do with all the senses. The Cambrian, I believe, evolved a change (via lensed eyes) to the mind/brain that allowed the mind/brain to quest a new way that requires different ‘machinery’ to extend a physical measurement (line) into both a logic measurement and/or a physical measurement (plane). Perhaps the questing of the logic side that became available through the evolution of eyes and mind/brain is the start of the consciousness that philosophers’ appear to be seeking, and that could be when our thinking went two-dimensional.

 

Thus, a definition of logic is a recipe and is a co-mingling of world P measurement/entanglement [duality] and world O concept/context [duality] using that part of the mathematics of concepts [(a+b)=1] that is chosen with the assigning/recognition of the attractors used [snapshot, to acknowledge relativity] to gain a solution [proverbs are simple solutions, forming a normal curve of attractor’s desirability] that fits the quest that has evolved/survived Life’s reality.

 

Plato’s problem is a lack of absolutes, and this is necessary and they must be assigned and has been dealt with before in chapter 67, however, there is another absolute from the solution of the interval (a+b) [Golden ratio] that has traditionally been associated with beauty/pleasure/contentment/ecstasy and provides an answer to why we have been able to use these properties and agree on them amongst ourselves. I have included this field for completeness, but its derivation will have to wait, but notice that it is an exception to Plato’s lack of absolutes.

 

A prediction/example might clarify the overall picture because statistical mechanics takes a concept, such as photons leaving a point source and assumes that enough photons are leaving so that there is an even distribution. I am saying that an independent/orthogonal entanglement ensures that there is an even distribution (context) and further, in more complicated cases, such as diffraction, a specific sequence occurs that becomes an enigma and unexplainable according to our present laws of physics.

 

. Consider abeam of light passing through a small hole [comparable to the wavelength] and Newton’s laws of motion says that the beam passes through as it entered because no force acts on it, however, I am saying that entanglement provides a logical reason for the photon to change direction without a force. [Newton’s law is a simplification with no context as will become apparent]. The beam is diffracted and spreads out according to Huygens’ principle, where Huygen’s ‘wavelets’, generated at each instant are, I believe, probabilities and the photon changes direction in accordance with the logic/entanglement to make a new total semicircular wavefront, and this derivation will have to be left for later.

 

To simplify, a photon has a measurement/entanglement duality, a constant speed/energy (concept), but direction is a context, and in the same way that a vector has force and direction, the photon has energy/speed and a direction and obeys Newton’s law ‘unless acted upon by a force or entanglement’ [my addition]. Force is a world O concept and in world P we have to use energy/logic, or more accurately, energy-measurement/entanglement. Whilst my derivation is more complicated, it predicts and explains independent/orthogonal outcomes, and as an example, ‘one unrealistic prediction of Huygens’ principle is that if all these new wavelets are sources of wave energy then they should generate a reverse wave as well as a forward wave. So why does a wave propagate only forwards? Huygens did not have an answer’. (50 physics ideas, Joanne Baker, p63)

 

If the wavelets are considered probability fronts, the probability of the photon reversing is zero given the simple thought experiment and that solves that problem. If we bring the real world into the picture by introducing a dust mote, the probability front increases behind because of the entanglement of photon and dust mote as they approach and at some point the probability becomes unity and reflection occurs as a logical effect. Notice that if the photon energy is sufficient, the probabilities include the photoelectric effect and it can be seen that the iteration inherent in the mathematics of concepts is becoming apparent. This interpretation makes more sense/logic than photons ‘bouncing off’, which is nonsensical as it is an entanglement, as will be shown at a later date.

 

The above answers, to my satisfaction the question of what is the ‘common-sense’ logic [two-dimensional] that we use daily and why it works [a product of our reality], the question of formal logic has been side-stepped and the logic of the physical world [one-dimensional] along with the associated dualities of measurement/entanglement and concept/context have been considered as part of the fifth dimension of a probability space.

 

We have taken the logic that must exist for us to be here [out of the multiverse] and used it along with the mathematics of concepts, questing/entanglement and relevance/entanglement to produce Life. We have done this because we could do it, and have demonstrated logical decisions, but these decisions are not based on logic, only possibilities that work because we live in a probability space and what we call logic exists as a complex ‘recipe’ that works. In other words, what we think of as measurement/logic [thinking], really is measurement/entanglement/multiverse/questing/relevance/mathematics of concepts, and the word ‘logic’ is only a convenient word for a complex interplay of physical/mental/sociological/environmental effects.

 

In a ‘nutshell’:

(1) We are the selection out of the multiverse because we are here.

(2) The one ‘dimensional’ use of the properties of world P that are properties of the space and could be called logical [as a machine is logical], but most important is Occams’ razor because simplicity is paramount.

(3) The two ‘dimensional’ use of worlds O and P by Life, and concept/context can perhaps be replaced by concept/quest/relevance/entanglement, where the concept evolved through forward-planning by the mind/brain and measurement by the eyes etc.

(4) Formal logic.

(5) Proverbs are a ‘higher’ logic/thinking that uses the mathematics of concepts to provide quick responses.

(6) The solution of (a +/and b)=1 is an absolute [Michelson-Morley] that the speed of light is a constant and all other measurements must have an assigned absolute [Plato’s problem] except for (7).

(7) The solution of the interval (a +/and b) is an absolute [Golden ratio] that makes beauty/appreciation/enjoyment logical/repeatable/relatable.

 

Conclusion: a photon is ‘pure’ energy that must move at a constant speed in vacuo and is whatever the measurer wants it to be [a quest] and is relativised continually and this motion, I believe, creates the expanding universe without which, we wouldn’t be here. The conservation of [no] energy means that ALL energy must be accounted for, even the infinitely infinitesimal that could occur in photons and there is no ‘machinery’/carrier in the motion. It is important to realize that the photon is energy transference AND has to move as a kinetic energy AND has to be relativised continuously AND has to create space, time and the splitting of energy.

 

Logic is a quest that ties everything together and is based on the factors above that can be derived from the dimensions, but the dimensions provide the tools, such as mathematics, mathematics of concepts, the computer of evolution, the proverbs, what we are taught etc. So, how do the great thinkers get away with enigmas, such as Huygens, Newton, Einstein, Feynman etc? I think that we have a great capacity to change ‘creation myths’ when we change tribes and can ignore inconsistencies when necessary, but it is interesting that, if a probability space is assumed, these enigmas, I believe, disappear.

 

As a justification of this statement, evolution [questing] is composed of Survival of the Fittest and sexual selection and the latter is obvious from our experience and bird’s plumage. But, is it [top down concept, Newtonian] obvious? I say that the absolute [Golden rule, interval (a+b), bottom up] evokes a concept of facial beauty or plumage and a context of all agreeing that that beauty/colour evokes a feeling/logic across the reality. [Aristotelian is a guess, Bacon supports experiments such as Newton did for some of his ideas (concept), whereas I advocate concept and context] I believe that the second [bottom up] explanation is not only superior, but is correct. Q.E.D.

 

References: (1) all quotations are fully referenced in the body and earlier chapters can be found on   http://darrylpenney.com  if required.

