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.

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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.

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

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**Trick or Truth: The Mysterious Connection Between Physics and Mathematics**

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Current Essay Contest

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Previous Contests

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

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

Contest Partner: The Peter and Patricia Gruber Fund.

read/discuss • winners

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RECENT POSTS IN THIS TOPIC

**Jonathan Dickau**: *on* 4/17/15 at 18:03pm UTC, wrote I want to thank you Daniel.. I had not seen the Lloyd and Dreyer paper...

**Jonathan Dickau**: *on* 4/17/15 at 3:39am UTC, wrote Thanks for the thoughtful reply Daniel.. Sorry someone else pushed your...

**Daniel Braun**: *on* 4/16/15 at 8:39am UTC, wrote Hello Jonathan, thank you very much for your kind words and pushing my...

**Jonathan Dickau**: *on* 4/15/15 at 23:53pm UTC, wrote Hello Daniel, I greatly enjoyed your excellent essay. As luck would have...

**Joe Fisher**: *on* 4/8/15 at 15:45pm UTC, wrote Dear Daniel, I think Newton was wrong about abstract gravity; Einstein was...

**Daniel Braun**: *on* 4/7/15 at 12:07pm UTC, wrote Dear Marc, no, that equation is supposed to be exact (incidentally, I just...

**Marc Séguin**: *on* 4/6/15 at 19:17pm UTC, wrote Dear Daniel, That's quite an equation in your paper! If I understand...

**Daniel Braun**: *on* 4/6/15 at 13:54pm UTC, wrote Dear Marc, thank you very much for your kind remarks, and bumping up the...

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Physicists are using optogenetics techniques to make a rudimentary agent, from cellular components, which can convert measurements into actions using light.

Investigating how quantum memory storage could aid machine learning and how quantum interactions with the environment may have played a role in evolution.

A proposed quantum set-up that could predict your game-playing strategy resurrects Newcomb’s classic quiz show paradox.

Investigating how the quantum measurement process might be related to the emergence of intelligence, agency and free will.

Why do we remember the past and not the future? Untangling the connections between cause and effect, choice, and entropy.

FQXi FORUM

June 3, 2020

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

TOPIC: Thoughts on a Theory of Theories by Daniel Braun [refresh]

TOPIC: Thoughts on a Theory of Theories by Daniel Braun [refresh]

I analyze the set of possible physical theories using the mathematical tool of set theory. The analysis starts from simple classical theories and extends all the way to quantum field theories. Guided by the analysis of existing theories of Nature, we explore how these theories could be generalized while still qualifying as a physical theory. This allows us to calculate the cardinality of the set of possible physical theories, and therefore to quantify how special our mathematical descriptions of Nature are.

I studied physics in Stuttgart, and, with a Fulbright grant, in Stony Brook. Then I moved to Paris and got a Ph.D. in physics at the University Paris Sud (Orsay) with work in mesoscopic solid state physics. Quantum chaos was center stage during my post-doc time in Essen, at the end of which I moved into quantum information theory. After four years in semi-conductor industry developing MRAM, I went back to academia as professor for theoretical physics in Toulouse, France. Since 2013 I am professor for theoretical physics in Tuebingen with a focus on quantum optics and quantum information.

Dear Professor Braun,

We read your essay with lot of interest, and enjoyed it, especially for the novelty of the idea.

We have a question in the context of non relativistic quantum mechanics and the process of quantum measurement. Do you adhere to the Copenhagen interpretation (this is the impression we get from reading your essay)? Many physicists including us regard this interpretation as problematic, because of the artificially assumed quantum - classical divide between system and apparatus. Let us consider the following three popular alternatives to Copenhagen:

Many worlds interpretation: no collapse of the wave-function, branching of alternatives [origin of Born probability rule obscure]

Bohmian mechanics as an equivalent mathematical reformulation of quantum mechanics - probabilities arise because of the so-called typicality assumption of initial condirions [We could not understand your remark "The lack of a consistent hidden variable description of the microscopic world entails a jump in cardinality of the set of possible physical theories from א2 to א3! "....to our understanding non-local hidden variable theories (generally referred to as Bohmian mechanics nowadays) are consistent at the non-relativistic level].

