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[back]

TOPIC: The utterly prosaic connection between physics and mathematics by Matt Visser [refresh]

TOPIC: The utterly prosaic connection between physics and mathematics by Matt Visser [refresh]

Eugene Wigner famously argued for the “unreasonable effectiveness of mathematics” for describing physics and other natural sciences in his 1960 essay. That essay has now led to some 55 years of (sometimes anguished) soul searching — responses range from “So what? Why do you think we developed mathematics in the first place?”, through to extremely speculative ruminations on the existence of the universe (multiverse) as a purely mathematical entity — the Mathematical Universe Hypothesis. In the current essay I will steer an utterly prosaic middle course: Much of the mathematics we develop is informed by physics questions we are tying to solve; and those physics questions for which the most utilitarian mathematics has successfully been developed are typically those where the best physics progress has been made.

Matt Visser is a mathematical physicist based in the Mathematics Department at the Victoria University of Wellington in New Zealand. He obtained his PhD at UC Berkeley, working on supergravity field theories. Since then he has (among other things) worked on QFT under external conditions, quantum scattering, general relativity, cosmology, black holes, Lorentzian wormholes, and “analogue spacetimes”. He has published over 200 scientific articles, one single-author research monograph on wormholes, and three edited volumes.

Hi Matt,

this is a beautiful essay. I'm sympathetic to your middle road practical point of view on this subject, though I'm also somewhat sympathetic to the "So what? why do you think we developed mathematics in the first place?" point of view that you use as a straw man. (I also like that you managed to bring in one of my favorite science fiction novels: The Dispossessed). ...

view entire post

this is a beautiful essay. I'm sympathetic to your middle road practical point of view on this subject, though I'm also somewhat sympathetic to the "So what? why do you think we developed mathematics in the first place?" point of view that you use as a straw man. (I also like that you managed to bring in one of my favorite science fiction novels: The Dispossessed). ...

view entire post

report post as inappropriate

Hi David:

Thanks for the comments. Regarding the quantum analogue of the "middle ground" between general relativity's PPN formalism (parameterized post-newtonian formalism) and rigorous Christodoulou-Klainerman-type global existence theorems; there is already an issue with quantum mechanics, let alone quantum field theory...

Quantum mechanics (as currently formulated) has no PPC...

view entire post

Thanks for the comments. Regarding the quantum analogue of the "middle ground" between general relativity's PPN formalism (parameterized post-newtonian formalism) and rigorous Christodoulou-Klainerman-type global existence theorems; there is already an issue with quantum mechanics, let alone quantum field theory...

Quantum mechanics (as currently formulated) has no PPC...

view entire post

Hi David:

To follow up and respond to your comments regarding the unreasonable effectiveness of complex numbers in quantum mechanics. I interpret your essay as saying something along these lines: "Complex numbers are the minimal extension of the real numbers; the real numbers are known to be useful for classical physics; so when one goes beyond classical physics it is perhaps not all that...

view entire post

To follow up and respond to your comments regarding the unreasonable effectiveness of complex numbers in quantum mechanics. I interpret your essay as saying something along these lines: "Complex numbers are the minimal extension of the real numbers; the real numbers are known to be useful for classical physics; so when one goes beyond classical physics it is perhaps not all that...

view entire post

Dear Matt Visser,

Maybe, complex numbers are already the minimal extension of the rational numbers? Anyway, already the extension of the natural numbers to the integer numbers may be interpreted as a trick to allow convenient calculation without shift operations.

In principle, 19th century physics could also be formulated without negative and complex numbers. This is not just an idea that I adopted from other engineers; it was also admitted by Pauli (cf. Der Pauli-Jung-Dialog). Don't get me wrong, I don't deny the practical necessity of using complex calculus.

While your superb essay confirms your excellence, you and virtually all physicists might nonetheless have failed to get aware of a trivial trifle; the use of complex calculus in physics and technology has been based on Heaviside's trick to attribute zeros to the not yet existing future and split the continued. This implies fourfold redundancy due to omission. Well, one can easily avoid the dilemma by following Einstein and Hilbert and denying the distinction between past and future. However, this way the logic consistency gets lost. Instead I prefer using complex calculus properly, step by step.

So far, nobody could show in what I am wrong when I state that cosine transformation of measured data is as good as their Fourier transformation.

MPEG demonstrated, it actually works. Therefore, I doubt with all unbelievable consequences that ict and ih are absolutely indispensable for physical reasons. Again, don't get me wrong. I don't claim that they can actually be replaced.

Faithfully yours,

Eckard Blumschein

report post as inappropriate

Maybe, complex numbers are already the minimal extension of the rational numbers? Anyway, already the extension of the natural numbers to the integer numbers may be interpreted as a trick to allow convenient calculation without shift operations.

In principle, 19th century physics could also be formulated without negative and complex numbers. This is not just an idea that I adopted from other engineers; it was also admitted by Pauli (cf. Der Pauli-Jung-Dialog). Don't get me wrong, I don't deny the practical necessity of using complex calculus.

While your superb essay confirms your excellence, you and virtually all physicists might nonetheless have failed to get aware of a trivial trifle; the use of complex calculus in physics and technology has been based on Heaviside's trick to attribute zeros to the not yet existing future and split the continued. This implies fourfold redundancy due to omission. Well, one can easily avoid the dilemma by following Einstein and Hilbert and denying the distinction between past and future. However, this way the logic consistency gets lost. Instead I prefer using complex calculus properly, step by step.