 

Abstract: the name Unified Field Theory promises a theory that is wide-reaching and includes all fields including the local football field. This derivation does just that, because the theory uses the mathematics of concepts that allows all desired fields with any desired priority to be set for the speciality of fields to be considered.  In other words, the theory presented here ticks all the boxes and is infinitely adaptable to the users’ wants, answers the  ‘why?’ in a deeper way by widening the definitions of the ‘particles of action’, ‘show-cases’ the mathematics of concepts and truly becomes the Unified Field Theory that does away with all assumptions and rests only on the dimensions of a probability space and the associated measurement/entanglement/ecstasy of the physical universe and the concept/context/beauty of Life.

I believe that I have given sufficient proof that our universe is a probability space and literally everything (until now), apart from space-time, has been taken (top-down) from the fifth dimension and so, I will use a bottom-up approach from the dimensions to show how wide-sweeping the fifth dimension is and it will allow me to build on the Unified Field Theory that appears to have caused trouble over many years. Perhaps the problem is, as shown in the two paragraphs below, that Newton’s ideas have been slavishly followed and a new direction is needed, and especially a new type of mathematics.

 

‘Let me raise a few points which seem not to have been made the subject of scholarly investigation. I have always been puzzled by the strange wording of the definitions of mass, momentum, and force, at the beginning of the Principia. For example, Definition I states “the quantity of matter is the measure of the same, arising from its density and its bulk conjointly”. Why does Newton again and again identify a physical property or quantity with its measure? There is surely more to a physical quantity than a statement of how it is measured? The answer is possibly to be found in Newton’s early Scholium on absolute space and time. Since, according to Newton, we can only measure relative space and time, and not absolute space and time, all we can know about physical quantities are not the absolute quantities themselves but merely their relative substitutes – that is, their measures. This argument is not well worked out by Newton.’ (Let Newton be!, John Henry, p 59, edited by John Fauvel)

 

‘It is not always appreciated that, 60 years ago, the makers of modern quantum theory were totally steeped, immersed, educated, brainwashed, if you like – in the mathematical methods of Lagrange and Hamilton; these ideas had grown out of, and were the natural evolution of, Newton’s dynamical ideas.’ (p 244) Further, ‘as we now know, his faith in forces was justified to such an extent that it is widely regarded as Newton’s most important scientific innovation.’ (p 128) ‘A slightly naughty thought can come to one’s mind here. Is it due to the nature of physics that the mathematical tools started by Newton are so essential for many parts of physics through the centuries? Or is our selection of worked-on parts of physics still largely Newtonian? (p 244)

 

This last quotation is what I call a chaotic statement [both correct and not correct at the same time] and it will take the whole chapter to make it clear, and that will be done, but it is at the moment a prediction and as the sixth dimension shows, a forward-plan makes things easier/possible. Newton missed/assumed the logic half of physics and also used mathematics, which is a special case of the mathematics of concepts, and mathematicians and physicists etc. have built on his vision and, as a consequence, we face a world-catastrophe/Extinction-event. The basic-problem/error that science has pursued may well be ‘simplification’ that [perhaps] came about from the simple inverse square law relationship of gravity, in world O units, and that aim [of science in general] is at odds with the indeterminacy of quantum mechanics, Life, social sciences etc. Everything is related, so we can start anywhere and I have chosen the Unified Field Theory to illustrate the failings of ‘following the herd’.

‘According to the current understanding of physics, forces are not transmitted directly between interacting objects, but instead are described by intermediary entities called fields. All four of the known fundamental forces are mediated by fields, which in the Standard Model of particle physics result from exchange of gauge bosons. Specifically the four fundamental interactions to be unified are:

• Strong interaction: the interaction responsible for holding quarks together to form hadrons, and holding neutrons and also protons together to form atomic nuclei. The exchange particle that mediates this force is the gluon.
• Electromagnetic interaction: the familiar interaction that acts on electrically charged particles. The photon is the exchange particle for this force.
• Weak interaction: a short-range interaction responsible for some forms of radioactivity, that acts on electrons, neutrinos, and quarks. It is mediated by the W and Z bosons.
• Gravitational interaction: a long-range attractive interaction that acts on all particles. The postulated exchange particle has been named the graviton.

Modern unified field theory attempts to bring these four interactions together into a single framework.’ (Wikipedia, Unified field theory)

Firstly, I have to say that I know little about this subject, and wish to comment on existing theory even less and that is the problem for the generalist and (possibly) why most people are content with a speciality, but, there is a need for a new approach, and that, is written in the dimensions. The missing word is ‘context’ and that, I believe, underlies the Extinction event that we have caused, our modern diseases and even the approaching Armageddon of our planet.

‘As the only nonanimal source of vitamin D, mushrooms are undoubtly important for many animals, especially species that are nocturnal and/or burrowing. All fungi contain ergosterol in quantity; it’s transformed into vitamin D by irridation with sunlight, often to an astonishing degree.’ (Trees, Truffles, and Beasts: How Forests Function, Maser, Claridge and Trappe, p 96) This quotation is apt for a number of reasons but is a little misleading in one context, and that is that we and all animals evolved from fungi and still retain the ability to form vitamin D from sunlight.

So important are these contextual ramifications to modern living, ‘”the implications are that vitamin D could be regulated by the controlled exposure of dried mushrooms to sunlight.” Therefore, squirrels that hang mushrooms or truffles in trees to dry in the sun ….  are producing vitamin D supplements in their diets’ (p 96) that this suggests that neglecting context is (possibly) the reason that modern diseases are so prevalent. These quotations are illustrating where we have gone wrong and in simple terms: context is a duality/orthogonality that we have not realized is attached to each and every concept. Throughout the ages, people have ‘reached’ into the fifth dimension and used logic, concepts and context without realizing where they come from, or how to use them properly.

 

Secondly, I believe that the Big-Bang/Big-Whoosh created a probability of existence universe composed of matter/energy [always totalling zero] that are states of energy in various forms with varying lifetimes and the universe has the dimensions space-time and (a+b)=1 as an illustration of measurement/entanglement of a probability space (a+b+c…)=1 where a and b are measurement/observers. This is the universe/basic-space of what we call energy and encompasses everything that allows us to investigate and make [mathematical/logical] sense of the parts with a measurement/entanglement duality [concept/context duality] using the mathematics of concepts.

 

Thirdly, (a+b)=1 can, as the questing of quantum mechanics [being necessarily indeterminate until measured] be written as (a +/and b)=1 to show the logic of entanglement and this leads to the quantum/evolution-logic/gravity description of the universe and this logic [as part of all energy] relativises the dimensions [mass/energy, space and time passing] so that the conservation of energy remains zero (see chapter 72). Hence, I offer an alternative to the postulate of ’gravitons’ and believe that gravity is both a logic and an energy and believe that I can offer better understanding by using a bottom-up approach through the dimensions.

 

Fourthly, whilst not an objection, the relationship of radioactivity to the ‘weak interaction’ seems to be a probability/half-life function that suggests/aligns with the idea that our universe is a probability space. In other words, as it stands, it requires half-life/probability additional to existence whilst a probability space contains that probability [is less complicated logically and so, more likely].

