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September 21, 2021

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

TOPIC: Math tells us what works, not what is real or why: a study in comparative dimensional physics by Neil Bates [refresh]

TOPIC: Math tells us what works, not what is real or why: a study in comparative dimensional physics by Neil Bates [refresh]

Just how "unreasonably effective" is mathematics, anyway? First, why does math accomplish so much for us in (apparently, in practice at least) understanding the "real world" around us? Then, what are the limits of what it can accomplish? Can it tell us why there is anything substantial at all, and why the world is the way it is? Here I argue related theses. First, mathematics is good at judging relative consistency (such as, whether a given model universe will be able to satisfy conservation of mass-energy.) This is demonstrated through a novel argument explaining why our universe must have three large spatial dimensions, in terms of the self-consistency of electromagnetic relations. Then, I argue that math has no ability to explain its own effectiveness in a "real world," or to explain the particular foundational properties of our world. Furthermore, math cannot explain why some possible worlds have "concrete" or "real existence" and others do not. Indeed, the very idea there is such a distinction is surprisingly problematic and questionable, as argued by Max Tegmark and others. Finally: any such existential distinction would be inaccessible to computational (AI-theoretical) intelligences.

I am an independent scholar interested in foundational questions. This is my fifth FQXi Essay Contest submission.

Greetings. First, I realized I made a typo in submitting my little bio to the web form (also, if I write something I want to use first person to show that.) Then I appreciated, it was sort of cute - I do want to be "interesting" not just interested. Along with the others here, this essay delves into the fundamental question of how well, and why, does mathematics model reality.

Asking these...

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Asking these...

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Hi Neil -

Very interesting essay! I am in full agreement with several of your conclusions: "Math and logic don't have the tools to reach beyond their realms and characterize the status of another existential level." "We are free to decide what intuitions to trust in our quest for the horizon of what we and the universe are, and why."

I got to these conclusions with a very different approach and would love your thoughts!

Regards - George Gantz

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Very interesting essay! I am in full agreement with several of your conclusions: "Math and logic don't have the tools to reach beyond their realms and characterize the status of another existential level." "We are free to decide what intuitions to trust in our quest for the horizon of what we and the universe are, and why."

I got to these conclusions with a very different approach and would love your thoughts!

Regards - George Gantz

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Dear Neil,

A logically strong presentation of views that I am in agreement with. Your essay is a vital contribution to this contest. Good luck.

James

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A logically strong presentation of views that I am in agreement with. Your essay is a vital contribution to this contest. Good luck.

James

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Dear Neil Bates ,

I agree with the essence of your essay: “math can tell us what works, but not what is real or why it is real”. Then the next question arises: Why is it that math can tell us 'what works' and 'what does not work'? My essay is based on this question. The simple answer lies in the nature of 'working', which can be defined as a 'change'. For any change to happen, bodies or its constituents should physically move. Or it is motion that causes changes. Motion is a space- time relation that can be mathematically described. So all changes follow mathematical laws. So maths can tell us what works.

As pointed out by you, maths cannot say why a body has mass, why a body has volume, why a body attracts, why bodies can move. In my opinion, we have to distinguish between properties and laws. Once the bodies have the given properties, it is mathematical laws that decide how bodies change with time. Please go through my essay: A physicalist interpretation of the relation between Physics and Mathematics.

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I agree with the essence of your essay: “math can tell us what works, but not what is real or why it is real”. Then the next question arises: Why is it that math can tell us 'what works' and 'what does not work'? My essay is based on this question. The simple answer lies in the nature of 'working', which can be defined as a 'change'. For any change to happen, bodies or its constituents should physically move. Or it is motion that causes changes. Motion is a space- time relation that can be mathematically described. So all changes follow mathematical laws. So maths can tell us what works.

As pointed out by you, maths cannot say why a body has mass, why a body has volume, why a body attracts, why bodies can move. In my opinion, we have to distinguish between properties and laws. Once the bodies have the given properties, it is mathematical laws that decide how bodies change with time. Please go through my essay: A physicalist interpretation of the relation between Physics and Mathematics.

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A very closely reasoned essay.

I think you might want to consider the implications of operationalism (P. W. Bridgman, The Logic of Modern Physics.)

Best, TOm Phipps

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I think you might want to consider the implications of operationalism (P. W. Bridgman, The Logic of Modern Physics.)

Best, TOm Phipps

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Dear Neil Bates,

I enjoyed your essay, starting with your comment "*math can tell us what works, but not what is real or why it is real*", a statement I completely agree with. I liked discussion following "*but our critical question here is: what does it tell us about "reality"? By reality, I mean what the person in the street means: "stuff" that actually "exists," not just mathematical models like the ones used to prove this point.*"

I have taken a little different approach to this same problem my essay here. My goal was to find "real" objects (in the sense that they can be modeled visually) that match the mathematical models of the particles of the standard model. I hope you get a chance to have a look and offer a rating.

A well done and well thought out essay, best of luck, you deserve a good rating.

Regards,

Ed Unverricht

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I enjoyed your essay, starting with your comment "

I have taken a little different approach to this same problem my essay here. My goal was to find "real" objects (in the sense that they can be modeled visually) that match the mathematical models of the particles of the standard model. I hope you get a chance to have a look and offer a rating.

A well done and well thought out essay, best of luck, you deserve a good rating.

Regards,

Ed Unverricht

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Dear Neil Bates,

I very much enjoyed your essay, and its support for the intuitively obvious fact that we live in a 3-dimensional world. I will have to carefully review your arguments for '*EMI equivalent mass*', but, given that these arguments lead to your equations (2) and (5) you very nicely derive the result D - 2 = 1 / ( D - 2 ) => D = 3.