So far, nobody could show in what I am wrong when I state that cosine transformation of measured data is as good as their Fourier transformation.

MPEG demonstrated, it actually works. Therefore, I doubt with all unbelievable consequences that ict and ih are absolutely indispensable for physical reasons. Again, don't get me wrong. I don't claim that they can actually be replaced.

Faithfully yours,

Eckard Blumschein

report post as inappropriate

Dear Matt Visser

I liked your essay and your collection of ``common sense’’ points about quantum mechanics. And I believe that the topic of ``collapse and reification’’ is key and indeed requires better physics more than mathematics. As fundamental mystery, perhaps entanglement might compete equality with this (the strangeness of writing a multi-particle wave-function in configuration space) and also require new physical thinking more than mathematics. Also, I just saw that Kastner’s latest paper (arXiv:1502.03814, Haag's Theorem as a Reason to Reconsider Direct-Action Theories) also stressed the importance of Haag’s theorem. I see the discipline of mathematical-physics as a porthole encouraging the transfer of possibly useful math into physics as needed and showing interesting physics problems to the mathematical community for cross fertilization.

Thanks again for your interesting contribution. Dave.

report post as inappropriate

I liked your essay and your collection of ``common sense’’ points about quantum mechanics. And I believe that the topic of ``collapse and reification’’ is key and indeed requires better physics more than mathematics. As fundamental mystery, perhaps entanglement might compete equality with this (the strangeness of writing a multi-particle wave-function in configuration space) and also require new physical thinking more than mathematics. Also, I just saw that Kastner’s latest paper (arXiv:1502.03814, Haag's Theorem as a Reason to Reconsider Direct-Action Theories) also stressed the importance of Haag’s theorem. I see the discipline of mathematical-physics as a porthole encouraging the transfer of possibly useful math into physics as needed and showing interesting physics problems to the mathematical community for cross fertilization.

Thanks again for your interesting contribution. Dave.

report post as inappropriate

Dear Matt Visser,

Your fine essay was a joy to read; your less-than-worshipful analysis of quantum mechanics and QFT, a breath of fresh air. As you note, math is simply a way of codifying regularities. Assuming Kronecker's dictum, then the question of the non-mystical source of integers would appear the key question, and I argue that these arise directly from the physical logic of AND and NOT 'gates' at all levels of physical reality. As you say, prosaic. Your observations on the obfuscations of mystics, and the horrible price paid by trees, is quite astute.

I find your discussion of quantum pedagogy very well done and agree with all of your major points, including those concerning the uncertainty relation, 'tunneling', collapse of the wave function, and decoherence, and that these require new*physical understanding*, not new mathematics.

As for 'collapse of the wave function' implying no physical basis of the notion of memory, history, or trajectory, I hope you will find time to read my current essay, The Nature of Bell's Hidden Constraints, which analyzes a local model of spin based on the**physics** of particles in the Stern-Gerlach apparatus, entirely overlooked by Bell's oversimplified assumptions, and precluded by his "hidden" constraints.

Your observations on utility versus precision are extremely appropriate and those on the non-ontological, non-interpretive essence of "*shut up and calculate*" ring decidedly true.

Thank you for entering this insightful essay,

My best wishes,

Edwin Eugene Klingman

report post as inappropriate

Your fine essay was a joy to read; your less-than-worshipful analysis of quantum mechanics and QFT, a breath of fresh air. As you note, math is simply a way of codifying regularities. Assuming Kronecker's dictum, then the question of the non-mystical source of integers would appear the key question, and I argue that these arise directly from the physical logic of AND and NOT 'gates' at all levels of physical reality. As you say, prosaic. Your observations on the obfuscations of mystics, and the horrible price paid by trees, is quite astute.

I find your discussion of quantum pedagogy very well done and agree with all of your major points, including those concerning the uncertainty relation, 'tunneling', collapse of the wave function, and decoherence, and that these require new

As for 'collapse of the wave function' implying no physical basis of the notion of memory, history, or trajectory, I hope you will find time to read my current essay, The Nature of Bell's Hidden Constraints, which analyzes a local model of spin based on the

Your observations on utility versus precision are extremely appropriate and those on the non-ontological, non-interpretive essence of "

Thank you for entering this insightful essay,

My best wishes,

Edwin Eugene Klingman

report post as inappropriate

Dear Matt Visser,

On page 4 of your essay you asked the question, 'So where are the "real" open questions in quantum physics?' I allege that, according to Alan Kogut's NASA science team that discovered the space roar, there are 3 independent empirical data sets that confirm the space roar. Do you agree or disagree with my allegation?

— D. B.

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On page 4 of your essay you asked the question, 'So where are the "real" open questions in quantum physics?' I allege that, according to Alan Kogut's NASA science team that discovered the space roar, there are 3 independent empirical data sets that confirm the space roar. Do you agree or disagree with my allegation?

— D. B.

report post as inappropriate

Dear DB:

There are really two questions here: (1) is the "space roar" real? (2) is the "space roar" important? (Since many people will not know what the "space roar" is, observationally there seems to be excess signal in the radio frequencies normally associated with radio galaxies, with the observed signal intensity being roughly six times what was naively expected.) But should we really get all that excited by a factor six discrepancy between observation and naive theory in a small part of the electromagnetic spectrum where we already know there are plenty of radio sources? Overall, at least for the time being, I think this is best left to the radio astronomers to worry about...

