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FQXi FORUM

February 7, 2023

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Trick or Truth Essay Contest (2015)
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TOPIC: On Finding Meaning in the Language of Physics by Conrad Dale Johnson [refresh]

TOPIC: On Finding Meaning in the Language of Physics by Conrad Dale Johnson [refresh]

Galileo spoke of the universe as a book, written in the language of mathematics. Following his metaphor, we ask – why does the language of physics include so many different kinds of math, some simple, others extremely complex? Like any language, this one has both a formal structure and a web of semantic relationships, that give contexts of meaning to its terms and expressions. In physics the formal, mathematical structures have been studied in depth, and despite their difficulties, this aspect of the language is quite well understood. The semantic aspect of physics, though, remains unexplored. We tend just to take it for granted that the many terms that appear in the equations are physically meaningful – terms like space and time, mass and charge, etc. Yet none of these is observable or even definable by itself, apart from the contexts given by other terms in the language. Each physical variable and constant appears in many key equations, which together define its meaning in relation to other terms. This essay considers what it takes for a language to do this – to make all its expressions meaningful in terms of each other. This kind of semantic self-sufficiency is unique to physics, since in any other language, expressions have meaning primarily by referring to things beyond the language itself. But the language of the physical world is fundamental; there’s no deeper level of meaning to which it can refer. We consider the diverse mathematics involved in atomic structure to illustrate how physics is able to give meaning to the complex variety of facts and regularities on which everything else in the universe depends.

I’ve lived mainly in the US. My interest in the foundations of physics goes back to my graduate-school days at the University of California at Santa Cruz, where I earned my Ph.D. in the History of Consciousness, focusing on the evolution of Western philosophy and science. I’ve contributed essays on related topics to the FQXi contests since 2012.

Hi Conrad Dale Johnson,

Enjoyed reading your essay. You caught me with this comment "What’s not at all understood is why the universe should be built on such strangely diverse mathematical structures." and "Physics has succeeded brilliantly in explaining a vast range of phenomena by uncovering their underlying mathematical structures."

And I agree with your comment "The question now becomes, how can we explain the peculiarly various architecture of the mathematical language itself?" where "the existence of atomic matter in our universe depends on all these very different mathematical structures."

Very nice ideas starting with "The formal structure of this language is represented in our equations; its vocabulary consists of all the parameters that appear in the equations." In the words of Schrödinger, "The world extended in space and time is but our representation."

Regards, Ed

report post as inappropriate

Enjoyed reading your essay. You caught me with this comment "What’s not at all understood is why the universe should be built on such strangely diverse mathematical structures." and "Physics has succeeded brilliantly in explaining a vast range of phenomena by uncovering their underlying mathematical structures."

And I agree with your comment "The question now becomes, how can we explain the peculiarly various architecture of the mathematical language itself?" where "the existence of atomic matter in our universe depends on all these very different mathematical structures."

Very nice ideas starting with "The formal structure of this language is represented in our equations; its vocabulary consists of all the parameters that appear in the equations." In the words of Schrödinger, "The world extended in space and time is but our representation."

Regards, Ed

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Dear Conrad Dale Johnson,

Your interesting essay focused on the physical world as unique in giving meaning to language and particularly mathematical language. Whereas languages are defined in basic terms, the physical world is a seamless web that presents all definitions in terms of itself, i.e., it's own self-consistent reality. The language may contain truth or falsity. The physical reality is true only. As you note, this truth is not the truth of a "proof", it is in the contextual or semantic meaning.

In one example you refer to*tracking a particle in a magnetic field*. My essay focuses on finding the meaning of physical reality based on this very key experiment in physics and it's oversimplification in the standard (i.e., Bell) narrative. The interesting point is that his mathematical 'proof' is correct, but his physical theory that is being 'proved' is incorrect. I hope you will find the time to read my essay and comment upon it.

Whereas many interesting essays deal with the specifics of the mathematical language, I very much like your focus on the ultimate reality that underlies all descriptions, whatever the language, natural or mathematical. I believe that some of the more esoteric languages and narratives popular at the moment will fall by the wayside relatively soon, while there will be no change at all in the underlying physical reality, just better understanding of it.

