Chapter 117: Economics From First Principles

Abstract: organization and economics have never been comfortable within science, but a new and expanded definition of relativity shows that they actually hold a prime position and can be derived from first principles. The expanded definition also shows that bottom-up organization is the key to completing philosophy, Newtonian physics and traditional mathematics and that allows us to explain long-standing enigmas as well as enabling new insights through the amalgamation.

Context: I am writing this letter because I believe that there are problems in economics and business that need widespread discussion and this has now become possible through a new definition of relativity obtained from first principles. This letter-form was chosen to reach as many readers as possible, and especially those that normally ‘throw up their hands in horror’ at words like relativity, quantum gravity, gravity, quarks etc. that are other specialists’ areas that show the problems within Newtonian physics. Economists are supposed to be generalists according to John Maynard Keynes … “the master-economist must possess a rare combination of gifts,” he wrote. “He must be a mathematician, historian, statesman, philosopher … He must study the present in the light of the past for the purposes of the future. No part of man’s nature or his institutions must be entirely outside his regard.” (Doughnut Economics: Seven Ways to Think Like a 21^st-Century Economist, Kate Raworth, p 288) This quotation, from a specialist economist lauding the generalist, highlights the core problem, and that problem has come about because we do not understand relativity. The quotation is wrong in that it asks for an impossibility because a specialist and generalist are (literally) orthogonal and independent and, in the limit, cannot understand each other, but both are needed. This is a fundamental problem like the wave/particle duality of quantum mechanics and we must accept it.

Economics has always been like a ship in deep water with only its experiments for truths and no anchor and relativity says that I can only describe economics relative to physics because physics describes the universe and our planet, but Newtonian physics is incomplete and lacks organization, so we have to add completeness. Also, traditional mathematics is woefully incomplete and to make economics accountable, we have to find economic and organizational solutions, and to do that, we need a new mathematic that I call the mathematics of concept/context. To make this understandable to specialists [as economists are not supposed to be, but are] and not have a multitude of references, I am going to start from first principles. It is important that the reader is comfortable with this, so I have included a ‘side-box’ that could be read later and, to show its usefulness, it contains derivations of Newton’s law of gravity that has never been derived before.

Concept: Doughnut Economics presents a planet with certain defined limits on its resources and defined wants of the population and I am taking this to be the upper limit or upper bound on economic thought, though, I am more interested in restarting evolution by controlling population than allocating resources to infinite wants, they lie on the same path. The lower limit is the creation equation that generates the universe and also shows the mathematics that we can use [truth]. To be more precise, the creation equation generates a measuring space [(1+(-1))=0], whilst Life has evolved to use a probability space [(a+b)=1] for all concepts a, b and you will notice that both are orthogonal equations that show relativity [1 and (-1), a and b].

‘If only – just before that apple fell – young Isaac had also marvelled at how it grew: in a fascinating, ever-evolving interplay of trees and bees, sun and leaves, roots and rain, blossom and seeds’. (p 129) This request leads into the answer in the box, and it is exactly what was sought because organization is on an equal footing with energy.

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 [‘a single particle could seemingly span a field as would a wave, a paradox still eluding satisfactory explanation’ Wikipedia, Elementary particle]. 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 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 all 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 in a measuring space [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.

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:

Attraction equals 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 reasoning’ [Robert Hooke maintained that it was stolen from him] and Einstein used an ‘analogy’. Clearly, this explanation shows that the inverse-square law has nothing to do with it!

We now understand gravity completely in that it’s effect has and will always be constant, it cannot exist except between two objects [relativity], its value depends only on the total amount of energy/organization and the separation and shimmer [from particle to wave] has no effect because two terms are involved as a sum. Also, the equation E=mc2 is misleading because mass and energy are the same thing and the equation is a conversion of the units that we have assigned, but what is not so obvious is that all of energy/mass and all of organization contribute equally [relativity]. It was accepted in Newton’s time that mass had an attraction and in Einstein’s time that energy [photon] had the same attraction, but the fact that organization had an attraction [curved space] and gave the correct experimental answer was a ‘step too far’ and fundamental physics closed down.

This enigma is a result of the short-comings of Newtonian physics, and it is not an enigma when it is realized that energy and organization are ‘two sides of the same coin’ and further, that this complexity is a mathematical physics solution because the first orthogonality [energy/organization] produces a second where, in part, organization gives gravity [organization] and energy [of gravity] through the absolute. To maintain the condition that the universe is expanding [(1) and (-1) kept separate] gravity must be a solution and be non-zero because a zero gravity produces random walk, which, in the limit, is not stable. The “e” in Euler’s equation determines a constantly growing universe [“e” is the driver in compounded interest].

From above, the statement that ‘the absolutes produce stability’ needs expansion, firstly, ‘the absolutes produce stability’ is, of course, true because they define the structure of the universe, secondly, ‘Occam’s razor and the principle of least action’ are an organizational requirement that only the simplest and least energetic response is possible if the organization is to have unique answers. In other words, the universe does measures organization and the measurement requires that the lowest energy be used [first absolute]. Thirdly, the requirement that all of energy/mass, length and time obey the Lorentz contraction together is an organizational requirement in that it is simpler that all change proportionately than to list an order of change.