 

Fifthly, the quotation about Newton’s lead/guidance as being the ‘guiding light’ of physicists ‘cries out’ for radically different ideas of space/fields and what I am proposing fits perfectly with his perception of force. If he had asked the additional question of why the apple kept repeating the same motion, he would have (perhaps) seen the logic side of the space/field, or perhaps not, because force is a world O creation and already contains the logic. A world O [our] measurement requires a mind/brain to apply the question [containing logic], whereas a world P [physical] does not. This concept of consciousness [of the apple] is continuous and seamless over evolution and thus forms a reality that is the Theory of Everything. In other words, the Unified Field Theory and the Theory of Everything are similar/linked.

 

I would like to offer a quotation from chapter 73, ‘there may be no a priori reason why the correct description of nature has to be a unified field theory. However, this goal has led to a great deal of progress in modern theoretical physics and continues to motivate research.’ (Wikipedia, Unified field theory) However, there is a description of the universe that I have called ‘quantum/evolution-logic/gravity’ and it is derived from the five dimensions, above, and they are the a priori and all that is needed to create the universe.

 

From chapter 72: ‘concept/measurement: 0 = kinetic (energy) + gravity (energy) + mass + dark matter + dark energy + photon energy + chemical etc. acting at the speed of photons in vacuo as a maximum.

 

Context/logic: 0 = kinetic + gravity (logic) + mass + dark matter + dark energy + photon energy + chemical etc. acting at an infinite speed where gravity is always negative and all the other energies are positive.’

 

This shows the separation of gravity (energy) and gravity (logic) and is the start of the logic side of the fields becoming apparent.

 

From chapter 73: deriving organization, ‘given that relativisation (1), the mathematics of concepts (2) and setting out the concepts/attractors and setting the context (3), the use of an [assigned] absolute (4) [forward-planning] chosen by the universities (5) [the ‘best’ absolute] are derived above. Further, (6) is experimentation/trials/measurement etc., as suggested by Francis Bacon to bring about a ‘scientific method’ that has proved spectacularly successful in science/technology and this could be considered a ‘break-through’ because most ‘science’ was derived by ‘thought’ for thousands of years. However, the duality of concept/context and measurement/logic means that theorists (7) should be included and it is apparent that a mathematics of concepts has been set up [(1) to (7) in total] where more factors produce a better organization, but what is the purpose of an organization? An organization is set up for a number of reasons, but basically it is to satisfy a need and/or to evolve (8), and I should stress that these eight points are (possibly) the most important of many more that may need to be considered.’

 

I should mention that (4) [forward-planning] is a sixth dimension and point (8) shows the gradation of evolution from iteration [Survival of the Fittest] to Survival of the Best when we decide what evolution should become and this concept drastically changes most life on earth and so we must be careful to use the correct tools for the job. Another crucial point is that relativisation is on-going and a decision/measurement must have the concepts and contexts (that were used) recorded so that they are seen to remain relevant over time.

 

Further, from chapter 73: ‘the comparison of the above with the below shows that the success of science was organizationally lucky/fortuitous, because, from above, many of our organizations are inadequate, such as the process of law, the making of laws by public servants, the food offered by shops, the fishing industry [a commons] etc. are deficient, but science was a ‘stroke’ of luck because acceptance (1) of a theory is required by scientists in general and that theory requires the mathematics of concepts (2) [to compare theories] and invites additions and checking (3) of the result (4) by those with a long-time career (5) in the subject and this often requires experimentation (6) and theorists (7) to fit it all together, and finally, the overall idea of science is to ‘push’ the boundaries (8) of what we know. It is hard to resist a giggle that science has been using the fifth dimension, top-down without acknowledging its existence.’

 

Keeping these thoughts in mind, from above, firstly, the splitting of gravity into a physical and logical duality, and secondly, a logical field of organization that embraces literally everything because everything is part of everything else [organization, entanglement, mathematics of concepts] have rendered the existence of ‘particles of action’ of the existing theory too restrictive. The application of the current use of the methods of science shows that science/universities are based/aligned with the theory, above, and the success of science/technology offers a ‘proof’ [by exception] of its power. Notice that as we moved down the list of the Unified Field Theory above, we moved from the physical to the physical/logic of gravity to the logic of organization.

 

The next step is to move to other fields, bearing in mind that I have relaxed the requirement that there must be a particle to transmit the ‘action’ because the instantaneous speed of logic is a property of the space, not the energy in the space. It is delving top-down into the fifth dimension to say that there must be a ‘something’ to cause ‘scary action at a distance’ and, of course there is, but it is a property of the probability space and relativisation was not recognised. Of course there must be something to ‘affect’ the ‘something’ at a distance, but it can take many forms, such as trust [monetary fields], logic [gravitation], measurement, relativisation, love etc. [The word ‘logic’ is used as a ‘rag’/mixed bag and will be considered/derived properly at a later date]

 

Another aspect, that emerges from the name Unified Field Theory, that was considered to be a theory of physics, becomes part of a much larger theory because it promises a theory that is wide-reaching and include all fields including the local football field. This comes about as part of the bottom-up requirement of the all-encompassing name and this derivation does just that, and more, because the theory uses the mathematics of concepts that allows all desired fields with any desired priority to be set for the speciality of fields to be considered.  In other words, the unified field theory presented here ticks all the boxes and is infinitely adaptable to the users’ wants as the area of interest can be prioritised by selection, whilst bringing other concepts into consideration as needed. To simplify further, a general mathematics of concepts must involve ALL concepts and contexts and that is why it has to be used, and why the ‘exact’ Newtonian thinking cannot adequately describe fields of all types.

 

The next to be considered is the ‘quantum’ field which could be defined as a ‘questing’ field because a probability field must consider all options [questing] and to do that it must be indeterminate at each point until measured, and it is the measurement, not a particle, that causes the wave/particle to become determinant. This, in the light of the above, could be resolved by saying that questing is a property of the space, but that might be ‘splitting hairs’ as the space is a field, so, we could say that a and b [as measurement/observers], as (a+b)=1, also shows that measurement and entanglement are a duality and comprise two independent fields.

 

Another field that must be considered is the singularity field and the associated relativity relativisation, because the dimensions require that the speed of all photons be a constant and this (logical) maximum allows the possibility of a singularity occurring. This possibility is handled in the simplest logical way [Occam’s razor] by relativisation of all the dimensions [energy/mass, space and time vary by the Lorentz transformation] as a frame of reference approaches the speed of light with respect to a [stationary] frame. This is a logical necessity because the measuring ‘stick’ is the speed of light and if it is exceeded, chaos occurs and cannot be eliminated/reversed because entropy cannot be simply returned/reversed. We are here because it has not happened in any of 400 billion galaxies over 14 billion years and nor is it likely to occur because relativisation works well, and that is why it is a field [‘it works’ field, multiverse selection logic].

