Re: [math-fun] fine structure constant, Pi, euler formula and approximations : Atiyah paper on the F.S. constant
How can it be possible for a proof of RH to be so short? As an aside, these Todd polynomials have some pretty interesting properties for approximating stuff, so they must have been utilized for other things already, right?? At 10:43 AM 9/25/2018, Fred Lunnon wrote:
The text of MFA's Monday lecture (weirdly unreadable on YouTube) is at https://drive.google.com/file/d/17NBICP6OcUSucrXKNWvzLmrQpfUrEKuY/view
Generally speaking, even when a paper is concerned with a topic of which I know next to nothing, I can very quickly form an impression of whether it is ground-breaking, authoritative, pedestrian, amateurish, crackpot, etc.
But not on this occasion ... WFL
On 9/25/18, Simon Plouffe <simon.plouffe@gmail.com> wrote:
Hello,
I have found the article of Atiyah about the Todd function and the fine structure constant, in this paper Atiyah reinvent Euler's Formula : exp(I*Pi) + 1 = 0 in a very surprising way.
https://drive.google.com/file/d/1WPsVhtBQmdgQl25_evlGQ1mmTQE0Ww4a/view
If you can't get it, I made a copy here: plouffe.fr/2018-The_Fine_Structure_Constant.pdf
Bonne lecture, best regards,
Simon Plouffe
Erm --- bottom of page 1 in https://drive.google.com/file/d/1WPsVhtBQmdgQl25_evlGQ1mmTQE0Ww4a/view << factors of Type II in which dimensions take all (positive) real values, >> Alright, I'll buy it: where can I find an example of a C*-algebra with finite non-integer dimension? (Only another 16 pages ...) WFL On 9/25/18, Henry Baker <hbaker1@pipeline.com> wrote:
How can it be possible for a proof of RH to be so short?
As an aside, these Todd polynomials have some pretty interesting properties for approximating stuff, so they must have been utilized for other things already, right??
At 10:43 AM 9/25/2018, Fred Lunnon wrote:
The text of MFA's Monday lecture (weirdly unreadable on YouTube) is at https://drive.google.com/file/d/17NBICP6OcUSucrXKNWvzLmrQpfUrEKuY/view
Generally speaking, even when a paper is concerned with a topic of which I know next to nothing, I can very quickly form an impression of whether it is ground-breaking, authoritative, pedestrian, amateurish, crackpot, etc.
But not on this occasion ... WFL
On 9/25/18, Simon Plouffe <simon.plouffe@gmail.com> wrote:
Hello,
I have found the article of Atiyah about the Todd function and the fine structure constant, in this paper Atiyah reinvent Euler's Formula : exp(I*Pi) + 1 = 0 in a very surprising way.
https://drive.google.com/file/d/1WPsVhtBQmdgQl25_evlGQ1mmTQE0Ww4a/view
If you can't get it, I made a copy here: plouffe.fr/2018-The_Fine_Structure_Constant.pdf
Bonne lecture, best regards,
Simon Plouffe
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
He's referring to von Neumann's Continuous Geometry: https://en.wikipedia.org/wiki/Continuous_geometry On Tue, Sep 25, 2018 at 6:10 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Erm --- bottom of page 1 in https://drive.google.com/file/d/1WPsVhtBQmdgQl25_evlGQ1mmTQE0Ww4a/view << factors of Type II in which dimensions take all (positive) real values,
Alright, I'll buy it: where can I find an example of a C*-algebra with finite non-integer dimension? (Only another 16 pages ...)
WFL
On 9/25/18, Henry Baker <hbaker1@pipeline.com> wrote:
How can it be possible for a proof of RH to be so short?
As an aside, these Todd polynomials have some pretty interesting properties for approximating stuff, so they must have been utilized for other things already, right??
At 10:43 AM 9/25/2018, Fred Lunnon wrote:
The text of MFA's Monday lecture (weirdly unreadable on YouTube) is at https://drive.google.com/file/d/17NBICP6OcUSucrXKNWvzLmrQpfUrEKuY/view
Generally speaking, even when a paper is concerned with a topic of which I know next to nothing, I can very quickly form an impression of whether it is ground-breaking, authoritative, pedestrian, amateurish, crackpot, etc.
