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RECENT POSTS IN THIS TOPIC

Alan Kadin: on 5/15/20 at 0:26am UTC, wrote Dear Dr.Guthrie, Let me suggest another topic that applied mathematicians...

Alyssa Adams: on 5/11/20 at 2:12am UTC, wrote Hi Dr. Guthery! This is an excellent point, that math should be driven by...

Eckard Blumschein: on 5/6/20 at 1:03am UTC, wrote Dear Scott Guthery, Do mathematicians like you consider a reference point...

Manfred Pohl: on 5/5/20 at 16:31pm UTC, wrote Dear Scott Guthery, i enjoyed your essay a lot. I agree much on your...

Eckard Blumschein: on 5/4/20 at 4:56am UTC, wrote Dear Scott Guthery. Is counting the only fundamental of mathematics? Well,...

Charles Sven: on 4/24/20 at 15:43pm UTC, wrote Greetings Scott Guthery ADAPT MATHEMATICS TO SCIENCE,NOT SCIENCE TO...

Boris Egorov: on 4/18/20 at 11:07am UTC, wrote Dear Scott, I agree with you that math is a language and should supplement...

Eckard Blumschein: on 4/16/20 at 21:47pm UTC, wrote Dear all, Isn't the complex Fourier transformation an example of how...


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FQXi FORUM
September 28, 2021

CATEGORY: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) [back]
TOPIC: Adapt Mathematics to Science, Not Science to Mathematics by Scott Guthery [refresh]
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Author Scott Guthery wrote on Mar. 31, 2020 @ 16:56 GMT
Essay Abstract

This essay argues that the mathematics being created by the research mathematics community is not responsive to the needs of the physical science community; that undecidability, uncomputability, and unpredictability are evidence of this gap. The essay goes on to suggest four research initiatives that could led to the creation of mathematics that was responsive to the needs of the physical sciences.

Author Bio

Dr. Guthery received his graduate degree in probability and statistics from Michigan State University in 1969. After working as applied mathematician for Bell Laboratories, Schlumberger, and Microsoft, he founded Docent Press which publishes books in the history of mathematics, computation, and technology.

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basudeba mishra wrote on Mar. 31, 2020 @ 17:47 GMT
Dear Sir,

I thoroughly enjoyed your basic research.

You have addressed one of the fundamental flaws of modern physics. Four years ago, I had written a paper here pleading on the same lines. My this year’s essay is also on similar lines. Both our views have much commonality, though explained differently.

Language is the unambiguous transposition of one’s/a system’s thoughts/command on another person’s/system’s mind/CPU. Mathematics does that with numbers. Hence mathematics is a language of Nature. But it only depicts quantitative aspect of Nature – scaling up or down the numbers with consequential changes in other aspects. It does not cover all aspects, though. Hence what is true for mathematics may or may not be true for physics or biology. For example, if by paying $3000 we can get a bike, by paying $1000 we can get 1/3 of a bike. This statement is mathematically correct. But physically it does not make any sense. There is no equation for the observer, but it has an important role in physics. Thus, physics beyond mathematics cannot be denied. Extending the limited scope of mathematics (scalar numbers) to (vector) physics or biology, makes us fall in the trap of reductionism. As you say: “mathematics (developed by physicists) that was subsequently abstracted and generalized by the mathematics community” or vice versa.

You have hit the target precisely when you point to the modern practice: “to adapt theories to available mathematical constructs and abstractions however flawed or inappropriate they may be”. I can add the process of renormalization and brute-force approach to your list. However, I beg to partially differ from your view on infinities. You can refer to my essay here for details.

Your views on irrational numbers matches my paper, where I had brought out the historical perspective. Similarly, your views on “Algorithms in Addition to Functions” complements my view.

Regards,

basudeba

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H.H.J. Luediger wrote on Mar. 31, 2020 @ 19:00 GMT
Scott,

your suggestion that mathematicians ought to make mathematics useful to physicists reminds me of the wondrous regularity making meteorites always land in craters...

I'm not convinced that e.g.

some clever (say) Egyptian one day sat down and invented numbers leaving it to following generations to make some use of them.

or

Newton invented his fluxions and only then noticed that they are useful means to describe the motion of bodies.

Heinz (believer in the fact that meteorites make craters)

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Author Scott Guthery replied on Mar. 31, 2020 @ 20:38 GMT
Heinz ...

Thanks much for your comments.

