by Darryl Penney

 

Abstract: much of philosophy today would be intelligible to the ancient Greeks and this lack of change lies, I believe, in the abandonment of the mathematics of concepts within the rise of mathematics. A return to the mathematics of concepts, the recognition of the fifth dimension and the properties of a probability space allow a bottom-up base of concept and context that allows philosophy to be unfolded and de-cluttered. Two other derivations are necessary, logic and organization, again as concept and context and examples are given of the necessity of re-writing Newton’s laws of motion and the classic problem of the Unity of the Virtues.

 

I have said before that the subject of Philosophy is a ‘closed book’ to me and I have often wondered why that is so, and one explanation could be that we are not supposed to find answers. ‘Bertrand Russell in The Problems of Philosophy: Thus, to sum up our discussion of the value of philosophy; Philosophy is to be studied, not for the sake of any definitive answers to its questions, since no definitive answers can, as a rule, be known to be true, but rather for the sake of the questions themselves; because these questions enlarge our conception of what is possible, enrich our intellectual imagination and diminish the dogmatic assurance which closes the mind against speculation’ (Is God a Mathematician?, Mario Livio, p 252)

 

On the other hand, it occurred to me that perhaps philosophy may not be as logical as it suggests/claims! After all, I found that what we call logic often exists as a ‘chimera’ where what appears to be logic is a mathematical entity and the following two paragraphs (from chapter 75) indicate that the universe is based on mathematics and not logic, and further, that we are the means of turning mathematics into logic.

 

‘An example of questing the fifth dimension [(a+b)=1] comes to mind because the total energy of the Big-Bang/Big-Whoosh is zero at all times, and yet, from chapter 72: “One requirement any law of nature must satisfy is that it dictates that the energy of an isolated body surrounded by empty space is positive, which means that one has to do work to assemble the body. That’s because if the energy of an isolated body were negative, it could be created in a state of motion so that its negative energy was exactly balanced by the positive energy due to its motion…. Empty space would therefore be unstable.” (The Grand Design, Stephen Hawking and Leonard Mlodinow, p 179). This is logical, but is it really logic or mathematics, which is a special case of the mathematics of concepts that is apparent from the dimensions?’ On the other hand, is it the context of a concept that requires a mind/brain?

 

‘In a simple planetary system, the total energy equation zero = (p+q) where p and q are kinetic energy and potential energy and mirrors the fifth dimension in context [measuring each other continuously and instantaneously] to the concept of “Newton’s inverse square law of gravity explained in one equation the orbits of all the planets as described in the three laws of Johannes Kepler.” (50 physics ideas, Joanne Baker, p 17) Notice that I mentioned concept and context, but Newton used world O thinking of the force of attraction between the planets and this invokes a determination and subsumes the logic/context.’

 

So, logic, from 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.’

From (3) above (and chapter 78):

 concept/forward-planning/quest/relevance/beauty/context

for Life in world O, bearing in mind that Life lives in a deterministic reality that must be complete and continuous and the physical world P, that is totally entangled, becomes:

 

measurement/quest/relevance/entanglement

 

and for “something” to be “logical”, it must contain answers to all six conditions because it is a restatement of the dimensions, absolutes and the properties of the probability space. This is a concept because it is limited in scope and contains concept/forward-planning/beauty (bearing in mind that forward-planning is a construction by the mind/brain of Life) and context is quest/relevance/context. This context was discussed in chapter 73, ‘given that relativisation (A), the mathematics of concepts (B) and setting out the concepts/attractors and setting the context (C), the use of an absolute (D) [forward-planning] chosen by the universities (E) [the ‘best’ absolute] are derived above.’

‘Further, (F) is experimentation/trials/measurement etc., as suggested by Francis Bacon to bring about a ‘scientific method’ that has proved spectacularly successful in science/technology and this could be considered a ‘break-through’ because most ‘science’ was derived by ‘thought’ for thousands of years. However, the duality of concept/context and measurement/entanglement means that theorists (H) should be included and it is apparent that a mathematics of concepts has been set up [(A) to (H) in total] where more factors produce a better organization, but what is the purpose of an organization? An organization is set up [forward-planned] for a number of reasons, but basically it is to satisfy a need and/or to evolve (I), and I should stress that these eight points are (possibly) the most important of many more that may need to be considered.’

 

It should be noted from (6) and (7) that major solutions/absolutes exist from the entanglement simplification (a+b)=1 that show that the speed of light is constant and that a measure of beauty, in the form of a ratio is available to Life. In particular, I believe that Life uses the Golden ratio as part of its reality and the form of reality (completeness and continuity) requires/ensures that the criterion of beauty is a reality having completeness and continuity across the reality (chapter78).