My best regards,

Edwin Eugene Klingman

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Your interesting essay focused on the physical world as unique in giving meaning to language and particularly mathematical language. Whereas languages are defined in basic terms, the physical world is a seamless web that presents all definitions in terms of itself, i.e., it's own self-consistent reality. The language may contain truth or falsity. The physical reality is true only. As you note, this truth is not the truth of a "proof", it is in the contextual or semantic meaning.

In one example you refer to

Whereas many interesting essays deal with the specifics of the mathematical language, I very much like your focus on the ultimate reality that underlies all descriptions, whatever the language, natural or mathematical. I believe that some of the more esoteric languages and narratives popular at the moment will fall by the wayside relatively soon, while there will be no change at all in the underlying physical reality, just better understanding of it.

My best regards,

Edwin Eugene Klingman

report post as inappropriate

Dear Edwin Eugene,

Thanks for your note. The way you're talking about language -- as a means of describing an underlying reality -- is very reasonable. But the point of my essay is that the physical reality itself functions as a unique kind of language, in making each of its constituent elements meaningful in terms of other elements.

It's not just self-consistency that makes this possible. In fact, I'm not sure it's necessary for all the different mathematical structures we find in physics to be strictly consistent. For example, it might be that the large-scale gravitational structure of spacetime and the sub-microscopic quantum structure of particle interaction can't be described within the same mathematical framework. What's important is that each of them contributes something different to the semantic web that physically defines and measures everything.

Thanks again -- Conrad

Thanks for your note. The way you're talking about language -- as a means of describing an underlying reality -- is very reasonable. But the point of my essay is that the physical reality itself functions as a unique kind of language, in making each of its constituent elements meaningful in terms of other elements.

It's not just self-consistency that makes this possible. In fact, I'm not sure it's necessary for all the different mathematical structures we find in physics to be strictly consistent. For example, it might be that the large-scale gravitational structure of spacetime and the sub-microscopic quantum structure of particle interaction can't be described within the same mathematical framework. What's important is that each of them contributes something different to the semantic web that physically defines and measures everything.

Thanks again -- Conrad

Dear Conrad,

I liked some of your concepts: math is built into the physical world and is more than just a convenient tool, articulating our universe, speaking in the language of physics (``it has nothing beyond itself to depend on or refer to’’), interrelated definitions, measurement provides context, complex web of interaction, and emphasis on stable structured matter. As you say, the mathematical language of the physical world is pretty well understood. But for the quantum world, I’m sure you know that the interpretation of the math is becoming increasingly contentious – and that is also part of understanding. And unlike math, Nature is the owner of definitions for physics; so physics has to continually improve its definitions to match (quantum state, photon, electron, vacuum,…) —and you mentioned measurement. The math is precise, but terms are often unclear. E.g., Sometimes, measurement means a projection (magnetic orientation, polarization) and sometimes collapse to a point with no surviving state.

On the whole, nice essay!

Regards, Dave.

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I liked some of your concepts: math is built into the physical world and is more than just a convenient tool, articulating our universe, speaking in the language of physics (``it has nothing beyond itself to depend on or refer to’’), interrelated definitions, measurement provides context, complex web of interaction, and emphasis on stable structured matter. As you say, the mathematical language of the physical world is pretty well understood. But for the quantum world, I’m sure you know that the interpretation of the math is becoming increasingly contentious – and that is also part of understanding. And unlike math, Nature is the owner of definitions for physics; so physics has to continually improve its definitions to match (quantum state, photon, electron, vacuum,…) —and you mentioned measurement. The math is precise, but terms are often unclear. E.g., Sometimes, measurement means a projection (magnetic orientation, polarization) and sometimes collapse to a point with no surviving state.

On the whole, nice essay!

Regards, Dave.

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David --

I appreciate your interest, and I'm really glad you were able to make some sense out of all those ideas. You're certainly right that even when the math is well understood, the interpretation is still highly problematic, especially regarding measurement. A large part of the problem is that measurement isn't a single well-defined process; it involves very different kinds of procedure depending on what you’re measuring. This is something I discussed in my 2012 FQXi essay and again in 2013.

