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RECENT POSTS IN THIS TOPIC

Jonathan Dickau: on 3/20/15 at 3:14am UTC, wrote Thanks for sharing this Marni, As usual, you bring a perspective it's hard...

Edwin Klingman: on 3/13/15 at 18:00pm UTC, wrote Dear Marni Dee Sheppeard, Since MacLane and Birkhoff I have avoided the...

Michael Rios: on 3/10/15 at 6:15am UTC, wrote Marni It's a pleasure to read an essay from you. Charge quantization...

lutz kayser: on 3/8/15 at 3:07am UTC, wrote Dear Marni Dee, what you explain is for me a surprising and refreshing...

Marni Sheppeard: on 3/7/15 at 21:51pm UTC, wrote Essay Abstract Category theory is a type of mathematics that...


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FQXi FORUM
December 17, 2017

CATEGORY: Trick or Truth Essay Contest (2015) [back]
TOPIC: On the Origin of Unreasonable Abstraction by Marni Dee Sheppeard [refresh]
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Author Marni Dee Sheppeard wrote on Mar. 7, 2015 @ 21:51 GMT
Essay Abstract

Category theory is a type of mathematics that challenges us to rethink fundamental ideas about numbers, as experimental outcomes. Essential to quantum field theory, its role in gravity remains elusive. Such nonsense is introduced under the assumptions that (i) unification is a valid goal for physics and (ii) relativistic causality holds for local observables. Is fermionic spin analogous to Boolean truth? If so, we should remember that whatever is divided is also non separable, and this ultimate reality cares nought for all our vanity.

Author Bio

Marni grew up in Sydney and completed her BSc(Hons) in Physics in 1989. After years of tutoring, research and working in the real world, she returned to study in the 1990s, but was unfortunately forced to give it up again. Marni finally completed her PhD in Theoretical Physics in 2007, with a thesis on Quantum Logic. She currently resides in Auckland, and apologises for being unable to participate in online discussions.

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lutz kayser wrote on Mar. 8, 2015 @ 03:07 GMT
Dear Marni Dee,

what you explain is for me a surprising and refreshing upgrade of the Standard model of QM. You return to the fact, that we can give every ponderable object a flag and recognise it when required. This gives us hope that one day we can begin to understand QM.

Help us to end the frustration Longo described : "We understand QM when we have understood that there is nothing to understand".

Best

Lutz

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Michael Rios wrote on Mar. 10, 2015 @ 06:15 GMT
Marni

It's a pleasure to read an essay from you. Charge quantization indeed forces one into the countable. This allows lattices to play a more central role, and by doing quantum mechanics in this integral form, many (once murky) mathematical relationships become manifest.

Your linear topos thesis foreshadowed much of the motivic amplitude results one sees today. In such amplitudes particles are assigned to projective space points, which are idempotent morphisms in a magma-like structure.

Suppose we scatter n-(indistinguishable bosonic) particles and study the MHV amplitude in CP^3. Geometrically, the n-particles localize on a single copy of the projective space, on a curve of some given degree and genus. Any given individual particle is equivalent to another particle through an isometry that maps an idempotent to another idempotent. This is a higher level morphism, mapping idempotents to each other.

Going higher, one can map projective lines, or degree one genus zero curves to each other via collineations. It takes two idempotents to define a line, hence such morphisms map pairs of idempotents. By induction, in complex projective n-space, one can envision ever higher levels of k-idempotent maps, which map hyperplanes to each other. This is where the Grassmannian structure becomes obvious, and combinatorial structures like the amplituhedron organize the hyperplane configurations quite effectively.

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Edwin Eugene Klingman wrote on Mar. 13, 2015 @ 18:00 GMT
Dear Marni Dee Sheppeard,

Since MacLane and Birkhoff I have avoided the square logic map diagrams, but I nevertheless managed to find quite interesting remarks in your essay.

Your abstract states "all we can really do is count." I begin my essay (and other essays) based on counting as the prototypical logic machine, constructed from NOTs and AND 'gates' which are ubiquitous in physical reality and manifest at all levels, RNA/DNA/proteins to telomeres, to insects, crows, neurons, silicon, etc. It is also the case that the key quantum field theory operator is the Number operator, or counter. So, with Kronecker, counting seems to be the sufficient basis for "all the rest" of math.

You note of the Standard Model, which is poorly understood, that enormous effort went into maintaining locality, while quantum physics would abandon it. My essay offers a novel analysis of this problem, which a recent comment on my thread describes as having a "self-concealing nature", thus making it extremely hard for physicists to see the error in logic. It is not a mathematical error, but a mapping error.

I do not believe classical physics requires distinguishability of particles as you seem to suggest, although, as you further suggest "for truly non-separable concept of existence, we must reinterpret the continuum of C."

I'm sure I've missed some of the more subtle issues of your essay, but I hope you will read my essay and try to understand the subtlety within it.

Best regards,

Edwin Eugene Klingman

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Jonathan J. Dickau wrote on Mar. 20, 2015 @ 03:14 GMT
Thanks for sharing this Marni,

As usual, you bring a perspective it's hard to find anywhere else.

Regards,

Jonathan

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