If you are aware of an interesting new academic paper (that has been published in a peer-reviewed journal or has appeared on the arXiv), a conference talk (at an official professional scientific meeting), an external blog post (by a professional scientist) or a news item (in the mainstream news media), which you think might make an interesting topic for an FQXi blog post, then please contact us at forums@fqxi.org with a link to the original source and a sentence about why you think that the work is worthy of discussion. Please note that we receive many such suggestions and while we endeavour to respond to them, we may not be able to reply to all suggestions.

Please also note that we do not accept unsolicited posts and we cannot review, or open new threads for, unsolicited articles or papers. Requests to review or post such materials will not be answered. If you have your own novel physics theory or model, which you would like to post for further discussion among then FQXi community, then please add them directly to the "Alternative Models of Reality" thread, or to the "Alternative Models of Cosmology" thread. Thank you.

Please also note that we do not accept unsolicited posts and we cannot review, or open new threads for, unsolicited articles or papers. Requests to review or post such materials will not be answered. If you have your own novel physics theory or model, which you would like to post for further discussion among then FQXi community, then please add them directly to the "Alternative Models of Reality" thread, or to the "Alternative Models of Cosmology" thread. Thank you.

Contests Home

Current Essay Contest

*Contest Partners: Nanotronics Imaging, The Peter and Patricia Gruber Foundation, and The John Templeton Foundation*

Media Partner: Scientific American

Previous Contests

**Undecidability, Uncomputability, and Unpredictability Essay Contest**

*December 24, 2019 - April 24, 2020*

Contest Partners: Fetzer Franklin Fund, and The Peter and Patricia Gruber Foundation

read/discuss • winners

**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*

read/discuss • winners

Current Essay Contest

Media Partner: Scientific American

Previous Contests

Contest Partners: Fetzer Franklin Fund, and The Peter and Patricia Gruber Foundation

read/discuss • winners

read/discuss • winners

How can mindless mathematical laws give rise to aims and intention?

Contest Partner: The Peter and Patricia Gruber Fund.

read/discuss • winners

Media Partner: Scientific American

read/discuss • winners

read/discuss • winners

read/discuss • winners

Which of Our Basic Physical Assumptions Are Wrong?

read/discuss • winners

read/discuss • winners

read/discuss • winners

read/discuss • winners

Forum Home

Introduction

Terms of Use

RSS feed | RSS help

Introduction

Terms of Use

*Posts by the author are highlighted in orange; posts by FQXi Members are highlighted in blue.*

RSS feed | RSS help

RECENT POSTS IN THIS TOPIC

**Thomas Ray**: *on* 5/6/15 at 14:33pm UTC, wrote Some of my further work in the origin of probability Tom

**Vladimir Tamari**: *on* 4/25/15 at 4:20am UTC, wrote Thank you Tom for your kind words about my graphics. I do understand and...

**Thomas Ray**: *on* 4/24/15 at 8:03am UTC, wrote Dear Alma, A writer's greatest reward is to be understood. Thank you! I...

**Alma Ionescu**: *on* 4/23/15 at 17:22pm UTC, wrote Dear Tom, Since the reply button is still active so I’m back to tell you...

**Thomas Ray**: *on* 4/23/15 at 1:52am UTC, wrote Alma, Your essay is an absolute treasure, as I commented in your forum. ...

**Thomas Ray**: *on* 4/23/15 at 1:49am UTC, wrote Thanks, Akinbo. Looking forward to it. :-) You got my upvote, too. Best...

**Thomas Ray**: *on* 4/23/15 at 1:47am UTC, wrote Cristi, I'm honored. Thanks. Tom

**Cristinel Stoica**: *on* 4/22/15 at 21:00pm UTC, wrote Dear Tom, I kept some of the most beautiful essays for the end. Yours is...

RECENT FORUM POSTS

**Cabal Owen**: "I have learned this while my research - What are the types of BCI’s ..."
*in* Expanding the Mind...

**Georgina Woodward**: "Compare: "Wild', existentially free particle, unmeasured, unperturbed, in..."
*in* Quantum Physics and the...

**Georgina Woodward**: "1. The 'magic rabbit' does not come into being, upon the photo being seen...."
*in* Quantum Physics and the...

**Deserdi Chapas**: "Report on ongoing Holographic Physics work at deserdi.xyz As humanity has..."
*in* Alternative Models of...

**umair zaheer**: "Travel is the movement of people between distant geographical locations...."
*in* Anatomy of spacetime and...

**robin 435**: "rsvsfascxseaczcfadv"
*in* Anatomy of spacetime and...

**David Vognar**: "Electron Doping? by David Vognar I think it helps to visualize physics so..."
*in* The Present State of...

**Nick Fury**: "Hi, when you get older there is not a single part of your body that is..."
*in* Quantum Measurement and...

RECENT ARTICLES

*click titles to read articles*

**The Entropic Price of Building the Perfect Clock: Q&A with Natalia Ares**

Experiments investigating the thermodynamics of clocks can teach us about the origin of time's arrow.

**Schrödinger’s A.I. Could Test the Foundations of Reality**

Physicists lay out blueprints for running a 'Wigner's Friend' experiment using an artificial intelligence, built on a quantum computer, as an 'observer.'

**Expanding the Mind (Literally): Q&A with Karim Jerbi and Jordan O'Byrne**

Using a brain-computer interface to create a consciousness 'add-on' to help test Integrated Information Theory.

**Quanthoven's Fifth**

A quantum computer composes chart-topping music, programmed by physicists striving to understand consciousness.

**The Math of Consciousness: Q&A with Kobi Kremnitzer**

A meditating mathematician is developing a theory of conscious experience to help understand the boundary between the quantum and classical world.

RECENT FORUM POSTS

RECENT ARTICLES

Experiments investigating the thermodynamics of clocks can teach us about the origin of time's arrow.

Physicists lay out blueprints for running a 'Wigner's Friend' experiment using an artificial intelligence, built on a quantum computer, as an 'observer.'

Using a brain-computer interface to create a consciousness 'add-on' to help test Integrated Information Theory.

A quantum computer composes chart-topping music, programmed by physicists striving to understand consciousness.

A meditating mathematician is developing a theory of conscious experience to help understand the boundary between the quantum and classical world.

FQXi FORUM

December 8, 2022

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

TOPIC: Mathematics: Science of the Possible, or the Probable? by Thomas Howard Ray [refresh]

TOPIC: Mathematics: Science of the Possible, or the Probable? by Thomas Howard Ray [refresh]

Mathematics is not physics. Rationally speaking, though, a physical result that corresponds one-for-one to a mathematical model forms a closed logical judgment on the truth of a falsifiable physical theory. Because it is not possible to make a closed logical judgment on physical probability for more than two possible outcomes of one event—no mathematical model can be one-for-one correspondent to the physics of probability, in a rationally complete scientific theory. We show that parity between all mathematical models and all physical results is possible if, and only if, probability exists independent of random events. Therefore, Max Tegmark’s Mathematical Universe Hypothesis is probably true.

A student of complex systems, Tom Ray is a retired technical writer-editor whose newest contribution to the field of complex systems science, on net-centric logistics, was published by Springer in January 2015, in the book collection Conflict and Complexity. http://www.springer.com/physics/complexity/book/978-1-4939-1

704-4

Hi Tom,

Your essay contains fascinating information. Although many statements exist to the effect that*experiments prove non-locality*, the fact is that the experiments prove [or come very close to proving] that *the experimentally found correlations agree with the correlations predicted by quantum mechanics*. It is not physical experiment, but *mathematics*, that proves...

view entire post

Your essay contains fascinating information. Although many statements exist to the effect that

view entire post

report post as inappropriate

Hi Edwin,

Thanks for the kind comments. In fact, I had read your essay previously, and was impressed -- it's your clearest and most direct, in my opinion, of all your entries over these years. I am finally convinced that we're talking about the same thing.

Key to our agreement in principle is the value of a continuous function. Just as Einstein originally formulated mass-energy...

view entire post

Thanks for the kind comments. In fact, I had read your essay previously, and was impressed -- it's your clearest and most direct, in my opinion, of all your entries over these years. I am finally convinced that we're talking about the same thing.

Key to our agreement in principle is the value of a continuous function. Just as Einstein originally formulated mass-energy...

view entire post

Tom,

I had meant to get back and discuss more about your fine essay. But time is running out, so at least I can give you an appropriate score.

Best,

Edwin Eugene Klingman

report post as inappropriate

I had meant to get back and discuss more about your fine essay. But time is running out, so at least I can give you an appropriate score.

Best,

Edwin Eugene Klingman

report post as inappropriate

Tom,

Your essay is as usual, a Tour de Force of highly condensed mathematical acumen. I've given it two readings and find much I have to learn more about. In general, however, the theme is clear and is concisely stated where you say,

"- if nothing exists in reality save random events, there is no natural correspondence of mathematics to physics."

I was impressed by your carefully avoiding a philosophic character of argument, and keeping matters very much on message of the nuts and bolts of math needing an independent yet true correspondence to physics being about that which is physical, without any ad hoc contrivance of the math to match the physical empiricism. The point you make about QM conventionally constraining measurement space to the Bloch sphere provides a conceptual 'visual aid' when contemplating that a continuous function must exist in metamorphizing a spherical (curved) space and a cubic (flat) space. The 1500 year old edifice Hagia Sophia comes to mind, and with it the geometric sense of strength in physical spacetime.