Newton makes my point. He was surely as much a scientist as he was a mathematician. He developed the mathematics he needed to describe his scientific theory; that is, he adapted mathematics to his science not his science to existing mathematics. If he had confined himself to only using the mathematics papers on the shelf at the time who knows where we'd be now. The same is true for Leibnitz.

As far as the clever Egyptian goes, counting is pretty fundamental whether you're a mathematician, a scientist, or just keeping track of your livestock. Once again, the mathematics was developed in response to a scientific need; viz. counting things. Your Egyptian didn't invent numbers and then go around seeing if anybody could make use of them.

Cheers, Scott

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Eckard Blumschein replied on May. 4, 2020 @ 04:56 GMT
Dear Scott Guthery.

Is counting the only fundamental of mathematics? Well, Cantor/Hilbertian mathematics is finitistic, I say it is pragmatic but not without carefully hidden problems.

A main obstacle for physics is the pretended freedom alias the need to choose a reference point. Why do physicists claim that R+ is effectively forbidden putatively "for mathematical reason"?

It is obviously taboo to attribute the point between past and future to the zero of a time scale which is absolutely identical with the ordinary one. Why?

Curious,

Eckard

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Yehonatan Knoll wrote on Mar. 31, 2020 @ 21:16 GMT
The curse of backward-compatibility.

I'm sure some people are trying to do precisely what you endorse; I certainly did (noting that all of mathematical physics is currently being converted to computer code, so why not model the phenomenon directly as code, including the symmetry group of the problem etc.). The problem is that current physical phenomena are way more complex than Newtonian dynamics, yet we are not correspondingly smarter than Newton. I, for example, had to make a choice: be a mathematician, and develop a novel code-physics, or use whatever is available `on the shelf' and model physical phenomena. When trying to be both, progress was very slow. So slow that today I believe that that most significant time scale in physics is not the planck scale, nor the inverse Hubble constant; it is the lifespan of a human being!

Thank you for a very enjoyable essay.

Yehonatan

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Branko L Zivlak wrote on Apr. 1, 2020 @ 10:11 GMT
Dear Scott,

when I read the following sentence in your essay, I interrupted my reading:

“We need to create mathematics that serves the needs of today’s physics and is free of those shortcomings.”

The reason is that elementary math was enough for me to lead to predictable formulas, which you can see on the last page of my essay.

Regards Branko

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Satyavarapu Naga Parameswara Gupta wrote on Apr. 1, 2020 @ 15:43 GMT
Dear Prof Scott Guthery,

Wonderful essay please.

You are exactly correct, mathematics can not describe nature fully. There are so many constraints. Math may explain some concepts well, does not mean what ever the math said correctly in some situations is always correct for all situations.

The theme your essay is essentially the same as my essay. Hope you will have a look at ....

" A properly deciding, Computing and Predicting new theory’s Philosophy"

Best Regards

=snp

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adel sadeq replied on Apr. 2, 2020 @ 19:27 GMT
Dear Gupta ,

I think you should read his essay again, he is not saying what you think he is saying.

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Martin van Staveren wrote on Apr. 2, 2020 @ 07:34 GMT
Physics is based on data, i.e. on measurements. Without data we only have empty speculation.

Mathematicians do not like measurements, because measured data are never exact.

This is the short version of why there is a cultural gap between physics and mathematics.

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S.E. Grimm wrote on Apr. 2, 2020 @ 18:34 GMT
Dear Scott Guthery,

I really enjoined your paper and I fully agree with the contents. However, I have an addition.

In physics we can only measure differences between observable/detectable phenomena. Actually, every measurement can only show the mutual relations between the distinct phenomena. Unfortunately, mutual relations create uncertainty, even if the distinct phenomena are compositions of simple building blocks (e.g. the relation between an even and an odd number).

But the universe is constantly creating the transformation of the observable phenomena. That means that there is an underlying creating structure we never can observe. What kind of underlying structure – for example the structure of the basic quantum fields (QFT) – is subject of discussion between physicists. But to describe a non-observable reality we need a precise “basis” language. Besides that, it should be really strange if the creating underlying reality is not responsible for the foundations of mathematics. That’s why I suppose that the foundations of mathematics will become more and more a subject of interest for philosophers and physicists.

With kind regards, Sydney

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Eckard Blumschein wrote on Apr. 3, 2020 @ 11:40 GMT
Dear Scott Guthery,

You criticized that the three impossibilities of the topic don't address "the needs of the" community of physicists. Yes,"a torrent of new definitions and theorems about old definitions" is certainly unnecessary.

