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

**Anonymous**: *on* 4/21/15 at 0:26am UTC, wrote Dear Paul, I appreciated and enjoyed your very concise yet lucid essay. I...

**Joe Fisher**: *on* 4/3/15 at 16:24pm UTC, wrote I think Newton was wrong about abstract gravity; Einstein was wrong about...

**Alexey/Lev Burov**: *on* 4/3/15 at 3:16am UTC, wrote Dear Paul, your essay is like a breath of fresh air. I agree with the...

**Edwin Klingman**: *on* 3/15/15 at 21:24pm UTC, wrote Dear Paul Merriam, Your brief essay focuses powerfully on the key argument...

**Akinbo Ojo**: *on* 3/9/15 at 14:06pm UTC, wrote Hi Paul, Your essay touches on aspects of physics of interest to me,...

**Gary Simpson**: *on* 3/5/15 at 0:07am UTC, wrote Paul, Physics deals with measurements. The color green has a wavelength....

**Sujatha Jagannathan**: *on* 2/26/15 at 17:33pm UTC, wrote Your representation is independent with your views, equations and the...

**Tommaso Bolognesi**: *on* 2/25/15 at 9:53am UTC, wrote Dear Paul, not many of the essays I’ve read so far discuss what...

RECENT FORUM POSTS

**Marcel-Marie LeBel**: "Georgina, There is no instantaneity along the rod or within the coffee. It..."
*in* The Nature of Time

**Stefan Weckbach**: "Hi Lorraine, thanks for your explanations. I think I now better..."
*in* The Present State of...

**Georgina Woodward**: "Consider ice cream in hot coffee. They stay together, 'in time', as..."
*in* The Nature of Time

**Mykel Waggoner**: "This is a link to a paper I wrote, as it explains how Quantum Entanglement..."
*in* Alternative Models of...

**Lorraine Ford**: "Hi Stefan, Replying to your last couple of posts, this is the way I would..."
*in* The Present State of...

**Robert McEachern**: ""There are more things in heaven and earth, Horatio, than are dreamt of in..."
*in* Undecidability,...

**Georgina Woodward**: "Max? Why?"
*in* Anatomy of spacetime and...

**Steve Agnew**: "Mueller opens his essay with... "As the argument goes, there are truths..."
*in* Undecidability,...

RECENT ARTICLES

*click titles to read articles*

**The Quantum Clock-Maker Investigating COVID-19, Causality, and the Trouble with AI**

Sally Shrapnel, a quantum physicist and medical practitioner, on her experiments into cause-and-effect that could help us understand time’s arrow—and build better healthcare algorithms.

**Connect the Quantum Dots for a New Kind of Fuel**

'Artificial atoms' allow physicists to manipulate individual electrons—and could help to reduce energy wastage in electronic devices.

**Can Choices Curve Spacetime?**

Two teams are developing ways to detect quantum-gravitational effects in the lab.

**The Quantum Engine That Simultaneously Heats and Cools **

Tiny device could help boost quantum electronics.

**The Quantum Refrigerator**

A tiny cooling device could help rewrite the thermodynamic rule book for quantum machines.

RECENT FORUM POSTS

RECENT ARTICLES

Sally Shrapnel, a quantum physicist and medical practitioner, on her experiments into cause-and-effect that could help us understand time’s arrow—and build better healthcare algorithms.

'Artificial atoms' allow physicists to manipulate individual electrons—and could help to reduce energy wastage in electronic devices.

Two teams are developing ways to detect quantum-gravitational effects in the lab.

Tiny device could help boost quantum electronics.

A tiny cooling device could help rewrite the thermodynamic rule book for quantum machines.

FQXi FORUM

September 21, 2021

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

TOPIC: Limits of Mathematical Representation by Paul Merriam [refresh]

TOPIC: Limits of Mathematical Representation by Paul Merriam [refresh]

There are fundamental limits to what physicists can represent by mathematics. It would seem that at least three empirical phenomena cannot be entirely represented by mathematics. These three phenomena are 1. qualia, 2. that aspect of time we call the unique 'now', and 3. existence.

I am a degreed independent researcher. I've been thinking about these things for a long time, and reading the mountain of recent papers online.

Hello. I just gave you the highest rate because this is the first essay I see in this contest (apart from mine) that is fully relevant to the topic and does not contain any nonsense. Indeed I saw most other essays as full of nonsense and still getting much higher rates than they deserve (as so many authors rate essays absurdly, having little clue about modern physics, or the foundations of maths, or about which ideas make sense). Then, while I cannot correct that by giving most of them the lowest rate, I considered searching for no-nonsense essays, even with only modest but correct value, to give them higher rates for contrast, which I finally found here. Indeed you correctly pointed out the core aspects of the non-mathematical side of reality.