For instance, mis-estimating the average distance between radio galaxies by a factor of two will mis-estimate their number density by a factor of eight, and more than adequately account for the "space roar"... There are also many other possibilities one might think of... So while the "space roar" appears to be a real signal, it may not be indicative of "fundamentally new physics". There is an old adage: "When you hear hoofbeats --- think horses, not zebras".

Regards

Matt

There are really two questions here: (1) is the "space roar" real? (2) is the "space roar" important? (Since many people will not know what the "space roar" is, observationally there seems to be excess signal in the radio frequencies normally associated with radio galaxies, with the observed signal intensity being roughly six times what was naively expected.) But should we really get all that excited by a factor six discrepancy between observation and naive theory in a small part of the electromagnetic spectrum where we already know there are plenty of radio sources? Overall, at least for the time being, I think this is best left to the radio astronomers to worry about...

For instance, mis-estimating the average distance between radio galaxies by a factor of two will mis-estimate their number density by a factor of eight, and more than adequately account for the "space roar"... There are also many other possibilities one might think of... So while the "space roar" appears to be a real signal, it may not be indicative of "fundamentally new physics". There is an old adage: "When you hear hoofbeats --- think horses, not zebras".

Regards

Matt

Dear Mat Visser,

A well written essay, I enjoyed reading it. I totally agree with your line of thought, “The problem is not with mysticism per se, but with excessive mysticism used as a tool to obfuscate....Heisenberg uncertainty relations (as commonly presented) suffer from their own level of excessive mysticism and obfuscation".

However, your conclusion, “ the close relationship between mathematics and physics is not at all surprising — the reason for the close relationship is in fact utterly prosaic”, denies that there can ever be any reason for that relation. Your kind attention is invited to my essay,**'A physicalist interpretation of the relation between physics and mathematics'**, wherein I propose a prosaic (not at all mystic) reason for the relation: Changes in the physical world happen entirely by way of motion; motion is a space- time relation that can be expressed mathematically; so all changes follow mathematical rules; so it is no wonder the patterns we observe in the world are mathematically explainable.

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A well written essay, I enjoyed reading it. I totally agree with your line of thought, “The problem is not with mysticism per se, but with excessive mysticism used as a tool to obfuscate....Heisenberg uncertainty relations (as commonly presented) suffer from their own level of excessive mysticism and obfuscation".

However, your conclusion, “ the close relationship between mathematics and physics is not at all surprising — the reason for the close relationship is in fact utterly prosaic”, denies that there can ever be any reason for that relation. Your kind attention is invited to my essay,

report post as inappropriate

Dear Prof. Visser:

I enjoyed reading your clear and cogent essay on how math and physics are mutually supportive but distinct. I especially appreciated your analysis of “Quantum Conundrums”, where you (or perhaps Dr. Shevek) question whether the accepted interpretation of QM really makes sense.

The accepted view of QM is that the physics (and mathematics) of the microworld are fundamentally different from those of the macroworld, which of course creates an inevitable boundary problem. I take the radical (and heretical) view that the fundamental organization is the same on both scales, so that the boundary problem immediately disappears. Quantum indeterminacy, superposition, and entanglement are artifacts of the inappropriate mathematical formalism. QM is not a universal theory of matter; it is rather a mechanism for distributed vector fields to self-organize into spin-quantized coherent domains. This requires nonlinear mathematics that is not present in the standard formalism.

My essay is entitled "Remove the Blinders: How Mathematics Distorted the Development of Quantum Theory", and presents a simple realistic picture that makes directly testable experimental predictions, based on little more than Stern-Gerlach measurements. Remarkably, these simple experiments have never been done.

Alan Kadin

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I enjoyed reading your clear and cogent essay on how math and physics are mutually supportive but distinct. I especially appreciated your analysis of “Quantum Conundrums”, where you (or perhaps Dr. Shevek) question whether the accepted interpretation of QM really makes sense.

The accepted view of QM is that the physics (and mathematics) of the microworld are fundamentally different from those of the macroworld, which of course creates an inevitable boundary problem. I take the radical (and heretical) view that the fundamental organization is the same on both scales, so that the boundary problem immediately disappears. Quantum indeterminacy, superposition, and entanglement are artifacts of the inappropriate mathematical formalism. QM is not a universal theory of matter; it is rather a mechanism for distributed vector fields to self-organize into spin-quantized coherent domains. This requires nonlinear mathematics that is not present in the standard formalism.

My essay is entitled "Remove the Blinders: How Mathematics Distorted the Development of Quantum Theory", and presents a simple realistic picture that makes directly testable experimental predictions, based on little more than Stern-Gerlach measurements. Remarkably, these simple experiments have never been done.

Alan Kadin

report post as inappropriate

"QM is not a universal theory of matter; it is rather a mechanism for distributed vector fields to self-organize into spin-quantized coherent domains. This requires nonlinear mathematics that is not present in the standard formalism."

I concur. QM is due to a rotating wave or field. The wave is rotating and corkscrewing through space tracing out a long helical path. Effects of the inclined planar wave front traversing the longer path of rotation exhibits relativistic effects such as length contraction, time dilation, inductance, and mass increase.

The basic vector math I resolved was C = Vv + Vr + Vt

Vv = translational motion (forward motion of the partical

Vr = rotational motion of the wave

Vt = radial motion of the wave spiralling out in a gravitational field

Limit Vt goes to zero and you have just the Lorentz invariance.