However, what about your suggestions to use numerical mathematics in terms of rational numbers and algorithms with sharp corners instead of e.g. Bourbaki style infinite differentiability, isn't this already successful common practice?

When I am suggesting some "calculate as if - but"s, this might be even more unwelcome in the sense I intend to make aware of possible mistakes that hinder physics. You might correct me. I am not a mathematician.

Best,

Eckard Blumschein

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Eckard Blumschein replied on Apr. 16, 2020 @ 21:47 GMT
Dear all,

Isn't the complex Fourier transformation an example of how mathematics was unfortunately adapted to the fatalistic block universe instead to reasonable physics with a natural, not an arbitrarily chosen point t=0 of reference between past and future?

Correct science is causal. If we adapt mathematics to correct science, then this avoids non-causality in physics and also the mathematical obstacles that hinders restriction of measured data to R+.

Even in case you rated my essay already low, I urgently ask to check my reasoning. The mistakes I refer to are located between mathematics and fzndamentals of physics.

Eckard Blumschein

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Steve Dufourny wrote on Apr. 3, 2020 @ 14:58 GMT
Hello Dr Guthery

I enjoyed your relevant essay , I agree with what you tell us about the mathematics and their importance for better physics. All seems a question of interpretations it seems to me and a kind of wisdom about this tool. I wish you all the best in this Contest, your essay merits to be very very well ranked , best regards

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Edwin Eugene Klingman wrote on Apr. 3, 2020 @ 19:21 GMT
Dear Scott B Guthery,

A wonderful essay, thanks. I enjoyed your first section on motivation, but I really enjoyed your 2.1 “the Role of Mathematical Proofs” as ’baked in tautologies’. I had never seen such a clear statement of this reality! And that this, in and of itself, can make no contribution to our understanding of the world around us.

You say this beautifully again:

“...no amount of computation will lead you to the discovery of a pattern in the physical world that wasn’t in the data in the first place.”

and

“...the output of a computational algorithm is by design and intent a re-expression of the input.”

Your statement s of irrelevance of each of the ‘un’s are concise and clear [and agree with my essay.]

You have clearly put much effort into understanding the issues. And you express this beautifully.

I hope you find my essay as fascinating as I find yours: Deciding on the nature of time and space

Best regards and good luck!

Edwin Eugene Klingman

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John C Hodge wrote on Apr. 5, 2020 @ 17:34 GMT
You say "We need to create mathematics that serves the needs of today's physics..."

Agree and would suggest there are mathematics currently used the do this. The difficulty is that there are many more math concepts that introduce usefulness, even flawed, physical conclusions. "Flawed" in the sense that experiment rejected the conclusion. However, the flaw may be in the physics postulates rather than the math. So, the physics community may outline the acceptable math assumptions and operations. This is my paper -"...determine the characteristics of the mathematics that is needed to support an emerging theory..."

Use of other math than physically useful does create knowledge which will be rejected by observation. You list examples. The major problem is that time and resources are wasted in discussing such models.

I disagree with your suggestion that only rational numbers (which are a count of standard units) should be used. I suggest Cardinal numbers. Irrational numbers can be used to a number of significant digits greater than the measurement uncertainty. Many irrational numbers result from converting geometrical relations to algebraic notation such as pi which is part of physics.

I like your approach to algorithms and enumeration.

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John David Crowell wrote on Apr. 9, 2020 @ 15:45 GMT
Scott. Interesting essay. I may have “discovered“ a solution to the problem. In my essay”Clarification of Physics....” I describe a Successful Self Creation process that creates its own mathematics as it progresses from chaos to the creation of the universe and its contents. The “created mathematics” fit the self creation methods. Thereby, creating a mathematics that can be used to describe the resulting universe, its contents and their measurements. I would appreciate comments based on your perspective on my essay. John Crowell

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Israel Perez wrote on Apr. 16, 2020 @ 05:02 GMT
Dear Scott

Thanks for your essay which I found it very illuminating. You are definitely right that pure math is completely disconnected from sciences; and it is hard to find a connection. As far as I know, there is a field of math, called applied mathematics whose aim is to see how math can be applied to other sciences. Although, as you say, it would be a waste of time, trying to find the math required to describe a phenomenon.

