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.