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RECENT POSTS IN THIS TOPIC

**Eckard Blumschein**: *on* 5/26/15 at 3:07am UTC, wrote Part 3 A mathematics that is relevant for physics should be free of...

**Eckard Blumschein**: *on* 5/3/15 at 6:43am UTC, wrote Aldo Filomeno replied on Apr. 30, 2015 @ 18:28 GMT ... Your essay looks...

**Eckard Blumschein**: *on* 4/24/15 at 8:48am UTC, wrote Part 2 At the time of Cauchy and Gauss in the middle of 19th century, the...

**Eckard Blumschein**: *on* 4/23/15 at 5:08am UTC, wrote Dear Edwin Eugene Klingman, Thank you for your warm words. I added some...

**Eckard Blumschein**: *on* 4/23/15 at 4:57am UTC, wrote Corrections to part 1: ? in a-? and a+? should read epsilon 1873 and...

**James Hoover**: *on* 4/22/15 at 22:50pm UTC, wrote Eckard, Shark time as they pull you down, so I am revisiting essays I’ve...

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FQXi FORUM

October 6, 2022

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

TOPIC: Physics Suffers from Unwarranted Interpretations by Eckard Blumschein [refresh]

TOPIC: Physics Suffers from Unwarranted Interpretations by Eckard Blumschein [refresh]

Some seemingly mysterious interpretations of mathematics by physicists are just unwarranted. When the ancient mathematicians attributed abstract notions like number and shape to physical objects, they didn’t distinguish these notions from real objects and didn’t accept fictitious numbers, numbers in excess of the pebbles of abacus. The progress of science stagnated until with Renaissance mathematicians ignored the restriction to countable elements of reality. By liberating mathematics they paved the way for calculus and complex calculus; these then boosted physics and technology. Later on, free evolution of mathematics was proclaimed. Such freedom contradicts discovered laws of nature rather than invented ones. By means of clever restricted constructs, modern set theory promised rigorously avoiding the gap between Euclid’s point that has no parts and Peirce’s continuum every part of which has parts. Belonging inconsistencies in physics gave rise to suggest a more natural foundation of mathematics. It renders CH, ZFC, EPR, and Bell not even wrong. Physics mainly suffers from bad habit to maximally generalize models and to interpret results immediately in an artificial mathematical domain as if they were automatically valid in reality too. Hilbert may be blamed for his denial of the now and for his untenable strategy to formulate axioms and then to deduce physics. Let’s instead reinstall obedience to natural restrictions on the results of calculations and reject arbitrarily enforced rigor that misled us into futile increasingly speculative theories. For instance: It is not warranted to ascribe singular points to reality; time symmetry is an artifact due to careless use of complex calculus; translation from fiction back to reality is a must.

See http://www.fqxi.org/community/essay/topic/369

Dear Eckhard,

Once again your essay delights me. Your erudite analysis of the history of mathematics and your focus on application to physics is excellent preparation for this essay topic.

As I do not believe there is anything corresponding to infinity in physics, I have never bothered (except in math classes eons ago) to think much about infinity. I intuitively accept a physical...

view entire post

Once again your essay delights me. Your erudite analysis of the history of mathematics and your focus on application to physics is excellent preparation for this essay topic.

As I do not believe there is anything corresponding to infinity in physics, I have never bothered (except in math classes eons ago) to think much about infinity. I intuitively accept a physical...

view entire post

report post as inappropriate

Dear Edwin,

Are pebble-like numbers sufficient for the analysis of measurement data? My anything but erudite reasoning arrives at a no. Hopefully at least you will not take me wrong; I very much enjoy using and correctly interpreting complex calculus. My emphasis is on CORRECTLY.

Formally, the Heaviside-based theory of analyzing data measured in real time is not even wrong. Nonetheless, the natural solution is still by far superior. It took me quite a while until I revealed the decisive reason and excluded not yet existing future data from analysis. Proponents of pebble-like numbers cannot accept this.

Akinbo Ojo suggests splitting pebble-like non-zero dimensional numbers. Giovanni Prisinzano came closer to me by modifying this idea and speaking of Dedekind’s cut as a binding instead of severing point, a point that is common to the left as well as to the right surrounding. While such maneuvers seem to resolve the EPR paradox too, I don’t sacrifice Euclid’s and Peirce’s definitions.

More later.

My very best regards,

Eckard Blumschein

Are pebble-like numbers sufficient for the analysis of measurement data? My anything but erudite reasoning arrives at a no. Hopefully at least you will not take me wrong; I very much enjoy using and correctly interpreting complex calculus. My emphasis is on CORRECTLY.