 

The dimensions, when used bottom-up are a powerful tool that links the speed of light with our reality [Michelson-Morley] and shows the intertwining of the physical and our worlds. In fact, everything in the universe can be derived from five dimensions if we live in a probability universe, and I believe that I have proved that to my satisfaction, the key to tackling the problems of society and of the world become solvable and the key is in chapter 67 that describes a modern means of attaining Plato’s political aspirations and the basis to that is organization, above.

 

‘Plato hankered, in his search for real knowledge, after the kind of certainty which the truths of mathematics have, but because he was after things and not truths, the things had to be necessarily existing things. Looked at in this light, even the road to Larissa does not really qualify (it might be washed away, as roads in Greece sometimes are).’ (Greek Philosophers, R. M. Hare, p 142) Mathematics did not exist in Plato’s time and certainty does not exist except in constructs such as mathematics,  similarly, uncertainty always exists in the mathematics of concepts unless we change the field to a reality because Life is uncomfortable with uncertainty, but questing is basic to a probability space and requires uncertainty until a measurement is made.

 

This quotation should be sufficient to establish my points, but is Plato relevant today? ‘Philosophy, as it is studied in the West today, is an invention of the ancient Greeks. So too, to a great extent, are science and mathematics. But today’s science and mathematics so far transcend the achievement of the Greeks that no modern scientist is likely to study Euclid or Hippocrates or Archimedes for other than purely antiquarian reasons. Modern philosophers, by contrast, continue to discuss problems which were first raised some two thousand five hundred years ago, and they often do so in terms which their Greek predecessors would have found fully intelligible.’ (p v)

 

So, Plato needed mathematics, which did not exist in his day, and great strides have been made since, using mathematics/science/technology over the last 2,500 years, but not, it appears, in philosophy. Philosophy needs the mathematics of concepts, that contains mathematics as a special case, and this is immediately apparent from the fifth dimension (a+b)=1. Science has forged ahead using mathematics, but more importantly it used the organizational context above that provided the impetus. This fact of organizational context can be shown simply by looking at the simplicity/inapplicability of Newton’s laws of motion.

 

From chapter 73, ‘the comparison of the rules of organization, above, with the basis of science, below, shows that the success of science was organizationally lucky/fortuitous, because, from above, many of our organizations are inadequate, such as the process of law, the making of laws by public servants, the food offered by shops, the fishing industry [a commons] etc. are deficient, but science was a ‘stroke’ of luck because acceptance (A) of a theory is required by scientists in general and that theory requires the mathematics of concepts (B) [to compare theories] and invites additions and checking (C) of the result (D) by those with a long-time career (E) in the subject and this often requires experimentation (F) and theorists (G) to fit it all together, and finally, the overall idea of science is to ‘push’ the boundaries (H) of what we know. It is hard to resist a giggle that science has been using the fifth dimension, top-down without acknowledging its existence!’

 

However, a small digression that shows how ‘tenuous’/unscientific the top-down method can be, is shown by the three laws of motion put forward by Descartes. “In order to avoid such notions of occult powers of motion, much of Descartes’ Principles of philosophy was devoted to an explanation of how or why matter moves, and what keeps it in motion.” (Let Newton be!, p 133, edited by John Fauvel) and the three laws given were very close to those of Newton, but, “Descartes insisted that the amount of motion in the universe is constant.” (p 134) “Newton … did not deny the occult nature of his active principles” (p 135) “A slightly naughty thought can come to one’s mind here. Is it due to the nature of physics that the mathematical tools started by Newton are so essential for many parts of physics through the centuries? Or is our selection of worked-on parts of physics still largely Newtonian?” (p 244) That these ideas have flowed through physics for 300 years shows, I believe, that the ‘selection of worked-on parts of physics is still largely Newtonian’!

 

A point should be made, and I keep repeating it because it is so important, about top-down and bottom-up, that Descartes looked for a universal ‘base’ because he believed that speed was conserved. This is the bottom-up approach and he made a valiant attempt to do this, but Newton looked in a ‘non-base’ description of motion and that was accepted. I am proposing a return to the ‘base’ idea of conservation of energy and that the total energy in the universe is zero at all times and that is a statement of relativisation. Remember that relativisation is a concept (two observers measure the speed of light to be the same, and that is an enigma except in a probability space) and context ((a+b+c …)=1).