I think you have made a good argument that what distinguishes where math is exemplary of physical reality is where there is continuity, and your approach to the Contest Topic by way of probabilities is challenging. I still have my sticky note of your conjecture and think it has a good fit in your presentation. Good Luck, don't let the back-biters bug. jrc

report post as inappropriate

Your essay is as usual, a Tour de Force of highly condensed mathematical acumen. I've given it two readings and find much I have to learn more about. In general, however, the theme is clear and is concisely stated where you say,

"- if nothing exists in reality save random events, there is no natural correspondence of mathematics to physics."

I was impressed by your carefully avoiding a philosophic character of argument, and keeping matters very much on message of the nuts and bolts of math needing an independent yet true correspondence to physics being about that which is physical, without any ad hoc contrivance of the math to match the physical empiricism. The point you make about QM conventionally constraining measurement space to the Bloch sphere provides a conceptual 'visual aid' when contemplating that a continuous function must exist in metamorphizing a spherical (curved) space and a cubic (flat) space. The 1500 year old edifice Hagia Sophia comes to mind, and with it the geometric sense of strength in physical spacetime.

I think you have made a good argument that what distinguishes where math is exemplary of physical reality is where there is continuity, and your approach to the Contest Topic by way of probabilities is challenging. I still have my sticky note of your conjecture and think it has a good fit in your presentation. Good Luck, don't let the back-biters bug. jrc

report post as inappropriate

Hi John,

It's been a constant source of pleasure and delight to me, that you truly get what I'm saying. And I don't just mean the words -- I mean the essential message of a committed rationalist.

Thank you and all best,

Tom

It's been a constant source of pleasure and delight to me, that you truly get what I'm saying. And I don't just mean the words -- I mean the essential message of a committed rationalist.

Thank you and all best,

Tom

Tom,

The pleasure has been mine, I can only understand rationalists and have learned much from you. I was especially pleased to learn from your essay the logic of Euler's equation. It never bothered me that he once said that any first rate mathematician would immediately see it, because I've never imagined myself a mathematician. But it has pestered me that I couldn't see it. Forest for the trees sort of thing, I was hung up on the numerical values. The manner you introduced it in your argument displays the simple logic both geometrically of a 1pi rotation, and algebraically of 'e'; it is the real function of each, not the arithmetic values that are at work! My horizons have been greatly enlarged. Thank-you very much. jrc

report post as inappropriate

The pleasure has been mine, I can only understand rationalists and have learned much from you. I was especially pleased to learn from your essay the logic of Euler's equation. It never bothered me that he once said that any first rate mathematician would immediately see it, because I've never imagined myself a mathematician. But it has pestered me that I couldn't see it. Forest for the trees sort of thing, I was hung up on the numerical values. The manner you introduced it in your argument displays the simple logic both geometrically of a 1pi rotation, and algebraically of 'e'; it is the real function of each, not the arithmetic values that are at work! My horizons have been greatly enlarged. Thank-you very much. jrc

report post as inappropriate

Hi John,

I think it was Gauss who said that. You're right, though -- analysis is far more compelling as a physical language than arithmetic. We actually experience geometry, as 3-dimension beings with 4-dimension brain-minds. Einstein in fact made what seems a mystical statement on first blush -- that he experienced relativity kinesthetically. Rotation, though, is a physical sense in more basic terms than a simple discrete point or line.

Best,

Tom

I think it was Gauss who said that. You're right, though -- analysis is far more compelling as a physical language than arithmetic. We actually experience geometry, as 3-dimension beings with 4-dimension brain-minds. Einstein in fact made what seems a mystical statement on first blush -- that he experienced relativity kinesthetically. Rotation, though, is a physical sense in more basic terms than a simple discrete point or line.

Best,

Tom

John,

Haters gonna hate. :-) I know from past experience that a couple of knuckleheads will knock a new entry down without reading it, just to try and suppress competition. Along with some others, I have been critical of the 'peer' voting system; it does no service to science that the peer group is limited only by one's capacity to use a keyboard.

You write, "Could you briefly...

view entire post

Haters gonna hate. :-) I know from past experience that a couple of knuckleheads will knock a new entry down without reading it, just to try and suppress competition. Along with some others, I have been critical of the 'peer' voting system; it does no service to science that the peer group is limited only by one's capacity to use a keyboard.

You write, "Could you briefly...

view entire post

Dear Tom

I liked your quote of John Barrow’s interpretation of Gödel: “if mathematics is a religion, it is the only religion that can prove it is a religion”. As I discussed in my 2012 essay I have found such a proof. The problem is that we have a religion that doesn’t want to admit the truth that it is a religion. The expedient way of dealing with such a proof is to deny it exists. As you discuss in your essay, Bell-like analysis on the border between maths and physics is not straightforward. It is possible to make implicit assumptions that undermine the generality of the result – as you are saying about Bell. In my essay I adopt a physics realism approach to the same questions on the basis that the true physical dynamics is hidden by simply being too fast for any experiment to measure. This option isn’t covered by Bell, and I find that quantum theory results can be reproduced. Where my essay was cut short by the word count, is on the issues of probability, locality and non-locality you discuss in your essay. I would be interested in your view of my new approach to Bell-like analysis, and what it implies for probability and non-locality.

Regards

Michael Goodband

report post as inappropriate

I liked your quote of John Barrow’s interpretation of Gödel: “if mathematics is a religion, it is the only religion that can prove it is a religion”. As I discussed in my 2012 essay I have found such a proof. The problem is that we have a religion that doesn’t want to admit the truth that it is a religion. The expedient way of dealing with such a proof is to deny it exists. As you discuss in your essay, Bell-like analysis on the border between maths and physics is not straightforward. It is possible to make implicit assumptions that undermine the generality of the result – as you are saying about Bell. In my essay I adopt a physics realism approach to the same questions on the basis that the true physical dynamics is hidden by simply being too fast for any experiment to measure. This option isn’t covered by Bell, and I find that quantum theory results can be reproduced. Where my essay was cut short by the word count, is on the issues of probability, locality and non-locality you discuss in your essay. I would be interested in your view of my new approach to Bell-like analysis, and what it implies for probability and non-locality.

Regards

Michael Goodband

report post as inappropriate

Dear Tom,

I am so sorry that you apparently cannot understand written English.

Remedial courses are available at very low cost.

Congenially,

Joe Fisher

report post as inappropriate

I am so sorry that you apparently cannot understand written English.

Remedial courses are available at very low cost.

Congenially,

Joe Fisher

report post as inappropriate

Dear Tom,

I am having an awful time with my credentialed fellow essayist. Several of them have reported my post as being inappropriate and had it removed.Thank you for your gracious humorous response to my comment.

Thankfully,

Joe Fisher

report post as inappropriate

I am having an awful time with my credentialed fellow essayist. Several of them have reported my post as being inappropriate and had it removed.Thank you for your gracious humorous response to my comment.

Thankfully,

Joe Fisher

report post as inappropriate

Joe, you're not wrong. There's just no possible framework in which you could be proved right, that isn't self-referential.

As Popper said, "All life is problem solving." The problem here is that life can't apparently communicate with sentient life other than by using abstract symbols and signals. How do you know, in fact, that you aren't communicating with an abstract being (me) through the abstract symbols on your keyboard that you are using? How do you know that I am 'real'?

I don't know your level of knowledge or interest in philosophy or philosophical problems; however, if you agree with Wittgenstein's view, there are no philosophical problems at all -- just "language games and forms of life." At the end of the day, that may be a great truth, and it's still a philosophy I reject outright -- for the same reason that I reject your claim that the world includes no abstractions:

Your conclusions, and Wittgenstein's, are based on inductive inference -- "Seeing is believing."

I am a rationalist, though. In order to solve a problem, one must identify it -- even a guess is good -- and find the logical correspondence between the problem and its solution in order to consider it solved. I quote J. Bronowski often: "All science is the search for unity in hidden likenesses."

Rationalism unites the world. Inductive inference divides it.

All best,

Tom

As Popper said, "All life is problem solving." The problem here is that life can't apparently communicate with sentient life other than by using abstract symbols and signals. How do you know, in fact, that you aren't communicating with an abstract being (me) through the abstract symbols on your keyboard that you are using? How do you know that I am 'real'?

I don't know your level of knowledge or interest in philosophy or philosophical problems; however, if you agree with Wittgenstein's view, there are no philosophical problems at all -- just "language games and forms of life." At the end of the day, that may be a great truth, and it's still a philosophy I reject outright -- for the same reason that I reject your claim that the world includes no abstractions:

Your conclusions, and Wittgenstein's, are based on inductive inference -- "Seeing is believing."

I am a rationalist, though. In order to solve a problem, one must identify it -- even a guess is good -- and find the logical correspondence between the problem and its solution in order to consider it solved. I quote J. Bronowski often: "All science is the search for unity in hidden likenesses."

Rationalism unites the world. Inductive inference divides it.

All best,

Tom

Tom,

I must confess that I have not yet mastered the erudite arguments you pose, but knowing a small bit about Tegmark's MUH, I wondered about the "independence of humans" aspect of the ERH. Current physics theories are the math equations and structures describing the theory and their concepts, thus explaining the connections to our observations. The equations are built by humans and are their baggage. I don't see the separation.

