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What Is “Fundamental”
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Trick or Truth: The Mysterious Connection Between Physics and Mathematics
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It From Bit or Bit From It
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Is Reality Digital or Analog?
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RECENT POSTS IN THIS TOPIC

Joe Fisher: on 4/8/15 at 15:47pm UTC, wrote Dear Jairo, I think Newton was wrong about abstract gravity; Einstein was...

Jairo da Silva: on 3/23/15 at 10:01am UTC, wrote Thanks, Alan. Please read my reply below.

Joe Fisher: on 3/17/15 at 15:30pm UTC, wrote Dear Professor da Silva, FQXi.org has labeled my work “OBNOXIOUS...

Jairo da Silva: on 3/16/15 at 17:46pm UTC, wrote Dear Joe. Thanks for your comments. You ask me what physical reality is....

Joe Fisher: on 3/16/15 at 15:55pm UTC, wrote Dear Professor da Silva, You wrote: “Physical reality, in short, is a...

Jairo da Silva: on 3/16/15 at 3:18am UTC, wrote Dear Alan. Thank you very much for your comments. I must first call your...

Alan Kadin: on 3/14/15 at 15:12pm UTC, wrote Dear Prof. da Silva: Your essay makes a coherent and cogent argument that...

Jairo da Silva: on 3/13/15 at 18:14pm UTC, wrote I´d like to highlight the points I believe worth noticing in my paper. 1)...


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FQXi FORUM
May 31, 2020

CATEGORY: Trick or Truth Essay Contest (2015) [back]
TOPIC: Mathematics, the Oracle of Physics by Jairo Jose da Silva [refresh]
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Author Jairo Jose da Silva wrote on Mar. 10, 2015 @ 14:03 GMT
Essay Abstract

Mathematics studies abstract patterns, either instantiated in structured system of things given to perception or in imagination, or freely invented and characterized axiomatically. The method of modern physics, which defines it, consists in studying the reality man perceives by means of abstract patterns extracted from it and idealized as mathematical patterns, which, then, can be freely extended. In this way, modern physics invites mathematics in. By an elaborate interplay between symbolic mathematics and creative semantics of mathematical systems, or by purely formal analogies between the mathematical surrogate science substitutes for perceptual reality and no matter which mathematical domain, mathematics manages to play a fundamental role in scientific heuristics. The mystery of the applicability of mathematics in empirical science is a consequence of the belief that physical and mathematical realities are two completely isolated and self-sufficient domains which can only communicate by mysterious means. Here, I strive to show that this belief is false.

Author Bio

Professor of Mathematics, Department of Mathematics, University of the State of São Paulo at Rio Claro, SP, BRAZIL. Member of the Centre for Logic, Epistemology and the History of Science (CLE), University of Campinas, Campinas, BRAZIL. Member of the Institute of Philosophy of the University of Lisbon, Portugal. Researcher of the National Council for Scientific Development (CNPq), Ministry of Science and Technology, BRAZIL. Chief-editor of Cahiers of History and Philosophy of Science, published by CLE.

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Author Jairo Jose da Silva wrote on Mar. 13, 2015 @ 18:14 GMT
I´d like to highlight the points I believe worth noticing in my paper. 1) I work with three different concepts of reality, sensorial, perceptual and physical; each level admits a different amount of mathematization, from the most basic to the most elaborate (perception may have a topological structure, but not a metrical one; physical reality, on the other hand, can be given a metrical structure proper). 2) Physical reality is a mathematical construct, its process of constitution takes perceptual reality and delivers physical reality after a considerable amount of "cutting" (abstraction), "polishing" (idealization) and "refurnishing" (substitution of percepts by mathematical representatives); physical reality is not simply a "representation" of perceptual reality. 3) Only physical reality, as the mathematical realm it is, admits full-blown mathematical treatment; the theories of mathematical physics are mathematical theories of the mathematical domain physical reality is. 3) the applicability of mathematics in physics, then, is only an instance of the applicability of mathematics in mathematics, with all its advantages. 4) The mathematical treatment of physical reality may disclose noteworthy formal regularities that can (but need not!) be given material content in perceptual reality; this accounts for the "unreasonable effectiveness" of mathematics in physics.