Phenomenologically Modified QM : GRW / Continuos spontaneous Localisation (CSL): Born rule arises from the stochastic nature of the modification.

While all these three variants have their own limitations and may turn out to be wrong eventually, it is our impression they do better than the Copenhagen interpretation.

We were wondering if the cardinality issue gets modified (looking more like classical) f you consider many-worlds / Bohemian / CSL, or is there no change compared to standard QM? We would be very interested to know what the answer is.

Thanks and regards,

Anshu, Tejinder

report post as inappropriate

We read your essay with lot of interest, and enjoyed it, especially for the novelty of the idea.

We have a question in the context of non relativistic quantum mechanics and the process of quantum measurement. Do you adhere to the Copenhagen interpretation (this is the impression we get from reading your essay)? Many physicists including us regard this interpretation as problematic, because of the artificially assumed quantum - classical divide between system and apparatus. Let us consider the following three popular alternatives to Copenhagen:

Many worlds interpretation: no collapse of the wave-function, branching of alternatives [origin of Born probability rule obscure]

Bohmian mechanics as an equivalent mathematical reformulation of quantum mechanics - probabilities arise because of the so-called typicality assumption of initial condirions [We could not understand your remark "The lack of a consistent hidden variable description of the microscopic world entails a jump in cardinality of the set of possible physical theories from א2 to א3! "....to our understanding non-local hidden variable theories (generally referred to as Bohmian mechanics nowadays) are consistent at the non-relativistic level].

Phenomenologically Modified QM : GRW / Continuos spontaneous Localisation (CSL): Born rule arises from the stochastic nature of the modification.

While all these three variants have their own limitations and may turn out to be wrong eventually, it is our impression they do better than the Copenhagen interpretation.

We were wondering if the cardinality issue gets modified (looking more like classical) f you consider many-worlds / Bohemian / CSL, or is there no change compared to standard QM? We would be very interested to know what the answer is.

Thanks and regards,

Anshu, Tejinder

report post as inappropriate

Dear Tejinder,

Thank you very much for your kind remarks and interest.

I did not make an assumption about the interpretation of quantum mechanics, and I don't think it enters into the cardinality calculation. The reason is that I consider possible QM theories as mappings from Hamiltonians to time evolution laws (plus possibly representations of operators for relevant physical...

view entire post

Thank you very much for your kind remarks and interest.

I did not make an assumption about the interpretation of quantum mechanics, and I don't think it enters into the cardinality calculation. The reason is that I consider possible QM theories as mappings from Hamiltonians to time evolution laws (plus possibly representations of operators for relevant physical...

view entire post

Dear Daniel,

Many thanks for your answer. I tend to agree with you. Many worlds is likely to be different, because no collapse takes place, and probabilities are likely only an apparent effect.

Best regards,

Tejinder

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Many thanks for your answer. I tend to agree with you. Many worlds is likely to be different, because no collapse takes place, and probabilities are likely only an apparent effect.

Best regards,

Tejinder

report post as inappropriate

Dear Daniel,

Thank you for an interesting and ambitious essay. You raise original questions about calculating the cardinality of the ensemble of all physical quantities and physical theories. I found the following sentence particularly interesting:

"We can safely claim that no useful physical quantity is known that involves powers larger than say one hundred."

Indeed, of all the SI derived units (newton, joule, watt, etc.), only 4 involve a third (or minus third) power, and only one, the farad, involves a fourth power : F = 1 kg^−1 x m^−2 x s^4 x A^2. I had never really given a second thought about the issue... very interesting! NASA engineers that worked on the Hubble space telescope found it useful to define the jounce as the fourth derivative of the position, so its units are m/s^-4, but once again, we don't get higher than fourth power!

Later on in your essay, I think you made an interesting distinction between physical laws of "fundamental type" and of "secondary type" (that involve weird and arbitrary functions of dimensionless ratios).

Your essay deals in an original and interesting way with the question of the cardinality of possible physical laws compared to the cardinality of all possible mathematical laws, and it makes a worthwhile contribution to the ideas that have been put forward in this contest. Strangely enough, it has been a bit forgotten so far in the competition, and I hope bumping it higher will make it more noticeable. Good luck!