Thanks very much -- Conrad

I appreciate your interest, and I'm really glad you were able to make some sense out of all those ideas. You're certainly right that even when the math is well understood, the interpretation is still highly problematic, especially regarding measurement. A large part of the problem is that measurement isn't a single well-defined process; it involves very different kinds of procedure depending on what you’re measuring. This is something I discussed in my 2012 FQXi essay and again in 2013.

Thanks very much -- Conrad

Dear Conrad,

rather impressed by your insightful words I want to cite one sentence:

" So the world is in a very deep sense mathematical, yet not in the sense imagined by the long tradition of philosophical speculation that extends from Pythagoras and Plato to Max Tegmark. What’s fundamental in this universe is not its mathematical pattern per se, but what all these highly diverse kinds of 5

patterning are able to accomplish."

I wish you luck in continuing your quest for a deeper understanding of math and physics being complementary.

Best

Lutz

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rather impressed by your insightful words I want to cite one sentence:

" So the world is in a very deep sense mathematical, yet not in the sense imagined by the long tradition of philosophical speculation that extends from Pythagoras and Plato to Max Tegmark. What’s fundamental in this universe is not its mathematical pattern per se, but what all these highly diverse kinds of 5

patterning are able to accomplish."

I wish you luck in continuing your quest for a deeper understanding of math and physics being complementary.

Best

Lutz

report post as inappropriate

Interesting essay. The language may lead to misunderstanding.

Take for example scientists saying that the universe is this or is that...

To say "IS" is to commit oneself to the description of what this thing is by itself .i.e metaphysics / ontology; not the experience we have of it.

Be more appropriate when talking physics/physicality to say that things "appear" to be.... Then, one does not pretend knowing something, when in fact he doesn't.

Good luck,

Marcel,

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Take for example scientists saying that the universe is this or is that...

To say "IS" is to commit oneself to the description of what this thing is by itself .i.e metaphysics / ontology; not the experience we have of it.

Be more appropriate when talking physics/physicality to say that things "appear" to be.... Then, one does not pretend knowing something, when in fact he doesn't.

Good luck,

Marcel,

report post as inappropriate

Hello Conrad,

It is interesting how our essays superficially seem to tackle the same set of questions, but arrive at drastically different places! I particularly liked how you incorporated the idea that "[...] nothing is meaningful in and of itself; meanings always depend on the possibility of other meanings." This is certainly the strength of your essay - it's the linguistic equivalent of "background independent".

Having said that, I have two major reservations:

1) Since we don't have a complete understanding of the universe, it seems we can't be sure our choice of parameters which we assign meanings (mass, charge, etc) are correct, or even remotely reasonable. The mass of an electron shows up in many places, but at the end of the day this is simply a parameter we picked, and without a complete theory showing how this parameter is really connected to the unified whole, I would be worried about deluding ourselves. In some sense, by using the background independence you've removed the "invariance of meaning". If the very definition of the quality you are talking about is not fixed, how can this idea be logically consistent? Isn't this something like saying "meaning only has meaning if it has meaning", and leave it up to the observer to supply their own definition of meaning?

2) When you talk about atoms being fundamental to the functionality of the physical world, it seems like you are really referring to how we experience the physical world - to the act of measurement. We have no idea if space and time make sense in the absence of stable atoms - all we know is that they do make sense in the presence of them. This further suggests to me that correct interpretation of "meaning" in this context requires input from an observer.

In any case, I think the self-consistency shown in this essay is exemplary, and it's basic thesis is excellent. I wish you the best of luck in the contest.

Chris

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It is interesting how our essays superficially seem to tackle the same set of questions, but arrive at drastically different places! I particularly liked how you incorporated the idea that "[...] nothing is meaningful in and of itself; meanings always depend on the possibility of other meanings." This is certainly the strength of your essay - it's the linguistic equivalent of "background independent".

Having said that, I have two major reservations:

1) Since we don't have a complete understanding of the universe, it seems we can't be sure our choice of parameters which we assign meanings (mass, charge, etc) are correct, or even remotely reasonable. The mass of an electron shows up in many places, but at the end of the day this is simply a parameter we picked, and without a complete theory showing how this parameter is really connected to the unified whole, I would be worried about deluding ourselves. In some sense, by using the background independence you've removed the "invariance of meaning". If the very definition of the quality you are talking about is not fixed, how can this idea be logically consistent? Isn't this something like saying "meaning only has meaning if it has meaning", and leave it up to the observer to supply their own definition of meaning?

