Chapter 100: The Equation of Everything, a General Mathematical Physics Developed and Used to Resolve ‘How Species Form?’

by Darryl Penney

Abstract: Newtonian physics and traditional mathematics have proved to be resistant to change and this is, I believe, because they use the units and methods that are natural to us and are based on the predator/prey situation with which we evolved even though enigmas necessarily abound because Newtonian physics and traditional mathematics are at odds with the universe around us. This paper uses the basic construction of orthogonality of a fractal/probability universe to derive a bottom-up mathematics of concept/context and organisational physics that augments the traditional approach and explains relativity, quantum mechanics, quantum gravity, magnetism, organisation etc. and a mathematics of concept and context that especially suits the social sciences. Further, the fractal/probability space links the mind/brain to the physical through two relationships, firstly, for Life, ‘concept/forward-planning/quest/relevance/beauty/context’ and secondly, for the physical ‘measurement/quest/relevance/entanglement’. Whilst the top-down/bottom-up orthogonality explains the long-standing enigmas, it is necessary to consider the orthogonality that mathematics is a concept and physics is a context that defines the logic of the mathematics of concept/context upon which the workings of the mind/brain is built and that they cannot be separated because of the Principle of Relativity. The end result derives a general mathematical physics and proves that it is the only combination of mathematics that can exist and be a complete description of everything and that traditional mathematics and Newtonian physics are special cases that have frustrated humanity for a long time. An example is given of Darwin’s problem of how speciation occurs that illustrates the fractal/probabilistic nature of the universe and the problems of measurement of species, quantum mechanics and relativity by highlighting the three absolutes that are required to ‘open the null space’ to our view.

It was the best of times [with technology] and it was the worst of times [with overpopulation, overuse of resources etc.] and the cause is a mathematical physics mired in (somewhat) antiquity and even the (so-called, 120 years ago) ‘modern’ physics has not been able to push mathematical physics into a more useful form. We cannot control civilization because mathematical physics is very resistant to change, presumably because it is top-down and no one has a clear idea of where it is going. Novelists had a clearer picture [of orthogonality], as above, and it will be shown that orthogonality is the basic construction technique used by the universe and that we have neglected it (probably) because it is too simple.

This paper shows that mathematical physics was led up the wrong [of two] path and I have derived a general mathematical physics that can be appended to the current usage. Notice the use of the combination ‘mathematical physics’ because there must always be concept and context to make sense [relativity] and this shows that there must always be specialists and generalists and that this fundamental requirement is usually overlooked [especially by universities]. I will use difference [orthogonality/independence] as well as sameness [equations] on which to base a ‘new’ mathematical physics that is complete in two orthogonalities because we will also be using bottom-up as well as the top-down guesses that Newton and others have ‘set in concrete’. I will stress the use of ‘two orthogonalities’ because of the requirements of the Principle of Relativity [apart from the absolutes] requires orthogonalities in all cases except for the absolutes.

Newtonian physics and traditional mathematics have been resistant to change because we have used the units of the predator/prey situation and the counting of sheep, both of which are pertinent to ourselves and have ignored the physical world. This is not an isolated use because we tend to ignore the environment and the physical world and think in terms of the use that we can gain for ourselves, but the difference equation shows that every independent concept is related to every other. This is enigmatic that independent things can be related, but obvious when it is pointed out [e.g. conservation of total energy] but it is a general rule that affects everything and is as enigmatic as the wave/particle duality until its use is understood [to create atoms from neutrons].

Mathematics and physics are stuck ‘in a rut’ and need a fundamental change to make them applicable to the social sciences as well as modern physics and this paper presents a proof that this is so, and shows how the fractal/probability space that must be used [to view the null space], supports four axioms that link our mind/brain with the physical and provide bottom-up methods to link the traditional into a ‘new’/absolute mathematical physics. Bottom-up (physical) and top-down (Life) link orthogonally in the same way that mathematics (concept) and physics (context) need to go together and it is the only way to truly understand the organisational problems that our current methods have inflicted on the planet.

