To the Editor of the Journal of the Australian Mathematical Society

I am writing this letter because your journal has a duty to notify readers, but the establishment is resistant to change and will tend to ignore it [two opposing truths]. This theory is completely new but one example that is well known is Newton’s law of gravitation [inspired guess], corrected by Einstein [by analogy] and is given as a simple derivation, below. This result is usually ascribed to physics, but the derivation is mathematical showing the necessity [and means] of bringing physics and mathematics together. A couple of mathematical enigmas are also linked to physics. The following letter outlines enough to show that the existing philosophy, mathematics, physics etc. are woefully incomplete and how to mend and use them properly.

Mathematics From First Principles – The New Renaissance

Abstract: the mind/brain is considered complex, but viewing it in a new way makes it simple and similar happens when the method is applied to the subject of mathematics where it is found that mathematics and physics are related [orthogonal] and must be brought together via a common truth [creation equation]. A new principle of relativity is derived that defines the basis of the universe and, in particular the properties of gravity and Newton’s law of gravitation, (in its correct form) is immediately apparent from the absolute truths of the creation equation as well as the type of spaces in which Life and the universe exist, the lack of knowledge of which has stalled fundamental modern physics for a century. Traditional mathematics does not change, but its relativity to everything does and it becomes part of a general mathematical physics that must be based on the creation equation. Two examples of enigmas [the series defining the mathematical constants and Euler’s equation] are explained and shown to lie in the (erstwhile) realm of physics.

“I was told by my professor that ‘If the brain were so simple that we could understand it, we would be so simple that we couldn’t.'” (Unthinkable, Helen Thomson, p 264) The reason for this letter is to refute this suggestion that the mind/brain, the universe and (fundamental) science are too complicated to understand, and to show that they only appear complicated because of our lack of understanding and appreciation of organization. The consequence of this lack places our civilization in danger from global warming etc. and stifles evolution, so we need to rewrite science from the bottom-up and combine it with the top-down that we have been using. In particular, traditional mathematics is not ‘the handmaiden of the sciences’, but an intrinsic part of a whole. Newtonian physics has been found wanting and fundamental modern physics has been curtailed for the last century because it does not adequately describe relativity and so, a new approach is needed. Einstein and Bohr’s difference of opinion on the type of space that we inhabit has held up fundamental physics for a hundred years and made it a ‘no go’ zone.

[http://bostonreview.net/science-nature-philosophy-religion/tim-maudlin-defeat-reason]

Both were wrong and this letter will hopefully renew interest, not only to revitalize fundamental physics, but also show how traditional mathematics has common ‘roots’ with physics when ‘adjusted’ fundamentally.

Traditional mathematics has gone to great lengths to define itself as a ‘statement of the mind’ and divorce mathematics from reality, but Life has evolved the mind/brain [(a+b)=1, all a, b] as a probability space, instead of the measuring space [(1+(-1))=0)] that defines the physical universe. In other words, traditional mathematics is relative to the axioms that many books have defined over thousands of years and so they do not align with the relativity of the creation equation [(1+(-1))=0] that, I believe, formed the universe. This is serious because traditional mathematics is used in the real world, so I will derive the universe from bottom-up and that allows me to derive Newton’s law of gravitation for the first time.

In the beginning there was nothing (0) and it is a property of orthogonality to make two independent things, but entangled [at the origin], such as (1) and (-1) [first fractal] and that forces the second fractal (1+(-1))=0 [this equation I call the creation equation because it yields the form of the universe] and it’s orthogonal is the logic of the half-truth [true, false, both true and false simultaneously] that yields ‘physical choice’ [shimmer presents opportunities for a reaction through the wave/particle duality] that leads to the working of the universe. Life employs a mind/brain to make better choices based on the structure of the probability equation [mathematics of concept/context] in the brain as well as thought [(-1), organization] from the burning of a simple sugar [(1), glucose]. That is the answer to the quotation, above, but with a ‘twist’ because Life uses a probability space [(a+b)=1] that is similar to the measuring space [(1+(-1))=0], but allows different concepts a, b to be considered.

Notice that the creation equation exits only if (1) and (-1) are kept apart and this logic requires an expanding universe, which we have [Big Bang], and this expansion produces the dimensions of space-time, energy and organization. The equation also says that everything is relative to something else, with no exceptions, except that ratios naturally become absolutes and they are the conservation of (total) energy/organization [energy/time], constant speed of light [distance/time], dark energy [energy/space] and gravity [energy/separation] and this becomes the principle of relativity [and replaces the present one that the laws of physics are the same in constantly moving frames]. The absolutes produce stability – the first leads to Occam’s razor and the principle of least action, the second to the constant [to the measurer, Michelson-Morley] speed of light, the third to the infill energy/organization [dark energy] to balance the expanding energy/organization of the universe and the fourth to gravity that measures energy.