In my essay A Mind/Mathematics Dualistic Foundation of Physical Reality I explained the logical articulation between these non-mathematical aspects and the mathematical ones, which also have their share of truth as shown by the amazing success of modern mathematical physics.

report post as inappropriate

In my essay A Mind/Mathematics Dualistic Foundation of Physical Reality I explained the logical articulation between these non-mathematical aspects and the mathematical ones, which also have their share of truth as shown by the amazing success of modern mathematical physics.

report post as inappropriate

Dear Paul,

All the issues that you are addressing has already been addressed extensively.

1. The assumption that reality exists outside of us is the basis of all our successful theories.

2. Time issue has been looked at from many perspectives. The issue is which one is the best or what could be a better one. Not that there is no solution.

3. first part has already been addressed in point 1. The mathematical part has no direct bearing on the issue at hand.

report post as inappropriate

All the issues that you are addressing has already been addressed extensively.

1. The assumption that reality exists outside of us is the basis of all our successful theories.

2. Time issue has been looked at from many perspectives. The issue is which one is the best or what could be a better one. Not that there is no solution.

3. first part has already been addressed in point 1. The mathematical part has no direct bearing on the issue at hand.

report post as inappropriate

Dear Paul,

not many of the essays I’ve read so far discuss what mathematics is*not* good at describing, while you provide three valuable and convincing examples. It is hard to disagree with you. But it seems to me that the three aspects that you mention are indeed related - they fit under the unique umbrella of consciousness. I optimistically suppose that, once a solid, scientific theory of consciousness is found (if ever!), then we shall also be able to assign a precise meaning to the concept of ‘now’, to qualia, and perhaps even to the elusive concept of ‘existence’. What do you think?

Indeed, one of the things I like in Tegmark’s work is that the Mathematical Universe can well include conscious entities (SAS - Self Aware Substructures), opening the door for the mathematical description of a universe (rather, multiverse) that includes not just one, but multiple forms of consciousness, as boldly claimed by a fictional character in my essay…

Best regards

Tommaso

report post as inappropriate

not many of the essays I’ve read so far discuss what mathematics is

Indeed, one of the things I like in Tegmark’s work is that the Mathematical Universe can well include conscious entities (SAS - Self Aware Substructures), opening the door for the mathematical description of a universe (rather, multiverse) that includes not just one, but multiple forms of consciousness, as boldly claimed by a fictional character in my essay…

Best regards

Tommaso

report post as inappropriate

Your representation is independent with your views, equations and the peripheral calculations suspect deviation recurring with the digits.

With regards,

Miss. Sujatha Jagannathan

report post as inappropriate

With regards,

Miss. Sujatha Jagannathan

report post as inappropriate

Paul,

Physics deals with measurements. The color green has a wavelength. That can be measured. The only way one might hope to measure the qualia of experiencing green would be with a brain scan.

Physics can measure the interval between successive "nows" but it cannot measure now.

Existence - historically, physics deals with measurements of things that exist. You can not measure something that does not exist. So physics does not attempt to address such an issue.

Best Regards and Good Luck,

Gary Simpson

report post as inappropriate

Physics deals with measurements. The color green has a wavelength. That can be measured. The only way one might hope to measure the qualia of experiencing green would be with a brain scan.

Physics can measure the interval between successive "nows" but it cannot measure now.

Existence - historically, physics deals with measurements of things that exist. You can not measure something that does not exist. So physics does not attempt to address such an issue.

Best Regards and Good Luck,

Gary Simpson

report post as inappropriate

Hi Paul,

Your essay touches on aspects of physics of interest to me, especially 'now' and 'existence'.

Can you clarify your statement,*"Time can also be conceived as a collection D of durations d. But this has the same problems"*. What kind of problems?

When you say, "*Attempts to prove something exists using logic fail, because existence proofs can be traced back to an assumption about whether some primitive or first thing exists...*". A different perspective and deduction from this is therefore that we should trace existence proofs differently, amending the statement to, "Attempts to prove something exists using logic WILL SUCCEED, IF existence proofs can be traced back to an assumption about NON-EXISTENCE...". In other words, existence can only arise from non-existence and vice-versa the ultimate fate of what exists is non-existence.

If I may ask your opinion, can what exists perish or is it eternally existing? Can the universe perish? Parmenides believes what exists does so eternally. I argue otherwise in my essay.

Best regards and all the best in the competition,

Akinbo

report post as inappropriate

Your essay touches on aspects of physics of interest to me, especially 'now' and 'existence'.

Can you clarify your statement,

When you say, "

If I may ask your opinion, can what exists perish or is it eternally existing? Can the universe perish? Parmenides believes what exists does so eternally. I argue otherwise in my essay.