But not on this occasion ... WFL
On 9/25/18, Simon Plouffe <simon.plouffe@gmail.com> wrote:
Hello,
I have found the article of Atiyah about the Todd function and the fine structure constant, in this paper Atiyah reinvent Euler's Formula : exp(I*Pi) + 1 = 0 in a very surprising way.
https://drive.google.com/file/d/1WPsVhtBQmdgQl25_evlGQ1mmTQE0Ww4a/view
If you can't get it, I made a copy here: plouffe.fr/2018-The_Fine_Structure_Constant.pdf
Bonne lecture, best regards,
Simon Plouffe
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
So these "dimensions" (sic) are potentially infinite in everyday terms, rescaled (as it were) so that the "dimension" of the entire space equals unity; I'm guessing this is somehow connected to formalising quantum-theoretic renormalisation? WFL On 9/26/18, Tom Duff <td@pixar.com> wrote:
He's referring to von Neumann's Continuous Geometry: https://en.wikipedia.org/wiki/Continuous_geometry
On Tue, Sep 25, 2018 at 6:10 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Erm --- bottom of page 1 in
https://drive.google.com/file/d/1WPsVhtBQmdgQl25_evlGQ1mmTQE0Ww4a/view << factors of Type II in which dimensions take all (positive) real values,
Alright, I'll buy it: where can I find an example of a C*-algebra with finite non-integer dimension? (Only another 16 pages ...)
WFL
On 9/25/18, Henry Baker <hbaker1@pipeline.com> wrote:
How can it be possible for a proof of RH to be so short?
As an aside, these Todd polynomials have some pretty interesting properties for approximating stuff, so they must have been utilized for other things already, right??
At 10:43 AM 9/25/2018, Fred Lunnon wrote:
The text of MFA's Monday lecture (weirdly unreadable on YouTube) is at https://drive.google.com/file/d/17NBICP6OcUSucrXKNWvzLmrQpfUrEKuY/view
Generally speaking, even when a paper is concerned with a topic of which I know next to nothing, I can very quickly form an impression of whether it is ground-breaking, authoritative, pedestrian, amateurish, crackpot, etc.
But not on this occasion ... WFL
On 9/25/18, Simon Plouffe <simon.plouffe@gmail.com> wrote:
Hello,
I have found the article of Atiyah about the Todd function and the fine structure constant, in this paper Atiyah reinvent Euler's Formula : exp(I*Pi) + 1 = 0 in a very surprising way.
https://drive.google.com/file/d/1WPsVhtBQmdgQl25_evlGQ1mmTQE0Ww4a/view
If you can't get it, I made a copy here: plouffe.fr/2018-The_Fine_Structure_Constant.pdf
Bonne lecture, best regards,
Simon Plouffe
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Hoping to get to page 2 any day now ... << In particular there appeared to be no quaternionic version of Euler's formula >> What is this supposed to mean? Euler's formula is just as true in |H as in |C ! WFL On 9/26/18, Fred Lunnon <fred.lunnon@gmail.com> wrote:
So these "dimensions" (sic) are potentially infinite in everyday terms, rescaled (as it were) so that the "dimension" of the entire space equals unity; I'm guessing this is somehow connected to formalising quantum-theoretic renormalisation?
WFL
On 9/26/18, Tom Duff <td@pixar.com> wrote:
He's referring to von Neumann's Continuous Geometry: https://en.wikipedia.org/wiki/Continuous_geometry
On Tue, Sep 25, 2018 at 6:10 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Erm --- bottom of page 1 in
https://drive.google.com/file/d/1WPsVhtBQmdgQl25_evlGQ1mmTQE0Ww4a/view << factors of Type II in which dimensions take all (positive) real values,
Alright, I'll buy it: where can I find an example of a C*-algebra with finite non-integer dimension? (Only another 16 pages ...)
WFL
On 9/25/18, Henry Baker <hbaker1@pipeline.com> wrote:
How can it be possible for a proof of RH to be so short?
As an aside, these Todd polynomials have some pretty interesting properties for approximating stuff, so they must have been utilized for other things already, right??
At 10:43 AM 9/25/2018, Fred Lunnon wrote:
The text of MFA's Monday lecture (weirdly unreadable on YouTube) is at https://drive.google.com/file/d/17NBICP6OcUSucrXKNWvzLmrQpfUrEKuY/view
Generally speaking, even when a paper is concerned with a topic of which I know next to nothing, I can very quickly form an impression of whether it is ground-breaking, authoritative, pedestrian, amateurish, crackpot, etc.