I'm surprised that Dirac did not even consider this, plus Einstein as well.

Maybe others consider it a pilot wave wrapping around a particle, but it's simply a rotating wave - see attached.

Bill Christie

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I concur. QM is due to a rotating wave or field. The wave is rotating and corkscrewing through space tracing out a long helical path. Effects of the inclined planar wave front traversing the longer path of rotation exhibits relativistic effects such as length contraction, time dilation, inductance, and mass increase.

The basic vector math I resolved was C = Vv + Vr + Vt

Vv = translational motion (forward motion of the partical

Vr = rotational motion of the wave

Vt = radial motion of the wave spiralling out in a gravitational field

Limit Vt goes to zero and you have just the Lorentz invariance.

I'm surprised that Dirac did not even consider this, plus Einstein as well.

Maybe others consider it a pilot wave wrapping around a particle, but it's simply a rotating wave - see attached.

Bill Christie

report post as inappropriate

Hi Matt,

I enjoyed reading your essay. I especially like that you address some problem areas including the interpretation of wave function collapse. You paint mathematics and physics as being loosely allied for convenience- rather than in a fundamental inseparable relationship. Which is I should think true of the disciplines (you would know best being involved with both). Though perhaps it is not so within nature. Getting to the end you reiterate your prosaic view of mathematics. That is a view I used to hold. I used to argue that it is just a a language. However I confess to now holding the more romantic notion that: in a changing universe, rather than just the 'stuff' it is made of, it is at least as much the totality of unmeasured 'mathematical' relations between the elements of (Object)reality that bestows its character, and provides the specific forces for change. If we were to ask;' which is more important substance or relation?' it would be hard to promote one over the other. Thinking about chemistry it is the form of molecules, the internal and external relations that gives their characteristic properties and behaviour not just the constituent elements. There is of course a difference between mathematics 'in vivo', in the wild, just as the living organism in vivo is different from the one (however accurately) described on paper.Can there be such a thing as wild mathematics rather than imagined and written,belonging to different facets of reality- I'd like to think so.

A very good read, good luck, Georgina

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I enjoyed reading your essay. I especially like that you address some problem areas including the interpretation of wave function collapse. You paint mathematics and physics as being loosely allied for convenience- rather than in a fundamental inseparable relationship. Which is I should think true of the disciplines (you would know best being involved with both). Though perhaps it is not so within nature. Getting to the end you reiterate your prosaic view of mathematics. That is a view I used to hold. I used to argue that it is just a a language. However I confess to now holding the more romantic notion that: in a changing universe, rather than just the 'stuff' it is made of, it is at least as much the totality of unmeasured 'mathematical' relations between the elements of (Object)reality that bestows its character, and provides the specific forces for change. If we were to ask;' which is more important substance or relation?' it would be hard to promote one over the other. Thinking about chemistry it is the form of molecules, the internal and external relations that gives their characteristic properties and behaviour not just the constituent elements. There is of course a difference between mathematics 'in vivo', in the wild, just as the living organism in vivo is different from the one (however accurately) described on paper.Can there be such a thing as wild mathematics rather than imagined and written,belonging to different facets of reality- I'd like to think so.

A very good read, good luck, Georgina

report post as inappropriate

Dear Matt Visser,

I identify closely with much that you have professed in your essay. Moderation is not mean; it simply means the exclusion of extremes. Your points "Clarity is typically more important than precision", and "The key issue here is usability versus precision" are acknowledged.

The essence of our problem concerning the relation between mathematics and physics is that what we seek (and often find) are utility values that are applicable to our personal needs. Relativity is more important (more useful) than precision (aka absolute truth).

"So the close connection between mathematics and physics is dynamic not static" follows naturally. The term 'dynamic' in this context means variable. Could the connection work any other way if the intention is to generate useful information under changing circumstances?

When we look at the very large we see an assemblage of many things, and their relatedness. When we look at the very small it is the same. In time we find ways of dividing even the smallest things into smaller, related things. We are unable to define the smallest units of existence or to say with any degree of certainty that they do not exist. What we have are relations, and relations to other relations, but no fixity. There is no absolute standard of motionless fixity except that to which individuals attach in their minds. Since such motionless fixity assumes a god-like lacking in confirmation; in the macrocosm of ‘all-there-is’; all there are are relations. All there is for mankind to understand is our appropriate relationship to all there is.

Gary Hansen

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I identify closely with much that you have professed in your essay. Moderation is not mean; it simply means the exclusion of extremes. Your points "Clarity is typically more important than precision", and "The key issue here is usability versus precision" are acknowledged.

The essence of our problem concerning the relation between mathematics and physics is that what we seek (and often find) are utility values that are applicable to our personal needs. Relativity is more important (more useful) than precision (aka absolute truth).

"So the close connection between mathematics and physics is dynamic not static" follows naturally. The term 'dynamic' in this context means variable. Could the connection work any other way if the intention is to generate useful information under changing circumstances?

When we look at the very large we see an assemblage of many things, and their relatedness. When we look at the very small it is the same. In time we find ways of dividing even the smallest things into smaller, related things. We are unable to define the smallest units of existence or to say with any degree of certainty that they do not exist. What we have are relations, and relations to other relations, but no fixity. There is no absolute standard of motionless fixity except that to which individuals attach in their minds. Since such motionless fixity assumes a god-like lacking in confirmation; in the macrocosm of ‘all-there-is’; all there are are relations. All there is for mankind to understand is our appropriate relationship to all there is.