Thank you for the simple demonstration

Your discussion of 'existence' and 'reality' is also very cogent and well argued, and also that "*math and logic ultimately constitute a self-referential universe*", working on "structure not essence", and incapable of reaching the level of substantial reality.

You say, "*all that mathematics can do for us, is make relative judgment about model worlds in terms of various internal criteria*."

I fully agree with your conclusions about 'reality' and 'mind', so I would like to focus on your statement about "relative judgment about model worlds…". You say [p. 7] "*all that math knows and can tell us in effect, is about math. When we think it is telling us something about "the world", we are just finding out about the model that we are using*."

In my essay I discuss the oversimplified physical model of Stern-Gerlach based on precession in a constant field, which leads to a null result; 0 not ±1. This contradiction is the basis upon which Bell builds his model, with the well-known "logical" consequences. I investigate a physical model of Stern-Gerlach that does not immediately lead to a contradiction, and attempt to see where that takes us. I invite you to read my essay and welcome your comments.

Best,

Edwin Eugene Klingman

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I very much enjoyed your essay, and its support for the intuitively obvious fact that we live in a 3-dimensional world. I will have to carefully review your arguments for '

Thank you for the simple demonstration

Your discussion of 'existence' and 'reality' is also very cogent and well argued, and also that "

You say, "

I fully agree with your conclusions about 'reality' and 'mind', so I would like to focus on your statement about "relative judgment about model worlds…". You say [p. 7] "

In my essay I discuss the oversimplified physical model of Stern-Gerlach based on precession in a constant field, which leads to a null result; 0 not ±1. This contradiction is the basis upon which Bell builds his model, with the well-known "logical" consequences. I investigate a physical model of Stern-Gerlach that does not immediately lead to a contradiction, and attempt to see where that takes us. I invite you to read my essay and welcome your comments.

Best,

Edwin Eugene Klingman

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Edwin,

Thanks for your comments. My argument about electromagnetic mass is somewhat complex but starts to come together for anyone with solid background who just follows along carefully. I appreciate that you are another of us, who realizes that math cannot just be glibly substituted as map for territory. There are many ways for the project to go wrong, both in terms of practical effect as well as deep questions of mind, determinism versus free action, etc. See my remarks about your essay at its link.

Thanks for your comments. My argument about electromagnetic mass is somewhat complex but starts to come together for anyone with solid background who just follows along carefully. I appreciate that you are another of us, who realizes that math cannot just be glibly substituted as map for territory. There are many ways for the project to go wrong, both in terms of practical effect as well as deep questions of mind, determinism versus free action, etc. See my remarks about your essay at its link.

Dear Neil,

I have read your essay in the spirit of the Cartesian doubt with great interest. I totally agree with you:

"Math and logic don't have the tools to reach beyond their realms and characterize the status of another existential level. Such systems can neither describe a more "substantial" realness per se, nor distinguish nor explain the high-level "accidents" of phenomenal...

view entire post

I have read your essay in the spirit of the Cartesian doubt with great interest. I totally agree with you:

"Math and logic don't have the tools to reach beyond their realms and characterize the status of another existential level. Such systems can neither describe a more "substantial" realness per se, nor distinguish nor explain the high-level "accidents" of phenomenal...

view entire post

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Vladimir,

Thank you very much! Yes, we can't just put together an "explanation of the world" out of the thinking applicable to pure math itself (which does not tell us which of those should be picked out for further manifestation). We need to look at our experiences in the world, but it isn't clear yet just how all of this adds up. Since we experience the world through our minds, we have to...

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Thank you very much! Yes, we can't just put together an "explanation of the world" out of the thinking applicable to pure math itself (which does not tell us which of those should be picked out for further manifestation). We need to look at our experiences in the world, but it isn't clear yet just how all of this adds up. Since we experience the world through our minds, we have to...

view entire post

Vladimir, I will look at your essay soon in more detail and make some comments. Here is my preliminary observation: like the last time, I see you had some translation issues regarding which English word or phrase is best to state certain concepts. If I knew more Russian I could help, but alas I do not.

PS: I apologize in general for my low activity in making comments etc. in this contest so far. More time will open up soon.

PS: I apologize in general for my low activity in making comments etc. in this contest so far. More time will open up soon.

Hi Neil--

Your essay is excellent. I agree with your bottom-line: that math, being a closed set of rules, is best at handling self-consistency, but is unable to help us on matters "out there". For that, we need physics. Your analysis involving Eq. (2) was great--but why did you call the result "obscure"? Finally, I admit that I am a fan David K. Lewis and "Modal Realism". So, I was on your side from the start.

Best regards,

Bill.

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Your essay is excellent. I agree with your bottom-line: that math, being a closed set of rules, is best at handling self-consistency, but is unable to help us on matters "out there". For that, we need physics. Your analysis involving Eq. (2) was great--but why did you call the result "obscure"? Finally, I admit that I am a fan David K. Lewis and "Modal Realism". So, I was on your side from the start.

Best regards,

Bill.

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William,

Thank you very much. The paradox of math indeed is that it can tell us about anything else only through itself. If our world happens to parallel (is isomorphic to) some mathematical system, that same math cannot explain*why* it is the model for a world - unless the world literally is that mathematical system. Then it is a case of identity, not a mysterious echo. I don't...

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Thank you very much. The paradox of math indeed is that it can tell us about anything else only through itself. If our world happens to parallel (is isomorphic to) some mathematical system, that same math cannot explain

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Well, I got unwittingly logged out, and that happens to lots of us. The reply to William Parsons was from me.