But not on this occasion ... WFL
On 9/25/18, Simon Plouffe <simon.plouffe@gmail.com> wrote:
Hello,
I have found the article of Atiyah about the Todd function and the fine structure constant, in this paper Atiyah reinvent Euler's Formula : exp(I*Pi) + 1 = 0 in a very surprising way.
https://drive.google.com/file/d/1WPsVhtBQmdgQl25_evlGQ1mmTQE0Ww4a/view
If you can't get it, I made a copy here: plouffe.fr/2018-The_Fine_Structure_Constant.pdf
Bonne lecture, best regards,
Simon Plouffe
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Can anyone make head or tail of Atiyah’s article? I looked in vain for a clear statement of how to calculate the fine structure constant, which would be great whether or not it has anything to do with the Riemann hypothesis. But paragraphs like "The value of ð(n) that emerges from these calculations varies with the arithmetic mod 16 of the starting point. To eliminate this variation, we should start with 0 mod 16, so that we get unbroken blocks. Musicians, following Pythagoras, will notice the close analogy with octaves in both major and minor keys. Our starting point, to avoid dissonance, should be the key of C major.” ...seem completely hallucinatory. - Cris
On Sep 25, 2018, at 4:22 PM, Henry Baker <hbaker1@pipeline.com> wrote:
How can it be possible for a proof of RH to be so short?
As an aside, these Todd polynomials have some pretty interesting properties for approximating stuff, so they must have been utilized for other things already, right??
At 10:43 AM 9/25/2018, Fred Lunnon wrote:
The text of MFA's Monday lecture (weirdly unreadable on YouTube) is at https://drive.google.com/file/d/17NBICP6OcUSucrXKNWvzLmrQpfUrEKuY/view
Generally speaking, even when a paper is concerned with a topic of which I know next to nothing, I can very quickly form an impression of whether it is ground-breaking, authoritative, pedestrian, amateurish, crackpot, etc.
But not on this occasion ... WFL
On 9/25/18, Simon Plouffe <simon.plouffe@gmail.com> wrote:
Hello,
I have found the article of Atiyah about the Todd function and the fine structure constant, in this paper Atiyah reinvent Euler's Formula : exp(I*Pi) + 1 = 0 in a very surprising way.
https://drive.google.com/file/d/1WPsVhtBQmdgQl25_evlGQ1mmTQE0Ww4a/view
If you can't get it, I made a copy here: plouffe.fr/2018-The_Fine_Structure_Constant.pdf
Bonne lecture, best regards,
Simon Plouffe
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On the assumption that the answer to that question is negative, progress may yet be possible via pooling the resources of a hive mind of determined and capable specialists to unpack the substantial amount of context which evidently lurks behind these superficially naïve assertions. Suggestions, anybody? WFL On 9/26/18, Cris Moore <moore@santafe.edu> wrote:
Can anyone make head or tail of Atiyah’s article? I looked in vain for a clear statement of how to calculate the fine structure constant, which would be great whether or not it has anything to do with the Riemann hypothesis. But paragraphs like
"The value of ð(n) that emerges from these calculations varies with the arithmetic mod 16 of the starting point. To eliminate this variation, we should start with 0 mod 16, so that we get unbroken blocks. Musicians, following Pythagoras, will notice the close analogy with octaves in both major and minor keys. Our starting point, to avoid dissonance, should be the key of C major.”
...seem completely hallucinatory.
- Cris
On Sep 25, 2018, at 4:22 PM, Henry Baker <hbaker1@pipeline.com> wrote:
How can it be possible for a proof of RH to be so short?
As an aside, these Todd polynomials have some pretty interesting properties for approximating stuff, so they must have been utilized for other things already, right??
At 10:43 AM 9/25/2018, Fred Lunnon wrote:
The text of MFA's Monday lecture (weirdly unreadable on YouTube) is at https://drive.google.com/file/d/17NBICP6OcUSucrXKNWvzLmrQpfUrEKuY/view
Generally speaking, even when a paper is concerned with a topic of which I know next to nothing, I can very quickly form an impression of whether it is ground-breaking, authoritative, pedestrian, amateurish, crackpot, etc.
But not on this occasion ... WFL
On 9/25/18, Simon Plouffe <simon.plouffe@gmail.com> wrote:
Hello,
I have found the article of Atiyah about the Todd function and the fine structure constant, in this paper Atiyah reinvent Euler's Formula : exp(I*Pi) + 1 = 0 in a very surprising way.
https://drive.google.com/file/d/1WPsVhtBQmdgQl25_evlGQ1mmTQE0Ww4a/view
If you can't get it, I made a copy here: plouffe.fr/2018-The_Fine_Structure_Constant.pdf
Bonne lecture, best regards,
Simon Plouffe
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
http://www.preposterousuniverse.com/blog/2018/09/25/atiyah-and-the-fine-stru... On Wed, Sep 26, 2018 at 10:53 AM Cris Moore <moore@santafe.edu> wrote:
Can anyone make head or tail of Atiyah’s article? I looked in vain for a clear statement of how to calculate the fine structure constant, which would be great whether or not it has anything to do with the Riemann hypothesis. But paragraphs like
"The value of ð(n) that emerges from these calculations varies with the arithmetic mod 16 of the starting point. To eliminate this variation, we should start with 0 mod 16, so that we get unbroken blocks. Musicians, following Pythagoras, will notice the close analogy with octaves in both major and minor keys. Our starting point, to avoid dissonance, should be the key of C major.”