Gary Hansen

report post as inappropriate

Dear Matt,

We have enjoyed reading your essay and broadly agree with you. Fully agree about the dynamic tension between physical theories and mathematics...what we call `frailty of the connection'.

A few remarks on the middle ground between quantum and classical mechanics, in the light of your conversation above with David Garfinkle. We fully agree there is a big difference...

view entire post

We have enjoyed reading your essay and broadly agree with you. Fully agree about the dynamic tension between physical theories and mathematics...what we call `frailty of the connection'.

A few remarks on the middle ground between quantum and classical mechanics, in the light of your conversation above with David Garfinkle. We fully agree there is a big difference...

view entire post

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Hi Matt,

This was a pretty good essay. I had three main complaints, though. First, I found it a bit disjointed. Perhaps the ten page limit was a hindrance. For example, I'm not sure how the technical end notes were meant to connect to the rest of the essay.

The second issue I had was with your characterization of the problems in quantum theory. While de Broglie's momentum-wavenumber relation and Einstein's energy frequency relation are certainly intriguing aspects of quantum physics, I'm not sure I would call them the "central mystery." Take the notion of contextuality, for example. It's a topic that has been central to a good number of papers on quantum foundations in the last decade or two, and yet, arguably, it has nothing to do with the concept of a "wavicle." Certainly within the quantum foundations community, contextuality is seen, these days, as a deeper issue.

Honestly, I'm not really sure how the issues in quantum theory really had/have anything to do with the nature of mathematics at all. At least you didn't make a convincing argument that they do from my reading of the essay.

Finally, I would say that "usability versus precision" is a false dichotomy. While I sympathize that many mathematical physicists over-extrapolate meaning from their results and that a healthy dose of operational realism ought to be included, I see no reason we must sacrifice one for the other. Certainly there is nothing that is a priori necessarily mutually exclusive about the two ideas.

Cheers,

Ian

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This was a pretty good essay. I had three main complaints, though. First, I found it a bit disjointed. Perhaps the ten page limit was a hindrance. For example, I'm not sure how the technical end notes were meant to connect to the rest of the essay.

The second issue I had was with your characterization of the problems in quantum theory. While de Broglie's momentum-wavenumber relation and Einstein's energy frequency relation are certainly intriguing aspects of quantum physics, I'm not sure I would call them the "central mystery." Take the notion of contextuality, for example. It's a topic that has been central to a good number of papers on quantum foundations in the last decade or two, and yet, arguably, it has nothing to do with the concept of a "wavicle." Certainly within the quantum foundations community, contextuality is seen, these days, as a deeper issue.

Honestly, I'm not really sure how the issues in quantum theory really had/have anything to do with the nature of mathematics at all. At least you didn't make a convincing argument that they do from my reading of the essay.

Finally, I would say that "usability versus precision" is a false dichotomy. While I sympathize that many mathematical physicists over-extrapolate meaning from their results and that a healthy dose of operational realism ought to be included, I see no reason we must sacrifice one for the other. Certainly there is nothing that is a priori necessarily mutually exclusive about the two ideas.

Cheers,

Ian

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Dear Ian:

Thanks for your comments.

--- Technical note 1 was there to make sure I minimized the number of formulae in the main text of the essay itself.

--- Technical note 2 was there of keep the essay more focussed, by allowing me to avoid bringing specific technical details of electro-magnetism and acoustics into the body of the essay.

--- Regarding the difference between the "Einstein--de Broglie" relations on the one hand, and "contextuality" on the other; it seems to me a little odd that the inequalities coming from contextuality-related arguments never seem to involve Planck's constant, while the Einstein--de Broglie relations do very explicitly involve Planck's constant. Somehow the presence of Planck's constant screams "quantum" to me in a fundamental manner.

--- Regarding the tension between usability and precision (more precisely, hyper-technical and excessive precision), consider for instance the Henstock-Kurzweil integral, which is even more powerful than the Lebesgue integral, which in turn is more powerful than the Riemann integral. There are purists who feel we should of course be teaching the Henstock-Kurzweil integral in freshman calculus; I have very strong reservations... Indeed I would be very leery of being a passenger in any vehicle whose design depended critically on the engineers using the Henstock-Kurzweil integral instead of the Riemann integral. (In fact, I'd probably prefer the engineers to stick to upper and lower Riemann sums to obtain explicit bounds on quantities of interest.) Now there are places where the Henstock-Kurzweil integral is useful, but just because you can develop such a mathematical formalism does not mean it it always desirable to do so... I am not saying that usability and precision are exclusive, I am saying that it is probably not worth setting up a formalism that is significantly more precise than what you really need to get the job done...

Regards

Matt

Thanks for your comments.

--- Technical note 1 was there to make sure I minimized the number of formulae in the main text of the essay itself.

--- Technical note 2 was there of keep the essay more focussed, by allowing me to avoid bringing specific technical details of electro-magnetism and acoustics into the body of the essay.

--- Regarding the difference between the "Einstein--de Broglie" relations on the one hand, and "contextuality" on the other; it seems to me a little odd that the inequalities coming from contextuality-related arguments never seem to involve Planck's constant, while the Einstein--de Broglie relations do very explicitly involve Planck's constant. Somehow the presence of Planck's constant screams "quantum" to me in a fundamental manner.

