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FQXi FORUM

February 23, 2018

CATEGORY:
Trick or Truth Essay Contest (2015)
[back]

TOPIC: Demistifying the astonishing success of mathematics: the case of gauge symmetry by Aldo Filomeno [refresh]

TOPIC: Demistifying the astonishing success of mathematics: the case of gauge symmetry by Aldo Filomeno [refresh]

This paper argues against a strong philosophical interpretation of the leading role of mathematics in all of physics. To do so the paper focuses on a specific case study, that of the truly astonishing success of symmetry groups in modern particle physics. Specifically, I analyze the case of one local gauge symmetry, that of the strong nuclear interaction. I would say this is an especially pertinent case study, as gauge symmetry applies throughout most of our current best fundamental physics and the intimate relation with the physics it describes is particularly astonishing. The paper advocates for an understanding of mathematics only as an (especially appropriate) language which does nothing but describe patterns, a subset of which are instantiated in Nature. With such an understanding I argue that the effectiveness of mathematics is not unreasonable; on the contrary, it is to be expected. Such an explanation undermines the viewpoint that takes gauge symmetry principles as a priori reasonable or as some sort of necessary meta-laws. Likewise, such an explanation weakens the reasons to endorse a strong ontological commitment to the mathematical entities (as the diverse variants that suggest that the universe is fundamentally mathematical, like [Tegmark, 2014] or [French, 2014]).

From March 2015 Aldo Filomeno will join the UNAM at Mexico DF as a postdoctoral researcher in philosophy. He defended last October his PhD in Philosophy of science. His thesis dealt with the notion of law of nature and is entitled: "On the possibility of stable regularities without assuming fundamental laws". Previously he studied engineering of telecommunications and philosophy. More details of his research can be found on: https://unam.academia.edu/AldoFilomeno

Dear Aldo Filomeno,

While many essays speak of Grothendieck's 'dessin d'enfants', or the Langlands program, or the Monster group, etc. in hopes that these will answer some questions, you address probably the most significant mathematics of the last 60 years, gauge theory – and you properly put it in its place.

As no other general field of math has had the impact on physics as has...

view entire post

While many essays speak of Grothendieck's 'dessin d'enfants', or the Langlands program, or the Monster group, etc. in hopes that these will answer some questions, you address probably the most significant mathematics of the last 60 years, gauge theory – and you properly put it in its place.

As no other general field of math has had the impact on physics as has...

view entire post

report post as inappropriate

Dear Eugene Klingman,

I very much appreciate your compliments and especially the comments.

Your point about the inexactitude of the symmetries seems to me particularly appealing: scientific or philosophical research should be carried out pursuing this line. So far I do not know which side I would bet on. I envisage arguments refusing the importance of such inexactitudes as well as arguments that might employ such inexactitudes against a too idealized view of the laws of nature.

I also agree that one could interpret symmetries and conservation principles as you suggest (being the latter more fundamental). Then, we face questions regarding the conservation principles: Are they a plausible unexplained primitive of our ontology, or should the postulation of the conservation of some property be somehow explained?

Finally, I'll read your essay which looks really interesting!

Warm regards,

Aldo Filomeno

I very much appreciate your compliments and especially the comments.

Your point about the inexactitude of the symmetries seems to me particularly appealing: scientific or philosophical research should be carried out pursuing this line. So far I do not know which side I would bet on. I envisage arguments refusing the importance of such inexactitudes as well as arguments that might employ such inexactitudes against a too idealized view of the laws of nature.

I also agree that one could interpret symmetries and conservation principles as you suggest (being the latter more fundamental). Then, we face questions regarding the conservation principles: Are they a plausible unexplained primitive of our ontology, or should the postulation of the conservation of some property be somehow explained?

Finally, I'll read your essay which looks really interesting!

Warm regards,

Aldo Filomeno

Dear Aldo Filomeno,

Your essay is an interesting and great read. My interest started with your question "Why is group theory so central to describing the physical world?" You introduce symmetry and spend time on SU(3) - "The color invariance is represented by the symmetry group SU(3), the Special Unitary group of degree 3". I have always been troubled by the naming these 3 properties "colors" and calling them Red, Blue and Green. Doesn't the subject require a better description of something so important and fundamental to world of hadrons?

My essay takes a very specific look at the SU(3) symmetry and extends the two properties (spin and handedness) of the electrons SU(2) symmetry to the world of hadrons and the SU(3) symmetry by adding a specific property of flow as the third property. I hope you get a chance to comment on it.

Finally, your comment "The ”unreasonable” success of symmetry principles in physics" begs an explanation and your essay makes a big contribution to the subject.

Regards and good luck in the contest.

Ed Unverricht

report post as inappropriate

Your essay is an interesting and great read. My interest started with your question "Why is group theory so central to describing the physical world?" You introduce symmetry and spend time on SU(3) - "The color invariance is represented by the symmetry group SU(3), the Special Unitary group of degree 3". I have always been troubled by the naming these 3 properties "colors" and calling them Red, Blue and Green. Doesn't the subject require a better description of something so important and fundamental to world of hadrons?