My "Connection of Math, Physics and Mind," I know, seem mundane, but I don't see the physical world as completely independent of humans.

What am I missing? Many scientists say that humans adhere to the ERH concept.

Jim

report post as inappropriate

I must confess that I have not yet mastered the erudite arguments you pose, but knowing a small bit about Tegmark's MUH, I wondered about the "independence of humans" aspect of the ERH. Current physics theories are the math equations and structures describing the theory and their concepts, thus explaining the connections to our observations. The equations are built by humans and are their baggage. I don't see the separation.

My "Connection of Math, Physics and Mind," I know, seem mundane, but I don't see the physical world as completely independent of humans.

What am I missing? Many scientists say that humans adhere to the ERH concept.

Jim

report post as inappropriate

Well, Jim, all I can say is that if you agree with Max's ERH table (slide 14 in this PowerPoint: www.fqxi.org/iceland/images/Iceland%20Talks/tegmark.ppt) you'll find my view at the extreme of "less baggage."

I am a rationalist. An external reality and metaphysical realism are fundamental assumptions.

Thanks for the note. I'll get to your essay when I can.

Best,

Tom

I am a rationalist. An external reality and metaphysical realism are fundamental assumptions.

Thanks for the note. I'll get to your essay when I can.

Best,

Tom

Tom,

Thank for taking the time to read my essay. I am not a mathematician but more another reading brought me closer to your well-thought-out vision and argument.

Jim

report post as inappropriate

Thank for taking the time to read my essay. I am not a mathematician but more another reading brought me closer to your well-thought-out vision and argument.

Jim

report post as inappropriate

Tom,

I'll start a new thread to get back on topic. I detect a hidden variable in your essay approach, namely the original EPR wave equation which seems to be ignored in speculative arguments about the double slit experiment. EPR's argument was that it could be possible to discover a state of position or momentum of a particle following the correlating event of impact with another without...

view entire post

I'll start a new thread to get back on topic. I detect a hidden variable in your essay approach, namely the original EPR wave equation which seems to be ignored in speculative arguments about the double slit experiment. EPR's argument was that it could be possible to discover a state of position or momentum of a particle following the correlating event of impact with another without...

view entire post

report post as inappropriate

Tom,

I crammed the EPR argument a bit. Their wave equation finds foundation in the momentum imparted to the screen by both particles and the known measured separation of the two slits. Their point being that direct observation would naturally disturb the q,p state of a particle, but simply knowing other parameters does not constitute an action. jrc

report post as inappropriate

I crammed the EPR argument a bit. Their wave equation finds foundation in the momentum imparted to the screen by both particles and the known measured separation of the two slits. Their point being that direct observation would naturally disturb the q,p state of a particle, but simply knowing other parameters does not constitute an action. jrc

report post as inappropriate

Very nice, John! I delayed replying until I could read a few times without distraction.

We are fortunate to have you in the forum.

I'll just add one comment -- you say, mirroring the EPR view, that " ... if QM is a complete theoretical description of reality, we really needn't resort to arguments on QM's terms."

In fact, though, the argument from binary probability does meet QM terms -- it just limits the probability distribution and eliminates prior probability. I am gratified that you agree that the prior probability of randomness obviates free will.

Best,

Tom

We are fortunate to have you in the forum.

I'll just add one comment -- you say, mirroring the EPR view, that " ... if QM is a complete theoretical description of reality, we really needn't resort to arguments on QM's terms."

In fact, though, the argument from binary probability does meet QM terms -- it just limits the probability distribution and eliminates prior probability. I am gratified that you agree that the prior probability of randomness obviates free will.

Best,

Tom

Tom,

I also agree that arguments must also address QM probabilities. As the saying goes, 'to beat a mathematician you have to hit'em in the math'. I don't want to be a distraction, and hope you get some competent feedback. Probabilities become anavoidable in complex systems, and systems don't need to be very extended to become complex. Not my bag of tricks though, and I tend to look at probability as a pry-bar to open inquiry as to what it evolves from. Good Luck, jrc

report post as inappropriate

I also agree that arguments must also address QM probabilities. As the saying goes, 'to beat a mathematician you have to hit'em in the math'. I don't want to be a distraction, and hope you get some competent feedback. Probabilities become anavoidable in complex systems, and systems don't need to be very extended to become complex. Not my bag of tricks though, and I tend to look at probability as a pry-bar to open inquiry as to what it evolves from. Good Luck, jrc

report post as inappropriate

Tom,

Looking in from outside of your universe, you continue to present your case brilliantly.

James

report post as inappropriate

Looking in from outside of your universe, you continue to present your case brilliantly.

James

report post as inappropriate

James, that is very kind of you.

In this context, I interpret Bar-Yam's theory of multi-scale variety thus: Though we may all see the world through our own unique eyes, it doesn't make the world any different for any of us. It only means that the marvelous variety of viewpoints available is many times bigger than any one of us. Isn't it the greatest pleasure to participate in, and increase, that variety?

Thanks, and all best to you in the essay competition!

Tom

In this context, I interpret Bar-Yam's theory of multi-scale variety thus: Though we may all see the world through our own unique eyes, it doesn't make the world any different for any of us. It only means that the marvelous variety of viewpoints available is many times bigger than any one of us. Isn't it the greatest pleasure to participate in, and increase, that variety?

Thanks, and all best to you in the essay competition!

Tom

Hi Thomas,

Great essay! You provide compelling arguments for the mathematical universe hypothesis. However, my essay takes an opposing view; I would be glad to take your opinion.

Best regards,

Mohammed

report post as inappropriate

Great essay! You provide compelling arguments for the mathematical universe hypothesis. However, my essay takes an opposing view; I would be glad to take your opinion.

Best regards,

Mohammed

report post as inappropriate

Tom, it's a very fascinating essay and a great contribution. Your philosophical approach on non-locality and Bell's theorem which you backed up by a thorough technical analysis, is quite inspiring. Also very enlightening is the last section on the Correspondence Principle and Popper Falsifiability. Thanks again, Steve

report post as inappropriate

report post as inappropriate

Also (as I mentioned in my reply to your post)- congratulations on being published by Springer :)

report post as inappropriate

report post as inappropriate

Thanks, Steve -- as I posted in your forum, we are in accord on many things, and the foundations of computability is, I think, the most important issue in frontier science.

Beyond the scope of the essay question, the growing fields of brain science and artificial intelligence depend strongly on resolving the issues of network robustness and integrity -- i.e., the amount of information...

view entire post

Beyond the scope of the essay question, the growing fields of brain science and artificial intelligence depend strongly on resolving the issues of network robustness and integrity -- i.e., the amount of information...

view entire post

Hi Tom,

As I told you in my FQXi page, I have read your intriguing Essay. Here are my comments:

1) Although I am a collector of aphorisms (particularly of Einstein's ones) I did not know the aphorism of Bronowski that "All science is the search for unity in hidden likenesses". It is very nice.

2) I think that black hole physics and its importance in the route to quantize gravity is an example of your beautiful statement that "Mathematics research will uncover further physical regularities in nature". I also find intriguing your extending to symmetry between mathematics and physics the Tegmark's MUH.

3) I find profound your question "What determines the objective result of a measurement - hidden variables or hidden assumptions?".

4) Can you give details on your statement that "Hawking radiation is a theoretical example of a locally real quantum phenomenon with simultaneous past and future equality"? This could indeed have implications for the black hole information puzzle.

5) I find very nice your Einstenian equation M=Pb^2=4P

6) I think your pretty final sentence that "In this game of unlimited possibilities called mathematics, our bet is on human imagination" should have been appreciated by Einstein.

In any case, the reading of your very nice Essay enjoyed me a lot. It deserves the highest score that I am going to give you.

I wish you best luck in the Contest.

Cheers, Ch.

report post as inappropriate

As I told you in my FQXi page, I have read your intriguing Essay. Here are my comments:

1) Although I am a collector of aphorisms (particularly of Einstein's ones) I did not know the aphorism of Bronowski that "All science is the search for unity in hidden likenesses". It is very nice.

2) I think that black hole physics and its importance in the route to quantize gravity is an example of your beautiful statement that "Mathematics research will uncover further physical regularities in nature". I also find intriguing your extending to symmetry between mathematics and physics the Tegmark's MUH.

3) I find profound your question "What determines the objective result of a measurement - hidden variables or hidden assumptions?".

4) Can you give details on your statement that "Hawking radiation is a theoretical example of a locally real quantum phenomenon with simultaneous past and future equality"? This could indeed have implications for the black hole information puzzle.

5) I find very nice your Einstenian equation M=Pb^2=4P

6) I think your pretty final sentence that "In this game of unlimited possibilities called mathematics, our bet is on human imagination" should have been appreciated by Einstein.

In any case, the reading of your very nice Essay enjoyed me a lot. It deserves the highest score that I am going to give you.

I wish you best luck in the Contest.

Cheers, Ch.

report post as inappropriate

Thanks, Christian!

The Bronowski quote is from his collection of post-war essays in the 1950s, called, *Science and Human Values.* It is a very inspiring little volume that I return to often to renew my optimism for the future of the human race and the role of science in it.

My view on Hawking radiation is based on the Hawking-Hartle no-boundary/imaginary time proposal: "This absence of boundaries means that the laws of physics would determine the state of the universe uniquely, in imaginary time. But if one knows the state of the universe in imaginary time, one can calculate the state of the universe in real time. One would still expect some sort of Big Bang singularity in real time. So real time would still have a beginning. But one wouldn't have to appeal to something outside the universe, to determine how the universe began. Instead, the way the universe started out at the Big Bang would be determined by the state of the universe in imaginary time."