Traditional mathematics and Newtonian physics are constructs that we use because they are useful, but they have no place in the physical universe. Firstly, the units of speed and distance are familiar to us because they are necessary in the predator/prey situation to set up zones where we feel safe, and secondly, because they are both based on equality, whereas, the universe is built on differences [note the relativity/orthogonality of same/different]. An example is that the textbooks are filled with derivations and theorems that rely on equality through the use of the equation, but I believe that the physical universe uses orthogonality, which uses independence not sameness because, in general, independence builds whereas similarity is static.

Sameness is 1=1, whereas, difference is (1 + (-1))=0 and you might say that there is no difference but I say that there is a huge difference between these two equations and that difference produces the universe and everything in it, and shows why traditional mathematics and Newtonian physics [that use 1=1] are only special cases of a general mathematical physics [uses (1 + (-1))=0]. The difference between the two equations is organisation and yet traditional mathematics, in particular, tries to eliminate it! Clearly, we have been engaging in a fishing expedition [top-down] because we have no clear idea of what is below the surface and we have got mathematics and science so wrong for so long! Bottom-up gives a unique view and the proof is that the enigmas disappear.

The above paragraph is a blunt statement, but, I believe, true nonetheless and indicates why traditional mathematics is having so much trouble with the social sciences and Newtonian physics is having so much trouble describing modern physics. The answer is ‘sameness is 1=1, whereas, difference is (1 + (-1))=0’ and we complicate our view because we do not recognise this fact. As an example, Euler’s equation has been known to be true for hundreds of years, but no one understands it because it is in the form of the difference (the latter equation) as described in chapter 98. The universe is a fractal/probability space and everything is repeated in a fractal space because it is generated from a simple equation [(1 + (-1))=0] and Euler’s equation thus shows the form of the creation of the universe. [Note that Euler’s equation does not contain a Big Bang singularity, but does allow splitting.]

A small digression that traditional mathematics is inbred and not helping itself and is based on methods that have little to do with the real world, and this is why it is unnatural without a context [of physics, relativity]. As an example, what I am saying about differences is already (somewhat) known and excluded from traditional mathematics, and that is computing that is based on the comparison of differences, literally, in the processor, is the 1 or 0, the same or different to the 1 or 0 in the register. In other words, is the number/letter/symbol is determined as the same or different.

The equation that generates the fractal is, not surprisingly, (1 + (-1))=0, and that is why I say that the universe is built on this equation, and the reference to a probability space is because a probability space is a measuring space also built on (1 + (-1))=0. However, a probability space is much more than that because it is a measuring space and is actually (a+b)=1 where a and b are general and this allows Life to evolve a mind/brain that uses concepts and context [a and b] between the orthogonals [the independent axes of the Cartesian coordinates]. We will return to this later because there are four ‘search axioms’, derived from the spaces that link the mind/brain to the physical universe.

If we take the equation (1 + (-1))=0 and using the same technique [of difference over sameness], this orthogonates to (1 + (-1))=0 and (1 and (-1))=0 and ‘(1)’ might represent energy and ‘(-1)’ might represent organisation, to use common terms, and in the same way, ‘+’ might represent the physical [energy] and ‘and’ might represent logic [organisation]. This ‘up/down’ and ‘sideways’ orthogonality lead to the interesting possibility that ‘(1)’ and ‘(-1)’ have a number of properties, firstly, that the equation is only stable if ‘(1)’ and ‘(-1)’ are moving apart from each other. I believe that the universe is expanding for this reason, and, the expansion is needed to generate the dimensions of space and time. Secondly, that ‘(1)’ and ‘(-1)’ are independent [physically and logically], but entangled organisationally

This statement appears to be an enigma because when two things are independent, we consider them to be completely independent, but the difference equation says differently, and it is correct, in that two things are independent, but are always entangled. An example is that the total energy is zero [law of conservation of (total) energy] because the sum has to always be zero irrespective of what happens at every point and the sum is the entanglement of the independent points/values. This makes the general point that we must use organisational physics to see/consider [as a context] our logic because it must be based on the spaces in which we exist. To try to set up a traditional mathematics based on something that we consider important is somewhat heroic, but a little futile and a special case when the mathematics of concept/context is staring us in the face [(a+b)=1] and that contains traditional mathematics as a special case and allows a mathematic for the social sciences.