Dear Neil,

Thanks for the arguments advanced in your essay.Where I do not seem to agree with you is your proposition that "mathematics cannot tell us about anything more than itself".

What!Has mathematics ceased to be the language of nature?Are you making a nulity of the Pythagorean thesis that "numbers rule the world;and all is number"?Are you also making a nulity of the vauntings expressed by Galileo Galilei that "The book of nature is written in the language of mathematics"?Or are you in effect contradicting yourself with an allusion that NATURE IS EXCLUSIVELY MATHEMATICAL?

Grateful,please oblige.

Lloyd Tamarapreye Okoko.

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Thanks for the arguments advanced in your essay.Where I do not seem to agree with you is your proposition that "mathematics cannot tell us about anything more than itself".

What!Has mathematics ceased to be the language of nature?Are you making a nulity of the Pythagorean thesis that "numbers rule the world;and all is number"?Are you also making a nulity of the vauntings expressed by Galileo Galilei that "The book of nature is written in the language of mathematics"?Or are you in effect contradicting yourself with an allusion that NATURE IS EXCLUSIVELY MATHEMATICAL?

Grateful,please oblige.

Lloyd Tamarapreye Okoko.

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Dear Neil,

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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Hello Neal,

Quite a number of good ideas to think about and take home from your essay.

I got mixed up a bit on the inertia of charges. Are you suggesting the inertia of an electron for example is other than its mass?

Then talking of mathematical models and "stuff" that actually "exists", in which category would you put Space. Is it a mathematical model or stuff that actually exists?

In my essay., I look at the consequences where "stuff" are not eternally existing but can be created and can perish. You may want to read and comment. You may also want to volunteer your opinion on 'how to cut a line', either from a mathematical model or real world perspective.

Regards,

Akinbo

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Quite a number of good ideas to think about and take home from your essay.

I got mixed up a bit on the inertia of charges. Are you suggesting the inertia of an electron for example is other than its mass?

Then talking of mathematical models and "stuff" that actually "exists", in which category would you put Space. Is it a mathematical model or stuff that actually exists?

In my essay., I look at the consequences where "stuff" are not eternally existing but can be created and can perish. You may want to read and comment. You may also want to volunteer your opinion on 'how to cut a line', either from a mathematical model or real world perspective.

Regards,

Akinbo

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Dear Akinbo,

First of all, I'm sorry for the delay in answering your question or in looking at your essay or commenting there (indeed, in general to everyone - I have been too busy.) The electron: no, I'm not suggesting a difference between its inertia and other effective definitions of "mass" such as energy equivalent, basis for deBroglie matter wavelength, etc. However, it has long been controversial as to how MUCH of the electron's mass-inertia is electromagnetic in origin (see for example Feynman's wonderful discussion in V. II of his Lectures). Much of this is due to issues of QED, but there has still long been a problem in general: the direct interactions, even for extended charge distributions, give the wrong answer ("4/3 problem") unless there is some correction due to stress.

That correction has been somewhat controversial because of arguments over von Laue's "energy current" (as per attempted solutions of the paradox of the right-angle lever, etc.) In any case, we make the problem simpler by consider only the CHANGE in EM inertia due to changes in charge configuration. Then we don't have to wonder, how much of the total is from EMI to start with.

In my essay, I explain how to derive that correction properly, and in a space of any number of dimensions. This only gives the correct answer (correct EM inertia) for three macro dimensions.

First of all, I'm sorry for the delay in answering your question or in looking at your essay or commenting there (indeed, in general to everyone - I have been too busy.) The electron: no, I'm not suggesting a difference between its inertia and other effective definitions of "mass" such as energy equivalent, basis for deBroglie matter wavelength, etc. However, it has long been controversial as to how MUCH of the electron's mass-inertia is electromagnetic in origin (see for example Feynman's wonderful discussion in V. II of his Lectures). Much of this is due to issues of QED, but there has still long been a problem in general: the direct interactions, even for extended charge distributions, give the wrong answer ("4/3 problem") unless there is some correction due to stress.

That correction has been somewhat controversial because of arguments over von Laue's "energy current" (as per attempted solutions of the paradox of the right-angle lever, etc.) In any case, we make the problem simpler by consider only the CHANGE in EM inertia due to changes in charge configuration. Then we don't have to wonder, how much of the total is from EMI to start with.

In my essay, I explain how to derive that correction properly, and in a space of any number of dimensions. This only gives the correct answer (correct EM inertia) for three macro dimensions.

Neil,

"Mathematics cannot tell us about anything more than itself."

Tegmark would say that conscious experience takes the form of mathematical "self-aware substructures" so itself is your perception.

I guess I am just an old-fashioned guy who likes to think it's all real and not a mathematical structure.I agree, "mere 'math brains' could not have real feelings: love, nausea, itches and pains, delight, experiences of pretty color sensations, and above all: the basic "sense" of being alive and real."

My "Connections" operate in a real world which connects math, mind, and physics into spectacular accomplishments in quantum biology, DNA mapping, and LHC discoveries.

Not having a stellar math background, I certainly could be wrong, having a math-stunted perspective.

Jim

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"Mathematics cannot tell us about anything more than itself."

Tegmark would say that conscious experience takes the form of mathematical "self-aware substructures" so itself is your perception.

I guess I am just an old-fashioned guy who likes to think it's all real and not a mathematical structure.I agree, "mere 'math brains' could not have real feelings: love, nausea, itches and pains, delight, experiences of pretty color sensations, and above all: the basic "sense" of being alive and real."

My "Connections" operate in a real world which connects math, mind, and physics into spectacular accomplishments in quantum biology, DNA mapping, and LHC discoveries.