The state of the universe in imaginary time is local -- every point of the Minkowski space-time in an expanding universe, is the origin of creation. (I'll send you something privately that explains it in more technical terms.)

Thanks again, and all best -- looking forward to more dialogue,

Tom

The Bronowski quote is from his collection of post-war essays in the 1950s, called, *Science and Human Values.* It is a very inspiring little volume that I return to often to renew my optimism for the future of the human race and the role of science in it.

My view on Hawking radiation is based on the Hawking-Hartle no-boundary/imaginary time proposal: "This absence of boundaries means that the laws of physics would determine the state of the universe uniquely, in imaginary time. But if one knows the state of the universe in imaginary time, one can calculate the state of the universe in real time. One would still expect some sort of Big Bang singularity in real time. So real time would still have a beginning. But one wouldn't have to appeal to something outside the universe, to determine how the universe began. Instead, the way the universe started out at the Big Bang would be determined by the state of the universe in imaginary time."

The state of the universe in imaginary time is local -- every point of the Minkowski space-time in an expanding universe, is the origin of creation. (I'll send you something privately that explains it in more technical terms.)

Thanks again, and all best -- looking forward to more dialogue,

Tom

Tom,

You've got to be one of the most eloquent mathematical writers I have ever read. Phenomenal clarity and rigor.

I've given you my highest mark in this contest so far.

Best of luck!

Rick

report post as inappropriate

You've got to be one of the most eloquent mathematical writers I have ever read. Phenomenal clarity and rigor.

I've given you my highest mark in this contest so far.

Best of luck!

Rick

report post as inappropriate

Tom,

Its great to see your essay getting attention of serious and informed people, and free of those whom like to dance on the bar and start fights. That's probably because your approach of possible vs. probable is presented with math results that many people don't know enough about what they come from. I sure can't contribute much! I do have more a curio than a question that might be pertenent...

Steven Sax provided an e-address for a thesis on laser experiments with Rubidium that I've waded into and think you would find interesting, and from which he launches his discourse on decidability. Here 'tis; http://www.bgu.ac.il/atomchip/Theses/Amir_Waxman_MSc_2007.pd

f

Its QM, of course, and uses the Bloch Sphere as the spin co-ordinate system. I realized that in their protocols what they specify as 'free precession' is in fact 'freely gimballed', in that the axis of precession intersects the origin at intersection of the orthogonals. To be 'free precession', the antipodal points of the axis of precession must be free to wander like the magnetic poles of the earth, the p-axis does not necessarily intersect the orthogonal. Intuitively this must fundamentally alter the landscape of co-ordinate pairs. And what seems to be already decided in QM is symmetric precession. Would that not impose an undecidable condition?

I don't get into coin tossing, I pinch pennies like to bring a tear to Lincoln's eye. So maybe this niave observation is a standard issue. Your comment would be instructive, at your leisure, I'm just now off on errands.

All the best, as always. jrc

report post as inappropriate

Its great to see your essay getting attention of serious and informed people, and free of those whom like to dance on the bar and start fights. That's probably because your approach of possible vs. probable is presented with math results that many people don't know enough about what they come from. I sure can't contribute much! I do have more a curio than a question that might be pertenent...

Steven Sax provided an e-address for a thesis on laser experiments with Rubidium that I've waded into and think you would find interesting, and from which he launches his discourse on decidability. Here 'tis; http://www.bgu.ac.il/atomchip/Theses/Amir_Waxman_MSc_2007.pd

f

Its QM, of course, and uses the Bloch Sphere as the spin co-ordinate system. I realized that in their protocols what they specify as 'free precession' is in fact 'freely gimballed', in that the axis of precession intersects the origin at intersection of the orthogonals. To be 'free precession', the antipodal points of the axis of precession must be free to wander like the magnetic poles of the earth, the p-axis does not necessarily intersect the orthogonal. Intuitively this must fundamentally alter the landscape of co-ordinate pairs. And what seems to be already decided in QM is symmetric precession. Would that not impose an undecidable condition?

I don't get into coin tossing, I pinch pennies like to bring a tear to Lincoln's eye. So maybe this niave observation is a standard issue. Your comment would be instructive, at your leisure, I'm just now off on errands.

All the best, as always. jrc

report post as inappropriate

Hey, John -- I have always thought of *you* as a serious and informed person! :-)

Give me your email address, and I'll send you something privately that addresses your question.

Thanks for the link to Steve's research -- it's on my list.

All best,

Tom

Give me your email address, and I'll send you something privately that addresses your question.

Thanks for the link to Steve's research -- it's on my list.

All best,

Tom

One of the advantages of being as old as I am, is that distant memories come into sharp focus with the right trigger.

The trigger to my recollection of Jim Cowan's wonderful short story was David Hestenes's discussion of modeling in his essay forum.

The Cowan story ("The Spade of Reason") and Jose Luis Borges's "Library of Babel" are two pieces of fiction that have had a deep impact on my intellectual life. Remarkably enough, Borges's story is referenced in Cowan's story.

All best,

Tom

The trigger to my recollection of Jim Cowan's wonderful short story was David Hestenes's discussion of modeling in his essay forum.

The Cowan story ("The Spade of Reason") and Jose Luis Borges's "Library of Babel" are two pieces of fiction that have had a deep impact on my intellectual life. Remarkably enough, Borges's story is referenced in Cowan's story.

All best,

Tom

Dear Thomas,

I just read Jim Cowan's short story "The Spade of Reason" at your suggestion. Indeed, it is great: philosophical science-fiction just the way I like it! I especially like it when the main character says that "one kind of madness is not knowing that the model is all we will ever know."

Marc

report post as inappropriate

I just read Jim Cowan's short story "The Spade of Reason" at your suggestion. Indeed, it is great: philosophical science-fiction just the way I like it! I especially like it when the main character says that "one kind of madness is not knowing that the model is all we will ever know."

Marc

report post as inappropriate

Dear Thomas,

Thank for the comments on my blog and the high rate. I had your essay in my list and you write about CHSH!

You can expect my feedback soon.

All the best,

Michel

report post as inappropriate

Thank for the comments on my blog and the high rate. I had your essay in my list and you write about CHSH!

You can expect my feedback soon.

All the best,

Michel

report post as inappropriate

Thanks, Michel! I look forward to productive dialogue and wish all the best to you and your essay in the competition.

Tom

Tom

Dear Tom,

Your essay is multivalued in the sense that

* you clarify the relationship between physics P and mathematics M, postulating a linear (Tegmarkian) equation E = k*P,

* you put this in perspective with Bell's (or CHSH) inequality and a establish a link to number theory (the unsoved Goldbach conjecture as revisited by Popper),

* you question the role of probabilty in the MP correspondance (as commented by John Cox in his post),

* you relate to Euler's identity (James Hoover has an essay on this topic as you know)...

All this aspects are justified in technical terms sometimes in an unexpected way. You received many valuable comments, a proof of respect. I add my congratulations and my good community mark.

Best wishes.

Michel

report post as inappropriate

Your essay is multivalued in the sense that

* you clarify the relationship between physics P and mathematics M, postulating a linear (Tegmarkian) equation E = k*P,

* you put this in perspective with Bell's (or CHSH) inequality and a establish a link to number theory (the unsoved Goldbach conjecture as revisited by Popper),

* you question the role of probabilty in the MP correspondance (as commented by John Cox in his post),

* you relate to Euler's identity (James Hoover has an essay on this topic as you know)...

All this aspects are justified in technical terms sometimes in an unexpected way. You received many valuable comments, a proof of respect. I add my congratulations and my good community mark.

Best wishes.

Michel

report post as inappropriate

Dear Thomas,

Thank you for your comments about my essay. I have left a reply on my page.

Yours is an intriguing and very ambitious essay!!! You tackle deep fundamental issues such as probability and free will, and I have to confess that I'm having some difficulty in following all the details, since I am not familiar enough with many theoretical results that you build upon.

I have questions about the "quadratic" relationship that you postulate between math M and physics P: M = P q^2, which becomes M = 4P because q = 2.

1. Why does the constant have to be the square of something? I see the parallel with E = m c^2, but I don't see why it has to hold.

2. Is your equation M = 4P dimensionless? In E = m c^2, E is in joules, m is in kilograms and c^2 is in joules per kilogram (or in meters squared by seconds squared). What are the "units" (if any) of physics P and math M?

So far, your essay is looking good in the ratings... Good luck!

Marc

report post as inappropriate

Thank you for your comments about my essay. I have left a reply on my page.

Yours is an intriguing and very ambitious essay!!! You tackle deep fundamental issues such as probability and free will, and I have to confess that I'm having some difficulty in following all the details, since I am not familiar enough with many theoretical results that you build upon.

I have questions about the "quadratic" relationship that you postulate between math M and physics P: M = P q^2, which becomes M = 4P because q = 2.

1. Why does the constant have to be the square of something? I see the parallel with E = m c^2, but I don't see why it has to hold.

2. Is your equation M = 4P dimensionless? In E = m c^2, E is in joules, m is in kilograms and c^2 is in joules per kilogram (or in meters squared by seconds squared). What are the "units" (if any) of physics P and math M?