Marc

report post as inappropriate

Thank you for an interesting and ambitious essay. You raise original questions about calculating the cardinality of the ensemble of all physical quantities and physical theories. I found the following sentence particularly interesting:

"We can safely claim that no useful physical quantity is known that involves powers larger than say one hundred."

Indeed, of all the SI derived units (newton, joule, watt, etc.), only 4 involve a third (or minus third) power, and only one, the farad, involves a fourth power : F = 1 kg^−1 x m^−2 x s^4 x A^2. I had never really given a second thought about the issue... very interesting! NASA engineers that worked on the Hubble space telescope found it useful to define the jounce as the fourth derivative of the position, so its units are m/s^-4, but once again, we don't get higher than fourth power!

Later on in your essay, I think you made an interesting distinction between physical laws of "fundamental type" and of "secondary type" (that involve weird and arbitrary functions of dimensionless ratios).

Your essay deals in an original and interesting way with the question of the cardinality of possible physical laws compared to the cardinality of all possible mathematical laws, and it makes a worthwhile contribution to the ideas that have been put forward in this contest. Strangely enough, it has been a bit forgotten so far in the competition, and I hope bumping it higher will make it more noticeable. Good luck!

Marc

report post as inappropriate

Dear Marc,

thank you very much for your kind remarks, and bumping up the rating of my essay. Given the small number of ratings so far, this had an immediate positive effect :-) [as an aside, initially the essay was in the top 5 for several days, till a community member shot it down by apparently giving it only 1 point, whereupon it ended up in the middle range and slipped into oblivion. I...

view entire post

thank you very much for your kind remarks, and bumping up the rating of my essay. Given the small number of ratings so far, this had an immediate positive effect :-) [as an aside, initially the essay was in the top 5 for several days, till a community member shot it down by apparently giving it only 1 point, whereupon it ended up in the middle range and slipped into oblivion. I...

view entire post

Dear Daniel,

That's quite an equation in your paper! If I understand correctly, it has been obtained by expanding some parameters to the tenth order, so it could be even "worse" if it was expanded further?

I agree with your that FQXi should organize a mock contest on the subject of the most ugly fundamental physical equation! Maybe next April 1st? :)

Marc

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That's quite an equation in your paper! If I understand correctly, it has been obtained by expanding some parameters to the tenth order, so it could be even "worse" if it was expanded further?

I agree with your that FQXi should organize a mock contest on the subject of the most ugly fundamental physical equation! Maybe next April 1st? :)

Marc

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Dear Marc,

no, that equation is supposed to be exact (incidentally, I just learned that it might contain some sign error, so I have to recheck it and possible write an Erratum. But other than that it should be exact). It results from an exact Gaussian integration of a high-order polynomial.

And yes, such a mock contest on April 1st (with the ugly equation to be found still required to be non-trivial and correct) might change a little bit the perspective of us beauty-hungry physicists :-)

Best regards,

Daniel

no, that equation is supposed to be exact (incidentally, I just learned that it might contain some sign error, so I have to recheck it and possible write an Erratum. But other than that it should be exact). It results from an exact Gaussian integration of a high-order polynomial.

And yes, such a mock contest on April 1st (with the ugly equation to be found still required to be non-trivial and correct) might change a little bit the perspective of us beauty-hungry physicists :-)

Best regards,

Daniel

Dear Daniel,

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

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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

Hello Daniel,

I greatly enjoyed your excellent essay. As luck would have it; I use the term 'theory of theories' in my own essay, but in a rather different way. Phil Gibbs put forward a theory of theories in his 'Cyclotron Notebooks' referring to the idea that the reality we observe may not be the product of a singular mathematical pattern or model (a GUT or TOE), but rather that the universe results from a kind of path integral whose output is shaped by the full range of applicable theories - as a weighted average. In this way; we would not have to choose between loops and strings, for example, because the laws of nature employ the regularity of the Maths in both cases at once.

This notion has shaped my thinking for quite some time, but I had not thought before now that one might be able to determine the cardinality of the full array of possible theories. So you give me a lot to think about! I have boosted your score a bit, but I hope others push it higher, because you deserve a higher standing than you presently enjoy.