My essay takes a very specific look at the SU(3) symmetry and extends the two properties (spin and handedness) of the electrons SU(2) symmetry to the world of hadrons and the SU(3) symmetry by adding a specific property of flow as the third property. I hope you get a chance to comment on it.

Finally, your comment "The ”unreasonable” success of symmetry principles in physics" begs an explanation and your essay makes a big contribution to the subject.

Regards and good luck in the contest.

Ed Unverricht

report post as inappropriate

Dear Ed Unverricht,

thank you very much for your comments!

In principle, the property has been named 'color' as it could have been named in any other way. How we could have a better scientific description of such properties I do not know. Philosophers have historically struggled to better understand what are properties, but it is hard to attain an answer (as usual in philosophical matters). This reminds me of a paper from a great philosopher and physicist called Alyssa Ney entitled: "Are There Fundamental Intrinsic Properties?" (available online). Perhaps you enjoy it. (Let me know!)

I'll read your essay, it looks very pertinent to what I say!

Warm regards,

Aldo Filomeno

thank you very much for your comments!

In principle, the property has been named 'color' as it could have been named in any other way. How we could have a better scientific description of such properties I do not know. Philosophers have historically struggled to better understand what are properties, but it is hard to attain an answer (as usual in philosophical matters). This reminds me of a paper from a great philosopher and physicist called Alyssa Ney entitled: "Are There Fundamental Intrinsic Properties?" (available online). Perhaps you enjoy it. (Let me know!)

I'll read your essay, it looks very pertinent to what I say!

Warm regards,

Aldo Filomeno

Dear Aldo,

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

report post as inappropriate

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

report post as inappropriate

Dear Aldo Filomeno,

While I will not vote and not even comment on your essay because I seem to be at odds with mainstream. You wrote: "the acceptance of (A) is hardly disputable, (B) should be justified". If you had a look into my essays, you may hopefully understand why I consider from the perspective not of a mathematical model but of conjectured reality the acceptance of (A) hardly indisputable. Concerning symmetries, I observed that ideal symmetries tend to be mathematical artifacts that just reflect redundancies. Real symmetries are rarely or maybe never absolutely perfect. Isn't the harmonic oscillator an unphysical ideal? What is wrong with this view?

I should add that I maintain that I consider it unjustified to integrate in case of frequency analysis over available past and not yet written future data. Cosine transformation is evidently as good as Fourier transformation except for it omits an arbitrarily chosen zero.

Genuinely curious,

Eckard Blumschein

report post as inappropriate

While I will not vote and not even comment on your essay because I seem to be at odds with mainstream. You wrote: "the acceptance of (A) is hardly disputable, (B) should be justified". If you had a look into my essays, you may hopefully understand why I consider from the perspective not of a mathematical model but of conjectured reality the acceptance of (A) hardly indisputable. Concerning symmetries, I observed that ideal symmetries tend to be mathematical artifacts that just reflect redundancies. Real symmetries are rarely or maybe never absolutely perfect. Isn't the harmonic oscillator an unphysical ideal? What is wrong with this view?

I should add that I maintain that I consider it unjustified to integrate in case of frequency analysis over available past and not yet written future data. Cosine transformation is evidently as good as Fourier transformation except for it omits an arbitrarily chosen zero.

Genuinely curious,

Eckard Blumschein

report post as inappropriate

Dear Eckard,

thanks for your comments. Your essay looks interesting and original; I'll certainly read it when I have the time. As to your comments, I'm curious to see how you argue that (A), i.e. that the world displays spatiotemporal patterns, is hardly indisputable. How could it be disputed? I took it as a premise of my argument (an obvious statement but it was important to make it explicit for the clarification of my conclusion).

Your view of symmetries as informing of redundancies in the world is clearly one standard possible interpretation of them. I would say it is not incompatible at all with the moral I wanted to highlight in my paper (if any, it's in the same line), namely the lack of any special or necessary status of the laws of current physics.

(By the way I don't understand your last observation!)

When I read your paper I'll let you know, warm regards,

Aldo

thanks for your comments. Your essay looks interesting and original; I'll certainly read it when I have the time. As to your comments, I'm curious to see how you argue that (A), i.e. that the world displays spatiotemporal patterns, is hardly indisputable. How could it be disputed? I took it as a premise of my argument (an obvious statement but it was important to make it explicit for the clarification of my conclusion).

Your view of symmetries as informing of redundancies in the world is clearly one standard possible interpretation of them. I would say it is not incompatible at all with the moral I wanted to highlight in my paper (if any, it's in the same line), namely the lack of any special or necessary status of the laws of current physics.

(By the way I don't understand your last observation!)

When I read your paper I'll let you know, warm regards,

Aldo

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