 

However, as I will have to foreshadow to some extent, Newton’s laws of motion have remained untouched for over 300 years and, in the light of the above, a re-thinking and re-writing might be in order, and the concept/attractor that science continually ‘re-builds’ its ‘house’ need to be reinstated and re-applied, and I suggest the following from chapter 77.

 

‘1 A particle remains at rest or in uniform motion unless acted upon by an energy gradient, except that it will be continually relativised, and in the case of a photon, the speed is always constant and an absolute, and only the energy is relativised.’

 

‘It is a property of a probability space that ‘free’ energy moves at the speed of light, unless energetic enough to form a particle as is indicated by the space-time and fifth dimension/energy. The interval of time is a world (our) O invention that was needed for survival in a predator/prey situation, and that takes speed and acceleration out of world (physical/probability) P.’

 

‘2 The modulus of energy, if greater than zero, can be transmitted to, or form, other types of energy without loss, at any distance via a change in the dimensions (space, time and energy/mass) equally through the Lorentz contraction acting between two frames of reference to prevent a singularity.’

 

‘Gravitational potential/energy is negative, all other energies are positive and the sum is zero (conservation of energy), but energy contains an orthogonal measurement/entanglement and this entanglement/relativisation is instantaneous and universe wide (a and b)=1, whereas positive energies are restricted to at, or below, the speed of light (a+b)=1.  This is a logical requirement [Lorentz contraction] that affects the dimensions equally and if exceeded, produces chaos everywhere.’

 

‘A Newtonian force is a combination of concept and measurement that down-plays entanglement and in Newton’s day ‘the only allowable notion of force, therefore, was force of impact; all other concepts of force, such as attraction and repulsion, were regarded by these natural philosophers as occult.’ (p 127) Also, Einstein used ‘spooky action at a distance’ for these same forces, yet a probability space contains the mechanism in relativisation to explain this.’

 

‘3 Locally, momentum is conserved and local entanglement (a+b)=1 allows action and reaction to be equal and opposite and that is necessary to generate space so that matter can condense as solar systems etc., but energy is conserved (at zero) universe-wide (measurement) and adjusted continually and instantly (entanglement, (a and b)=1).’

 

‘Decartes thought that momentum was conserved universally and that non-occult forces are the physical world of collisions and was incorrect in the first instance and correct in the second, but Newton combined world O and P in a local scenario that has taken 300 years to understand/unravel. The use of force subsumes context/entanglement and combines world O and P, which is acceptable when the separation is understood.’

 

First, it is useful to give a quick and easy description of the use of the mathematics of concepts from chapter 75.

 

‘If we take the Cartesian system of the X-Y plane, we can say that some point is composed of two independent variables (x, y), and the mathematics of concepts can be handled similarly, bearing in mind that an iteration or mind/brain initiates a measurement and we are dealing with world O and world P. A little foreshadowing will make it easier to understand, that world P is a probability space and only has iteration, whereas Life has made world O into a “determinate”/non-entanglement world because of the necessity of creating a reality as part of questing/Survival-of-the-Fittest.’

 

‘So, taking the easy case of world P, questing is: X-Y axes with the concepts to be examined spread equally spaced along the X axis, and a curve/^ is drawn between each concept and every other concept with a height ^ equal to its probability and the sum of all the ‘heights’ is 1. This comes straight from the entanglement/measurement of the probabilities in a probability space. To move it into world O in order to automate or use a mind/brain, move the concepts and the ^ to make a ‘normal’ curve and read off the best concepts and their context. If this looks simple, ask yourself ‘why should it be complicated?’, when the universe requires only 5 dimensions and life six dimensions.’

 

There is one further point, and that is that the decision that has been made is a concept and whilst the context has be taken into account, the context must be recorded and be re-evaluated periodically to maintain relevance. This is, of course, questing and relevance that are part of a probability space and we need measurement and entanglement as well, and for (our) world O [concept/forward-planning/quest/relevance/beauty/context] that is a combination of concept and context. Further, I believe that this is ‘elegant infinite’, which is the context to mathematics’ ‘elegant simple’, that is a concept.