 

Another field has been discovered by Life and is unique to Life and that is consciousness, and its major attribute is forward-planning that derives the sixth dimension [world O] and that has been formulated by organisms, including ourselves, as a necessary defence against predation by the mind/brain using distance and speed to judge a safe distance. Likewise, the predator has to judge speed and distance to control the level of success of an attack because each failed bid reduces the available resources [this is the source of world O versus world P]. The sixth dimension, I believe, is different to the other dimensions because it introduces future time and that requires a space/field of the mind/brain.

 

It is important to note that [world P] probability space is measurement/entanglement and a simple mathematical space, but the mind/brain has built on this [world O] with the sixth dimension [forward-planning] and reality has changed the space/field. Entanglement changes every point in the universe, but because of measurement, we are constrained by what we know and live in a world that is determinant because every organism must be able to live with every other for at least one breeding cycle. This is probably easier to understand if we consider that each of us has had an unbroken chain of ancestors that had offspring [for 3,000 million years], else we would not be here. In other words, the necessity of survival means that we can live with predators for a ‘reasonable’ time and recognise danger and avoid it, and if we cannot sense it, such as for bacteria, our immune system can, and does.

 

The space/field produced by the mind/brain is so important/overwhelming that it has instigated a mass extinction at the current time, every bit as ‘bad’ as the mass extinction caused by, I believe, the evolution of lensed eyes and the predator/prey forward-planned attack/avoidance evolved in the Cambrian. Now (a+b)=1 shows context for the concepts a and b, and I have said that concept/context [world O] is a duality [measurement/entanglement duality in world P] and the phrase ‘space/field produced by the mind/brain’ could be classed as a chaotic statement [both correct and incorrect at the same time], so I will explain with a digression.

 

Some time ago, I used the mathematics of concepts [or, as it was then, the Mathematics of the Mind] to derive three Laws of Life: (1) creation [iteration, componentization (like an atom, evolution etc.), time passing etc., (2) state of mind, nutrition and exercise etc. and (3) family life and teaching the young etc. These are expressed in the terms of the mathematics of concepts [hence the etc.] and, given that mathematics is a recent invention, it is not surprising that these Laws mirror the Trinity of the Bible and suggest that the Holy Spirit, that has been ‘lost’ for 2,000 years is the second Law (2) (see chapter 1). The first Law is the Creation [God the Father] and the third Law is God the Son. It is well known that the Church has always believed that the environment was for man’s use, but that idea must change in view of the current extinction event.

 

From above, every concept has an associated context, and the concept of the mind/brain has the second and third Laws as context because we must relate ourselves to the environment [Law (2)] and prepare offspring for the environment on their own [Law (3)]. Thus, the mind/brain field/space has two contexts whereby we keep ourselves healthy [considering that 60% of adults are overweight or obese] and prepare our children to enter the community. The mind is a ‘higher’ use of a brain that is composed of a multitude of cells and by coming together, produce an organization that has new properties that tie into the surrounding universe through improved measurement [lensed eyes leading to forward-planning etc.].

 

The above is, as in the mathematics of concepts, laying out the most pertinent concepts ready to apply the context to derive a version of the Unified Field Theory and it may pay to ‘lay to rest’ a couple of ‘urban myths’ considering quantum mechanics and relativity. They are simple concepts and will allow us to appreciate the concept and context of fields. Relativity is a logical requirement because the ratio of space to time dimensions demands a constant speed of light [for all/different energies] that becomes indeterminate and produces logical chaos if a particle exceeds the speed of our measuring rod. Quantum mechanics arises because we live in a probability universe and a probability space ‘quests’ over every alternative and the result must be indeterminate unless a measurement forces it to become determinate. That has disposed of those two problems easily because we used concept/logic in both cases and that is the fifth dimension (a+b)=1.

 

Now, we find that fields have to belong in a space that holds them [much like the zeroth law was appended to this oversight of the three laws of thermodynamics] and that is the probability space of existence that over-arches everything, supports the Big-Bang/Big-Whoosh and holds energy in different states that ‘meshes’ with the two [strong and weak force], above. However, electromagnetic quanta, I believe, are constrained [by the dimensions] to a relatively slow speed and, I also believe, they are ‘free’ energy, however, quanta are essential to Life-fields in transferring energy [and balancing energy].

 

The total energy in the universe appears to be zero [not least for logical reasons] and that means that literally everything is the result of ‘splitting’ into matter/anti-matter, positive/negative electric charges, positive and negative energies and north/south magnetic poles and I believe that their effects are linked by the basic properties of measurement/entanglement in our probability universe. Notice that a different effect occurs when energy is created, because creation of energy [splitting] increases time and space].

 

 

Finally, I believe that there is another secondary absolute from the fifth dimension (a+b)=1 that makes an over-arching description of our physical universe be measurement/entanglement/ecstasy and this is carried into world O through the evolution of Life. Ecstasy, or a feeling of resonance through measurement/entanglement is ‘available’/we-have-made-use-of the questing of the solution of (a+b), and that is the Golden ratio that has intrigued scholars for hundreds, perhaps thousands of years as a source of beauty/contentment, and that concept will/has been dealt with more fully in the future. This concept/field entwines/involves a huge proportion of our lives as in the search for personal beauty including jewellery, high heels etc., the enjoyment of music, drugs, food etc.

The fundamental interactions to be unified are:

