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.