Formally, the Heaviside-based theory of analyzing data measured in real time is not even wrong. Nonetheless, the natural solution is still by far superior. It took me quite a while until I revealed the decisive reason and excluded not yet existing future data from analysis. Proponents of pebble-like numbers cannot accept this.

Akinbo Ojo suggests splitting pebble-like non-zero dimensional numbers. Giovanni Prisinzano came closer to me by modifying this idea and speaking of Dedekind’s cut as a binding instead of severing point, a point that is common to the left as well as to the right surrounding. While such maneuvers seem to resolve the EPR paradox too, I don’t sacrifice Euclid’s and Peirce’s definitions.

More later.

My very best regards,

Eckard Blumschein

Dear Eckhard,

Interpreting our math without physical constraints leads to abstract mathematical objects that do not exist in our universe. I invite you to read my essay and give me your informed comments. Thanks.

Ken Seto

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Interpreting our math without physical constraints leads to abstract mathematical objects that do not exist in our universe. I invite you to read my essay and give me your informed comments. Thanks.

Ken Seto

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Dear Ken Hon Seto,

My references include meanwhile heretical papers by Euclid and Galileo. Unfortunately you didn't refer to scientific work. Therefore I am not in position to judge your Model Mechanics. My difficulties begin with your claim for absolute time. What do you mean with it?

I consider the currently elapsed time the natural reference.

Eckard Blumschein

My references include meanwhile heretical papers by Euclid and Galileo. Unfortunately you didn't refer to scientific work. Therefore I am not in position to judge your Model Mechanics. My difficulties begin with your claim for absolute time. What do you mean with it?

I consider the currently elapsed time the natural reference.

Eckard Blumschein

Dear Eckard,

Your essay traces the historical origins of the debate. I am happy the effort you put into this came out with something worth reading and enjoying. You discussed very well the different sides of the debate. For example comparing Euclid's point as something that doesn’t have parts and C. S. Peirce's continuum as something every part of which has parts. As we have both argued in the past, I dispute the meaning of "not having parts" to imply being of zero magnitude. Rather, I prefer the definition of "having no parts" as implying an indivisible magnitude.

Why do you include volume among unphysical mathematical notions?

Also, let me ask you other questions: 1) Can the Universe perish (e.g. in a Big Crunch) or can the Universe be created from nothing (e.g. in a Big bang)? 2) If you answer is Yes, does that mean that the Peirce-continuum along with its points also perish? In my essay I make a hypothesis on this.

Your essay, made me to check up a bit more about Peirce's logic and I found this in the Stanford Encyclopedia:*"...Peirce says that if a line is cut into two portions, ***the point at which the cut takes place** actually **becomes two points**...".

Does this mean that 'the point at which the cut takes place' has two parts? If so, this contradicts the geometric definition.

All the best in the competition.

Regards,

Akinbo

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Your essay traces the historical origins of the debate. I am happy the effort you put into this came out with something worth reading and enjoying. You discussed very well the different sides of the debate. For example comparing Euclid's point as something that doesn’t have parts and C. S. Peirce's continuum as something every part of which has parts. As we have both argued in the past, I dispute the meaning of "not having parts" to imply being of zero magnitude. Rather, I prefer the definition of "having no parts" as implying an indivisible magnitude.

Why do you include volume among unphysical mathematical notions?

Also, let me ask you other questions: 1) Can the Universe perish (e.g. in a Big Crunch) or can the Universe be created from nothing (e.g. in a Big bang)? 2) If you answer is Yes, does that mean that the Peirce-continuum along with its points also perish? In my essay I make a hypothesis on this.

Your essay, made me to check up a bit more about Peirce's logic and I found this in the Stanford Encyclopedia:

Does this mean that 'the point at which the cut takes place' has two parts? If so, this contradicts the geometric definition.

All the best in the competition.

Regards,

Akinbo

report post as inappropriate

Akinbo,

Asking "Why do you include volume among unphysical mathematical notions?" you referred to this:

When Spinoza wrote "It is absurd to claim that bodies are composed of areas, areas of lines, and finally lines of points" he equated the physical notion "body" with the mathematical notion volume. ... A body in reality cannot at all be composed of abstract items.

I would...

view entire post

Asking "Why do you include volume among unphysical mathematical notions?" you referred to this:

When Spinoza wrote "It is absurd to claim that bodies are composed of areas, areas of lines, and finally lines of points" he equated the physical notion "body" with the mathematical notion volume. ... A body in reality cannot at all be composed of abstract items.