Not having a stellar math background, I certainly could be wrong, having a math-stunted perspective.

Jim

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James,

Yes we agree the world is more than math, although Tegmark's MUH shouldn't be waved off*a priori* because of anything immediately obvious about either logic, assumptions about ontology, or the way things *work* in the world. It is only by appreciating subtleties of randomness, mind, and time that one can really face up to "all this" being something beyond what any abstraction can fully describe (which, IMHO would be equivalent to it just being that abstraction.) BTW MUH neo-determinism just can't extract proper Born statistics out of its structure. I'll take a look at your essay in turn.

Yes we agree the world is more than math, although Tegmark's MUH shouldn't be waved off

Correction, I meant MWI neo-determinism (because of its branch structure and the isomorphism of compared systems differing only in the various relative amplitudes.) The many-worlds multiverse just cannot fairly generate observed statistics according to the Born rule, despite elaborate gymnastics attempting to square things, so to speak.

Greetings to the Community

I've gotten fed up with the roller-coaster ride of my point ratings, as have many others. At this point the percent change may not be much, but of course it's easy to calculate what the last rating was. Please: if you think this or any essay deserves a rating of say, three or less, you really should say why in a comment. Sure, you are justified to worry about consequences (not necessarily from the person rated!), so feel free to post as Anonymous - what matters is getting an explanation out. I'll do the same for anyone else. I don't like getting dinged with no idea what turned you off.

Even better, how about discussing things first before even giving a bad rating? And note for overall perspective: for the highest-rated essay on a 10-point scale to be in the six range, is rather sad, as is two distinguished physicists rating what would be an "F" (even if barely) on a standard public school grading system!

Thanks, I think I can say that for everyone.

I've gotten fed up with the roller-coaster ride of my point ratings, as have many others. At this point the percent change may not be much, but of course it's easy to calculate what the last rating was. Please: if you think this or any essay deserves a rating of say, three or less, you really should say why in a comment. Sure, you are justified to worry about consequences (not necessarily from the person rated!), so feel free to post as Anonymous - what matters is getting an explanation out. I'll do the same for anyone else. I don't like getting dinged with no idea what turned you off.

Even better, how about discussing things first before even giving a bad rating? And note for overall perspective: for the highest-rated essay on a 10-point scale to be in the six range, is rather sad, as is two distinguished physicists rating what would be an "F" (even if barely) on a standard public school grading system!

Thanks, I think I can say that for everyone.

Neil,

You are not alone. Of the 34 ratings, at least 6 (I haven't kept track throughout) are a rating of 1 w/o comments

Jim

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You are not alone. Of the 34 ratings, at least 6 (I haven't kept track throughout) are a rating of 1 w/o comments

Jim

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It is interesting to prove that the three dimensional space is the only possible for an electromagnetic, field; but this is true, if I understand well, only for a space with interacting particles, so that a single particle has not a constraint on the space dimension (ever if I understand well), so that the interaction create the space dimension.

I think that the electromagnetism and gravitation have equal fields (I think that there are duality between charges-Coulomb constant and masses-Gravitational constant), so that it can be that the constraint on a multi-particle mass is true for each field.

I must read with more attention, but it is important for me.

Cheers

Domenico

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I think that the electromagnetism and gravitation have equal fields (I think that there are duality between charges-Coulomb constant and masses-Gravitational constant), so that it can be that the constraint on a multi-particle mass is true for each field.

I must read with more attention, but it is important for me.

Cheers

Domenico

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Domenico,

The inconsistency isn't about being able to have an electromagnetic field at all, it's about subtle relationships pertaining to electromagnetic inertia (which are problematic even in three dimensions per the "4/3 problem.") The relationships just won't give the right answer for other dimensionalities. Gravity: it is not entirely analogous to EM so I can't assume the problem would be the same. Furthermore, self-energy works differently because it gravitates in turn, so the addition is not linear, and there are localization issues (good discussion in Penrose's "The Road to Reality." There have been extrapolations of gravitation to other dimensions. I appreciate your interest, will look at your essay.

The inconsistency isn't about being able to have an electromagnetic field at all, it's about subtle relationships pertaining to electromagnetic inertia (which are problematic even in three dimensions per the "4/3 problem.") The relationships just won't give the right answer for other dimensionalities. Gravity: it is not entirely analogous to EM so I can't assume the problem would be the same. Furthermore, self-energy works differently because it gravitates in turn, so the addition is not linear, and there are localization issues (good discussion in Penrose's "The Road to Reality." There have been extrapolations of gravitation to other dimensions. I appreciate your interest, will look at your essay.

I think that there is a complete analogy between gravitational field and electromagnetic field, because of the gravitoelectromagnetism formulation, that it is deeper for me because of:

so that, when I read your essay some weeks ago, I saw a possible gravity inertia application; that I had forgotten to consider, because of I had not taken notes because I read dozens of essay at a time (each essay is worth reading)..

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so that, when I read your essay some weeks ago, I saw a possible gravity inertia application; that I had forgotten to consider, because of I had not taken notes because I read dozens of essay at a time (each essay is worth reading)..

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I prefer not to comment on the essays, because they affect the votes, but in any case I would have informed you after the vote; I break the rule just because I consider polite to reply to my posts.

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Greetings Tyranno,

I certainly agree with the 3 dimensions of reality and arrive there from a different direction. A totally worthwhile essay, thank you.

Sherman Jenkins

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I certainly agree with the 3 dimensions of reality and arrive there from a different direction. A totally worthwhile essay, thank you.