1. a probability of existence space over-arches the fields that are defined by the dimensions: space-time and (a+b)=1, for simplicity and for measurement/observers a and b and remembering that energy, as the sole occupier of the space is effectively a dimension.
2. Strong interaction: the interaction responsible for holding quarks together to form hadrons, and holding neutrons and also protons together to form atomic nuclei. The exchange particle that mediates this force is the gluon.
3. Electromagnetic interaction: the familiar interaction that acts on electrically charged particles. The photon is the exchange particle for this energy [I have changed energy for force because force requires a measurement].
4. Weak interaction: a short-range interaction responsible for some forms of radioactivity, that acts on electrons, neutrinos, and quarks. It is mediated by the W and Z bosons [and invokes/requires probability].
5. Gravitational interaction: a long-range attractive interaction that acts on all energies (having a energy component and a logic component) [measurement/entanglement/logic]. The logic component is instantaneous and the energy component has a constant speed of light because the dimensions change by the same amount [Lorentz factor].
6. Measurement/entanglement duality from the equation/illustration (a+b)=1 that a and b have no absolute solution (except for the speed of light).
7. Measurement/entanglement duality from the equation/illustration (a and b)=1. Notice that F and G produce Plato’s problem of no absolute [of justice etc.] because the equation has a solution/absolute [speed of light].
8. Organization affects every relationship and through the fifth dimension (a +/and b)=1 can be derived concepts/attractors in the form of a mathematics of concepts that describes in a transparent way the concepts used in the prediction. This allows specialization  but still keeps the basic over-arching attractors.
9. Questing field can be derived from a probability space and is the requirement that measurements remain indeterminant until a measurement is made by an iteration or mind/brain. This is the basis of quantum mechanics, evolution, business growth etc.
10. Singularity field is the ability of a field to prevent a singularity occurring that would effect a logic or measurement chaotic effect universe-wide or within an attractor [necessitating a boundary]. Our universe relativises the dimensions of energy/mass, space and time-passing by the Lorentz factor as the relative speed of two frames of reference approach the speed of light in vacuo [logic limit]. Our universe has been successful in 400 billion galaxies over 14 billion years, otherwise we would not be here [logic of selection].
11. Mind/brain field is the building/evolving of a new type of field on top of the measurement/entanglement field that is the probability space [world P] turning it into a concept/context/determinate field of the mind/brain complete with special units of distance and speed to guage predator/prey behavior. This is the world O of mathematics and physics [limited context] that (probably) is causing an Extinction event on the planet.
12. Mathematics of the Mind is the correct/optimal [derivable from the dimensions] way of using the mind/brain and the bio-computer/evolution ‘proves’ that the Mathematics of the Mind and the mathematics of concepts are the same. In other words, the countless iterations of evolution have produced a mathematically optimal system (in the mind/brain).
13. Environmental field (second Law of Life) is the reality that allows organisms to co-exist and reproduce and contains a mathematical/logic ‘machine’ [componentization, atom, evolution etc.] that is the basis of Survival of the Fittest, where the fittest produce more offspring. The individual relies on state of mind, exercise and nutrition within the environment to increase the number of viable offspring.
14. Family field (third Law of Life) is the practice of protecting and teaching the young offspring to enhance their chances of survival on their own. Longer lived species tend to do this, presumably to increase the success rate per energy expended. This introduces sub-fields because continued breeding success requires that the old members should die before the younger inexperienced members [death orgene, illogical requirement that the more expeienced should die before the less experienced] and old long-lived females should stop breeding because birth defects increase with age.
15. Money field is a social convenience that everyone accepts by donating their time and energy at work in exchange for promises of future purchasing power and trusting that it will remain ‘stable’.
16. University field is a unique repository of knowledge and so forth through all the fields/orgainizations that are determinate to us. The Mathematics of concepts can hanle this multitude, but there are simple steps that must be followed as discussed in chapter 73.
17. Beauty/contentment/enjoyment field that, I believe, we have evolved from the absolute of the solution of the fifth dimension that we call the Golden ratio. [Notice that this is conceptually different to Plato’s problem, that is a lack of an absolute]
18. And so on.

It is readily apparent that these fields/organizations are concepts that are on-going and need the mathematics of concepts to use context to derive predictions by a mind/brain or iteration. At the same time it is apparent that the ‘array’ of concepts are a mathematics of concepts and can be ‘ranked’, or more fields that are of importance to a speciality/field-of-expertise can be added. Further, generalists are unwelcome within establishments, and I presume that the reason is that they know little of the field of endeavour and are thought to contribute little. However, if we equate specialists with concepts, we have to consider that generalists are context and given the above, that concept and context are independent but both are important/necessary [like orthogonalty], I believe, that this is why the world is in an Extinction event and perhaps Plato’s democracy is the place to start (chapter 67).

Conclusion: a Unified Field Theory, to unify everything cannot be simple [because it has to include everything], but it is simple when the mathematics of concepts is used, because the mathematics of concepts is immediately apparent from the fifth dimension and the dimensions embrace everything. The existing theory contains four fields ranging from sub-atomic to universe-wide, so this extension of the theory is simply filling in the ‘bits’ between. The ability of the mathematics of concepts to include mathematics, physics etc. is ‘complex/elegant’ [but the opposite to ‘simple/elegant’] and allows the areas of interest to be prioritised in a way that mathematics cannot do [without a mind/brain selecting them with some context in mind, which is, of course, the mathematics of concepts].

 

Further, the existing theory uses ‘common’ logic that assumes that a ‘particle’ affects the ‘object of interest’ but this ‘particle’ can be expanded into measurement, questing, trusting etc. In other words, this extension fills out the theory and gets rid of assumptions and relaces them with the dimensions, and unifies everything, so it could be called the Unifying Theory, or perhaps just ‘I’ve got it now’!

 

It is time that Newton’s work was updated and the mixture of measurement and logic in world O be sorted out. Newton has ‘carried’ science for far too long, and specialists rule the academic world, but it is time for generalists to expand context to its rightful 50/50 balance with concepts and ‘balance’ our civilization. Science has ‘mined’ the fifth dimension, to a limited extent, and done a lot better than the other organizations, as one would expect/hope, albeit, possibly by luck, but universities should be given their ‘due’ and are our best choice to give Plato a chance before fear/lack-of-change brings on Armageddon.

 

References: (1) all quotations are fully referenced in the body and earlier chapters can be found on   http://darrylpenney.com  if required.

 

 

Abstract: the mind/brain appears to have created an Extinction Event in the Cambrian and it is doing so again, at the present time, and the problem is being caused by our lack of adequate tools of organization/management that we are trying to use top-down and which make more sense when viewed from a bottom-up prospective using the dimensions of a probability space [our universe]. The quantum/evolution – logic/gravity description of the universe produces a range of conditions/understanding that can be applied to every organization/society, and science, as practiced today, struck it lucky in a top-down approach that ‘proves the rule’ and its success shows how effective the application of the science of organization/management can be to solving the world’s problems and re-establishing a meaningful evolution through Plato’s politics. The mathematics of concepts requires relevance/relativity and assigned absolutes and indicates how a Unified Field Theory is derivable.

There have been many Ages: the Stone Age, Computer Age etc. and they all had a concept and context, where the concept is a product of the Age but the context was the fitting of that age into human history. The Mind is the greatest concept of all and occurred when single cells ‘contracted’ [in the placebo/nocebo effect] to join together to create a higher/more-useful mind/brain, and together with the lensed eyes in the Cambrian, I believe, caused a massive change to evolution through an extinction event that led to the formation of hard fossils that laid out the study of evolution.

 

The Cambrian could be called the Age of the Mind because of the swift change from soft bodied creatures that (literally) had to bump into each other for a predator/prey situation to occur, to teeth and other hard parts that came about as lensed eyes made forward-planning possible [the blossoming of the sixth dimension]. The Theory of Everything suggests that consciousness has always been with us, from the repetition of a falling apple through the consciousness of life to the mind/brain of humans. Unfortunately, the present Age of the Mind is creating another Extinction Event, similar to that of the Cambrian, but now we have the means to control it, and I believe that that means is the Selection of the Best (mathematics of concepts) [concept] and using Plato’s political system [context] to help effect it.

 

Our world is in a mess because we moved out of the reality of Survival of the Fittest [an iteration] to our own creation of farming, that I call Survival of the Best (mathematics) and mathematics is a special case of the mathematics of concepts and we used concepts without adequate context and consequently are heading towards Armageddon and that shows how problems can quickly occur [in only 10,000 years] when a special case is used instead of the general/workable case. An Extinction Event can be avoided using the mathematics of concepts and the provision of a goal [sixth dimension, absolute] because these are basic/fundamental requirements that need to be understood about an organization. A simple example is that science sets up an experiment [goal/concept/assigned absolute] and brings the results into a context/theory. Contrast this method to the promises of politicians, and their lack of suitable goals, and it is little wonder why the world is in a mess.