--- Regarding the tension between usability and precision (more precisely, hyper-technical and excessive precision), consider for instance the Henstock-Kurzweil integral, which is even more powerful than the Lebesgue integral, which in turn is more powerful than the Riemann integral. There are purists who feel we should of course be teaching the Henstock-Kurzweil integral in freshman calculus; I have very strong reservations... Indeed I would be very leery of being a passenger in any vehicle whose design depended critically on the engineers using the Henstock-Kurzweil integral instead of the Riemann integral. (In fact, I'd probably prefer the engineers to stick to upper and lower Riemann sums to obtain explicit bounds on quantities of interest.) Now there are places where the Henstock-Kurzweil integral is useful, but just because you can develop such a mathematical formalism does not mean it it always desirable to do so... I am not saying that usability and precision are exclusive, I am saying that it is probably not worth setting up a formalism that is significantly more precise than what you really need to get the job done...

Regards

Matt

Dear Dr. Visser,

You wrote: “Mathematics is simply a way of codifying, in an abstract manner, various regularities we observe in the physical universe around us.”

Accurate writing has enabled me to perfect a valid description of untangled unified reality: Proof exists that every real astronomer looking through a real telescope has failed to notice that each of the real galaxies...

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You wrote: “Mathematics is simply a way of codifying, in an abstract manner, various regularities we observe in the physical universe around us.”

Accurate writing has enabled me to perfect a valid description of untangled unified reality: Proof exists that every real astronomer looking through a real telescope has failed to notice that each of the real galaxies...

view entire post

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Dear Joe:

There is no gentle way to put this --- your essay is failing to usefully communicate with the intended audience. To save other people the time that might be spent in reading your essay, let me provide three salient quotes therefrom:

"Had Isaac [Newton] had any concern for truth and a rudimentary grasp of reality..."

"Had Albert [Einstein] shown any interest in truth and had he had a rudimentary grasp of reality..."

"Had Hawking had even the most rudimentary grasp of reality..."

Comments along these lines will certainly influence people --- but not in a positive manner. Some of the other phrases you use, such as "erroneous abstract zero" and "invisible illuminant" are certainly striking; but for all the wrong reasons. I strongly feel you should carefully re-assess your entire essay, and your serious misconceptions regarding both mathematics and physics.

Regards

Matt

There is no gentle way to put this --- your essay is failing to usefully communicate with the intended audience. To save other people the time that might be spent in reading your essay, let me provide three salient quotes therefrom:

"Had Isaac [Newton] had any concern for truth and a rudimentary grasp of reality..."

"Had Albert [Einstein] shown any interest in truth and had he had a rudimentary grasp of reality..."

"Had Hawking had even the most rudimentary grasp of reality..."

Comments along these lines will certainly influence people --- but not in a positive manner. Some of the other phrases you use, such as "erroneous abstract zero" and "invisible illuminant" are certainly striking; but for all the wrong reasons. I strongly feel you should carefully re-assess your entire essay, and your serious misconceptions regarding both mathematics and physics.

Regards

Matt

Dear Dr. Visser,

Thank you ever so much for reading my essay. Alas you are correct in that my unified explanation of reality will not appeal to the utterly ignorant abstractions addicted community at this site.

Please either refute my contention that real light is inert and there is no physical space or accept it, but please do not leave me with the impression that you are also an abstraction addicted ignoramus.

Imploringly,

Joe Fisher

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Thank you ever so much for reading my essay. Alas you are correct in that my unified explanation of reality will not appeal to the utterly ignorant abstractions addicted community at this site.

Please either refute my contention that real light is inert and there is no physical space or accept it, but please do not leave me with the impression that you are also an abstraction addicted ignoramus.

Imploringly,

Joe Fisher

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Hi Matt,

I tend to agree with you that math is efficient because we have developed it for areas in which it is efficient, so it's kind of a pointless question if you interpret it literally. It's like asking why email is efficient at delivering messages.

However, I think you're missing the more relevant question, that is, are there aspects for which math cannot be used, or it is "efficient" for everything? I see you're not very convinced by the mathematical universe hypothesis. Arguably you are right that saying that there are more mathematical structures to be discovered is hardly a useful prediction, but the question is there a mathematical structure for ANY observation that we can make (natural science or any other), or not? Maybe you have a chance to look at my essay, I think you might find we have some things in common.

-- Sophia

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I tend to agree with you that math is efficient because we have developed it for areas in which it is efficient, so it's kind of a pointless question if you interpret it literally. It's like asking why email is efficient at delivering messages.

However, I think you're missing the more relevant question, that is, are there aspects for which math cannot be used, or it is "efficient" for everything? I see you're not very convinced by the mathematical universe hypothesis. Arguably you are right that saying that there are more mathematical structures to be discovered is hardly a useful prediction, but the question is there a mathematical structure for ANY observation that we can make (natural science or any other), or not? Maybe you have a chance to look at my essay, I think you might find we have some things in common.

-- Sophia

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Dear Matt Visser,

Great essay. Your comment "*unnecessary and excessive obfuscation*" leading to the example of "*distressingly common misconception that “uncertainty relations” are intrinsically a quantum phenomenon — utterly ignoring the fact that engineers have by now some 60 years of experience with utterly classical timefrequency uncertainty relations in signal processing, and that mathematicians have by now over 80 years experience with utterly classical time-frequency uncertainty relations in Fourier transform theory.*" is something I agree completely with.