Sherman Jenkins

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Dear Neil,

I appreciate the depth of your essay and its level; to my mind, it is among the top ones here. Although I disagree with some of your points, I give your essay very high rating. Your conclusions that

“math cannot either describe what "concreteness" is, nor which if any model worlds should be manifested as "actual worlds." It cannot explain why any such transcendently "more real" world should be mathematically elegant or "simple," instead of messy and not effectively accessible through math”

are extremely important and correct. However, physics is more than math, and its success with elegant mathematics tells something very important about the universe. I am inviting you to read our essay where we refute Tegmark’s MUH on the ground of fundamental physics.

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I appreciate the depth of your essay and its level; to my mind, it is among the top ones here. Although I disagree with some of your points, I give your essay very high rating. Your conclusions that

“math cannot either describe what "concreteness" is, nor which if any model worlds should be manifested as "actual worlds." It cannot explain why any such transcendently "more real" world should be mathematically elegant or "simple," instead of messy and not effectively accessible through math”

are extremely important and correct. However, physics is more than math, and its success with elegant mathematics tells something very important about the universe. I am inviting you to read our essay where we refute Tegmark’s MUH on the ground of fundamental physics.

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Dear Alexey/Lev,

Thank you. I read your essay at your request and was very impressed at the writing as well as the acute grasp of conceptual foundations and issues (like, the problem of existential asymmetry for specially-selected possible worlds.) Well put. First, I agree with you that physics is more than math, and that our world is not a math structure. Math "by itself" cannot tell us more than about its own contents (like, why there "are" five Platonic solids in that sense). However, as you well argue, the math we find in the universe can tell us much more. You correctly note the flaw in the argument that the fine-tuning we observe can be adequately explained (in Bayesian terms) as no more than a self-selection effect. True, if that were so, then the precision and elegance of the world would probably be less. (However, let's all admit that with continua we do have a measure problem. Still, even without enumerable sets to compare, the relative "areas" of numerical ranges give us a rough idea of what we should expect.)

Actually I think the problem is even worse. If we really consider the full range of math structures, then we have to include inconsistent ones like e.g. the splicing together of y = x^{2} with y = x^{4}. In that case, rules would not even be consistent over time etc. There are many more possible messy worlds than orderly ones, a problem noted about David Lewis' modal realism.

These foundational arguments are fascinating and important, but I am particularly proud of my novel (in its broad execution at least) argument for why space had to be three-dimensional. It constrains possible worlds more than previously realized, although as I noted: only to the extent that we expect lawful consistency in "worlds" in the first place. And what really makes "worlds" different from mere structures of math? I basically agree with the sentiments pleaded by Roger Penrose (whose diagram is borrowed for your essay). Quote:

"One can argue that a universe governed by laws that do not allow consciousness is no universe at all. I would even say that all the mathematical descriptions of a universe that have been given so far must fail this criterion. It is only the phenomenon of consciousness that can conjure a putative 'theoretical' universe into actual existence! ... Yet beneath all this technicality is the feeling that it is indeed 'obvious' that the conscious mind cannot work like a computer, even though much of what is actually involved in mental activity might do so. This is the kind of obviousness that a child can see--though that child may, in later life, become browbeaten into believing that the obvious problems are 'non-problems', to be argued into non-existence ... ."

- Roger Penrose, in The Emperor's New Mind (1988), pp. 447-448.

Thank you. I read your essay at your request and was very impressed at the writing as well as the acute grasp of conceptual foundations and issues (like, the problem of existential asymmetry for specially-selected possible worlds.) Well put. First, I agree with you that physics is more than math, and that our world is not a math structure. Math "by itself" cannot tell us more than about its own contents (like, why there "are" five Platonic solids in that sense). However, as you well argue, the math we find in the universe can tell us much more. You correctly note the flaw in the argument that the fine-tuning we observe can be adequately explained (in Bayesian terms) as no more than a self-selection effect. True, if that were so, then the precision and elegance of the world would probably be less. (However, let's all admit that with continua we do have a measure problem. Still, even without enumerable sets to compare, the relative "areas" of numerical ranges give us a rough idea of what we should expect.)

Actually I think the problem is even worse. If we really consider the full range of math structures, then we have to include inconsistent ones like e.g. the splicing together of y = x

These foundational arguments are fascinating and important, but I am particularly proud of my novel (in its broad execution at least) argument for why space had to be three-dimensional. It constrains possible worlds more than previously realized, although as I noted: only to the extent that we expect lawful consistency in "worlds" in the first place. And what really makes "worlds" different from mere structures of math? I basically agree with the sentiments pleaded by Roger Penrose (whose diagram is borrowed for your essay). Quote:

"One can argue that a universe governed by laws that do not allow consciousness is no universe at all. I would even say that all the mathematical descriptions of a universe that have been given so far must fail this criterion. It is only the phenomenon of consciousness that can conjure a putative 'theoretical' universe into actual existence! ... Yet beneath all this technicality is the feeling that it is indeed 'obvious' that the conscious mind cannot work like a computer, even though much of what is actually involved in mental activity might do so. This is the kind of obviousness that a child can see--though that child may, in later life, become browbeaten into believing that the obvious problems are 'non-problems', to be argued into non-existence ... ."

- Roger Penrose, in The Emperor's New Mind (1988), pp. 447-448.

Dear Neil,

Thanks for your good words and interesting remarks to our essay. I am glad to see that we agree on most important points, and there is a good potential for a productive discussion in many others. In particular, I wish to discuss your 3D arguments, but this requires different format. You can easily find my address; if you like, you may send me an email and we’ll find a better way to discuss that. Meanwhile, please do not miss out on rating our essay :)

Cheers,

Alexey.

