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.