The second example you mention "*“tunnelling”/“barrier penetration”. Despite yet more common misconceptions, tunnelling is a simply wave phenomenon; it is not (intrinsically) a quantum physics phenomenon. Under the cognomen “frustrated total internal reflection”, the classical tunnelling phenomenon has been studied and investigated for well over 300 years, with the wave aspects (the “evanescent wave”) coming to the foreground approximately 150 years ago ..*" adds more certainty to your argument.

I enjoyed the discussion on the standard model, where no one doubts it's accuracy, but perhaps time will give us a better understanding of some of the technical aspects and issues you highlight.

Finally, I agree with your comments on "usability". In my essay here, I start with the usability issue and argue that it can be greatly enhanced by providing visual models of objects that match the properties of the fundamental particles of the standard model. I would be very interested in your comments on any of the specific models provided.

Your essay was a very enjoyable and insightful read.

Thank you and regards,

Ed Unverricht

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Great essay. Your comment "

The second example you mention "

I enjoyed the discussion on the standard model, where no one doubts it's accuracy, but perhaps time will give us a better understanding of some of the technical aspects and issues you highlight.

Finally, I agree with your comments on "usability". In my essay here, I start with the usability issue and argue that it can be greatly enhanced by providing visual models of objects that match the properties of the fundamental particles of the standard model. I would be very interested in your comments on any of the specific models provided.

Your essay was a very enjoyable and insightful read.

Thank you and regards,

Ed Unverricht

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Dear Matt,

Great essay and very clear. I particularly liked your section on Quantum conundrums.

I liked the way you dealt with quantum complementarity and I also have an instinctive reaction against such ideas which do not present a unified and simple picture of natural phenomena.

In talking about the measurement problem or the problem of the collapse of the wavefunction you may be interested to read my essay "Solving the mystery". I take the position that the apparent mystery is because of our lack of understanding.

If we adopt a different interpretation of reality in which we are dealing with real physical waves, then the notional collapse of the wavefunction is in fact an interaction of a real physical wave with an atom of the detector or measuring device. The measurement problem then is resolved.

Best regards

Richard

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Great essay and very clear. I particularly liked your section on Quantum conundrums.

I liked the way you dealt with quantum complementarity and I also have an instinctive reaction against such ideas which do not present a unified and simple picture of natural phenomena.

In talking about the measurement problem or the problem of the collapse of the wavefunction you may be interested to read my essay "Solving the mystery". I take the position that the apparent mystery is because of our lack of understanding.

If we adopt a different interpretation of reality in which we are dealing with real physical waves, then the notional collapse of the wavefunction is in fact an interaction of a real physical wave with an atom of the detector or measuring device. The measurement problem then is resolved.

Best regards

Richard

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Dear Matt,

Thank you for your essay.

I liked your point that the back-and-forth connections between mathematics and physics will continue to twist and strain not only due to technological limitations, but also due to the personalities involved (i.e. mathematics and physics are both human endeavours).

I also liked your point that theorists pay heed to experimentalists who only adjust one aspect of an experiment at a time - similarly, theorists should not overlay speculation on speculation.

Adding to your point that mathematics encodes the patterns and regularities in the data stream, I would argue that the crux of the tension between mathematics and physics is that the data stream does not include the arrow of time - and therefore mathematics is not able to model this empirical feature of nature. That is, the act of measurement and quantification (combined with the use of the continuum) eliminates from the data stream the arrow of time before mathematics can do its magic. This, in my view, is why we end up with time-symmetric theories and,for example,the measurement problem you discuss.

Thank you for writing the essay.

Kind regards

Spencer Scoular

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Thank you for your essay.

I liked your point that the back-and-forth connections between mathematics and physics will continue to twist and strain not only due to technological limitations, but also due to the personalities involved (i.e. mathematics and physics are both human endeavours).

I also liked your point that theorists pay heed to experimentalists who only adjust one aspect of an experiment at a time - similarly, theorists should not overlay speculation on speculation.

Adding to your point that mathematics encodes the patterns and regularities in the data stream, I would argue that the crux of the tension between mathematics and physics is that the data stream does not include the arrow of time - and therefore mathematics is not able to model this empirical feature of nature. That is, the act of measurement and quantification (combined with the use of the continuum) eliminates from the data stream the arrow of time before mathematics can do its magic. This, in my view, is why we end up with time-symmetric theories and,for example,the measurement problem you discuss.

Thank you for writing the essay.

Kind regards

Spencer Scoular

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Hi Matt—

Your essay was a joy to read: passionately yet cogently argued and right to the point. To all of your points, I can only respond, “YES!” In particular, I subscribe to your thesis that what we do in physics is identity patterns and regularities in Nature, which we then codify using mathematics. There is no mystery here. Mathematics is so effective because we have spent the last 350 years industriously making it so.

On a minor note, I also enjoyed your use of quotations. You’ve got to be the only guy in the history of FQXi who has managed to work in a cite to Ken Wilber!

On a completely different note, I observe that your outstanding book, Lorentzian Wormholes, is 20 years old. To the best of my knowledge, you never put out a second edition. Don’t you think that it is about time?

Best regards,

Bill.