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Thanks for your good words and interesting remarks to our essay. I am glad to see that we agree on most important points, and there is a good potential for a productive discussion in many others. In particular, I wish to discuss your 3D arguments, but this requires different format. You can easily find my address; if you like, you may send me an email and we’ll find a better way to discuss that. Meanwhile, please do not miss out on rating our essay :)

Cheers,

Alexey.

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Dear Neil,

I found your essay quite interesting, so I added it to the list of quality essays in my review. Unfortunately I did not have the time to analyze in details your arguments about dimensions. But I found that we completely agree on the metaphysics which you expressed in your last 2 pages. I expressed the same idea in very short on the bottom of page 2 of my own essay. I also explained there how quantum physics is naturally interpreted in this way.

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I found your essay quite interesting, so I added it to the list of quality essays in my review. Unfortunately I did not have the time to analyze in details your arguments about dimensions. But I found that we completely agree on the metaphysics which you expressed in your last 2 pages. I expressed the same idea in very short on the bottom of page 2 of my own essay. I also explained there how quantum physics is naturally interpreted in this way.

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Dear Neil,

Thanks for your good words and interesting remarks to our essay. I am glad to see that we agree on most important points, and there is a good potential for a productive discussion in many others. In particular, I wish to discuss your 3D arguments, but this requires different format. You can easily find my address; if you like, you may send me an email and we’ll find a better way to discuss that. Meanwhile, please do not miss out on rating our essay :)

Cheers,

Alexey.

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Thanks for your good words and interesting remarks to our essay. I am glad to see that we agree on most important points, and there is a good potential for a productive discussion in many others. In particular, I wish to discuss your 3D arguments, but this requires different format. You can easily find my address; if you like, you may send me an email and we’ll find a better way to discuss that. Meanwhile, please do not miss out on rating our essay :)

Cheers,

Alexey.

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Dear Sylvain,

Thank you for noting my essay at your review site. This gem is among your top four picks:

"Genesis of a Pythagorean Universe," by Alexey and Lev Burov.

I consider this essay one of the best as well, as you might gather from my reply to their comment here. You group them in the Idealism/Dualism sector, where I put myself too. But I make clear, that stance is in terms of ultimate considerations.Operationally, I accept the practical and apparent reduction of most processes to objectively discernible laws, etc. I would compare the attitude to that of Penrose, whom the Burovs clearly admire as much as I do.

My argument about 3-D draws on contexts that just aren't part of most physics these days, because of concentration on particles, quantum and GR theory etc. Most physicists are out of touch with the relativistic dynamics of extended bodies and this sort of foundational reasoning by analogy. Yet it's straightforward application of SRT and the principles of retarded field projection. I hope that when readers have more time to work through it, the demonstration will become clear.

I'll take a look at your essay. I sometimes mull over them awhile before commenting but at least that means I didn't just skim and throw something out there without thinking much. Cheers.

PS: reminder to everyone to check if you are really still logged in and if you pick the link for the thread you want to reply to.

Thank you for noting my essay at your review site. This gem is among your top four picks:

"Genesis of a Pythagorean Universe," by Alexey and Lev Burov.

I consider this essay one of the best as well, as you might gather from my reply to their comment here. You group them in the Idealism/Dualism sector, where I put myself too. But I make clear, that stance is in terms of ultimate considerations.Operationally, I accept the practical and apparent reduction of most processes to objectively discernible laws, etc. I would compare the attitude to that of Penrose, whom the Burovs clearly admire as much as I do.

My argument about 3-D draws on contexts that just aren't part of most physics these days, because of concentration on particles, quantum and GR theory etc. Most physicists are out of touch with the relativistic dynamics of extended bodies and this sort of foundational reasoning by analogy. Yet it's straightforward application of SRT and the principles of retarded field projection. I hope that when readers have more time to work through it, the demonstration will become clear.

I'll take a look at your essay. I sometimes mull over them awhile before commenting but at least that means I didn't just skim and throw something out there without thinking much. Cheers.

PS: reminder to everyone to check if you are really still logged in and if you pick the link for the thread you want to reply to.

Well, to add more about the 3-D argument since I really shouldn't imply it's just about applying retardation of fields: a key element is the stress adjustment, which has been controversial. Few people think about it other than those with a specific interest, and it's mostly taken for granted as something in the background. IOW, few people think about the workings of it in a way that would allow insight into the generalization of that correction to *n* dimensions. So, the implications of it for comparative physics is neglected.

Neil,

I am revisiting essays I have read to make sure I rated them. I found that I rated your on the day of my comments 4/13/2015.

I would like to see your thoughts on mine. Mine, I must admit, is not as open-minded as yours: http://fqxi.org/community/forum/topic/2345

Thanks,

Jim

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I am revisiting essays I have read to make sure I rated them. I found that I rated your on the day of my comments 4/13/2015.

I would like to see your thoughts on mine. Mine, I must admit, is not as open-minded as yours: http://fqxi.org/community/forum/topic/2345

Thanks,

Jim

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James, thanks, will take a look. I recall that your essay last time was rather interesting. I don't say much about rating per se for obvious reasons, other than my overall opinions.

Dear Neal,

Your essay conjoins two topics I would not have immediately thought of as being closely related in an interesting way. A few comments:

1.Your eqn. 2 reminded me a little of Ehrenfest's argument already over 100 years ago that one way to answer the question about the dimensionality of space is to consider that in space dimensions other than 3 orbits become unstable. Now, I...