So far, your essay is looking good in the ratings... Good luck!

Marc

report post as inappropriate

Thanks, Marc. Indeed, I fretted all the time I was writing it, over whether this work might be *too* ambitious. Details can run away from one, if the scope gets too big. In the end, I could not escape the conclusion that if free will exists, it cannot be a property of random observer choice. This being so:

Only a binary decision that is square integrable can share a reciprocal relation *continuously* with a continuous range of variables in a finite interval of time (Buridan's principle is limiting). The linear relation M = 4P is not physically meaningful in the first degree, because it is not dynamic; M - 4P = 0. The second degree equivalent, M = Pq^2, q = 2, accounts for the full range of possible binary decisions in any finite interval where M = P. Tracing the relation back to the cosmological initial condition, the rest state of the universe is a "fourity" of possibilities in any locally bounded interval.

The units of M and P are dimensionless to the extent that M = P is unitary. In the reciprocal relationship M = Pq^2, the fundamental dimensionality M = 4P (P = M/4) gives us the division algebras we know to exist (R, C, O, H) as a complete algebraically closed range of computational fields relating binary choice to a continuous range of variables limited by a finite time interval.

Physical units are derived from empirical observations in a bounded measure space. Since four pure physical states imply the Hawking-Penrose singularity theorem, and insofar as four are the minimum necessary and sufficient for dynamic interaction between physics and mathematics (i.e., between measure and model), maybe we can move a little closer to Hawking's question of what "puts the fire in the equations" with number-theoretic arguments alone. Just thinking out loud here.

All best to you and your essay, too!

Tom

Only a binary decision that is square integrable can share a reciprocal relation *continuously* with a continuous range of variables in a finite interval of time (Buridan's principle is limiting). The linear relation M = 4P is not physically meaningful in the first degree, because it is not dynamic; M - 4P = 0. The second degree equivalent, M = Pq^2, q = 2, accounts for the full range of possible binary decisions in any finite interval where M = P. Tracing the relation back to the cosmological initial condition, the rest state of the universe is a "fourity" of possibilities in any locally bounded interval.

The units of M and P are dimensionless to the extent that M = P is unitary. In the reciprocal relationship M = Pq^2, the fundamental dimensionality M = 4P (P = M/4) gives us the division algebras we know to exist (R, C, O, H) as a complete algebraically closed range of computational fields relating binary choice to a continuous range of variables limited by a finite time interval.

Physical units are derived from empirical observations in a bounded measure space. Since four pure physical states imply the Hawking-Penrose singularity theorem, and insofar as four are the minimum necessary and sufficient for dynamic interaction between physics and mathematics (i.e., between measure and model), maybe we can move a little closer to Hawking's question of what "puts the fire in the equations" with number-theoretic arguments alone. Just thinking out loud here.

All best to you and your essay, too!

Tom

Tom,

An excellent essay. Although I am not certain I fully understand your solution, but the issue of whether or not reality is objective or observer dependent is critical to understanding how math integrates with science. Might it be the case that the reality is objective but measurement is observer dependent and is that consistent with your thinking?

thanks

Rob

report post as inappropriate

report post as inappropriate

An excellent essay. Although I am not certain I fully understand your solution, but the issue of whether or not reality is objective or observer dependent is critical to understanding how math integrates with science. Might it be the case that the reality is objective but measurement is observer dependent and is that consistent with your thinking?

thanks

Rob

report post as inappropriate

Rob, that's exactly right. The question -- "What determines the objective result of a measurement, hidden variables or hidden assumptions"? -- refers to metaphysical realism (measurement outcome) vs anti-realist assumptions.

The assumption of non-locality is obviated by the time parameter (Hess-Philipp) in that every point of a 4 dimension Minkowski space is an operator.

Because the time parameter is not real, independent of spacetime (special relativity), pairwise measurement outcomes are simultaneous with past-future local spacetime states that obviously include the observer as an element. The assumption of nonlocality is therefore superfluous, with the implication that the assumption of a nonlocal measurement value is superfluous. The observer -- whether human or point particle -- is one more degree of freedom than allowed by 3 dimension measure.

In a continuous function classical measure, the macroscopic description of position in time as well as space is bounded only by the cosmological state. A microscopic state is therefore dependent on the cosmological state, and not discontinuous with the operator that exists at every point of local 4 dimension spacetime.

All best,

Tom

The assumption of non-locality is obviated by the time parameter (Hess-Philipp) in that every point of a 4 dimension Minkowski space is an operator.

Because the time parameter is not real, independent of spacetime (special relativity), pairwise measurement outcomes are simultaneous with past-future local spacetime states that obviously include the observer as an element. The assumption of nonlocality is therefore superfluous, with the implication that the assumption of a nonlocal measurement value is superfluous. The observer -- whether human or point particle -- is one more degree of freedom than allowed by 3 dimension measure.

In a continuous function classical measure, the macroscopic description of position in time as well as space is bounded only by the cosmological state. A microscopic state is therefore dependent on the cosmological state, and not discontinuous with the operator that exists at every point of local 4 dimension spacetime.

All best,

Tom

Tom,

I was just looking in and your responses to both Robert and Marc are helpful to understanding your maths and your thinking. You do speak to mathematicians, and that assumes an 'ideal reader'. I've been hoping good questions would draw you into something of tutorial discussion.

Robert puts it succinctly that reality is objective and measurement is observer dependent. Math, like the color purple, is a figment of human imagination. The reality is that randominity is limited by necessity. 'There is no such thing as cold, cold is the absence of heat' - (Louie Ritchey). When we reach absolute Zero Kelvin, they can have pure randominity. I won't care. ;-> jrc

report post as inappropriate

I was just looking in and your responses to both Robert and Marc are helpful to understanding your maths and your thinking. You do speak to mathematicians, and that assumes an 'ideal reader'. I've been hoping good questions would draw you into something of tutorial discussion.

Robert puts it succinctly that reality is objective and measurement is observer dependent. Math, like the color purple, is a figment of human imagination. The reality is that randominity is limited by necessity. 'There is no such thing as cold, cold is the absence of heat' - (Louie Ritchey). When we reach absolute Zero Kelvin, they can have pure randominity. I won't care. ;-> jrc

report post as inappropriate

Tom,

Let me elaborate on my last comment before returning to some personal matters.

I think your identification of escape velocity with any point in space is a profound insight. It is both physical and at the same time mathematically versatile. It is where the path of least resistance is provided to the random walk. The escape velocity at any given point in space will naturally vary...

view entire post

Let me elaborate on my last comment before returning to some personal matters.

I think your identification of escape velocity with any point in space is a profound insight. It is both physical and at the same time mathematically versatile. It is where the path of least resistance is provided to the random walk. The escape velocity at any given point in space will naturally vary...

view entire post

report post as inappropriate

I find myself in the position of defending the views of both Alan Kadin and Michel Planat, who crossed swords in Alan's blog.

No surprise -- there is probably no sharper demarcation of philosophies in physics, than between Einstein-Bohm represented by Kadin, and Bohr-Peres represented by Planat.

I'm not neutral -- I agree with Karl Hess (*Einstein was Right* 2015) and the late...

view entire post

No surprise -- there is probably no sharper demarcation of philosophies in physics, than between Einstein-Bohm represented by Kadin, and Bohr-Peres represented by Planat.

I'm not neutral -- I agree with Karl Hess (*Einstein was Right* 2015) and the late...

view entire post

Tom,

'So how should one show what is being measured..." You do say a lot in short posts.

Many times we all have imperfect knowledge of the fullness of measures that have become used in particular ways that tend to relegate one parameter or another to obscurity. So what the quantum is as a measure, is generally treated as if it is only a specific quantity of energy because it doesn't tell us whether it is a particle or a wave. Added to that, the time normalization in QM denudes the quantum of its 'per second' realism.

But the original Quantum finds more measure than given credit for. Boltzman's Constant obtains from the Gas Constant/Avagadros Number, and so Boltzman is a physical proportion that gives the energy/temperature associated with a single source particle. By relation with Planck's Constant as a physical proportion of energy/time, there is a complex measure of a single physical wave at any specified frequency which carries the celebrated energy quantity per every 1/f from a single source. That's a lot of information to start with.

To an experimentalist, CHSH isn't half the story. What is the wave doing and how, such that some ranges of frequencies penetrate deep into the dirt and others bounce off airplanes? Each single wavelength carries the same energy. How's it do that?! - Duhhoohhhh - :) jrc

report post as inappropriate

'So how should one show what is being measured..." You do say a lot in short posts.

Many times we all have imperfect knowledge of the fullness of measures that have become used in particular ways that tend to relegate one parameter or another to obscurity. So what the quantum is as a measure, is generally treated as if it is only a specific quantity of energy because it doesn't tell us whether it is a particle or a wave. Added to that, the time normalization in QM denudes the quantum of its 'per second' realism.

But the original Quantum finds more measure than given credit for. Boltzman's Constant obtains from the Gas Constant/Avagadros Number, and so Boltzman is a physical proportion that gives the energy/temperature associated with a single source particle. By relation with Planck's Constant as a physical proportion of energy/time, there is a complex measure of a single physical wave at any specified frequency which carries the celebrated energy quantity per every 1/f from a single source. That's a lot of information to start with.

