Nature Is Fundamentally Discrete But Our Basic Formalism Is Not by Lev Goldfarb

Essay Abstract

In physics, we have been seriously confronted with the question of continuous vs. discrete since the beginning of the last century. Why is it still with us, and increasingly so in the last sixty years? The title of the essay suggests the reason: so far, we have relied on the "continuous", or vector space, mathematics (of spatial origin), the only one we have, while the experiments suggest that, at the bottom, the nature is non-continuous, or discrete, albeit in a sense unfamiliar to us. We have tried to save the situation by "discretizing" our conventional models, but for the reasons I discuss here such desperate attempts to transform our basic formalism (by destroying its integrity) are not meaningful. We may have no other choice than to set aside for a while the millennia-old numeric, or spatial, forms of representation and the associated measurement processes and to begin completely anew, by shifting to a non-numeric-- relational, or temporal--representational formalism, which should give the meaning to the nebulous concept of discreteness and, even more importantly, should remove the enormous present gap between the physical and the mental.

Author Bio

Lev Goldfarb obtained Diploma in Mathematics (St.-Petersburg University) and Ph.D. in Systems Design Engineering (University of Waterloo). For twenty five years he worked as an Assistant and Associate Professor in the Faculty of Computer Science, University of New Brunswick, Canada. Now he conducts research, development, and consulting through his company IIS. He has served on the editorial boards of Pattern Recognition, Pattern Recognition Letters, and now Cognitive Neurodynamics. Trained as a mathematician, he realized quite early the inadequacy of the conventional numeric models and has been working on the development of a fundamentally new formalism for structural representation.

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Hi Don,

I wanted to welcome you to the contest first, but you bit me to it. ;-) [I'm having a very hard time with my renovations, now a year and half in the making]

Regarding 3: there is really nothing new there (think of a more precisely depicted Feynman diagram.

Regarding 4: that's the idea.

Thanks for you comments!

Last night I remembered that several days ago I recommended to Ian Durham (on his essay page) R.G. Collingwood's book "The Idea of Nature" (1945), in particular the end of the first chapter. So today I decided to reread this part of the book, and suddenly one important point came to my mind. Before making this point, I would like to share with you the portion of the text that triggered this idea:

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If an historian had no more means of apprehending events that occupied more than an hour, he could describe the burning down of a house but not the building of a house; the assassination of Caesar but not his conquest of Gaul; ... the performance of a symphony but not its composition. If two historians gave each his own answer to the question: 'What kind of event happen, or can or might happen, in history?' their answers would be extremely different if one habitually thought of an event as something that takes an hour and the other as something that takes ten years; and a third who conceived an event as taking anything up to 1,000 years would give a different answer again.

... In general, making things takes longer than destroying them. The shorter our standard time-phase for an historical event, the more our history will consist of destructions, catastrophes, battle, and sudden death. But destruction implies the existence of something to destroy; and as this type of history cannot describe how such a thing came into existence, for the process of its coming into existence was ... too long to be conceived ..., its existence must be presupposed as given, ready-made, miraculously established by some force outside history.

... I have quoted late Mr. Sullivan's remark that the second law of thermodynamics applies only from the human point of view and would be unnecessary for an intelligent microbe. ... [A]n intelligent organism whose life had a [much] longer time-rhythm than man's might find it not so much unnecessary as untrue.

The natural processes that come most easily within ordinary human observation, it may be, are predominantly of a destructive kind, like the historical events that come most easily within the knowledge of the historian who thinks of an event as something that takes a short time. Like such an historian, the natural scientist, it may be, is led by this fact to think of events in nature as in the main destructive: releases or dissipations of energy ...; to think of the natural world as running down like a clock or being shot away like a store of ammunition. ...

May it not be the same in the world of nature? May it not be the case that the modern picture of a running-down universe, in which energy is by degrees exchanging a non-uniform and arbitrary distribution (that is, a distribution not accounted for by any laws yet known to us, and therefore in effect a given, ready-made, miraculously established distribution ...) for a uniform distribution, according to the second law of thermodynamics, is a picture based on habitual observation of relatively short-phase processes, and one destined to be dismissed as illusory at some future date, when closer attention has been paid to processes whose time-phase is longer? Or even if these long-phase processes should continue to elude human observation, may it not be found necessary to dismiss the same picture as illusory because, according to the principles of evolutionary physics, we shall find ourselves obliged to postulate such processes even though we cannot directly observe them?

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Now I come to one of the main points of my essay: together with Helmholtz and Poincaré, I postulated the processes related to the induction (class generating processes) to be the central/underlying informational processes. In the context of the above quote, they are the main constructive processes in Nature. This postulate also allows for a very direct link between the physical and the mental. Of course, the concrete 'physical' embodiment of such processes is yet to be determined.

Hello Jim,

The reason we cannot deal with the "reality", at least so far, has to do with our inability to approach it directly, without any special "language", or formalism, designed for that purpose.

In my essay, I suggested that our present difficulties have to do with the fact that the numeric formalism, which has served us for several millennia, has exhausted its usefulness and needs to be replaced by a new formalism which is supposed to capture reality in a much more direct manner.

Jim,

I'm sorry but I'm not quite following you.

Dear Peter,

I sincerely appreciate your interest in my essay!!

I already read your essay and would have commented on it if I felt confident/competent that those will be useful to you.

I believe your remark that "Perhaps a spectacular success in application is needed." is absolutely correct, and the main reason I participate (for the second time) in these contests is directly related to my hope that some people might be motivated to develop with or without me some "physical" applications of the proposed new form of data representation.

In fact, *all* I'm proposing is a fundamentally new (structural) form of data representation in science.

Best wishes,

--Lev

Thank you, Yuri, for pointing to the quotes by Feynman (in your essay page) and 't Hooft (in the link) supporting my doubts regarding the applicability of the logic of calculus to physics (the second paragraph of section 3 in my essay).