Fourthly, compare the treatment of organization in Newtonian physics where organization is allowed upon experiment or peer review. The English philosopher, Francis Bacon was correct that physics must be based on experiment because [repeatable] experiment is a truth and we can also use the long-term effects of evolution as truths. ‘The general idea of the importance and possibility of a sceptical methodology makes Bacon the father of the scientific method’. (Wikipedia) For example, ‘in loco parentis’ passes from parent to offspring and not visa versa as the major religions demand. Peer review is a half-truth that is true only for specialist subjects and false for general subjects because specialists think differently to generalists [relativity] plus two truths are violated [relativity, and evolution (the established resist change)]. Notice the ‘thread’ that I am using is not the usual [ancient Greeks to Newton to Einstein to the Snow White effect], but a different successful thread [ancient Greeks to Bacon (experimental truth) to this theory (absolutes, experimental truths and evolutionary truths)]

Fifthly, the principle of relativity, stated above could also be called the principle of orthogonality because they are relative to each other and everything contains elements that are either the same or independent to something else and it is the orthogonals that form the basis of the mathematics of concept/context that is immediately apparent from the probability equation.

Coulomb’s law for charges is similar in form to Newton’ law, and many people must have, like I, wondered about this, and both are, [inappropriately as it turns out] associated with the inverse square law. A simple explanation is to use the fractalness that the neutron [mass] is a special case of energy [photon] and orthogonates to a proton, electron and a neutrino and that Newton’s law describes the mass attraction, whilst Coulomb’s law describes the charge attraction. Obviously they must be equivalent, apart from sign and magnitude.

Consider the orthogonality of the creation equation [shape of everything] and the logic of the half-truth [functioning of everything]. The latter term allows shimmer to present choices in the physical and the same thing happens in our mind/brain when we make a choice. In other words, we compare two orthogonals and rate them and as an example, choosing between two new cars of different colours is an orthogonal choice on colour [because everything else is the same]. This can be seen from the equation of a probability space [(a+b)=1] where a and b can be any concept and “+” can be any correspondence operator [add, logic, truth from experiment, absolute truth], unlike mathematics that is restricted (mainly) to the number line.

The mathematics of concept/context is simply that the mind/brain allocates numbers/feelings ranking the desirability of alternates [a and b] and thus makes a choice. This process could be called ‘democracy’ because it requires interested, active participants to vote their choices to make an accumulated choice and a decision. Notice that we have defined democracy from bottom-up and it shows the shortcomings of our voting system. Clearly, to implement a democracy requires those that are interested [and knowledgeable] to vote referenda of social issues and is the key to promoting the limits that are needed for the planet’s protection and the implementation of Kate Raworth’s ideas. Notice that publicising this process results in a more transparent operation than at present.

Conclusion: this letter is an attempt to ‘anchor’ economics in truths so that it can become not only a science, but a complete science that include the present economics allied to the physical [bottom-up] and recognizing the sideways orthogonalities [creation equation]. I believe that this theory will prevail, eventually, and I cite the importance of the space that is used. 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 because the space, above, is a measuring space [physical] and a probability space [mind/brain].

There are some things that may need fixing in the light of the above. Firstly, Kate Raworth mentions problems of organized complexity (p 136), “the universe is messy. It is non-linear, turbulent, and chaotic.’ (p 141) and ‘theirs is one among several promising complexity approaches to understanding the effects of financial markets on the macroeconomy’ (p 147) On the contrary, the universe is a simple place built on the simple creation equation and that makes the space a fractal, which means that everything describes the creation equation and the explanation of Euler’s equation, below, is an example.

Secondly, Kate Raworth bemoans the fact that economics is out-of-date, but that is the result of academia because universities tend to ‘silo’ the departments and smother original research as stated above. The mathematics of concept/context shows that both concept [specialist] and context [generalist] are independent and (literally, in the limit) cannot understand the other. They must work together, literally, and this letter is an attempt by me, and Kate Raworth’s book to show that economics, as well as science in general, needs to get its act together. The reader [as a specialist] has the opposite problem in trying to understand this letter, but the problem of specialist/generalist is as fundamental as the wave/particle duality in quantum mechanics, so get use to it! The probability, I believe, comes about because our mind/brain is based on a probability space and the solution is forced on us that each specialist must consult with a generalist to achieve balance because we live in a measuring space and every measurement requires relativity.

Prediction (due to relativity): to further illustrate the ubiquity of organization I would like to explain the amazing success of the Mona Lisa, and as an example of the interdependency of the disciplines, Euler’s equation, the meaning of which has been an enigma in mathematics for centuries.

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 important contextually.

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 and that the creation equation only exists if the sphere is expanding [Big Bang]. 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 [speed of light] 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]. ‘Euler’s formula is ubiquitous in mathematics, physics, and engineering. The physicist Richard Feynman called the equation “our jewel” and “the most remarkable formula in mathematics”.’ (Wikipedia)

Finally, 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 darrylpenney.com when required.

[Darryl Penney, 20/11/2018, dwpenney2@bigpond.com 0410668511]