...seem completely hallucinatory.
- Cris
On Sep 25, 2018, at 4:22 PM, Henry Baker <hbaker1@pipeline.com> wrote:
How can it be possible for a proof of RH to be so short?
As an aside, these Todd polynomials have some pretty interesting properties for approximating stuff, so they must have been utilized for other things already, right??
At 10:43 AM 9/25/2018, Fred Lunnon wrote:
The text of MFA's Monday lecture (weirdly unreadable on YouTube) is at https://drive.google.com/file/d/17NBICP6OcUSucrXKNWvzLmrQpfUrEKuY/view
Generally speaking, even when a paper is concerned with a topic of which I know next to nothing, I can very quickly form an impression of whether it is ground-breaking, authoritative, pedestrian, amateurish, crackpot, etc.
But not on this occasion ... WFL
On 9/25/18, Simon Plouffe <simon.plouffe@gmail.com> wrote:
Hello,
I have found the article of Atiyah about the Todd function and the fine structure constant, in this paper Atiyah reinvent Euler's Formula : exp(I*Pi) + 1 = 0 in a very surprising way.
https://drive.google.com/file/d/1WPsVhtBQmdgQl25_evlGQ1mmTQE0Ww4a/view
If you can't get it, I made a copy here: plouffe.fr/2018-The_Fine_Structure_Constant.pdf
Bonne lecture, best regards,
Simon Plouffe
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.math.ucr.edu/~mike http://reperiendi.wordpress.com
Ah well, I didn't entirely waste my time --- I learnt about von Neumann algebras; and I might even manage to understand renormalisation at last. WFL On 9/26/18, Mike Stay <metaweta@gmail.com> wrote:
http://www.preposterousuniverse.com/blog/2018/09/25/atiyah-and-the-fine-stru... On Wed, Sep 26, 2018 at 10:53 AM Cris Moore <moore@santafe.edu> wrote:
Can anyone make head or tail of Atiyah’s article? I looked in vain for a clear statement of how to calculate the fine structure constant, which would be great whether or not it has anything to do with the Riemann hypothesis. But paragraphs like
"The value of ð(n) that emerges from these calculations varies with the arithmetic mod 16 of the starting point. To eliminate this variation, we should start with 0 mod 16, so that we get unbroken blocks. Musicians, following Pythagoras, will notice the close analogy with octaves in both major and minor keys. Our starting point, to avoid dissonance, should be the key of C major.”
...seem completely hallucinatory.
- Cris
On Sep 25, 2018, at 4:22 PM, Henry Baker <hbaker1@pipeline.com> wrote:
How can it be possible for a proof of RH to be so short?
As an aside, these Todd polynomials have some pretty interesting properties for approximating stuff, so they must have been utilized for other things already, right??
At 10:43 AM 9/25/2018, Fred Lunnon wrote:
The text of MFA's Monday lecture (weirdly unreadable on YouTube) is at https://drive.google.com/file/d/17NBICP6OcUSucrXKNWvzLmrQpfUrEKuY/view
Generally speaking, even when a paper is concerned with a topic of which I know next to nothing, I can very quickly form an impression of whether it is ground-breaking, authoritative, pedestrian, amateurish, crackpot, etc.
But not on this occasion ... WFL
On 9/25/18, Simon Plouffe <simon.plouffe@gmail.com> wrote:
Hello,
I have found the article of Atiyah about the Todd function and the fine structure constant, in this paper Atiyah reinvent Euler's Formula : exp(I*Pi) + 1 = 0 in a very surprising way.
https://drive.google.com/file/d/1WPsVhtBQmdgQl25_evlGQ1mmTQE0Ww4a/view
If you can't get it, I made a copy here: plouffe.fr/2018-The_Fine_Structure_Constant.pdf
Bonne lecture, best regards,
Simon Plouffe
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.math.ucr.edu/~mike http://reperiendi.wordpress.com
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (5)
-
Cris Moore -
Fred Lunnon -
Henry Baker -
Mike Stay -
Tom Duff