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Your essay conjoins two topics I would not have immediately thought of as being closely related in an interesting way. A few comments:

1.Your eqn. 2 reminded me a little of Ehrenfest's argument already over 100 years ago that one way to answer the question about the dimensionality of space is to consider that in space dimensions other than 3 orbits become unstable. Now, I...

view entire post

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Dear Armin,

You ask good questions. About your #1: it isn't enough to have some kind of stuff with whatever rules would be an extrapolation to other dimensions. The change in rules has to all add up to a consistent system. I showed that if we make the expected change in exponent for basic field law and combine that with requiring electromagnetic inertia and the stress correction, things don't work together harmoniously except for D = 3 (here just referring to space dimensions.) Yes, the 4/3 problem has been a wild ride and with lots of conflicting arguments, unbelievable (?) as that may seem. Yes Rorlich's book is a great read, and many interesting articles about such issues appear in American J. of Physics, while the more glamorous cutting-edge journals have mostly left this behind as unfashionable.

Yet a clear implication can be worked out, going back to Einstein's old argument about the effect relative simultaneity has on force-application times, and therefore momentum and energy. This in turn has specific implications for stressed bodies that are accelerated. Well I will add more later.

You ask good questions. About your #1: it isn't enough to have some kind of stuff with whatever rules would be an extrapolation to other dimensions. The change in rules has to all add up to a consistent system. I showed that if we make the expected change in exponent for basic field law and combine that with requiring electromagnetic inertia and the stress correction, things don't work together harmoniously except for D = 3 (here just referring to space dimensions.) Yes, the 4/3 problem has been a wild ride and with lots of conflicting arguments, unbelievable (?) as that may seem. Yes Rorlich's book is a great read, and many interesting articles about such issues appear in American J. of Physics, while the more glamorous cutting-edge journals have mostly left this behind as unfashionable.

Yet a clear implication can be worked out, going back to Einstein's old argument about the effect relative simultaneity has on force-application times, and therefore momentum and energy. This in turn has specific implications for stressed bodies that are accelerated. Well I will add more later.

Dear Neil,

Please pardon the misspelling of your name, I noticed it as soon as I posted my previous comment.

Armin

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Please pardon the misspelling of your name, I noticed it as soon as I posted my previous comment.

Armin

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Hi Neil,

You present an interesting case for why we probably do live in a 3 dimensional universe. But I'm mainly interested in your major thesis that "math can tell us what works, but not what is real or why it is real".

I think your argument is correct that "Math and logic don't have the tools to reach beyond their realms and characterize the status of another existential level." - "We must transcend math and logic to grasp this". I think you made a very good case.

As you have noted, our essays address the same sort of foundational questions.

Best wishes,

Lorraine

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You present an interesting case for why we probably do live in a 3 dimensional universe. But I'm mainly interested in your major thesis that "math can tell us what works, but not what is real or why it is real".

I think your argument is correct that "Math and logic don't have the tools to reach beyond their realms and characterize the status of another existential level." - "We must transcend math and logic to grasp this". I think you made a very good case.

As you have noted, our essays address the same sort of foundational questions.

Best wishes,

Lorraine

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Lorraine, thanks for writing. Please consider attending one of the Tucson interdisciplinary conferences on consciousness some day, I think you have much to contribute on the great mystery of the mind. I went to the 2000 event and gave a paper on willful choice. I've enjoyed your previous essays too. We can't really extract "worlds" from math, although Max Tegmark's heroic effort of the MUH deserves credit for audacity and creativity. It should not be dismissed casually (even though I don't agree with the thesis.)

Dear Neil,

My apologies for reading your essay so late, but each year there seem to be more and more notable pieces like yours and choosing the order is a hard thing to do. You have some delightful expressions, this one in particular reminding me of how Einstein saw the world, “the orderliness is the expression of the mind of God”. You are making a very interesting point approaching the self-energy problem, allow me to add to that the whole theory maybe deserves more attention than it receives nowadays, and perhaps a careful treatment in the framework of general relativity. Another good point of yours is that of structure and essence and I appreciate your treatment. I agree with "math can tell us what works, but not what is real or why it is real", and the final words conclude well that "Mathematics cannot tell us about anything more than itself".

My very best regards,

Cristi Stoica

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My apologies for reading your essay so late, but each year there seem to be more and more notable pieces like yours and choosing the order is a hard thing to do. You have some delightful expressions, this one in particular reminding me of how Einstein saw the world, “the orderliness is the expression of the mind of God”. You are making a very interesting point approaching the self-energy problem, allow me to add to that the whole theory maybe deserves more attention than it receives nowadays, and perhaps a careful treatment in the framework of general relativity. Another good point of yours is that of structure and essence and I appreciate your treatment. I agree with "math can tell us what works, but not what is real or why it is real", and the final words conclude well that "Mathematics cannot tell us about anything more than itself".

My very best regards,

Cristi Stoica

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Dear Christinel,

Thank you very much for your supporting comments. Many of us think that the order in the world is an expression of some deep "idea" or complex of ideas, aside from how a person wants to imagine that ultimate reality. We agree that math by itself can do the job, but ideas like MUH shouldn't be dismissed breezily. (Remember also that Max was instrumental in starting up...

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Thank you very much for your supporting comments. Many of us think that the order in the world is an expression of some deep "idea" or complex of ideas, aside from how a person wants to imagine that ultimate reality. We agree that math by itself can do the job, but ideas like MUH shouldn't be dismissed breezily. (Remember also that Max was instrumental in starting up...

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Christinel,

Sorry that I need to correct a statement that inadvertently misrepresented our positions. I should have written:

"We agree that math by itself CANNOT do the job, but ideas like MUH shouldn't be dismissed breezily. (Remember also that Max was instrumental in starting up FQXi!)"

Here the correction is in bold, I originally had "can do the job". Good luck in the finals.