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Alan M. Kadin wrote on Mar. 14, 2015 @ 15:12 GMT
Dear Prof. da Silva:

Your essay makes a coherent and cogent argument that much of both science and math are human constructions, rather than independent external entities, and it is this human connection that accounts for the usefulness of math in physics. I’m sure you realize that this is heresy to the prevailing scientific pseudo-religion, in which both science and math provide, in...

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Author Jairo Jose da Silva replied on Mar. 23, 2015 @ 10:01 GMT
Thanks, Alan. Please read my reply below.

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Author Jairo Jose da Silva wrote on Mar. 16, 2015 @ 03:18 GMT
Dear Alan. Thank you very much for your comments. I must first call your atention to a misinterpretation of my paper that I was afraid would be a common one, namely, that I take a somewhat "post-modern" point of view. It is true that I claim that mathematics is to a large extent an invention, since we can freely create mathematical patterns by explicitly stating their formal properties axiomatically. But mathematics can also be created by paying attention to patterns that we find in our experience of reality. The question whether mathematics is discovered or created has a trivial answer: both. Our colour experience, for example, has an obvious topological structure, and anyone could in principle have invented topology by paying enough attention to this particular structure. On the other hand, the arithmetic of quaternions is obviously invented. Now, the real question is how it is possibly that mathematics, be it invented or discovered, can be used in the empirical sciences. Some mathematics -for instance, topology - could be applied directly to perception but metrical geometry cannot. How come then that it is? Answer: because it is not to perception that we apply metrical geometry, but to an idealization of perception. In few words, in general our perception of reality can be mathematically treated because we substitute it by a mathematical surrogate. Once this surrogate is available we can use whatever mathematical instruments available to investigate it. It is mathematics as usual, like using heavy analytical machinary to investigate the numerical realm. There is nothing earth-shaking in anything that I said. The problem is that most philosophers in the Anglo-American analytical tradition are sworn empiricists and believe religiously that the reality investigated in physics is what it is independently of idealizations and other interventions that make it amenable to mathematical treatment. This where the "unreasonable effectiveness" nonsense begins.

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Joe Fisher wrote on Mar. 16, 2015 @ 15:55 GMT
Dear Professor da Silva,

You wrote: “Physical reality, in short, is a scientific construct.” What is physical reality in long?

This is my single unified theorem of how the real Universe is occurring: Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of abstract NOTHING. Proof exists that...

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Author Jairo Jose da Silva wrote on Mar. 16, 2015 @ 17:46 GMT
Dear Joe. Thanks for your comments. You ask me what physical reality is. Well, I use this term in a somewhat tecnical sense. What is "out there" is "out there" and it is at best a limit concept. Science is concerned only with what we perceive or can in principle perceive. But what we perceive is what is out there filtered through our sensorial and percentual systems (which, by the way, are not the same thing). This is what I called percentual reality. Perceptual reality has some structure, of course, and so can already be aproached mathematically, since mathematics is the science of structures. But the structure of percentual reality is already, to some extent, a contribution of percentual filtering systems. To ask what is "out there" but cannot be perceived is not a well-posed question, we do not even know what it means! Now, in order for mathematics to be really effective, science substitutes perceptual reality by a mathematical surrogate that, as I said in the paper, contains simultaneously more and less than what perception provides or can in principle provide. This is what I call physical reality. Not what is "out there", not even what we can perceive as being out there, but a mere formal, symbolic, mathematical representation of what perception indicates to be, maybe, out there.

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Joe Fisher replied on Mar. 17, 2015 @ 15:30 GMT
Dear Professor da Silva,

FQXi.org has labeled my work “OBNOXIOUS SPAM,” and removed it from several sites where I had posted it.

Sir, do you have a real complete skin surface? Does every animal, insect, and can of soda have a real complete surface? It is physically impossible to perceive a single real surface. No matter in which direction one looks, one will only ever see a plethora of real surfaces. At each point where surfaces touch, a real sub-surface forms. All surface travels at the same constant speed. Each sub-surface travels at a unique speed that remains less than the constant speed of surface. That is why although everything is traveling at the same speed, each object remains in its own unique position.

Grateful that you read my comment and at least made an answer to it.

Joe Fisher

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Joe Fisher wrote on Apr. 8, 2015 @ 15:47 GMT
Dear Jairo,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

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