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RECENT POSTS IN THIS TOPIC

jing boo: on 5/7/18 at 8:11am UTC, wrote Le mouvement d'horlogerie du mouvement de la montre mécanique fait tourner...

Phillip Helbig: on 4/22/15 at 9:25am UTC, wrote Thanks for the comments. I should have kept Sabine Hossenfelder's dictum...

Sylvia Wenmackers: on 4/21/15 at 20:30pm UTC, wrote Dear Phillip Helbig, I put your essay on my reading list, because you...

Armin Nikkhah Shirazi: on 4/21/15 at 7:11am UTC, wrote Dear Phillip, I just read your short essay and agree that mathematics in...

Joe Fisher: on 4/6/15 at 15:06pm UTC, wrote Dear Philip, I think Newton was wrong about abstract gravity; Einstein was...

Joe Fisher: on 3/11/15 at 19:47pm UTC, wrote Dear Dr. Helbig, You stated in the abstract of your essay: “I argue that...

Phillip Helbig: on 3/6/15 at 15:26pm UTC, wrote Thanks for the comments. There are certainly some contexts where it is...

Kevin Knuth: on 3/6/15 at 9:19am UTC, wrote Thank you for your interesting perspective on the relationship between...


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FQXi FORUM
October 22, 2019

CATEGORY: Trick or Truth Essay Contest (2015) [back]
TOPIC: Trick or truth, or just a treat? Is the connection between physics and mathematics mysterious? by Phillip Helbig [refresh]
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Author Phillip Helbig wrote on Feb. 28, 2015 @ 00:44 GMT
Essay Abstract

I argue that the connection between physics and mathematics has a simple, non-mysterious explanation, which also applies to connections between mathematics and other areas.

Author Bio

Phillip Helbig (b. 1964) has a (magna cum laude) degree in physics (major) and astronomy (minor) from the University of Hamburg. He has worked in cosmology at the Hamburg Observatory (University of Hamburg), Jodrell Bank (University of Manchester), and the Kapteyn Institute (University of Groningen). Other interests include Fortran, VMS, philology and linguistics, music, travel, photography, and cinema, financed via work as a systems analyst and database administrator (VMS and Rdb).

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Sujatha Jagannathan wrote on Feb. 28, 2015 @ 07:44 GMT
You probe connectivity in the up-holistic trend which classifies and differentiates from space-time.

Regards,

Miss. Sujatha Jagannathan

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Conrad Dale Johnson wrote on Feb. 28, 2015 @ 13:45 GMT
Phillip --

Your short essay explains the clear and simple connection between math and physics very nicely. Now it seems to me the evidence strongly indicates that there is in fact "true randomness at some level," so that not everything in the world can be explained by rules. But I don't see that this affects your explanation, that math will naturally be useful in describing whatever parts of the world do follow rules -- and of course that includes most of physics.

As to why rules exist in the physical world, and why so many different kinds of math are needed to describe them -- this is a problem I've tried to open up in my essay on semantics.

Thanks -- Conrad

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Author Phillip Helbig replied on Feb. 28, 2015 @ 13:52 GMT
I think the jury is still out on whether there is any real randomness in physical reality. In his book Our Mathematical Universe (worth reading even if you don't agree with the more speculative stuff), Tegmark makes a pretty good case for the lack of true randomness.

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Member Kevin H Knuth wrote on Mar. 6, 2015 @ 09:19 GMT
Thank you for your interesting perspective on the relationship between mathematics and physics. I have argued that one of the critical aspects of mathematics is that of symmetry, which is a special case of the concept of rules. This is important at the end of your where part of your argument hinges on the idea that there is no true randomness.

This is a little difficult for me because I am a Jaynesian (for lack of a better descriptive word) in the sense that I do not conceive of "randomness" as representing a quality of the system. Instead, I conceive of randomness as representing my lack of knowledge about the system (to the point where I am unable to make predictions about the system). That being said, if we imagine that we have a system that is random, either in the sense that I intend or the sense in which I assume you intend, then because of its randomness, it still may possess symmetries, which are describable by mathematical rules. So I don't think that "true" randomness (or lack of) has much, if at all of anything, to do with the problem.

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Author Phillip Helbig replied on Mar. 6, 2015 @ 15:26 GMT
Thanks for the comments.

There are certainly some contexts where it is useful to think of randomness as "representing my lack of knowledge about the system". By "true randomness" I don't mean randomness in this sense, but, well, true randomness at a fundamental level, as in the Copenhagen interpretation of quantum mechanics. Whether or not this exists is, I think, an open question. Certainly Tegmark has argued that it does not exist.