2) When you talk about atoms being fundamental to the functionality of the physical world, it seems like you are really referring to how we experience the physical world - to the act of measurement. We have no idea if space and time make sense in the absence of stable atoms - all we know is that they do make sense in the presence of them. This further suggests to me that correct interpretation of "meaning" in this context requires input from an observer.

In any case, I think the self-consistency shown in this essay is exemplary, and it's basic thesis is excellent. I wish you the best of luck in the contest.

Chris

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Chris – thanks very much for your comments. I did read your essay and note that it was worth reading twice – I’ll do that soon.

You’re right of course that all of physics is provisional, even the choice of parameters. And since our current physics was developed to stay as close as possible to the 19th-century picture of fields and particles, it is quite likely that we’re...

view entire post

You’re right of course that all of physics is provisional, even the choice of parameters. And since our current physics was developed to stay as close as possible to the 19th-century picture of fields and particles, it is quite likely that we’re...

view entire post

Hi Conrad,

I'm glad you wrote an essay in this contest. I read your essay before I wrote mine. So it might not be a coincidence, that there might be some parallels between our essays, although I tried to actively avoid the word 'meaning'.

But it might also be unavoidable to have some parallels between the essays, since yours point at the heart of the problem: how terms (physical or mathematical) accuire meaning.

That meaning is accuired in physics by the relation of the terms themselves would correspond to Heissenbergs 'Closed Theories'. Heisenberg states that the history of physics is a succession of closed theories, where the older theories are limiting cases of the newer ones. But also, that terms of the newer ones can only be understood by the terms of the older ones. Von Weizsäcker uses the term 'sematical consistency'.

A kind of circularity seems unavoidable. The means of verification or falsification of the theory (measurements) are described by the very same theory, that should be falsified or confirmed. This disturbed Lorenzen who tried to build a proto physics, where the basic terms like space, mass etc. are defined by operational procedures (for example the rubbing of a stone against other stones to get a flat space), that are independent of the physical theory.

I discuss this and other issues in my essay (hopefully soon to be shown), that I had to write really fast and I had no time to go into the details, but that I hope we find the time to discuss in the forums.

Best regards

Luca

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I'm glad you wrote an essay in this contest. I read your essay before I wrote mine. So it might not be a coincidence, that there might be some parallels between our essays, although I tried to actively avoid the word 'meaning'.

But it might also be unavoidable to have some parallels between the essays, since yours point at the heart of the problem: how terms (physical or mathematical) accuire meaning.

That meaning is accuired in physics by the relation of the terms themselves would correspond to Heissenbergs 'Closed Theories'. Heisenberg states that the history of physics is a succession of closed theories, where the older theories are limiting cases of the newer ones. But also, that terms of the newer ones can only be understood by the terms of the older ones. Von Weizsäcker uses the term 'sematical consistency'.

A kind of circularity seems unavoidable. The means of verification or falsification of the theory (measurements) are described by the very same theory, that should be falsified or confirmed. This disturbed Lorenzen who tried to build a proto physics, where the basic terms like space, mass etc. are defined by operational procedures (for example the rubbing of a stone against other stones to get a flat space), that are independent of the physical theory.

I discuss this and other issues in my essay (hopefully soon to be shown), that I had to write really fast and I had no time to go into the details, but that I hope we find the time to discuss in the forums.

Best regards

Luca

report post as inappropriate

Hi Luca,

I’m very glad to hear from you, and to find that an essay of yours is in the queue.

I hadn’t thought about the circularity of meaning between observation and theory, though that’s certainly another important aspect of the theme. The theories only have meaning by explaining observations, and the observations would be meaningless data (or would never even be made) apart from the theories.

It’s understandable that the concept of meaning is avoided in physics, since it has such a strong connotation of subjectivity and anthropocentrism. That’s unfortunate, since it makes it hard to think about how the physical world itself makes all its components meaningfully definable and observable.