I would...

view entire post

Akinbo,

While I answered your question "Why do you include volume among unphysical mathematical notions" I didn't yet answer the following numbered questions:

1) Can the Universe perish (e.g. in a Big Crunch) or can the Universe be created from nothing (e.g. in a Big bang)?

2) If you answer is Yes, does that mean that the Peirce-continuum along with its points also perish?

My answer is: The universe is by definition just a mental container of anything physical, the whole of space including all the stars, galaxies, and possible even multiverses.

I abstain from any comment on belonging speculations unless they look simply like obviously nonsensical artifacts. For instance, even H.-D. Zeh distrusted white holes ascribed to a Schwarzschild solution. A God is not trustworthy because he is to similar to hoe humans look.

When I attributed the definition of a genuine continuum to Peirce, I was aware that it was not a new insight by himself but just formulated the infinite divisibility. Why felt C.S. Peirce overwhelmed by set theory? Stanford Encyclopedia omits a lot. If I recall correctly, Peirce was proud of having found Dedekind's definition of infinity before Dedekind.

Having quoted: "Peirce says that if a line is cut into two portions, the point at which the cut takes place actually becomes two points..." you are asking:

"Does this mean that 'the point at which the cut takes place' has two parts? If so, this contradicts the geometric definition."

It looks as if you are aware of the calamity which I ascribe to Dedekind's notion of number as a pebble.

Regards,

Eckard

While I answered your question "Why do you include volume among unphysical mathematical notions" I didn't yet answer the following numbered questions:

1) Can the Universe perish (e.g. in a Big Crunch) or can the Universe be created from nothing (e.g. in a Big bang)?

2) If you answer is Yes, does that mean that the Peirce-continuum along with its points also perish?

My answer is: The universe is by definition just a mental container of anything physical, the whole of space including all the stars, galaxies, and possible even multiverses.

I abstain from any comment on belonging speculations unless they look simply like obviously nonsensical artifacts. For instance, even H.-D. Zeh distrusted white holes ascribed to a Schwarzschild solution. A God is not trustworthy because he is to similar to hoe humans look.

When I attributed the definition of a genuine continuum to Peirce, I was aware that it was not a new insight by himself but just formulated the infinite divisibility. Why felt C.S. Peirce overwhelmed by set theory? Stanford Encyclopedia omits a lot. If I recall correctly, Peirce was proud of having found Dedekind's definition of infinity before Dedekind.

Having quoted: "Peirce says that if a line is cut into two portions, the point at which the cut takes place actually becomes two points..." you are asking:

"Does this mean that 'the point at which the cut takes place' has two parts? If so, this contradicts the geometric definition."

It looks as if you are aware of the calamity which I ascribe to Dedekind's notion of number as a pebble.

Regards,

Eckard

Eckard,

You said you have trust only in the definition of a point as having no extension. In my opinion, this may be one example of "Your Physics Suffers from Unwarranted Interpretations", the title of your essay.

In my 2013 Essay, I briefly discussed how your definition came about. Let me copy and paste for your convenience the relevant portion, with bold and italics to highlight...

view entire post

You said you have trust only in the definition of a point as having no extension. In my opinion, this may be one example of "Your Physics Suffers from Unwarranted Interpretations", the title of your essay.

In my 2013 Essay, I briefly discussed how your definition came about. Let me copy and paste for your convenience the relevant portion, with bold and italics to highlight...

view entire post

report post as inappropriate

Dear Dr. Blumschein,

You make a number of points in your analysis, with the common theme of questioning whether mathematical models in physics may be improperly interpreted, leading to misleading or incorrect physics.

My own essay addresses a similar issue: "Remove the Blinders: How Mathematics Distorted the Development of Quantum Theory"

I argue that premature adoption of an abstract mathematical framework prevented consideration of a simple, consistent, realistic model of quantum mechanics, avoiding paradoxes of indeterminacy, entanglement, and non-locality. What’s more, this realistic model is directly testable using little more than Stern-Gerlach magnets.

Alan Kadin

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You make a number of points in your analysis, with the common theme of questioning whether mathematical models in physics may be improperly interpreted, leading to misleading or incorrect physics.

My own essay addresses a similar issue: "Remove the Blinders: How Mathematics Distorted the Development of Quantum Theory"

I argue that premature adoption of an abstract mathematical framework prevented consideration of a simple, consistent, realistic model of quantum mechanics, avoiding paradoxes of indeterminacy, entanglement, and non-locality. What’s more, this realistic model is directly testable using little more than Stern-Gerlach magnets.

Alan Kadin

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Dear Dr. Kadin,

I did of course read your again excellent essay. I had already quoted your topic 1993 in my topic 2012 and 1296 in 1364.