 

The mathematics of concepts is necessary to deal with the ‘soft’ sciences that can’t use the exactitude of mathematics and it took me years to develop this mathematics of concepts, only to find that it can be written elegantly as (a +/and b) =1 for concepts/measurements a and b, and the ‘+/and’ is shorthand for context/logic that forms a duality with concept/measurement. The problem with such simple relationships is that you have to realize what the concepts/contexts mean, and an example is that the basis/definition of quantum mechanics is to investigate every possibility. Another simple example, (a+b)=1 mathematically has no unique solution, and that solves Plato’s problem of no absolute of justice etc., and it will be shown, below, that there is one absolute, the speed of light in vacuo that is the same to all observers [Michelson-Morley].

 

It might seem unusual that justice etc. should be used in the same sentence as the speed of light, but the universe is composed of organizations of all different things [stars, businesses, tree growth etc.]  and the dimensions of our universe are the most fundamental part to use to build a bottom-up view of organizations. It is essential that a bottom-up view be taken because top-down does not answer the question ‘why?’, only ‘how?’ and this adds uncertainty to the answers. As an example, mathematics is a special case of the mathematics of concepts, and whilst I derived it in another way, when you know what it is, it is obvious from the dimension (a+b)=1.

 

Notice that there are two dualities, measurement/logic and concept/context, and [in chapter 72], measurement/logic applies to a mathematical (world P) probability space, such as our universe, but Life has evolved along a time-line as shown by the Theory of Everything and has evolved a mind/brain that uses a Mathematics-of-the-Mind/mathematics-of-concepts (world O). World O uses the same fifth dimension as world P, but with the addition of a new dimension six, that is forward-planning and concepts instead of probabilities.

 

In other words, cells took billions of years to evolve [the cell wall must remain small for strength] and so cells joined together to form multi-cellular organisms [an organization] and that resulted in the placebo/nocebo contract [two-way conversation] and allowed, I believe, the evolution of the much more efficient lensed eyes that led to predator/prey attacks and forward-planning [sixth dimension] evolving. The mind, I believe, is a mechanism that ‘quests’ concepts using the ‘principle’ of quantum mechanics, as quantum mechanics ‘quests’ the relation (a+b)=1 [fifth dimension] where every point in a probability space has a probability and the sum of all probabilities over all points remains 1, and this calculation is carried out instantly and continuously. Remember that a probability of existence space has an infinitely small chance of existing [at 1] and likewise, has an infinitely small chance of not existing [=0], and forms a ‘twilight zone’.

 

To digress, I have always had problems with why iteration and the mind/brain produced measurements and now realize that the questing of quantum mechanics is the answer and that is a basic property of a probability space and it is there for anything, such as a limit of an iteration or the questing of a mind/brain. In other words, why can an iteration or mind brain ‘force’/interact-with the universe to ‘register’ a ‘snap-shot’ of the universe going about its business and it must be that part of a probability space that quests, and that is a basic property shown by the fifth dimension (a +/and b)=1, that is ‘+/and’.

 

To repeat, the mind, I believe, is a mechanism that ‘quests’ concepts using a process that is the basis of quantum mechanics, but using the mathematics of concepts as a ‘plural’ [concepts/context duality] instead of the probability space’s ‘singular’ [measurement/entanglement duality] (see chapter 72) and produces a space that is not an entangled probability, but is a space restricted to our reality and as such, uses the mathematics of concepts with its intrinsic indeterminism.

 

Relativity only causes problems because of the way it is viewed and the Michelson-Morley experiment [(a+b)=1=(a+c) for the speed of light a and observers b and c, indicates b=c] shows that two observers are relativised by both seeing the speed of light [a] to be the same. Relativisation [(a +/and b)=1)] is a property of a probability space and is quite natural, and uses the Lorentz transformation on each of mass/energy, length and time, which are the five dimensions [space-time and (a +/and b) =1]. Notice that all of the dimensions are affected equally, as we would expect, as it is logically simpler to act on all dimensions equally [Occam’s razor, which is a simple solution to the mathematics of concepts] and the speed of light [a] is a ratio of distance [dimension] divided by time [dimension], so, the speed of light is constant and an absolute [the transformation cancels, the equation has a solution].

 

It is interesting that inflation in the Big Bang may have been caused by the same relativisation of dimensions being linked [energy increase/splitting produces space and time increases via the Lorentz transformation] and that, I believe, is the same simple process that is used by [constant] energy in the form of photons to maintain the internal ‘book-keeping’ of the conservation of energy [chapter 72] [and as a means of movement]. The dimensions determine everything and especially physics, above, but we can expand our view and produce/find a Unified Field Theory because there are a limited number of [distinct] possibilities that the fifth dimension can attain.

 

Unless we control our lives, we have problems such as obesity, overpopulation, crime, health problems etc. and these concepts have contexts attached [concept/context duality/orthogonality] and it is only when a measurement of a concept is made that it becomes determinant, as does the context. A simple example would be the obesity epidemic, (partially) caused by people ignoring the relationship of state of mind, exercise and nutrition [Second Law of Life] where our bodies evolved for the hunter/gatherer lifestyle of the Paleolithic and not the modern culture of laziness, poor nutrition [‘quality’ and lack of variety] and lack of exercise.

 

Another simple example, ‘we have found that a small truffle specialist, the California red-backed vole, usually has pieces of eight to twelve species of truffles in its stomach at any one time. Although a single, medium-sized truffle would fill its tiny stomach, it chooses instead to nip around on many species. The same holds true for a great number of other small mammals around the world, particularly the obligate and preferential mycophagists. Perhaps instinct or the varied attractive odors of the different species induce them to diversify their diet and thus minimize the risk of nutritional deficiencies. (Trees, Truffles, and Beasts: How Forests Function, Maser, Claridge and Trappe, p 100) I firmly believe that processed ‘foods’ and a severely restricted range of natural foods is helping cause the ‘obesity epidemic’ in the developed world, not to mention the ‘modern diseases’.

 

The fifth dimension [(a +/and b) =1] contains the logic operator ‘and’, and the proviso that an accounting and readjustment of (a+b+c+….)=1 [relativisation] is carried out instantaneously and given that the universe is [only] energy in various states, the Law of Conservation of Energy is nothing more than this relativisation of the logic component [of gravity] of the various forms of energy [gravity, kinetic, chemical, matter, dark energy, etc.] where gravity energy is negative and all the rest positive. The duality of measurement/entanglement leads to two equations of the form: 0=energy of all the terms (gravity + kinetic etc.) and logic of all the terms (gravity + kinetic etc.), the speed of gravity (logic) is infinite and the maximum speed of all other energies is the speed of light [an absolute]

 

An interesting point is that everything is indeterminate because a probability space must investigate every possibility and it can only do that if it is free to do it, and measurement by iteration or mind/brain makes a concept and context determinant, at that instant. Notice that this indeterminacy was one of the ‘oddities’ of quantum mechanics, but in this (logical) ‘light’/question is necessary. As an example, photons will be a wave or a particle depending on how we measure them. The key to a probability space is relativisation because every frame of reference is continually changing with respect to the conservation of energy and this is shown by the continual changing energy of electromagnetic quanta [Pound-Rebka].