The heart of the problem is a certain understanding of what it means to be fundamental, that goes back to the beginning of our intellectual tradition. We tend to assume that whatever’s truly basic in the world must be something that doesn’t need any basis itself, that just*is* in some absolute sense. Mach imagined that science could be built on pure, raw sense-data; you mention the idea that it could all be reduced to simple operational procedures. The FQXi contests are full of attempts to derive the physical world from mathematical axioms. One way or another, it seems there must be some sort of absolute starting-point.

I find the alternative difficult to articulate – that everything needs a basis, a context in which it can make a definable difference to other things. So, everything also has to contribute to contexts in which other things make a meaningful difference. That’s a very abstract way of putting it, though.

I look forward to reading your essay, no matter how rapidly written, and will surely find time to discuss it.

Thanks – Conrad

I’m very glad to hear from you, and to find that an essay of yours is in the queue.

I hadn’t thought about the circularity of meaning between observation and theory, though that’s certainly another important aspect of the theme. The theories only have meaning by explaining observations, and the observations would be meaningless data (or would never even be made) apart from the theories.

It’s understandable that the concept of meaning is avoided in physics, since it has such a strong connotation of subjectivity and anthropocentrism. That’s unfortunate, since it makes it hard to think about how the physical world itself makes all its components meaningfully definable and observable.

The heart of the problem is a certain understanding of what it means to be fundamental, that goes back to the beginning of our intellectual tradition. We tend to assume that whatever’s truly basic in the world must be something that doesn’t need any basis itself, that just

I find the alternative difficult to articulate – that everything needs a basis, a context in which it can make a definable difference to other things. So, everything also has to contribute to contexts in which other things make a meaningful difference. That’s a very abstract way of putting it, though.

I look forward to reading your essay, no matter how rapidly written, and will surely find time to discuss it.

Thanks – Conrad

Hi Conrad,

I think your essay is the first I've read in this contest that gave me something new to think about, thanks for that :) I never really thought about the self-referentialness of physics in the sense that you discuss it.

I am somewhat puzzled that you're not elaborating on the question of dimension (not spatial dimension, but dimension of parameters). These are, in some sense, that what distinguishes math from physics, that what makes it "real", if you wish. This has always been, still is, a great mystery to me. In my essay, of course, I have argued that for the pragmatist it doesn't really matter.

You should think over your opinion about the anthropic principle though. It isn't true that it's useless, this is just incorrect. That our theories must be so as to allow life to exist does put a constraint on the theories, and this can actually be used to obtain limits on certain parameters.

Let me add that your essay is very well and fluidly written :)

-- Sophia

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I think your essay is the first I've read in this contest that gave me something new to think about, thanks for that :) I never really thought about the self-referentialness of physics in the sense that you discuss it.

I am somewhat puzzled that you're not elaborating on the question of dimension (not spatial dimension, but dimension of parameters). These are, in some sense, that what distinguishes math from physics, that what makes it "real", if you wish. This has always been, still is, a great mystery to me. In my essay, of course, I have argued that for the pragmatist it doesn't really matter.

You should think over your opinion about the anthropic principle though. It isn't true that it's useless, this is just incorrect. That our theories must be so as to allow life to exist does put a constraint on the theories, and this can actually be used to obtain limits on certain parameters.

Let me add that your essay is very well and fluidly written :)

-- Sophia

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Sophia,

Thanks very much. You’re right, if we want to understand how the physical world defines itself, the big outstanding question is why there all these parameters with these particular dimensions. If I could have done it convincingly, I would have tried to sort this out in the essay. But this is one of those questions that’s so obvious and yet so difficult that even the most...

view entire post

Thanks very much. You’re right, if we want to understand how the physical world defines itself, the big outstanding question is why there all these parameters with these particular dimensions. If I could have done it convincingly, I would have tried to sort this out in the essay. But this is one of those questions that’s so obvious and yet so difficult that even the most...

view entire post

Dear Conrad,

It is indeed an important aspect of physics that you are pointing out, that is not usual to point out. However I would not exactly agree with the claim that "no other system has this sort of completeness, defining itself entirely in terms of itself. Mathematics in general certainly does not. Every branch of mathematics is built on certain primitive notions that are left...

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It is indeed an important aspect of physics that you are pointing out, that is not usual to point out. However I would not exactly agree with the claim that "no other system has this sort of completeness, defining itself entirely in terms of itself. Mathematics in general certainly does not. Every branch of mathematics is built on certain primitive notions that are left...