To an experimentalist, CHSH isn't half the story. What is the wave doing and how, such that some ranges of frequencies penetrate deep into the dirt and others bounce off airplanes? Each single wavelength carries the same energy. How's it do that?! - Duhhoohhhh - :) jrc

report post as inappropriate

Hi John,

Perceptive and interesting, as always. :-)

I expect you will relish reading this Andrei Khrennikov paper on sampling contextually with different statistical properties.

My own answer to the question of time-dependent quantum measurement in a number theoretic context is in the attached.

All best,

Tom

attachments: Something_I_discovered_from_my_research_into_the_properties_of_Sophie_Germain_primes.pdf

Perceptive and interesting, as always. :-)

I expect you will relish reading this Andrei Khrennikov paper on sampling contextually with different statistical properties.

My own answer to the question of time-dependent quantum measurement in a number theoretic context is in the attached.

All best,

Tom

attachments: Something_I_discovered_from_my_research_into_the_properties_of_Sophie_Germain_primes.pdf

Tom,

Thanks for the links, anybody looking in can access them also, and that is one of the real values of this forum. When participants assume the role of sounding board in the bouncing of ideas off one and another 'The Beat Goes On'. If it starts sounding like a Ping-Pong match, its time to quit the game.

The Khrennikov link is a free sign in to what looks to be an extensive archive, I'll content myself with the download of your att'mt but others might find it fruitful. You are obviously enjoying your retirement giving you the time to pursue what you have long wanted, and that's refreshing, and perhaps more satisfying than those whom have had careers requiring intense research and find themselves now in real proximity to 'publish or perish'. Enjoy! jrc

report post as inappropriate

Thanks for the links, anybody looking in can access them also, and that is one of the real values of this forum. When participants assume the role of sounding board in the bouncing of ideas off one and another 'The Beat Goes On'. If it starts sounding like a Ping-Pong match, its time to quit the game.

The Khrennikov link is a free sign in to what looks to be an extensive archive, I'll content myself with the download of your att'mt but others might find it fruitful. You are obviously enjoying your retirement giving you the time to pursue what you have long wanted, and that's refreshing, and perhaps more satisfying than those whom have had careers requiring intense research and find themselves now in real proximity to 'publish or perish'. Enjoy! jrc

report post as inappropriate

Hello Tom

I read your essay twice and am still not very clear about what you are saying. The fault is entirely mine - for example a lack of background in the type of mathematical/logical arguments you used. Another reason is that at my age (73) I was reading not to explore new ideas, but to confirm my own half-cooked ones in a view to develop them further! For example, based on my Beautiful Universe Theory concepts I think there is no inherent probability in Nature, nor is there particle-wave duality, no wave function collapse (which you agree with) and that Bell's Theorem only confuses the issue. At least about the latter I can point to Edwin Klingman's essay here for a more substantive analysis than my one-liners. In my essay here I argue that in a causal local absolute discrete Universe mathematics and physics reduce to the same thing - not themselves, but the micro structure of Nature itself. As always I value your feedback.

With best wishes

Vladimir

report post as inappropriate

I read your essay twice and am still not very clear about what you are saying. The fault is entirely mine - for example a lack of background in the type of mathematical/logical arguments you used. Another reason is that at my age (73) I was reading not to explore new ideas, but to confirm my own half-cooked ones in a view to develop them further! For example, based on my Beautiful Universe Theory concepts I think there is no inherent probability in Nature, nor is there particle-wave duality, no wave function collapse (which you agree with) and that Bell's Theorem only confuses the issue. At least about the latter I can point to Edwin Klingman's essay here for a more substantive analysis than my one-liners. In my essay here I argue that in a causal local absolute discrete Universe mathematics and physics reduce to the same thing - not themselves, but the micro structure of Nature itself. As always I value your feedback.

With best wishes

Vladimir

report post as inappropriate

Hi Vladimir,

I always enjoy your essays. They are delightfully illustrated, meaningful and fun to read.

Our views of science are diametrically opposed, though. I do not subscribe to the idea that if we just look at the evidence of nature in new ways, all will be clear and obvious. This trendy new philosophy (some call it "embodied cognition") is actually as old as Aristotle and...

view entire post

I always enjoy your essays. They are delightfully illustrated, meaningful and fun to read.

Our views of science are diametrically opposed, though. I do not subscribe to the idea that if we just look at the evidence of nature in new ways, all will be clear and obvious. This trendy new philosophy (some call it "embodied cognition") is actually as old as Aristotle and...

view entire post

Thank you Tom for your kind words about my graphics.

I do understand and respect how science works and am puzzled why you think I do not ! You quote from my Beautiful Universe theory which, as I stated at the outset, is an incomplete and speculative model of how the universe might work. I know I have not treated my ideas mathematically but I have certainly thought out their physical implications. For example in an absolute discrete universe in which signals travel at a maximum of c but at slower rates in regions of higher potential, moving meter sticks get shorter and moving clocks tick at a slower rate, not space and time as dimensions distort. Hence a physics bypassing SR and GR is possible. I did not yet prove it mathematically, but it certainly played out from physical arguments expressed in words and figures.

The math can be added later but the physical ideas have to come first. That is how Einstein worked - he thought of the weightlessness of a falling man, and it took him (and Grossman) 10 years to clothe the idea mathematically into his General Relativity theory of gravity. I do not see what the problem is with my how I do physics - ideas first and the math to be detailed later.

In no way do I downplay the importance of mathematics in describing physical ideas. In my fqxi essay I try to show why it can describe physics at its own level so well. What I do object to (the tricky part) is that mathematics is so prodigious it can also describe scenarios that have no parallel in Nature. Kepler's ellipses yes, Ptolemy's epicycles no. Both described the same phenomena - is it wrong for me to say we must choose the scenario that is closer to how nature actually works?

And even if I take your advice and work only with mathematics I would say I work with geometrical ideas - a friend swears only algebra can describe nature. It is all fun, and in the end what advances physics will remain.

With appreciation and all best wishes,

Vladimir.

report post as inappropriate

I do understand and respect how science works and am puzzled why you think I do not ! You quote from my Beautiful Universe theory which, as I stated at the outset, is an incomplete and speculative model of how the universe might work. I know I have not treated my ideas mathematically but I have certainly thought out their physical implications. For example in an absolute discrete universe in which signals travel at a maximum of c but at slower rates in regions of higher potential, moving meter sticks get shorter and moving clocks tick at a slower rate, not space and time as dimensions distort. Hence a physics bypassing SR and GR is possible. I did not yet prove it mathematically, but it certainly played out from physical arguments expressed in words and figures.

The math can be added later but the physical ideas have to come first. That is how Einstein worked - he thought of the weightlessness of a falling man, and it took him (and Grossman) 10 years to clothe the idea mathematically into his General Relativity theory of gravity. I do not see what the problem is with my how I do physics - ideas first and the math to be detailed later.

In no way do I downplay the importance of mathematics in describing physical ideas. In my fqxi essay I try to show why it can describe physics at its own level so well. What I do object to (the tricky part) is that mathematics is so prodigious it can also describe scenarios that have no parallel in Nature. Kepler's ellipses yes, Ptolemy's epicycles no. Both described the same phenomena - is it wrong for me to say we must choose the scenario that is closer to how nature actually works?

And even if I take your advice and work only with mathematics I would say I work with geometrical ideas - a friend swears only algebra can describe nature. It is all fun, and in the end what advances physics will remain.

With appreciation and all best wishes,

Vladimir.

report post as inappropriate

Hi Tom,

I have printed out your essay and I am going to study it on my next lie down rest my back break. :-)

Looks like you have been busy here but thought I would inform you if you don't already know that the core part of Joy Christian's model has been proven by Albert Jan Wonnink via the computer program GAViewer. For those interested look here.

Looks like FQXi's panel of experts were very wrong. But you already knew that.

report post as inappropriate

I have printed out your essay and I am going to study it on my next lie down rest my back break. :-)

Looks like you have been busy here but thought I would inform you if you don't already know that the core part of Joy Christian's model has been proven by Albert Jan Wonnink via the computer program GAViewer. For those interested look here.

Looks like FQXi's panel of experts were very wrong. But you already knew that.

report post as inappropriate

Richard Gill continues to attack Joy Christian's measurement framework. My response attached.

attachments: Continuing_misguided_attacks_by.docx

attachments: Continuing_misguided_attacks_by.docx

Yeah, it is rather sad that Gill seems to not realize that he has lost the debate since Albert Jan's computer proof of Joy's model. He quite frankly is carrying on like it didn't happen. Maybe some day he will understand geometric algebra and what Joy's true big discovery is. I'm not holding my breath though.

report post as inappropriate

report post as inappropriate

I would not hold my breath Fred..

Let each out breath inexorably lead to an in breath, then vice versa, and so on. That each inward path leads to an outward one, and outward to inward, is a suitable imitation of the connectedness of S3. I too enjoyed your summary, Tom, and I have to wonder what it would take - because it appears Gill's criteria are a moving target, just as he claims for Joy.

It is ironic that RG wants to use Joy's first paper as the bellwether, given that it is only a sketch of the full proof, and that he has ignored that Bell's first paper contained an error that was later glossed over or corrected - as clearly pointed out by M. Goodband. I think perhaps Joy's use of the Kronecker delta is partially at fault; it is a convenient but lossy abbreviation that leaves too much room for interpretation.