 

I gave the example of Newton’s laws and another example [that illustrates relevance over time] might be ‘the doctrine that virtue is knowledge is the key to understanding the so called thesis of the Unity of the Virtues, maintained by Socrates in Protagoras. In that dialogue Protagorus assumes a broadly traditional picture of the virtues as a set of attributes distinct from one another, as, for example, the different bodily senses are distinct.’ (Greek Philosophers, R. M. Hare, p 64) ‘The theory that virtue is knowledge is, as we have seen, flawed, in that one of its central propositions, that virtue is always in the agent’s interest, is nowhere adequately supported in the Socratic dialogues. It also has a deeper flaw in that it is incoherent.’ (p 66)

 

All life obeys questing, which is another name for Survival of the Fittest and as part of this, relevance is required and relevance is reality. We have to sense predators and live among them, but keeping a forward-plan if the predator gets too close and we need continuity and completeness, otherwise, magic/predators sneak in without us sensing them. The larger animals protect their offspring by teaching them and helping them until they ‘know the ropes’.

 

The Greek philosophers advocated a mentor, but the Bible was more formal by using, I believe, the mathematics of concepts to divide God into three parts to, I believe, make understanding easier, and I believe that over the last 2000 years the Church ‘lost’ the Holy Spirit. I derived three Laws of Life and they ‘mirror’ the Trinity. God the Father is creation, the Holy Spirit is the wider environment and God, the Son is family and other close relationships, see Chapter 1.

 

From bottom-up, questing and relevance through the untold generations make up an iteration/computer and what we see is what is logical/has-evolved given the conditions on the planet, we have done the best that we can and teaching offspring works, because we do it. ‘Socrates suggests that, on the contrary, the names of individual virtues, courage, self-control, etc., are all “names of one and the same thing” (329c-d)’ (p 65) This is true if time is taken into account because as we go back in time, these successful traits lead to success in the tribe even without names, just observation and as time passes, these attributes are progressively named. ‘Socrates suggests that, on the contrary, the names of the individual virtues, courage, self-control, etc., are all “names of one and the same thing” (329c-d)’ (p 65) is top-down thinking, and translated into bottom-up becomes ‘names of one successful concept of survival (emulation/knowledge through teaching) that has the context of those names (virtue, courage, self-control, etc.) as a means of attaining breeding success’. [using forward-planning in reverse]

 

‘The incoherence emerges when we ask “what is virtue knowledge of?” The answer indicated by Meno and Protagoras is that virtue is knowledge of the agent’s good, in that, given the standing motivation to achieve one’s good, knowledge of what that good is will be necessary if one is to pursue it reliably, and sufficient to guarantee that the pursuit is successful.’ (p 66) This suggests that knowledge of virtue (concept) is necessary and to pursue it (context) with the motivation being Survival of the Fittest and especially the family etc.

 

The dimension of time-passing culturally ‘splits off’ the virtues and are similar to the accumulation of the senses (feeling, smell, sight etc.) because it is part of reality and questing has, through evolution, determined relevance otherwise they would not exist at this time. These virtues have been with us for 3,000 million years when bacteria swapped DNA. The answer to “what is virtue knowledge of?” is answered by the parents to the best of their ability to enhance their investment by ‘on the job’ teaching as well as family input, and over time the adult becomes the agent of a group and it appears that doing the best for each person, as decided by the person, is the best that we can hope for.

 

From chapter 78, ‘The Nobel laureate Eugene Wigner, gave a celebrated lecture with the title, “The unreasonable effectiveness of mathematics in the natural sciences”…. The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it.’ (The Story of Measurement, Andrew Robinson, p 45) I need to say that there is a rational explanation that mathematics ‘works’ because mathematical/logical relationships are the fifth dimension and quests of a mathematical relationship (a+b)=1 are the basis of our universe and this will be explored later.’ (chapter 81)

 

Conclusion: the title: ‘When Philosophy Meets Mathematical Physics’ is, I believe, appropriate and is an opportunity to reorganize both philosophy and science from the bottom-up. As to why I cannot understand philosophy, I present the following quotation, again, but now I believe that it has been turned ‘on its head’.

 

‘Bertrand Russell in The Problems of Philosophy: Thus, to sum up our discussion of the value of philosophy; Philosophy is to be studied, not for the sake of any definitive answers to its questions, since no definitive answers can, as a rule, be known to be true, but rather for the sake of the questions themselves; because these questions enlarge our conception of what is possible, enrich our intellectual imagination and diminish the dogmatic assurance which closes the mind against speculation’ (Is God a Mathematician?, Mario Livio, p 252)

 

Thus, I do not know whether to apologise to philosophers that in my ignorance I have turned their mental exercise into a confrontation with the mathematical physicists, or giggle that they will have to work (or fight) together to straighten thing out. As an indication, Plato’s political system (chapter 67) needs to be implemented as soon as possible.

 

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