Mathematics can be seen as a language but language goes beyond a set of symbols and grammatical rules. Perhaps, you may find my essay interesting, since I also discuss how physicists have been lost in mathematical structures with a poor physical insight. The right math can not only be the right language but the right understanding of a phenomenon.

Good luck in the contest!

Regards

Israel Perez

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Boris Egorov wrote on Apr. 18, 2020 @ 11:07 GMT
Dear Scott,

I agree with you that math is a language and should supplement physics but not vice versa. I think that math can be made more physical.

I wish you good luck

Boris

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Charles John Sven wrote on Apr. 24, 2020 @ 15:43 GMT
Greetings Scott Guthery

ADAPT MATHEMATICS TO SCIENCE,NOT SCIENCE TO MATHEMATICS

From your last paragraph:

“…the disconnect between the current output of the research mathematics community and the needs of the physical science community.”

I must submit that math can and does obstruct –

especially when that math describes things not observed in real life that becomes the basis of physics – as in de Sitter’s expanding space – Friedman’s creation of the world from nothing – and Lemaître notation – “If the world has begun with a single quantum…” these all obscure applicable common 3D physics hiding the physics of the Big Bang.

It is proposed that any evidence describing the Big Bang is beyond science’s reach and yet this essay of mine entered January 18th“Common 3D Physics Depicts Universe Emerging From Chaos” presents a plausible explanation with plenty of current replicable evidence describing ‘Reality.’ Check it out.

Regards

Charles Sven

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Manfred U.E. Pohl wrote on May. 5, 2020 @ 16:31 GMT
Dear Scott Guthery,

i enjoyed your essay a lot. I agree much on your statement about rational numbers.

Although in the pysical theories are "flaws" too, but they are effect of physicist being conditioned to use wrong mathematics.

To me it looks like we must at least go back to Pythagoras Mathematics, but scientific community is in fear to do so, because physics and mathematics then become connected to political influence and economic system.

Physics about space and time is Philosophy ... not attached to Reality (physical)

"Physical" Physics is different mathematics, as each number (each °1°) must be connected to a "measurement" (empirical data).

irrational mathematics : 1+1=2 ???

rational mathematics :

1+1=1 (1 bread + 1 butter = 1 small meal)

1+1+1+1+1 = 1 (1 bread + 1 butter + 1 egg + 1 orange juice = 1 big meal.

one can find 1 piece of butter and create 1/3 + 1/3 + 1/3 = 3* 1/3 = 1 Piece

same concept is possible for Astronomy:

one find one sphere (sky) and can find 4 (or 4 Million) stars (shining objects) and use them as 4 million "clocks". Using them, there a 4 (million) different times at the same time.

in general, (as said by others too) "math" is our universal language and also "animals" are using maths as language: They use "waves" (sound, EM) to communicate.

Our mathematics (language-puzelling might be completely disconnected from physics at least for 2020 years.

Best wishes

Manfred Pohl

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Eckard Blumschein wrote on May. 6, 2020 @ 01:03 GMT
Dear Scott Guthery,

Do mathematicians like you consider a reference point an irrelevant detail because it is considered outside pure mathematics?

Eckard Blumschein

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Alyssa Adams wrote on May. 11, 2020 @ 02:12 GMT
Hi Dr. Guthery!

This is an excellent point, that math should be driven by physical observations! I definitely agree with this. Our models should inform us about the world around us, but we should also let the world around us inform us about new models. Actually, this is why I was so happy to be a data scientist for a few years! It gave me a very good perspective on the data-driven world and the advantages it has to offer. Now returning back to academia, I see a very big need for a two-way street between models and observations! It seems like it should be an iterative process between refining models and giving a causal explanation to data.

Cheers!

Alyssa

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Alan M. Kadin wrote on May. 15, 2020 @ 00:26 GMT
Dear Dr.Guthrie,

Let me suggest another topic that applied mathematicians should address: Nonlinear dynamics.

In particular, I believe that the behavior of solitons is central to a proper understanding of quantum mechanics, and solitons can occur only in certain nonlinear differential equations.

Note that the entire Hilbert space formalism of orthodox quantum theory is based on linearity. Linear algebra is well known as a powerful mathematical tool, but it does not apply to nonlinear systems.

In my own essay, ”The Uncertain Future of Physics and Computing”, I point out that an electron can be presented as a soliton-like wave, rather than a statistical distribution of point particles. The exclusion principle can be understood as a classical soliton-soliton interaction, rather than as a mysterious entanglement in Hilbert space. But we need the mathematics to address this.

Alan Kadin

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