More later,

Jonathan

report post as inappropriate

Let each out breath inexorably lead to an in breath, then vice versa, and so on. That each inward path leads to an outward one, and outward to inward, is a suitable imitation of the connectedness of S3. I too enjoyed your summary, Tom, and I have to wonder what it would take - because it appears Gill's criteria are a moving target, just as he claims for Joy.

It is ironic that RG wants to use Joy's first paper as the bellwether, given that it is only a sketch of the full proof, and that he has ignored that Bell's first paper contained an error that was later glossed over or corrected - as clearly pointed out by M. Goodband. I think perhaps Joy's use of the Kronecker delta is partially at fault; it is a convenient but lossy abbreviation that leaves too much room for interpretation.

More later,

Jonathan

report post as inappropriate

An enjoyable essay Tom..

It took me a while to work through this paper, but it appears your logical reasoning is solid, even though I found some portions confusing. There is a lot I agree with, though it runs counter to prevailing opinion. I especially like that you wove Euler's equation into the story in such a meaningful way. I'll likely have more to say, but a ratings boost is all for now.

Regards,

Jonathan

report post as inappropriate

It took me a while to work through this paper, but it appears your logical reasoning is solid, even though I found some portions confusing. There is a lot I agree with, though it runs counter to prevailing opinion. I especially like that you wove Euler's equation into the story in such a meaningful way. I'll likely have more to say, but a ratings boost is all for now.

Regards,

Jonathan

report post as inappropriate

Hi everyone

I see there is some discussion here of Albert Jan Wonnink's GAViewer program with which he attempted to verify one line in the first "Bell refutation" paper of J J Christian ... from way back in 2007: quant-ph/0703179

He immediately ran into Christian's trademark algebraic error. This is the (-1)^2 = -1 error which Christian needs in order to make embarassing...

view entire post

I see there is some discussion here of Albert Jan Wonnink's GAViewer program with which he attempted to verify one line in the first "Bell refutation" paper of J J Christian ... from way back in 2007: quant-ph/0703179

He immediately ran into Christian's trademark algebraic error. This is the (-1)^2 = -1 error which Christian needs in order to make embarassing...

view entire post

report post as inappropriate

Hi Richard,

Thanks for dropping by. I'll be happy to entertain an exchange here, if it remains collegial.

Your arguments vis a vis Christian always come back to, " ... because of Bell's theorem." Yes, of course, we know that the literature assumes quantum entanglement, such that spin zero decays to spin - 1/2, + 1/2. Because you don't acknowledge that quantum entanglement is no more than an assumption, your argument does not even address the issue of an alternative measurement framework.

Christian, on the other hand, HAS constructed a measurement framework -- published last year in the International Journal of Theoretical Physics -- that purports to demonstrate quantum correlations are NOT " ... because of Bell's theorem." Since one can't demonstrate constructively that the mathematical proof of Bell's theorem is independent of the experimental protocol -- any scientist should welcome an *objective* test that eliminates ad hoc assumptions.

That is what my essay is about -- the possibility of rational correspondence between mathematical model and physical result. Such correspondence cannot be shown valid, without demonstratiing independence of mathematics and physics. Otherwise, one appeals to mystical, non-realistic explanations for correlated phenomena. Should one prefer realism over mysticism? -- a rationalist is so compelled. If science is a rationalist enterprise, science is also so compelled.

Your interpretation of Joy's application of geometric algebra is wrong, and the answer to your title question is "yes." You have neglected Hestenes' interchangeability of geometric algebra with Minkowski space, as well as the topological property of simple connectedness in the 3-sphere. Both of which lead to spinor characteristics in our ordinary measure space, which is 4 dimensional.

Best,

Tom

Thanks for dropping by. I'll be happy to entertain an exchange here, if it remains collegial.

Your arguments vis a vis Christian always come back to, " ... because of Bell's theorem." Yes, of course, we know that the literature assumes quantum entanglement, such that spin zero decays to spin - 1/2, + 1/2. Because you don't acknowledge that quantum entanglement is no more than an assumption, your argument does not even address the issue of an alternative measurement framework.

Christian, on the other hand, HAS constructed a measurement framework -- published last year in the International Journal of Theoretical Physics -- that purports to demonstrate quantum correlations are NOT " ... because of Bell's theorem." Since one can't demonstrate constructively that the mathematical proof of Bell's theorem is independent of the experimental protocol -- any scientist should welcome an *objective* test that eliminates ad hoc assumptions.

That is what my essay is about -- the possibility of rational correspondence between mathematical model and physical result. Such correspondence cannot be shown valid, without demonstratiing independence of mathematics and physics. Otherwise, one appeals to mystical, non-realistic explanations for correlated phenomena. Should one prefer realism over mysticism? -- a rationalist is so compelled. If science is a rationalist enterprise, science is also so compelled.

Your interpretation of Joy's application of geometric algebra is wrong, and the answer to your title question is "yes." You have neglected Hestenes' interchangeability of geometric algebra with Minkowski space, as well as the topological property of simple connectedness in the 3-sphere. Both of which lead to spinor characteristics in our ordinary measure space, which is 4 dimensional.

Best,

Tom

I will give some further explanation about what Albert Jan did with GAViewer so that others are not hoodwinked by Gill's misrepresentations.

The geometric algebra program GAViewer is fixed in a right handed bivector basis. So in order to see the left handed bivector basis part of Joy's model, all one has to do is reverse the order of the geometric product AB to BA. IOW, from a right handed perspective, one sees the order reversed for the left handed part. Lambda simply toggles between the two orders to correctly represent the model from the right handed only perspective. Pretty easy to understand and the model works as advertised. And what Albert Jan did is simple and elegant.

report post as inappropriate

The geometric algebra program GAViewer is fixed in a right handed bivector basis. So in order to see the left handed bivector basis part of Joy's model, all one has to do is reverse the order of the geometric product AB to BA. IOW, from a right handed perspective, one sees the order reversed for the left handed part. Lambda simply toggles between the two orders to correctly represent the model from the right handed only perspective. Pretty easy to understand and the model works as advertised. And what Albert Jan did is simple and elegant.

report post as inappropriate

Fred,

Thanks for pointing that out, GAViewer sounds like 'graphic arts drawing' tool to me, and would not be built to select between a right or left mathematical handedness. It also points out the importance of thinking through any proposed experimental protocol, and especially with the growing reliance on computerized simulation. In Theory, a process is an interactive dynamic. In physical practice, a process is a something - like the bump at the end of a bone that the muscles connect to. In Theory all you need for a mathematical process to be complete is to specify an initial state, it will stick together just fine. In Experiment, to get two things to physically stick together initially, you need to add a mechanical process and that can introduce an asymmetry into an otherwise mathematically symmetrical dynamic. Measure twice, cut once. jrc

report post as inappropriate

Thanks for pointing that out, GAViewer sounds like 'graphic arts drawing' tool to me, and would not be built to select between a right or left mathematical handedness. It also points out the importance of thinking through any proposed experimental protocol, and especially with the growing reliance on computerized simulation. In Theory, a process is an interactive dynamic. In physical practice, a process is a something - like the bump at the end of a bone that the muscles connect to. In Theory all you need for a mathematical process to be complete is to specify an initial state, it will stick together just fine. In Experiment, to get two things to physically stick together initially, you need to add a mechanical process and that can introduce an asymmetry into an otherwise mathematically symmetrical dynamic. Measure twice, cut once. jrc

report post as inappropriate

This essay appears indeed highly erudite but I wonder how much the author has understood of the authors he is citing. Let me illustrate this with the citations he gives to papers in an area I know well: Bell inequalities.

Instead of plugging the Joy Christian model, Thomas Ray is now plugging Hess and Philipp, who more than ten years ago published a bunch of papers with the main theme that...

view entire post

Instead of plugging the Joy Christian model, Thomas Ray is now plugging Hess and Philipp, who more than ten years ago published a bunch of papers with the main theme that...

view entire post

report post as inappropriate

Gill's wordy reply support's Karl Hess's claim that Gill "makes himself a pretzel" to defend his views while disparaging constructive alternatives with irrelevant misdirection.

" ... Bell was very aware of the role of time, and gave specific experimental instructions so that one would *not* be able to blame a violation of his inequality on time".

Uh ... yeah. That's the core of what Hess-Philipp (and I) have been saying. The Bell-Aspect program does no more than prove its own assumptions.

Gill's "friend" Han Geurdes is cited (not quoted) as an example of a trivial proof that "The free will to choose both a proposition and the negation of that proposition is contradictory of free will in any physical sense." And I have discussed this with Han -- it is in fact, Gill himself who characterized the proof as 'trivial,' in the PubPeer discussion to which he refers, and I happen to agree with the characterization. The fact that it is trivial only underscores its importance to measure theory.

I have never "plugged" Joy Christian or anyone else. It is Gill who is so enamored of personality cults that he confuses science with scientist. At any rate, Joy Christian's program does not contradict the contents of the essay -- I just didn't need it to make my point.

Time and events to follow will reveal whether "the essayist knows what he is talking about." And whether the voice of authority is stronger than rational science.

Tom

" ... Bell was very aware of the role of time, and gave specific experimental instructions so that one would *not* be able to blame a violation of his inequality on time".

Uh ... yeah. That's the core of what Hess-Philipp (and I) have been saying. The Bell-Aspect program does no more than prove its own assumptions.

