Adapt Mathematics to Science, Not Science to Mathematics by Scott Guthery

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

Dear Gupta ,

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

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

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

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

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.

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

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

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

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

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

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

Dear Scott Guthery,

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

Eckard Blumschein

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

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