 

‘Let me raise a few points which seem not to have been made the subject of scholarly investigation. I have always been puzzled by the strange wording of the definitions of mass, momentum, and force, at the beginning of the Principia. For example, Definition I states “the quantity of matter is the measure of the same, arising from its density and its bulk conjointly”. Why does Newton again and again identify a physical property or quantity with its measure? There is surely more to a physical quantity than a statement of how it is measured? The answer is possibly to be found in Newton’s early Scholium on absolute space and time. Since, according to Newton, we can only measure relative space and time, and not absolute space and time, all we can know about physical quantities are not the absolute quantities themselves but merely their relative substitutes – that is, their measures. This argument is not well worked out by Newton.’ (Let Newton be!, John Henry, p 59, edited by John Fauvel)

 

‘It is not always appreciated that, 60 years ago, the makers of modern quantum theory were totally steeped, immersed, educated, brainwashed, if you like – in the mathematical methods of Lagrange and Hamilton; these ideas had grown out of, and were the natural evolution of, Newton’s dynamical ideas.’ (p 244) Further, ‘as we now know, his faith in forces was justified to such an extent that it is widely regarded as Newton’s most important scientific innovation.’ (p 128) ‘A slightly naughty thought can come to one’s mind here. Is it due to the nature of physics that the mathematical tools started by Newton are so essential for many parts of physics through the centuries? Or is our selection of worked-on parts of physics still largely Newtonian? (p 244)

 

These quotations are included to show the effect that Newton had on physics and his ideas on forces/action-at-a-distance/gravity set physics on a path of concept without the context of the repetition of the falling apple and it is apparent that forces/action-at-a-distance/gravity are simply and easily explained though measurement/entanglement/logic [concept/context]. The second quotation suggests that science has been ‘running’ with only ‘half of the ball’ and perhaps the time has come to put context to concepts. Even Newton ‘recognized’ relativity and measurement, but the use of ‘forces’ [instead of the logic duality] was top-down, and that has been the problem.

 

In other words, these quotations link together what I am saying in this chapter with the historical development of the ‘hole’ that has developed in physics that Newton (effectively) postulated and Einstein explicitly stated as ‘spooky action at a distance’. There is a reason for action at a distance if we consider our universe to be a probability space and I have proved it, to my satisfaction, at least, time and time again.

 

The fifth dimension is similar to the workings ascribed to a God by some religions and Life has evolved because evolution is very similar to quantum mechanics in that both record probabilities/possibilities as humans (and all living creatures) investigate every niche by trying every permutation of life-form and continuing to exist, if possible [mathematical/logical testing]. The biocomputer of life is there for us to guide ourselves and ‘human beings and their social orders are intrinsically imperfectible and fortunately so. In a constantly changing world, we need the flexibility that only imperfection provides.’ (The Social Conquest of Earth, Edward O. Wilson, p 241) In other words, the concepts behind relativity and quantum mechanics are wide-spread as relevance/relativity and ‘questing’ and are common organizational terms [it can be seen that a Unified Field Theory is emerging].

 

The above can be viewed as a ‘quantum/evolution – logic/gravity description of the universe’ and that seems to include enough descriptive components with the advantage that ‘quantum/evolution’ are concepts and ‘logic/gravity’ are contexts. Also, it is apparent that mathematics gives way to the elegance of the use of the mathematics of concepts, as above, and this should promote confidence of its use in the softer sciences and in particular, bringing reality [a steady state] to our planet because it is impractical for us to move to another planet. ‘If global change caused by HIPPO (Habitat destruction, Invasive species, Pollution, Overpopulation and Overharvesting, in that order of importance) are not abated, half the species of plants and animals could be extinct or at least among the “living dead” – about to become extinct – by the end of the century.’ (p 294)

 

The dimensions are fundamental and contain the solution if we work together to effect a Survival of the Best (mathematics of concepts) through state of mind, exercise, nutrition and getting on with the neighbours [second and third Laws of Life, reality]. The iteration of Survival of the Fittest was superseded about 10,000 years ago by farmers doing what they thought was best, and as a consequence, the average height dropped [assuming a poorer diet] by about four inches, whilst the mid-Victorians [How the Mid-Victorians Worked, Ate and Died, Paul Clayton and Judith Rowbotham] lived as long as we do [those after the age of five years due to infant mortality], in spite of modern medical care. This indicates that when we took over control, our health suffered and it is suffering now with 60% of adults overweight or obese, and further, I maintain that our chances of averting an Armageddon will improve if we use the general case of organization/management, as shown below.

 

The dimensions are used in, and dictate every-day life, and as examples, consider that forward-planning [sixth dimension applicable to us] is crucial to projects and it is apparent why politics is not saving the world [it has little forward-planning and our idea of democracy is flawed, Plato’s democracy, chapter (67)]. Another example is the ‘tragedy of the commons’ that assigns concept [anyone can use it] but no context of how it should be used, and similar, judges decide that the floor-covering in units is to be the owner’s choice because they are not common property [concept], but the hard flooring, instead of carpet that used to be required, creates noise for other residents [context] and the problem is that the judges used concept without context. The solution is a costly tribunal to try to force the owners to put down carpet and hardly worth the effort, so discomfort is forced on residents because the judges’ lack of context.

 

Examples like this abound because it is not understood that concept and context are always a duality/independent and when forced to consider both in the mathematics of concepts it becomes clear that the judges, the renovators and the managing agents form a ‘cascade’ of people ‘not doing their jobs properly’, and I maintain that the use of mathematics [or management, at present] is a special case and that it needs the general case to make the correct decisions. The mathematics of concepts is transparent and shows the concepts that were considered [a history/measurement that is always available, relevance/relativity] and anyone can introduce a new concept [and if relevant, and that shows why the history/measurement must be available] that changes the context by general agreement. There is no unique solution, and that is its strength, and that strength could be called relativisation because, as above, it keeps the overall result ‘constant’ [relevant], and that is what we need for the planet [to enter a reality, constant population].

 

Our concept of democracy, that the majority wins/controls, is flawed because the majority are as ignorant/misinformed/uninformed as the minority and a more sensible way is to change the two-way [politicians-media-voters] into a three-way [politicians-media-universities-media-voters, Plato’s democracy, chapter 67]. So, by combining a mathematics of concepts [context], Plato’s democracy [concept], forward- planning [sixth dimension] and setting a goal [absolute, using universities], we would have a much better chance of bringing the human race ‘to heel’ before Armageddon throws us back to Survival of the Fittest [an iteration not involving a mind/brain].

 

To repeat and clarify, the same ‘forces’/inevitability/evolution from the dimensions affect and describe the universe, above, and our daily life, and we live in the shadow of Armageddon, that we brought about and is our most pressing concern. The mathematics of concepts is basic [and new] to all parties and allows the basic attributes behind each law to be continually scrutinized and changed [relativisation, (1) below] if needed, as time goes by. The ‘quality’ of those laws needs the universities [(5) below] to keep the politicians ‘honest/relevant’ and long-term goals must be set [absolute, forward-planning, (4) below] to aim for.