Gill's "friend" Han Geurdes is cited (not quoted) as an example of a trivial proof that "The free will to choose both a proposition and the negation of that proposition is contradictory of free will in any physical sense." And I have discussed this with Han -- it is in fact, Gill himself who characterized the proof as 'trivial,' in the PubPeer discussion to which he refers, and I happen to agree with the characterization. The fact that it is trivial only underscores its importance to measure theory.

I have never "plugged" Joy Christian or anyone else. It is Gill who is so enamored of personality cults that he confuses science with scientist. At any rate, Joy Christian's program does not contradict the contents of the essay -- I just didn't need it to make my point.

Time and events to follow will reveal whether "the essayist knows what he is talking about." And whether the voice of authority is stronger than rational science.

Tom

I have never doubted Richard Gill's sincerity and expertise in defending Bell's theorem orthodoxy. He is certainly misguided, though, in his assumption that Bell's Bertlmann's Socks analogy eliminates the issue of a missing time parameter.

Consider Bell's illustrations 4 & 5. Bell (and Gill) would have us believe that the Stern-Gerlach magnet rotation produces separated groups (quantum mechanical pattern) of particle detections as a result of fundamental quantum non-locality.

Einstein, however -- using the mathematical convention of Minkowski space -- never considered this spatial parameter independent of the time parameter. The problem arises in the microscopic scale. Every point of spacetime in relativity carries its own clock independent of scale, a point that Karl Hess and Walter Philipp made quite elegantly to apply on the quantum microscopic scale, and which Gill's (with Weihs, Zeilinger and Zukowski) criticism -- despite his claim -- fails to refute.

A modified version of the 2-slit experiment (Young), where particles are sent one at a time through the slits -- and nevertheless arrange themselves in the classical wave interference pattern as if each particle "knows" where the other went -- is local and time dependent. It is unmotivated, other than by mere assumptions of quantum entanglement and non-locality, that measurement scale affects hidden-variable continuity in the spacetime subspace of local measure. (I have an existence proof of this claim that I am not yet ready to discuss publicly.)

In the words of Hess-Philipp " ... a properly chosen sum of what we call setting dependent subspace product measures (SDSPM) does not violate Einstein-separability and does lead to the quantum result ..."

Tom

Consider Bell's illustrations 4 & 5. Bell (and Gill) would have us believe that the Stern-Gerlach magnet rotation produces separated groups (quantum mechanical pattern) of particle detections as a result of fundamental quantum non-locality.

Einstein, however -- using the mathematical convention of Minkowski space -- never considered this spatial parameter independent of the time parameter. The problem arises in the microscopic scale. Every point of spacetime in relativity carries its own clock independent of scale, a point that Karl Hess and Walter Philipp made quite elegantly to apply on the quantum microscopic scale, and which Gill's (with Weihs, Zeilinger and Zukowski) criticism -- despite his claim -- fails to refute.

A modified version of the 2-slit experiment (Young), where particles are sent one at a time through the slits -- and nevertheless arrange themselves in the classical wave interference pattern as if each particle "knows" where the other went -- is local and time dependent. It is unmotivated, other than by mere assumptions of quantum entanglement and non-locality, that measurement scale affects hidden-variable continuity in the spacetime subspace of local measure. (I have an existence proof of this claim that I am not yet ready to discuss publicly.)

In the words of Hess-Philipp " ... a properly chosen sum of what we call setting dependent subspace product measures (SDSPM) does not violate Einstein-separability and does lead to the quantum result ..."

Tom

John Cox has an elegant way of bringing the issues in line with everyday experience.

Having devoted part of my misspent youth to the pool table, John's reference to the relation between shooting pool and moment-to-moment instinct got me thinking about Hess-Philipp's timelike correlated parameters (TLCPs) .

Because initial condition changes with time, moment-to-moment action (event...

view entire post

Having devoted part of my misspent youth to the pool table, John's reference to the relation between shooting pool and moment-to-moment instinct got me thinking about Hess-Philipp's timelike correlated parameters (TLCPs) .

Because initial condition changes with time, moment-to-moment action (event...

view entire post

More should be said about why the Karl Hess and Walter Philipp PNAS paper of 2001 is a breakthrough in our understanding of time dependent systems, because it accents the physical identities among time, information and energy that characterizes complex systems -- and as the authors make explicit, the problem of decidability between Einstein and Bohr.

Criticisms of Hess-Philipp have failed...

view entire post

Criticisms of Hess-Philipp have failed...

view entire post

attachments: Walter2002.pdf

Tom,

I'm glad I managed to get to your essay. Again I found little to disagree with, but then I'm now down to speed-reading so resolution is reduced! There's also now little time for discussion, which I suspect may be a blessing, though our fundamental views may have more in common than is often apparent. Certainly I found the essay beautifully 'bookended' with Bronowki's quote (always a guiding star for my own work) and your concluding paragraph.

"In this game of unlimited possibilities called mathematics, our bet is on human imagination."

As you're a mathematician I'm particularly impressed with that. I see you're struggling to make the break point so I hope my score helps.

best wishes.

Peter

report post as inappropriate

I'm glad I managed to get to your essay. Again I found little to disagree with, but then I'm now down to speed-reading so resolution is reduced! There's also now little time for discussion, which I suspect may be a blessing, though our fundamental views may have more in common than is often apparent. Certainly I found the essay beautifully 'bookended' with Bronowki's quote (always a guiding star for my own work) and your concluding paragraph.

"In this game of unlimited possibilities called mathematics, our bet is on human imagination."

As you're a mathematician I'm particularly impressed with that. I see you're struggling to make the break point so I hope my score helps.

best wishes.

Peter

report post as inappropriate

Peter,

Thank you, that's very kind. There's no mystery to why my score languishes below the cut -- never in my memory, from the first time I entered these competitions (which dates from the very beginning), has a fully relativistic viewpoint in foundational physics gotten due respect, while some of the fringiest views in quantum theory have won big prizes. So I have long abandoned any...

view entire post

Thank you, that's very kind. There's no mystery to why my score languishes below the cut -- never in my memory, from the first time I entered these competitions (which dates from the very beginning), has a fully relativistic viewpoint in foundational physics gotten due respect, while some of the fringiest views in quantum theory have won big prizes. So I have long abandoned any...

view entire post

We don't agree most times but we get to exchange ideas. It is good to rate those who are here come rain come shine and who have also contributed a nice essay. We continue our arguments (or 'quarrels') after the contest. You should now be able to make the list.

Akinbo

report post as inappropriate

Akinbo

report post as inappropriate

Dear Tom,

I'm sorry but it's late and I don't have time to comment properly, except to say that I really enjoyed your essay a lot; I hope to be able to comment properly tomorrow if the system still allows. I believe too that Vesselin should have received more attention. For what it's worth, you have my vote.

Alma

report post as inappropriate

report post as inappropriate

I'm sorry but it's late and I don't have time to comment properly, except to say that I really enjoyed your essay a lot; I hope to be able to comment properly tomorrow if the system still allows. I believe too that Vesselin should have received more attention. For what it's worth, you have my vote.

Alma

report post as inappropriate

Alma,

Your essay is an absolute treasure, as I commented in your forum. Thanks for reading mine.

By the way, though the spelling is different, you wouldn't be related to one of my favorite playwrights, Eugen Ionesco, would you? :-)

All best,

Tom

Your essay is an absolute treasure, as I commented in your forum. Thanks for reading mine.

By the way, though the spelling is different, you wouldn't be related to one of my favorite playwrights, Eugen Ionesco, would you? :-)

All best,

Tom

Dear Tom,

Since the reply button is still active so I’m back to tell you how much I enjoyed your essay and why. Firstly, I think you write really well, and here I mean your style and not the technical side. Actually it’s impressive that the essay itself is*very* technical and attacks *difficult* problems that I am sure took time to develop and yet it’s expressed in a very...

view entire post

Since the reply button is still active so I’m back to tell you how much I enjoyed your essay and why. Firstly, I think you write really well, and here I mean your style and not the technical side. Actually it’s impressive that the essay itself is

view entire post

report post as inappropriate

Dear Alma,

A writer's greatest reward is to be understood. Thank you! I sometimes feel I should apologize for being subtle, and yet I find that one can't apply natural language with the desired precision, without putting a fine point on it. Someday, I expect, we will communicate in a universal language -- if not mathematics as we know it, then something like mathematics -- that smooths...

view entire post

A writer's greatest reward is to be understood. Thank you! I sometimes feel I should apologize for being subtle, and yet I find that one can't apply natural language with the desired precision, without putting a fine point on it. Someday, I expect, we will communicate in a universal language -- if not mathematics as we know it, then something like mathematics -- that smooths...

view entire post

Dear Tom,

I kept some of the most beautiful essays for the end. Yours is really nice. I agree with many of your viewpoints, and you presented them so good. Many make confusion between Tegmark's MUH and mathematical Platonism, and it is great you clarify this. And the rest of the essay contains so many intriguing remarks. I hope your essay will do fine!

Best regards,

Cristi

report post as inappropriate

I kept some of the most beautiful essays for the end. Yours is really nice. I agree with many of your viewpoints, and you presented them so good. Many make confusion between Tegmark's MUH and mathematical Platonism, and it is great you clarify this. And the rest of the essay contains so many intriguing remarks. I hope your essay will do fine!

Best regards,

Cristi

report post as inappropriate

Login or create account to post reply or comment.