This point is very important because total energy is conserved through (1 + (-1))=0, but energy is always being created to necessarily balance the expansion of everything. Note that this can be confusing because we do not have unique words because (literally) everything (energy or organisation) orthogonate into energy and organisation Another example is the requirement that two frames of reference in a measurement between them do not exceed the speed of light in a vacuum [chapter 99 suggests that magnetism is the control]. This equation (1 + (-1))=0 also proves that electric charge is conserved and angular momentum, but linear momentum that is often said to be conserved is only a local special case. I have always been comfortable with conservation of charge, but not angular momentum, in a general conservational sense, until now.

Notice that the above explained the Big Bang, conservation of (total) energy, charge and angular momentum, the structure of magnetism, energy and organisation and we have hardly started! The equality equation is static, whereas the difference equation contains expansion that forms the universe and this constitutes a mathematical/physical/organisational proof that the difference is superior. In other words, the bottom-up mathematics and physics, I suggest, is superior, but both [top-down/bottom-up and equality/difference] are needed for a complete discipline [to accommodate us]. Notice also that expansion derives the dimensions to create a universe and that this proof actively involves organisation/mind/decision that is an ‘add-on’ to the traditional form of mathematics and physics.

Thirdly, these requirements can be simply derived from the dimensions of space/time above and from chapter 99, ‘I believe that the universe is constructed on orthogonality/choice and that we, by necessity, must view/expand the null space through a probability/fractal lens that allows that expanded view. The requirement of a probability/fractal space complicates our view of orthogonality and leads to the Principle of Relativity. From chapter 97, “in a probability/fractal space, the Principle of Relativity is that everything is relative to something else (1+(-1))=0, except for the conservation of total energy, the speed of electromagnetic waves in a vacuum and the increase in energy/organisation per unit of newly created space [dark energy].”’

The requirement of the separation of ‘(1)’ and ‘(-1)’ requires the production/definition of the dimensions of space and time passing as well as the creation of two types of energies and a simple ratio of the dimensions leads to the ‘absolute’ restrictions above. However, as an example of the importance of the requirement of expansion to the dimensions, the logical requirement of simplicity [Occam’s razor] applied to the Special Theory of Relativity accounts for the (apparent) enigma that all of time, length and mass [energy] being distorted by the same amount [Lorentz contraction] to satisfy the absolute conditions, above.
‘Whether or not the universe is five-dimensional is a topic of debate … German mathematician Theodore Kaluza and Swedish physicist Oscar Klein independently developed the Kaluza-Klein Theory in 1921, which used the fifth dimension to unify gravity with electromagnetic force. Although their approaches were later found to be at least partially inaccurate, the concept provided a basis for further research over the past century.’ (Wikipedia, Five-dimensional space)

It is apparent now that traditional mathematics and Newtonian physics are deficient in firstly, that they are based on sameness [‘sameness is 1=1, whereas, difference is (1 + (-1))=0’], but this is fortunate because sameness and difference are orthogonal. Secondly, physical/organisational [(1+(-1))=0 and (1 and (-1))=0] is (somewhat) lacking because the logical ‘and’ is relegated to an external mind/brain. Presumably this is done to simplify the construction of the traditional mathematics. Thirdly, entanglement [(1 +/and (-1))=0] is a physics concept because physics spreads the mathematical concepts across the various fields and provides the logic required by mathematics because we have to use the logic imposed by the fractal/probability space in the use of physics.

Further, more problems arise, fourthly, top-down and bottom-up [top-down is exploring-possibilities/guessing whereas bottom-up is derivable from the dimensions], fifthly, traditional use [the familiar units of the predator/prey situation are used], sixthly, the mind/brain extends the [axes of] orthogonality into [the plane of] concept/context that defines a mathematics of concept/context] and seventhly, putting it all together in a useful whole to make an absolute/general mathematical physics using orthogonality.