One can certainly have rules which apply to randomness, chance, odds and so on, but these are qualitatively different from those of the "if a then b" type.

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Joe Fisher wrote on Mar. 11, 2015 @ 19:47 GMT
Dear Dr. Helbig,

You stated in the abstract of your essay: “I argue that the connection between physics and mathematics has a simple, non-mysterious explanation, which also applies to connections between mathematics and other areas.”

Accurate writing has enabled me to perfect a valid description of untangled unified reality: Proof exists that every real astronomer looking through...

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Joe Fisher wrote on Apr. 6, 2015 @ 15:06 GMT
Dear Philip,

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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Armin Nikkhah Shirazi wrote on Apr. 21, 2015 @ 07:11 GMT
Dear Phillip,

I just read your short essay and agree that mathematics in some sense "exists" in some realm for which "mathematical mindscape" is as good a label as any. In my view, part of the reason that some people have problems with platonism is that we use the same word, existence, to describe the being of mathematical objects, which is however, of a very different kind than the being of physical objects. Ideally, one should come up with a different word to denote these different senses of existence.

It is very perceptive of you to identify that what sets being in the physical sense apart from other others is almost always its close association with a particular location. Mathematical objects, dreams, ideas, perceptions and feelings seem to have in common that they lack such an association.

(As a short digression, note that the mainstream view that objects characterized by v=c, which are almost universally taken to physically exist, do not have rest frames has the probably unwelcome consequence that it lumps such objects together with those mentioned above, which is one reason I find this view inadequate [Instead I would say they have no spacetime rest frames, which is a different kind of statement even though under the current paradigm it sounds the same]).

I think your identification of the factor that both physics and mathematics happen to be formulable in terms of rules that can be applied across the fields is a big part of the picture that explains how they relate to each other, but I feel that you did not go far enough with your argument. Specifically, when you say "In summary, if there is no true randomness, then every process is determined by rules." I would reply that even if there is true randomness (and QM suggests that there is) every process is determined by rules, for random processes the rules may not be deterministic but we can still formulate probabilistic rules.

I do not think that the argument you gave exhausts all possible explanations for the effectiveness of mathematics in physics but does supply an important ingredient. Your writing style is also very clear and accessible, and this is greatly appreciated.

Best wishes,

Armin

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Member Sylvia Wenmackers wrote on Apr. 21, 2015 @ 20:30 GMT
Dear Phillip Helbig,

I put your essay on my reading list, because you indicate right away that you are a mathematical Platonist, a position which I do not share, but which I want to understand better.

One of the pieces of advice that Daniel Dennett gives in his book on tools for thinking is to pay close attention when an author presents something as "obvious". You find mathematical Platonism obvious, although you do give one argument: you claim that otherwise non-humans would have a different sort of mathematics. I don't see how this follows. First of all, most non-humans don't have mathematics at all. (Think of trees for instance; sure, we may describe many aspects of trees with mathematics, but they don't engage in developing mathematics.) Second, if you are considering non-human aliens that may have developed their own mathematics, then it remains to be seen what kind of mathematics they have (if we can recognize it as such in the first place). But it may well be similar to ours, because these organisms live in the same physical universe as we do and will likely be subjected to similar cognitive limitations.

You characterize mathematics as a set of rules, you state that the subjects we apply mathematics to (natural sciences, games, music) are characterized by rules, and that such rules are easy enough for humans to understand. Hence, it is not clear that Platonism does much work in the second part of your essay. On your analysis, doesn't the initial question boil down to how humans manage to understand rules, in particular in the natural sciences? So wouldn't a naturalistic explanation be more appropriate after all?

Best wishes,

Sylvia Wenmackers - Essay Children of the Cosmos

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Author Phillip Helbig replied on Apr. 22, 2015 @ 09:25 GMT
Thanks for the comments. I should have kept Sabine Hossenfelder's dictum in mind: "Saying it's obvious doesn't make it obvious". :-) On the other hand, just because I say it's obvious doesn't mean that it is not obvious. :-)

I'm sure that evolution has played a role in determining what type of rules we recognize, which we consider important, and so on. However, my view is still that these are "objectively real" and not just products conditioned by our own evolution. I'm sure that no alien intelligence (indeed, this is what I had in mind, not non-human beings on Earth) would claim that Fermat's last theorem is not true.

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