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Your essay was a joy to read: passionately yet cogently argued and right to the point. To all of your points, I can only respond, “YES!” In particular, I subscribe to your thesis that what we do in physics is identity patterns and regularities in Nature, which we then codify using mathematics. There is no mystery here. Mathematics is so effective because we have spent the last 350 years industriously making it so.

On a minor note, I also enjoyed your use of quotations. You’ve got to be the only guy in the history of FQXi who has managed to work in a cite to Ken Wilber!

On a completely different note, I observe that your outstanding book, Lorentzian Wormholes, is 20 years old. To the best of my knowledge, you never put out a second edition. Don’t you think that it is about time?

Best regards,

Bill.

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Dear Matt,

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

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Dear Matt,

This is a well argued and well thought out exposition. I enjoyed reading it as much as I enjoy reading your relativity papers; you always bring up interesting topics and back them up with solid research. While I can think of counterexamples to the idea that much of the mathematics we develop serves a well defined purpose, I do agree with and enjoy your no-nonsense approach to the central theme of the contest. I also found particularly satisfactory your witty critique on how speculation gets disconnected from reality. Your mention of some of the interpretations and non-interpretations of QM made me wonder (again) which is your approach to the problem. I hope one day you'll write a paper about it.

Wish you good luck in the contest! Should you have the time and curiosity to read my essay, your comments are more than welcome.

Warm regards,

Alma

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This is a well argued and well thought out exposition. I enjoyed reading it as much as I enjoy reading your relativity papers; you always bring up interesting topics and back them up with solid research. While I can think of counterexamples to the idea that much of the mathematics we develop serves a well defined purpose, I do agree with and enjoy your no-nonsense approach to the central theme of the contest. I also found particularly satisfactory your witty critique on how speculation gets disconnected from reality. Your mention of some of the interpretations and non-interpretations of QM made me wonder (again) which is your approach to the problem. I hope one day you'll write a paper about it.

Wish you good luck in the contest! Should you have the time and curiosity to read my essay, your comments are more than welcome.

Warm regards,

Alma

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Dear Matt

30 year ago I was persuading my classmate, that a professor was wrong, I claimed, as you, that uncertainty principle is not only a quantum phenomenon. At your interpretation it is evident still more clearly something: that the purpose of hbar is also to make physics dimensionless. More is written in my essay.

I agree also with you, that Tegmark's multiverse is too speculative. It is based on a supposition that simplicity and beauty of formulae is not enough to suppose that other simple formulae exists. (As Burov's in FQXi 2015 write.) But these beatiful and simple physical formule should/must have one still unknown background explanation. I think, that dimensionless nature of physics, already reduced number of axioms, quantum gravity theory will still reduce number of physical postulates and theory of consciousness still more.

You like positivistic aspect ''shut up and calculate''. I like such view, but not 100 %. I think that interpretation of QM should be improved and clarified and that QM is not complete: it does not explain quantum gravity and consciousness. You also correctly mentioned unexplained measurement problem.

I like your realistic and simple approach to physics, except that you do not mentioned consciousness (except measurement problem). But I hope that you will read my essay and independent Poirer's essay about quantum consciousness, and that you will give opinion.

My essay.

Best regards

Janko Kokosar

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30 year ago I was persuading my classmate, that a professor was wrong, I claimed, as you, that uncertainty principle is not only a quantum phenomenon. At your interpretation it is evident still more clearly something: that the purpose of hbar is also to make physics dimensionless. More is written in my essay.

I agree also with you, that Tegmark's multiverse is too speculative. It is based on a supposition that simplicity and beauty of formulae is not enough to suppose that other simple formulae exists. (As Burov's in FQXi 2015 write.) But these beatiful and simple physical formule should/must have one still unknown background explanation. I think, that dimensionless nature of physics, already reduced number of axioms, quantum gravity theory will still reduce number of physical postulates and theory of consciousness still more.

You like positivistic aspect ''shut up and calculate''. I like such view, but not 100 %. I think that interpretation of QM should be improved and clarified and that QM is not complete: it does not explain quantum gravity and consciousness. You also correctly mentioned unexplained measurement problem.

I like your realistic and simple approach to physics, except that you do not mentioned consciousness (except measurement problem). But I hope that you will read my essay and independent Poirer's essay about quantum consciousness, and that you will give opinion.

My essay.

Best regards

Janko Kokosar

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Matt,

I consider your essay beautifully balanced and written, covering many important truths. Now speed-reading I may have missed much and have noted it down to return to. In particular we agree Dyson's quote is important, I think as important as Wigners.

I agree it's not new maths that's needed to resolve the issue of QM but to derive the complex physical mechanism to match the maths, and hopefully identify a viable 'quasi' classical' mechanism in my essay (and referenced paper). I hope you'll read it and advise or comment even after the scoring deadline.

I certainly consider your essay should be in the final group and found it well argued with no flaws to worthy of a high score. Best of luck.

Peter

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I consider your essay beautifully balanced and written, covering many important truths. Now speed-reading I may have missed much and have noted it down to return to. In particular we agree Dyson's quote is important, I think as important as Wigners.

I agree it's not new maths that's needed to resolve the issue of QM but to derive the complex physical mechanism to match the maths, and hopefully identify a viable 'quasi' classical' mechanism in my essay (and referenced paper). I hope you'll read it and advise or comment even after the scoring deadline.

I certainly consider your essay should be in the final group and found it well argued with no flaws to worthy of a high score. Best of luck.

Peter

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