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How can mindless mathematical laws give rise to aims and intention?
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Previous Contests
What Is “Fundamental”
October 28, 2017 to January 22, 2018
Sponsored by the Fetzer Franklin Fund and The Peter & Patricia Gruber Foundation
read/discuss • winners
Wandering Towards a Goal
How can mindless mathematical laws give rise to aims and intention?
December 2, 2016 to March 3, 2017
Contest Partner: The Peter and Patricia Gruber Fund.
read/discuss • winners
Trick or Truth: The Mysterious Connection Between Physics and Mathematics
Contest Partners: Nanotronics Imaging, The Peter and Patricia Gruber Foundation, and The John Templeton Foundation
Media Partner: Scientific American
read/discuss • winners
How Should Humanity Steer the Future?
January 9, 2014 - August 31, 2014
Contest Partners: Jaan Tallinn, The Peter and Patricia Gruber Foundation, The John Templeton Foundation, and Scientific American
read/discuss • winners
It From Bit or Bit From It
March 25 - June 28, 2013
Contest Partners: The Gruber Foundation, J. Templeton Foundation, and Scientific American
read/discuss • winners
Questioning the Foundations
Which of Our Basic Physical Assumptions Are Wrong?
May 24 - August 31, 2012
Contest Partners: The Peter and Patricia Gruber Foundation, SubMeta, and Scientific American
read/discuss • winners
Is Reality Digital or Analog?
November 2010 - February 2011
Contest Partners: The Peter and Patricia Gruber Foundation and Scientific American
read/discuss • winners
What's Ultimately Possible in Physics?
May - October 2009
Contest Partners: Astrid and Bruce McWilliams
read/discuss • winners
The Nature of Time
August - December 2008
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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...
RECENT FORUM POSTS
Georgina Woodward: "Robert, I though there was a problem with sorting the particles, that being..." in The Nature of Time
Eckard Blumschein: "Rob, You wrote: "Stern-Gerlach experiments do not "orient a particles..." in The Nature of Time
Sunil Sharma: "Really very happy to say,your post is very interesting to read. Online..." in FQXi'ers Debate the Deep...
Joe Fisher: "Dear Dr. Kuhn, Today’s Closer To Truth Facebook page contained this..." in Gravity's Residue
Roger Fedrer: "If people can act as individual agents,"—with free will—"this will..." in Constructing a Theory of...
Roger Fedrer: "Are you still facing any issue then check this website I hope you'll get..." in YouTube Video Lectures:...
Joe Fisher: "Dear Reality Fans, Any sensible person should know that reality could only..." in Gravity's Residue
Steve Dufourny: "After all if we want to unify G c and h , the general relativity with the..." in YouTube Video Lectures:...
RECENT ARTICLES
click titles to read articles
Gravity's Residue
An unusual approach to unifying the laws of physics could solve Hawking's black-hole information paradox—and its predicted gravitational "memory effect" could be picked up by LIGO.
Could Mind Forge the Universe?
Objective reality, and the laws of physics themselves, emerge from our observations, according to a new framework that turns what we think of as fundamental on its head.
Dissolving Quantum Paradoxes
The impossibility of building a perfect clock could help explain away microscale weirdness.
Constructing a Theory of Life
An all-encompassing framework of physics could help to explain the evolution of consciousness, intelligence, and free will.
Usurping Quantum Theory
The search is on for a fundamental framework that allows for even stranger links between particles than quantum theory—which could lead us to a theory of everything.
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...
RECENT FORUM POSTS
Georgina Woodward: "Robert, I though there was a problem with sorting the particles, that being..." in The Nature of Time
Eckard Blumschein: "Rob, You wrote: "Stern-Gerlach experiments do not "orient a particles..." in The Nature of Time
Sunil Sharma: "Really very happy to say,your post is very interesting to read. Online..." in FQXi'ers Debate the Deep...
Joe Fisher: "Dear Dr. Kuhn, Today’s Closer To Truth Facebook page contained this..." in Gravity's Residue
Roger Fedrer: "If people can act as individual agents,"—with free will—"this will..." in Constructing a Theory of...
Roger Fedrer: "Are you still facing any issue then check this website I hope you'll get..." in YouTube Video Lectures:...
Joe Fisher: "Dear Reality Fans, Any sensible person should know that reality could only..." in Gravity's Residue
Steve Dufourny: "After all if we want to unify G c and h , the general relativity with the..." in YouTube Video Lectures:...
RECENT ARTICLES
click titles to read articles
Gravity's Residue
An unusual approach to unifying the laws of physics could solve Hawking's black-hole information paradox—and its predicted gravitational "memory effect" could be picked up by LIGO.
Could Mind Forge the Universe?
Objective reality, and the laws of physics themselves, emerge from our observations, according to a new framework that turns what we think of as fundamental on its head.
Dissolving Quantum Paradoxes
The impossibility of building a perfect clock could help explain away microscale weirdness.
Constructing a Theory of Life
An all-encompassing framework of physics could help to explain the evolution of consciousness, intelligence, and free will.
Usurping Quantum Theory
The search is on for a fundamental framework that allows for even stranger links between particles than quantum theory—which could lead us to a theory of everything.
FQXi FORUM
February 21, 2019
CATEGORY:
Trick or Truth Essay Contest (2015)
[back]
TOPIC: On the Origin of Unreasonable Abstraction by Marni Dee Sheppeard [refresh]
TOPIC: On the Origin of Unreasonable Abstraction by Marni Dee Sheppeard [refresh]
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.
Download Essay PDF File
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.
Download Essay PDF File
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
report post as inappropriate
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
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.
report post as inappropriate
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.
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
report post as inappropriate
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
Thanks for sharing this Marni,
As usual, you bring a perspective it's hard to find anywhere else.
Regards,
Jonathan
report post as inappropriate
As usual, you bring a perspective it's hard to find anywhere else.
Regards,
Jonathan
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