The limitations of Newtonian physics have made gravity an enigma for a long time and I believe, it is not an attraction [Newton], not ‘bent’ space that introduced organization and shut down modern physics for a hundred years [Einstein, deflection of a photon by a solar mass], but simply an absolute [energy-organization/distance], where all matter is composed of energy and organization and the doubling effect that Einstein (eventually) found is due to relativity where:

E(1)/d times E(2)/d plus O(1)/d times O(2)/d where E is energy, O is organization and d is the separation of two masses (1) and (2).

This leads to twice the Newtonian value where only energy is considered and is in line with Einstein’s finding. Notice that this is the first time that Newton’s law of gravitation has been derived because Newton used an ‘inspired guess’ and Einstein used an ‘analogy’ and this derivation is a result of relativity and the equation only exist because of relativity.

Traditional mathematics grew out of counting sheep using the number line and it is obvious that the number line is (literally) infinitely more complex than the creation equation [(1+(-1))=0] and yet mathematics must be able to be derived from this equation which means that mathematics has unexplored possibilities at its base. In other words, in spite of the multitude of books defining mathematics, it is a fractal and the (simple) generator (1+(-1))=0 has been ignored. Thus, when physics and mathematics use the same base [(1+(-1))=0], they are not the same but orthogonal and entangled. No references are cited because everything can be derived simply from the first principles and the examples given above. However, it is pointless ‘reinventing the wheel’ and most of it will be on my website, when required.

The first enigma is that the concepts of the mathematical constants [pi, e, i etc.] can be expressed as infinite series and this can be explained through the concept of ‘orthogonality’ shown in the orthogonality equation [(1+(-1))=0] where Life uses a variant (a+b)=1 that describes a probability space for all concepts a, b, … as above. The entanglement “+” represents all possibilities, such as plus, minus, and, or, truths derived from experiment, evolution, creation equation etc., and clearly, this shows the restrictions placed on traditional mathematics. Tut, tut, enough said!

The second enigma carries on from the last paragraph, and if the universe is a fractal, everything in it reflects the creation equation and Euler’s equation is no exception. In Euler’s equation [e power i times pi plus 1 = 0] when rearranged and e power 0 replaces 1, the equation becomes an orthogonality equation that could be thought of as a fractal entangled with the creation equation. “Pi” is a circle/sphere operator and logically a mathematical construction like a point or circle could not exist, but the surface of a sphere could exist [Big Bang] and that the creation equation only exists if the sphere is expanding. The “e” is given in elementary textbooks as the growth of money under compound interest and this aptly describes the necessary [constant] expansion of the universe from the creation equation with time and compounding rate as absolutes. The “i” is an unexpected term that makes Euler’s equation so fearsome, and yet it has a logical simplicity as an orthogonality that must be there. The question is often asked ‘what happened before the Big Bang?’. The “i” provides the answer and it must be there to add completeness [relativity] to the equation because the opposite [orthogonality] to the universe is imaginary and if it is to be explored further, it must be a ‘mirror image’ orthogonality through the centre [because everything is relative]. Clearly, the equation should be able to be derived from the creation equation when mathematics is ‘realized’.

Conclusion: the simple message of this letter is that everything is relative. The absolutes are the ‘taming’ of relativity and show that the same basic truths must be used for physics and mathematics. The above is a taste of bottom-up organization together with the sideways orthogonality that can be combined with traditional top-down science to make a general mathematical physics [that includes philosophy through the mathematics of concept/context]. Have fun!

[Darryl Penney, 13/10/2018, dwpenney2@bigpond.com]

Post script: why mathematicians like or find beauty/interest/emotion/energy in mathematics is an oft asked question and ‘have fun!’ is literally true, so as an explanation, I am including the following [“1” is energy, “(-1)” is organization]: another example of orthogonality in the real world is the painting of Mona Lisa that is small [77 cm x 53 cm (30 “ x 21 “)], but is the most famous painting in the world because, I believe, that Leonardo da Vinci was conversant with mathematical organization [golden triangle, golden rectangle etc.], incorporated them into the paintings and the measurement [by looking] created energy [emotion] in the viewer. The production of emotion is common in art, music, church buildings and services, flags etc. and the more and better the organization inserted by song-writers, authors etc., the greater their success. Thus, the judgement of the worth of a piece of art, architecture or the golden triangle is simply the amount of emotion that it produces in the judges and viewers. This is obvious when pointed out, but it proves the point of this letter.

Post post script: it occurred to me that even the concept of momentum is an exercise in relativity and that solves a personal question of what is the momentum that Newtonian physics is built on? Clearly, momentum is not an absolute truth [energy times distance divided by time], but it does work [at low speed] as a basis for physics and Newton’s three laws of motion are all expressions of relativity. The obvious point is that neither traditional mathematics nor Newtonian physics are based on the simplest, nor on the same base, and that the base should be the creation equation.