So, where are we going with this derivation? The first three points have been investigated, but another example of current usage might shed light on where progress can be made. The operators ‘+’ and ‘and’ have the same importance, but neither traditional mathematics nor Newtonian physics likes to use the ‘and’, and one common reference (Dirac) is in anticipating the positron. This suggests that top-down versus bottom-up allows many surprises and I have mentioned a few [e.g. no Big Bang, but expansion is logically required]. Traditional use of units is important and must be part of any absolute/general mathematic/physics and the answer is at hand in that everything is orthogonal and orthogonality can be used to solve the problem [because it is so basic/intrusive].

Three aspects are needed, firstly, top-down traditional mathematics and Newtonian physics, secondly, bottom-up mathematics of concept/context and organisational physics. Note that the mathematics can be seen from (a+b)=1 for general concepts a and b. Thirdly, the four ‘search axioms’ that link the mind/brain through the probability/fractal space, see below.

The first question is ‘what will this affect?’ and the answer is ‘only what you want it to affect’. The big winners will be the social sciences and the social organisations through the mathematics of concept/context, including the (theoretical) ability to solve the planet’s problems with population etc. In other words, the concept of adding numbers of things has been expanded to include (literally) everything and especially the concepts themselves. In mathematical physics it will be changes to our thinking and concepts more than the ‘nuts and bolts’ because mathematics is the concept and physics is the context, but we must be careful of the equations (equality), for example.

Referring to the above, and quoting from chapter 99, ‘firstly, a digression, because [literally] everything is an orthogonality, but an orthogonality may be the same in some regards, but different [states such as water, steam and ice] or independent [such as the frequency and amplitude of a wave]. E=mc2 is a relationship that illustrates this because energy and mass are the same thing [states of each other] and the units that we use to describe energy and mass are (presumably) related through the speed of light. E=hf is another case in point, of the second kind, but not so trivial because energy is orthogonal to mass as well as organisation This might seem confusing because everything [in the universe] is an orthogonality if it is not identical [1=1 versus (1+(-1))=0], kept separate by expansion [the universe] or by orthogonality [the atom].’

Further, from chapter 99 it was suggested that the photon is a wave/particle duality with the wave turning into a particle every half wavelength so that choice is presented as is necessitated by the capture of the electron by a proton to form an atom. This is part of the expansion of the universe, otherwise the proton and electron de-orthogonate into a neutron and the hydrogen atom collapses, which would not be helpful to the general living space. Thus, the universe is an organisational solution that we cannot affect, and our top-down thoughts, such as equality are not universe-building and the equations E=mc2 and E=hf must be regarded as nonsensical as orthogonality intertwines them and they are one and the same [except in form/shape].

Is a ‘new’ mathematical physics proper? The answer is ‘yes’ if we think the correct way. After all of the above, it might be time to consider philosophy, which has been isolated as being without answers because the amenable parts have been ‘hived off’ as disciplines. The mathematics of concept/context is the mathematics of philosophy and will answer all questions, much like the Oracle of Delphi of legend, because answers will be probabilistic [we are looking through a probability space] and require a mind/brain, but we can see the philosophical ‘roots’. Every question must contain concept/oneness/equality as well as everything-else/context/difference as shown in the first orthogonality [1=1 and (1+(-1))=0] and the mathematical notation makes it easier to comprehend.

So again, is mathematical physics proper? The answer is ‘yes’ if we think the correct way. Traditional mathematics is exact and made of equations [equals], whereas traditional physics can be thought of as orthogonals [differences] and that creates an orthogonality together [the original orthogonality is equal/not-equal]. The mathematics of concept/context is iterative (orthogonal) and the organisational physics is exact because it is logic and together form an orthogonal. The four ‘search axioms’ are the link between the mind/brain and the physical and the mind/brain is based on the mathematics of concept/context (orthogonals) and the physical concept is exact [the reason that Euler’s equation appears in traditional mathematics]. Thus, instead of a humanity based on thinking in terms of equality, we have found a universe based on independence, entanglement and orthogonality and yet we can fit into it using a ‘proper’ organisational physics.