Sorry that I need to correct a statement that inadvertently misrepresented our positions. I should have written:

"We agree that math by itself CANNOT do the job, but ideas like MUH shouldn't be dismissed breezily. (Remember also that Max was instrumental in starting up FQXi!)"

Here the correction is in bold, I originally had "can do the job". Good luck in the finals.

Dear Neil,

Great essay. It is well-written and well-argued. I agree fully with your analysis, and there are some similarities between my essay and yours. Your essay deserves the highest rating.

Best regards and good luck in the contest.

Mohammed

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Great essay. It is well-written and well-argued. I agree fully with your analysis, and there are some similarities between my essay and yours. Your essay deserves the highest rating.

Best regards and good luck in the contest.

Mohammed

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Hi Neil,

It is nice to meet you again here in FQXi Essay Contest. Even this year, you made a very good work. I indeed found your Essay very interesting and enjoyable. In particular, I appreciate your pretty argument which explains why the Universe consists in three spatial dimensions.

More in general, I found the reading of your nice Essay very interesting and enjoyable. Thus, I am pleasured to give you a deserved highest rate.

I hope you will have a chance to read my Essay.

I wish you best luck in the contest.

Cheers, Ch.

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It is nice to meet you again here in FQXi Essay Contest. Even this year, you made a very good work. I indeed found your Essay very interesting and enjoyable. In particular, I appreciate your pretty argument which explains why the Universe consists in three spatial dimensions.

More in general, I found the reading of your nice Essay very interesting and enjoyable. Thus, I am pleasured to give you a deserved highest rate.

I hope you will have a chance to read my Essay.

I wish you best luck in the contest.

Cheers, Ch.

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Christian, thanks.

I haven't had time to read your essay in detail (and I'm neurotic about saying much unless I do), but I already appreciate that you address specific experimental results and predictions in light of particular theoretical expectations and critiques. That adds more than generalizations can do on their own. Note this curious irony: you correctly say that GR (now celebrating its 100th anniversary, so an apt time for your essay) is a geometrical theory, which constrains its form and predictions in certain ways. Yet you are boldly asserting that many physicists have missed an important insight, in their handling of clock synchronization in the rotating disk (all this I am gathering from your abstract alone.) How could this be?

Well if you are right, it means there are subtle problems of framing issues in this area - analogous to the problems dogging quantum mechanics and relativistic dynamics (such as arguments about the right-angle lever and the "energy current", how is angular momentum conserved in Thomas Precession, etc.)

I will go into more detail at your own essay.

Regards.

I haven't had time to read your essay in detail (and I'm neurotic about saying much unless I do), but I already appreciate that you address specific experimental results and predictions in light of particular theoretical expectations and critiques. That adds more than generalizations can do on their own. Note this curious irony: you correctly say that GR (now celebrating its 100th anniversary, so an apt time for your essay) is a geometrical theory, which constrains its form and predictions in certain ways. Yet you are boldly asserting that many physicists have missed an important insight, in their handling of clock synchronization in the rotating disk (all this I am gathering from your abstract alone.) How could this be?

Well if you are right, it means there are subtle problems of framing issues in this area - analogous to the problems dogging quantum mechanics and relativistic dynamics (such as arguments about the right-angle lever and the "energy current", how is angular momentum conserved in Thomas Precession, etc.)

I will go into more detail at your own essay.

Regards.

Neil,

I really appreciate your incisive review, including your constructive comments.

Best regards,

Jim

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I really appreciate your incisive review, including your constructive comments.

Best regards,

Jim

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My comment at the contest winners announced discussion site about the announcement of winners:

My reaction to hearing the list of number-place winners (unless there are special extra prizes to be awarded late), and based on omissions and not critique of winners, is the following: FQXi (or, the majority of judges) seems not really interested in finding new talent and rewarding people from "all walks" for daring thinking and trying to present genuine contributions (new physics.) I'm sorry to have to say that, and I'm disappointed. I see no real effort to identify talented amateurs trying to make even potentially important contributions, versus the philosophizing that most essays express. Shouldn't that be a top priority?

Sure, I can't be fully objective all along, especially about myself. Don't take my word for anything. So, if anyone is interested then do some spade work and tell me what you think.

--------------------------

Added here: they can't be bothered to be at least somewhat impressed, by a new argument to explain something as fundamental as the dimensionality of space?! I didn't even use "new theories" etc, it was creative extension of

known theory (retarded fields, stress tensor) applied to higher dimensions. I gamely went along four previous times, but after a fifth snub like this, it's started to feel like "trickle down." BTW feel free to also discuss at my FB page, facebook.com/tyrannogenius.

My reaction to hearing the list of number-place winners (unless there are special extra prizes to be awarded late), and based on omissions and not critique of winners, is the following: FQXi (or, the majority of judges) seems not really interested in finding new talent and rewarding people from "all walks" for daring thinking and trying to present genuine contributions (new physics.) I'm sorry to have to say that, and I'm disappointed. I see no real effort to identify talented amateurs trying to make even potentially important contributions, versus the philosophizing that most essays express. Shouldn't that be a top priority?

Sure, I can't be fully objective all along, especially about myself. Don't take my word for anything. So, if anyone is interested then do some spade work and tell me what you think.

--------------------------

Added here: they can't be bothered to be at least somewhat impressed, by a new argument to explain something as fundamental as the dimensionality of space?! I didn't even use "new theories" etc, it was creative extension of

known theory (retarded fields, stress tensor) applied to higher dimensions. I gamely went along four previous times, but after a fifth snub like this, it's started to feel like "trickle down." BTW feel free to also discuss at my FB page, facebook.com/tyrannogenius.

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