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Dear Sylvain –

Thanks for reading and commenting so extensively.

Your notion of a cyclically self-referential foundation of mathematics is interesting and apparently very unusual. The brief notes on this topic in my essay reflect a mainstream view that seems sensible to me, but I’m willing to believe there are other possibilities. Even so, I think there’s a basic difference...

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Thanks for reading and commenting so extensively.

Your notion of a cyclically self-referential foundation of mathematics is interesting and apparently very unusual. The brief notes on this topic in my essay reflect a mainstream view that seems sensible to me, but I’m willing to believe there are other possibilities. Even so, I think there’s a basic difference...

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Dear Conrad,

I found your essay to be very clear and I agree completely with your emphasis on the importance of language.

Physics depends greatly on the correct use of language to describe reality. Mathematics is to some extent less dependent on the English language as it has a language of mathematical symbols with its own rules.

I find that there is a need for greater attention to resolving the nature of reality at the descriptive level rather than, for example, the quantum theory acceptance of a lack of agreed physical interpretation.

As an example in your essay you mention the idea of 'which slit the photon passed through' in the interference experiment. It seems totally clear to me that the photon is a real physical wave that passes through both slits.

It is only when we have resolved at the descriptive level, the nature of light, of mass and charge and found a framework for unification that we can begin to apply mathematics effectively and build back in the ideas of quantum theory and the standard model within the new conceptual framework.

I have tried to make a start with this and my essay 'Solving the mystery' covers the main ideas.

It would be great if we could devise a 'language of physics' which was English and yet as precise as mathematics to construct a physical description of reality in a structured way. This would somehow allow us to agree on a valid description which then feeds into the mathematical modelling.

Regards

Richard

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I found your essay to be very clear and I agree completely with your emphasis on the importance of language.

Physics depends greatly on the correct use of language to describe reality. Mathematics is to some extent less dependent on the English language as it has a language of mathematical symbols with its own rules.

I find that there is a need for greater attention to resolving the nature of reality at the descriptive level rather than, for example, the quantum theory acceptance of a lack of agreed physical interpretation.

As an example in your essay you mention the idea of 'which slit the photon passed through' in the interference experiment. It seems totally clear to me that the photon is a real physical wave that passes through both slits.

It is only when we have resolved at the descriptive level, the nature of light, of mass and charge and found a framework for unification that we can begin to apply mathematics effectively and build back in the ideas of quantum theory and the standard model within the new conceptual framework.

I have tried to make a start with this and my essay 'Solving the mystery' covers the main ideas.

It would be great if we could devise a 'language of physics' which was English and yet as precise as mathematics to construct a physical description of reality in a structured way. This would somehow allow us to agree on a valid description which then feeds into the mathematical modelling.

Regards

Richard

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Dear Dr. Johnson,

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 Conrad,

I see your accent on meanings as interesting. One way to put meanings in a metaphysical center is by means of a transcendental mind as a source of meanings. Another way is to assume something like full-blown multiverse of Tegmark, where all logically possible options are realized. I tried to see what is your view on that but did not succeed. In our essay the Tegmark's multiverse is refuted, but you might think differently.

Regards,

Alexey Burov.

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I see your accent on meanings as interesting. One way to put meanings in a metaphysical center is by means of a transcendental mind as a source of meanings. Another way is to assume something like full-blown multiverse of Tegmark, where all logically possible options are realized. I tried to see what is your view on that but did not succeed. In our essay the Tegmark's multiverse is refuted, but you might think differently.

Regards,

Alexey Burov.

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Dear Conrad,

I finally had a chance to read all three of your FQXi essays and found that many of the themes you address are also those that I have spent time thinking and writing papers about. To just name two examples, on the issues of the context-dependence of "measurements" of physical quantities you may find this paper interesting, which deals exclusively with the measurement of time...

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I finally had a chance to read all three of your FQXi essays and found that many of the themes you address are also those that I have spent time thinking and writing papers about. To just name two examples, on the issues of the context-dependence of "measurements" of physical quantities you may find this paper interesting, which deals exclusively with the measurement of time...

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