All the Best,

Jonathan

report post as inappropriate

I greatly enjoyed your excellent essay. As luck would have it; I use the term 'theory of theories' in my own essay, but in a rather different way. Phil Gibbs put forward a theory of theories in his 'Cyclotron Notebooks' referring to the idea that the reality we observe may not be the product of a singular mathematical pattern or model (a GUT or TOE), but rather that the universe results from a kind of path integral whose output is shaped by the full range of applicable theories - as a weighted average. In this way; we would not have to choose between loops and strings, for example, because the laws of nature employ the regularity of the Maths in both cases at once.

This notion has shaped my thinking for quite some time, but I had not thought before now that one might be able to determine the cardinality of the full array of possible theories. So you give me a lot to think about! I have boosted your score a bit, but I hope others push it higher, because you deserve a higher standing than you presently enjoy.

All the Best,

Jonathan

report post as inappropriate

Hello Jonathan,

thank you very much for your kind words and pushing my score. I read the paper by Lloyd and Dreyer on the universal path integral but frankly couldn't make much sense out of it. So now I am curious to read your article, and the paper by Phil Gibbs that you mention.

I think it is an intriguing idea that laws of physics themselves might be the result of some interference, but is there even in principle a way to test this?

All the best,

Daniel

thank you very much for your kind words and pushing my score. I read the paper by Lloyd and Dreyer on the universal path integral but frankly couldn't make much sense out of it. So now I am curious to read your article, and the paper by Phil Gibbs that you mention.

I think it is an intriguing idea that laws of physics themselves might be the result of some interference, but is there even in principle a way to test this?

All the best,

Daniel

Thanks for the thoughtful reply Daniel..

Sorry someone else pushed your ranking back down. As regards to my essay's thesis in relation to an idea in your essay; exact determinations of various quantities may have a built-in difficulty, and this can present problems with mathematization. Iterating the squaring function on the complex plane yield a bounding surface at r = 1 - any value smaller converges to (0,0i) and seed values further from the origin all diverge or are repelling points, while a value whose distance is 1 from the origin stays on the boundary forever.

But this requires infinite precision, or the preservation of unitarity as a fundamental value. If there is any noise on our calculation, or a truncation due to limited precision, this imprecision will drive the successive iterands to 0 or infinity. This is sort of like what Hawking has lately said about the fluctuation of an event horizon for a black hole being like weather forecasting. A built-in uncertainty, indeterminacy, or measurement imprecision, can all have the same effect - to drive a system to a particular result.

If we use z^2 + z instead of just z^2, things become much more interesting, but perhaps a little jitter is part of the equation. This gives me much food for thought.

Regards,

Jonathan

report post as inappropriate

Sorry someone else pushed your ranking back down. As regards to my essay's thesis in relation to an idea in your essay; exact determinations of various quantities may have a built-in difficulty, and this can present problems with mathematization. Iterating the squaring function on the complex plane yield a bounding surface at r = 1 - any value smaller converges to (0,0i) and seed values further from the origin all diverge or are repelling points, while a value whose distance is 1 from the origin stays on the boundary forever.

But this requires infinite precision, or the preservation of unitarity as a fundamental value. If there is any noise on our calculation, or a truncation due to limited precision, this imprecision will drive the successive iterands to 0 or infinity. This is sort of like what Hawking has lately said about the fluctuation of an event horizon for a black hole being like weather forecasting. A built-in uncertainty, indeterminacy, or measurement imprecision, can all have the same effect - to drive a system to a particular result.

If we use z^2 + z instead of just z^2, things become much more interesting, but perhaps a little jitter is part of the equation. This gives me much food for thought.

Regards,

Jonathan

report post as inappropriate

I want to thank you Daniel..

I had not seen the Lloyd and Dreyer paper before your mention above (or had filed it away and forgot), but now I have downloaded it and it looks very interesting.

All the Best,

Jonathan

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I had not seen the Lloyd and Dreyer paper before your mention above (or had filed it away and forgot), but now I have downloaded it and it looks very interesting.

All the Best,

Jonathan

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