Best regards and all the best in the competition,

Akinbo

report post as inappropriate

Dear Paul Merriam,

Your brief essay focuses powerfully on the key argument against Platonic faith that phenomenal universe either "derives" or "emerges" from math; that is the apparent fact that mathematics cannot entirely or sufficiently represent 1.) Qualia, 2.) 'Now', or 3.) Existence. You conclude that mathematics is the language of pattern. I begin my essay describing the way in which such patterns can be extracted from measurement numbers and mapped into optimal 'pattern vectors' or 'feature vectors' as the basis of physics, then I consider the fact that the pattern vectors or maps are not unique and can, as FQXi suggests, "trick us". I consider the case in which we may have already been tricked for 50 years.

You state "**attempts to prove something exists using logic fails**", but for 50 years the attempt to prove the existence of "entanglement" has been strictly by use of logic. *Entanglement*, despite current beliefs, is not measured, it is inferred logically by belief that Bell's oversimplified physics assumptions are valid. As you refer to Spekkens, I see you are familiar with such logical inference, and I invite you to read a more physically-based approach.

I invite you to read my essay and welcome any comments you might have.

Best,

Edwin Eugene Klingman

report post as inappropriate

Your brief essay focuses powerfully on the key argument against Platonic faith that phenomenal universe either "derives" or "emerges" from math; that is the apparent fact that mathematics cannot entirely or sufficiently represent 1.) Qualia, 2.) 'Now', or 3.) Existence. You conclude that mathematics is the language of pattern. I begin my essay describing the way in which such patterns can be extracted from measurement numbers and mapped into optimal 'pattern vectors' or 'feature vectors' as the basis of physics, then I consider the fact that the pattern vectors or maps are not unique and can, as FQXi suggests, "trick us". I consider the case in which we may have already been tricked for 50 years.

You state "

I invite you to read my essay and welcome any comments you might have.

Best,

Edwin Eugene Klingman

report post as inappropriate

Dear Paul, your essay is like a breath of fresh air.

I agree with the limitations you pointed out, and would add to them one more: mathematics will never be able to answer the question about its 'unreasonable effectiveness in natural science'. The reason we think this way can be found in our essay.

Best regards,

Alexey Burov.

report post as inappropriate

I agree with the limitations you pointed out, and would add to them one more: mathematics will never be able to answer the question about its 'unreasonable effectiveness in natural science'. The reason we think this way can be found in our essay.

Best regards,

Alexey Burov.

report post as inappropriate

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

report post as inappropriate

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

report post as inappropriate

Dear Paul,

I appreciated and enjoyed your very concise yet lucid essay. I agree with you that as of its present state, mathematics is unable to represent the concepts you mentioned, but I also believe that at present we have barely touched the expressive power of mathematics.

The limitations you point out in your essay are, I believe, ultimately due to the fact that classical logic permits only a binary distinction between true and false propositions. However, there are many, many other kinds of logic, and who is to say that one cannot construct mathematical systems on these which can, if not completely represent the things you mentioned, cone much closer to doing so? The lowest hanging fruit among them is, in my opinion, existence, and in my own entry I argue that extending classical logic by two non-classical ones permits us to define modes of existence which can be mapped to a possible distinction that exists in the real world at microscopic scales. Note, this sort of endeavor is still, as far as I can tell, in its infancy, so even if it does not overcome some the limitations as you point them out, it is not necessarily the case, in my opinion, that it never will.

Nevertheless, I agree that it is a good idea to keep in the back of one's mind the limitations of mathematical representation, if only to try to break through them.

Best wishes,

Armin

report post as inappropriate

I appreciated and enjoyed your very concise yet lucid essay. I agree with you that as of its present state, mathematics is unable to represent the concepts you mentioned, but I also believe that at present we have barely touched the expressive power of mathematics.

The limitations you point out in your essay are, I believe, ultimately due to the fact that classical logic permits only a binary distinction between true and false propositions. However, there are many, many other kinds of logic, and who is to say that one cannot construct mathematical systems on these which can, if not completely represent the things you mentioned, cone much closer to doing so? The lowest hanging fruit among them is, in my opinion, existence, and in my own entry I argue that extending classical logic by two non-classical ones permits us to define modes of existence which can be mapped to a possible distinction that exists in the real world at microscopic scales. Note, this sort of endeavor is still, as far as I can tell, in its infancy, so even if it does not overcome some the limitations as you point them out, it is not necessarily the case, in my opinion, that it never will.

Nevertheless, I agree that it is a good idea to keep in the back of one's mind the limitations of mathematical representation, if only to try to break through them.

Best wishes,

Armin

report post as inappropriate

Login or create account to post reply or comment.