The above is new, different, full-on and concise and I have tried to give examples to make it easier, so, another example that cannot be answered by traditional methods has been an enigma for a long time. Why do species form? ‘Ironically, considering that Darwin called his book On the Origin of Species, the one thing that he couldn’t explain was how species originated. Darwin’s theory suggested a mechanism for how a species might become stronger or better or faster – in a word, fitter – but gave no indication of how it might throw up a new species.’ (A Short History of Nearly Everything, Bill Bryson, p 346)

The answer is to be found, I believe, in three parts, firstly [physically], by consulting the ‘opening of the null space’, above, because two measurement/species occur when the two elements are not entangled as in separation by a sea, mountain range etc. Secondly [organisationally], you can neither tell if two species are separate if their range is expanding nor if they are organisationally entangled. I can say this with complete confidence because it has been derived bottom-up and the answer has to do with measurement, or, more precisely, the lack of ability to measure, because we are looking through a probability space and are facing the same probabilistic problems as in quantum mechanics.

How do you know when two species have been formed and the answer is when they can not breed together and that is an unknown unless we can individually watch and take account of every individual to see if mating produces viable offspring. This problem is organisational and requires infinite speed of accounting as in quantum gravity, and on the ground, requires walking or driving, and in the modern sense, with its own problems, radio collars. Needless to say, the absolute (relatively) slow speed of measuring, of which we are capable, is analogous to the Theory of Relativity. Ho hum! When you derive from the bottom-up in a fractal space, the options are limited and the same options in evolution apply to mathematical physics as to the rest of the universe.

Thirdly [Life], from above, we have to incorporate the ‘opening of the null space’ and the Principle of Relativity into a combined mathematical physics that will handle examples of social science, politics, philosophy etc. with the same ease as speciation is being considered. This requires considering the properties of the probability space and that Life is a parasite that has evolved and in particular has taken advantage of the mathematical/physical space of the universe to evolve a place and this is clarified by the following quotation from chapter 86. ‘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 7), 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.’

The physical search for the cause of speciation was akin to quantum gravity with all the problems that unfolding a probability space entails, but including Life, as is necessary, shows, in the paragraph above that the probability space allows concept/forward-planning/quest/relevance/beauty/context and these are in the mind of the beholder and connect the mind/brain with the physical universe. Thus, there are both physical and mental reasons contributing to speciation and beauty [golden triangle (a+b)] is an unexpected player (chapter 78).

In conclusion, the mathematical physics [mathematics and physics do not exist on their own, relativity] of the universe is determined by (1+(-1))=0 [measurement/entanglement/choice] and a probability space has a more expansive definition of (a+b)=1, where a and b are completely general and Life has used this to evolve a mind/brain to explore the space between the orthogonals and produce the mathematics of concept/context. In other words, I believe that the mind/brain evolved to use the orthogonality of energy/organisation to produce thought [and forward planning] by consuming/burning large quantities of glucose [energy] in order to produce thought [organisation]. The concept of the creation of a mind/brain has been an enigma of long-standing and the orthogonality of energy/organisation presents a simple relationship between burning sugar and thought.

The ‘new’ physics and the ‘new’ mathematics have been ‘cobbled’ together to allow ‘common usage’ to use a systems of units that were useful in the predator/prey situation of the survival of the fittest, but using the physics of the universe. This general/absolute mathematical physics is the only general mathematical physics that can be derived through a fractal/probability space and our society needs it to put more emphasis on organisation to stop the population growing and outstripping resources. Clearly, concept, context and expansion form the basis of survival of the fittest and that is why it works, but, the misery of the participants is apparent in the competition and we need a better organisational means of limiting population to a sustainable level.

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

Chapter 99: The Principle of Relativity, the Role and Importance of Magnetism, the Amplitude of Electromagnetic Waves and Inside the Photon

Chapter 98: The Principle of Relativity, the Creation and Euler’s Equation Explained

Chapter 97: You Asked For A Simple Theory, Stephen Hawking, So, Enjoy It!

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

Chapter 86: How the Mind Works, Evolution in Mind-space, the Placebo/nocebo Effect Has Two Parts, Combating Chronic Pain, Why Eastern and Western Medicine are Similar, Unfolding Mind-space from the Fifth Dimension and the Law of Conservation of Minimum Energy

Chapter 32: Reality and the Mathematics of the Social Sciences