Hopefully, someone will perform the test you are suggesting. I just vaguely recall someone else repeatedly suggesting: Someone should look. Nobody did so. That's why I rather trust in other arguments too. Unfortunately, I have no background in quantum theory and can therefore not provide immediate support. Did you already deal with the essays by Klingman, McEachern, and Smolin?

Please don't disdain the "number of points" I made even if they may fundamentally contradict to what every academic has to learn. I would appreciate any serious hint to mistakes if mine.

Eckard

I did of course read your again excellent essay. I had already quoted your topic 1993 in my topic 2012 and 1296 in 1364.

Hopefully, someone will perform the test you are suggesting. I just vaguely recall someone else repeatedly suggesting: Someone should look. Nobody did so. That's why I rather trust in other arguments too. Unfortunately, I have no background in quantum theory and can therefore not provide immediate support. Did you already deal with the essays by Klingman, McEachern, and Smolin?

Please don't disdain the "number of points" I made even if they may fundamentally contradict to what every academic has to learn. I would appreciate any serious hint to mistakes if mine.

Eckard

Dear Sir,

You have hit the Bull’s eye with the naming of your essay. It could not have been described better. The Renaissance mathematicians did not ‘liberate’ mathematics; they led it astray ‘by means of clever restricted constructs’ ‘to maximally generalize models and to interpret results immediately in an artificial mathematical domain as if they were automatically valid in...

view entire post

You have hit the Bull’s eye with the naming of your essay. It could not have been described better. The Renaissance mathematicians did not ‘liberate’ mathematics; they led it astray ‘by means of clever restricted constructs’ ‘to maximally generalize models and to interpret results immediately in an artificial mathematical domain as if they were automatically valid in...

view entire post

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Dear basudeba,

You are blaming not just me wrong but also some experts in history of mathematics. I maintain: Renaissance, enlightenment predominantly in non-Catholic countries of Europe, and both application and upcoming scientific exchange LIBERATED mathematics by ignoring the ancient restriction to the forward countable elements of reality. Let me give a perhaps most simple example:

It is of course possible to describe sound in terms of absolute pressure of air. However, acoustics benefits a lot from what you called "going astray", a mathematical trick. Absolute pressure can be considered as two fictitious components, a constant one and a superimposed one that alternates between positive and negative values.

Thank you for pointing me to the somewhat strange ancient Indian mathematics and to the essay by Schneider. I will read his and yours.

Regards,

Eckard

You are blaming not just me wrong but also some experts in history of mathematics. I maintain: Renaissance, enlightenment predominantly in non-Catholic countries of Europe, and both application and upcoming scientific exchange LIBERATED mathematics by ignoring the ancient restriction to the forward countable elements of reality. Let me give a perhaps most simple example:

It is of course possible to describe sound in terms of absolute pressure of air. However, acoustics benefits a lot from what you called "going astray", a mathematical trick. Absolute pressure can be considered as two fictitious components, a constant one and a superimposed one that alternates between positive and negative values.

Thank you for pointing me to the somewhat strange ancient Indian mathematics and to the essay by Schneider. I will read his and yours.

Regards,

Eckard

Your outcome sourcing fines definite improving notions which attracted conventional sources of measuring.

With best regards,

Miss. Sujatha Jagannathan

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With best regards,

Miss. Sujatha Jagannathan

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Miss. Sujatha Jagannathan,

No matter how hard I am trying to understand your sentence, I have no clue what you meant. I am just a German. My dictionary tells me:

If you are fined, you are punished by being ordered to pay a fine.

A source is something from which something emerges. What is sourcing?

An outcome is the result of a process or an action.

What are definite notions?

Eckard Blumschein

No matter how hard I am trying to understand your sentence, I have no clue what you meant. I am just a German. My dictionary tells me:

If you are fined, you are punished by being ordered to pay a fine.

A source is something from which something emerges. What is sourcing?

An outcome is the result of a process or an action.

What are definite notions?

Eckard Blumschein

Hi Eckard,

Excellent, in-depth analytical essays in the spirit of hard Cartesian doubt. You talk about "unwarranted interpretations". Romanovskaya T.B. in Sovremennaya fizika i sovremennoye iskusstvo – paralleli stilya// Fizika v sisteme kultury [Modern physics and contemporary art – parallels of style // Physics in the culture system]. The author speaks about "crisis of interpretation and representation" in fundamental physics. Morris Cline says that "mathematics loss of certainty". The problem of the foundation of mathematics (better – justification or basification) for over a hundred years ... What are your ideas on a single foundation of "fundamental knowledge"? What interpretations "warranted"? What is "justified" basis of physics?...