 

I have said that the pressing problem of the world is Armageddon and the solution below will solve it, and I believe that this claim is true because the method was derived from the dimensions and is the general solution of organization/management that creates a science from, what has been called, the ‘art of management’ because all of the factors have been derived. Thus, given that relativisation (1), the mathematics of concepts (2) and setting out the concepts/attractors and setting the context (3), the use of an absolute (4) [forward-planning] chosen by the universities (5) [the ‘best’ absolute] are derived above.

 

Further, (6) is experimentation/trials/measurement etc., as suggested by Francis Bacon to bring about a ‘scientific method’ that has proved spectacularly successful in science/technology and this could be considered a ‘break-through’ because most ‘science’ was derived by ‘thought’ for thousands of years. However, the duality of concept/context and measurement/logic means that theorists (7) should be included and it is apparent that a mathematics of concepts has been set up [(1) to (7) in total] where more factors produce a better organization, but what is the purpose of an organization? An organization is set up for a number of reasons, but basically it is to satisfy a need and/or to evolve (8), and I should stress that these eight points are (possibly) the most important of many more that may need to be considered.

 

The comparison of the rules of organization, above, with the basis of science, below, shows that the success of science was organizationally lucky/fortuitous, because, from above, many of our organizations are inadequate, such as the process of law, the making of laws by public servants, the food offered by shops, the fishing industry [a commons] etc. are deficient, but science was a ‘stroke’ of luck because acceptance (1) of a theory is required by scientists in general and that theory requires the mathematics of concepts (2) [to compare theories] and invites additions and checking (3) of the result (4) by those with a long-time career (5) in the subject and this often requires experimentation (6) and theorists (7) to fit it all together, and finally, the overall idea of science is to ‘push’ the boundaries (8) of what we know. It is hard to resist a giggle that science has been using the fifth dimension, top-down without acknowledging its existence!

 

The above assertion is bottom-up [derived from first principles] and expands, not just science, but into organizations in general, and forms a seamless transition across science/social-science/organizations to, perhaps solving the world’s problems by organizing every organization into the scientific form. The basic structure in the United Nations, World Bank etc. is in place, and each country contains a similar police/judiciary/political-system, so that it would not be a large step to ‘fix’ the system, especially as the police and judiciary form a reality, although the political system needs work [politics freely acknowledges that it is biased, self-seeking, greedy etc.], but, there is a way to bypass the political system, as below.

 

So, the time has come to put these simple concepts together, and I stress that these concepts are simple, but elusive because unless we use bottom-up, simplicity is difficult to see [unless we use the biocomputer of evolution with its multitude of iterations]. For example, the Rule of Life uses the concept of the vast number of ‘iterations’/questing/logical-decisions [in the way of quantum-mechanics/probability space] to bring the mind/body to such a complicated state that there is the question [by some groups] as to whether the body evolved or was it ‘designed’?

 

The above is the derivation [bottom/up] of seemingly simple concepts, such as the ‘relevance’ of the market in which a business/organization is operating, but this concept is often overlooked [or relegated to a marginal cost scenario] and yet relativity/relevance is such a large part of modern physics and further, is a large part of living through a mind/brain [less relevant, by way of usage, leads to the ‘sub-conscious’]. The same applies to quantum mechanics, where the ‘questing’ is the important principle and leads to growth/evolution. These basic ‘qualities’ of organization, relevance and questing that we have been discussing are ‘fields of endeavour’ particular to our universe and can be ‘handled’/linked with a mathematics of concepts into the existing Unified Field Theory. The very reason why relativity and quantum mechanics are ‘difficult’ to envisage/manage/understand is because we lack/not-using the tools/understanding that I am suggesting here. Five dimensions does not lead to a complicated world when we understand it.

 

Given that these fundamental concepts have been dealt with previously, I will restrict the discussion to the following simple example of trying to avert Armageddon by indicating a pathway. I have previously mentioned Plato’s three-way concept of democracy [voters-media-university-media-politicians] and would like to add the above to it by stating that, of all the organizations, the universities/science are (perhaps) unique in that they (fortuitously, because at other periods, science did not) follow the basic principles of organization, above. So, given that we desire a democracy [of some sort] where voters are, to a large extent ignorant and selfish, that universities/science is the best that humanity can do, and that politicians are a necessary ‘evil’ and are ‘controlled’/limited in the damage that they can do [through monitoring and losing control to science], we have an answer that can guide all organizations.

 

In other words, given that a ‘democracy’ is generally considered to be better than other forms of government [history, bio-computer, placebo/nocebo] where the voters can only be trusted to exhibit general tendencies/choices/wants and that politicians are ‘limelight seeking’ individuals of no particular mental strengths, the universities, with their ‘proper’/formal organizational strength (as above) can bring the accumulated knowledge to the subject that is to be voted on, is crucial to success. Surely this must be better than watching Malcolm Turnball floundering in indecision whilst getting ‘advice’ from everyone except the universities.

 

Conclusion/prediction: to transform the governing of the planet requires only a simple change in several regards, as above, to bring the organization/management into a science, based on the dimensions that are shown to describe the universe as ‘quantum/environment – logic/gravity’ that contains our world and our ecological/political/social etc. systems. The move to renewable energy is an obvious first step, but population is the problem and there are ways to bring this under control and resume our evolution. The science of organization/management gives a bottom-up solution of the problem that we have got ourselves into and the success of our present science/technology has, in hind-sight, been (literally) a ‘stroke’ of luck, but does show what can be done with a bottom-up recognition of the solution. This ‘stroke’ of luck [of science] forms part of the proposed Plato’s democracy and, from bottom-up, shows the logical path to follow to avert Armageddon and re-start evolution.

 

Prediction: just as the mathematics of concepts requires a history to provide relevance/relativity, it forces a prediction [or quest], and I now realize that that prediction is an assigned absolute leading to forward-planning (sixth dimension) and (perhaps) the above could fit into one of the ‘dreams’ of a New World Order or Unified Field Theory. ‘There may be no a priori reason why the correct description of nature has to be a unified field theory. However, this goal has led to a great deal of progress in modern theoretical physics and continues to motivate research.’ (Wikipedia, Unified field theory) There is an a priori description of the universe that I have called ‘quantum/evolution-logic/gravity’ and it is derived from the five dimensions, above.

 

References: (1) this chapter (73) follows and adds to chapter (72): The Why and the How of the Big Bang, Why the Universe is ‘Flat’, Inflation and Quanta are Explained, Why Feynman was Correct, Why Matter Predominates over Antimatter, Why the Speed of Light is Constant and an Absolute, Relativisation is the Work-horse of the Universe, the ‘Face’ of God, Dark Energy Might be Necessary for Survival and the Super-world of the Mind

(2) all quotations are fully referenced in the body and earlier chapters can be found on   http://darrylpenney.com  if required.