**"Truth should be drawn …"** A.Zenkin "SCIENTIFIC COUNTER-REVOLUTION IN MATHEMATICS".

Kind regards,

Vladimir

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Excellent, in-depth analytical essays in the spirit of hard Cartesian doubt. You talk about "unwarranted interpretations". Romanovskaya T.B. in Sovremennaya fizika i sovremennoye iskusstvo – paralleli stilya// Fizika v sisteme kultury [Modern physics and contemporary art – parallels of style // Physics in the culture system]. The author speaks about "crisis of interpretation and representation" in fundamental physics. Morris Cline says that "mathematics loss of certainty". The problem of the foundation of mathematics (better – justification or basification) for over a hundred years ... What are your ideas on a single foundation of "fundamental knowledge"? What interpretations "warranted"? What is "justified" basis of physics?...

Kind regards,

Vladimir

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Hi Vladimir,

Dedekind and Georg Cantor were friends, at least for a while. I suspect a possible reason to Hilbert for popularizing Cantor instead of Dedekind to be found in Hilbert's admiration for stunning ideas. More than infinite, what a wonderful silly idea!

I quoted two authors besides Zenkin who shed light into the matter: Mückenheim and Spalt.

Meanwhile I am sure: The belonging key question relates already to Dedekind's changed notion of number. I see it unwarranted to abandon Euclid's definitions. My arguments arose from obvious inability of a professor of mathematics to explain logical inconsistencies. He pointed me to Weierstrass.

My primary concern was a strict separation between past and future. Read Phipps' essay in order to see from a quite different side that spacetime is indeed not warranted but IR+ is valuable.

When I dealt with IR+, I came the the history of negative and imaginary numbers.

My message is: Interpretations directly in complex plane is not necessarily warranted.

Kind regards,

Eckard

Dedekind and Georg Cantor were friends, at least for a while. I suspect a possible reason to Hilbert for popularizing Cantor instead of Dedekind to be found in Hilbert's admiration for stunning ideas. More than infinite, what a wonderful silly idea!

I quoted two authors besides Zenkin who shed light into the matter: Mückenheim and Spalt.

Meanwhile I am sure: The belonging key question relates already to Dedekind's changed notion of number. I see it unwarranted to abandon Euclid's definitions. My arguments arose from obvious inability of a professor of mathematics to explain logical inconsistencies. He pointed me to Weierstrass.

My primary concern was a strict separation between past and future. Read Phipps' essay in order to see from a quite different side that spacetime is indeed not warranted but IR+ is valuable.

When I dealt with IR+, I came the the history of negative and imaginary numbers.

My message is: Interpretations directly in complex plane is not necessarily warranted.

Kind regards,

Eckard

Thank you very much, Eckard! My highest appraisal and another "eternal question" which I ask all mathematics and physics. John Archibald Wheeler left to physicists and mathematicians a good philosophical precept: "Philosophy is too important to be left to the philosophers".When physicists and mathematicians speak about the structure and the laws of Universum for some reason they forget about lyricists that the majority on Mother Earth. I believe that the scientific picture of the world should be the same rich senses of the "LifeWorld» (E.Husserl), as a picture of the world lyricists , poets and philosophers:

*We do not see the world in detail,*

Everything is insignificant and fractional ...

Sadness takes me from all this.( Alexander Vvedensky,1930)

*It is by a mathematical point only that we are wise, *

as the sailor or the fugitive slave keeps the polestar in his eye;

but that is sufficient guidance for all our life.

We may not arrive at our port within a calculable period,

but we would preserve the true course. (Henry David Thoreau, 1854)

Do you agree with Henry David Thoreau?

Kind regards,

Vladimir

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Everything is insignificant and fractional ...

Sadness takes me from all this.

as the sailor or the fugitive slave keeps the polestar in his eye;

but that is sufficient guidance for all our life.

We may not arrive at our port within a calculable period,

but we would preserve the true course.

Do you agree with Henry David Thoreau?

Kind regards,

Vladimir

report post as inappropriate

Yo put the same question to Tom Phipps. I largely agree with his answer with a few caveats.

Quote: "I do not have any particular religion of my own. That would partly close my mind, which I prefer to keep open. I do, however, have a sort of frankly irrational suspicion -- which is akin to faith -- that when we understand the fundamental ways in which nature works we shall be far more stunned, shocked, amazed than even the lyricists, poets, etc. have it in their power to imagine." Unquote.

Reasoning tells me that irrational analogy between e.g. Nemzov and Jean Jaurès is hopefully unwarranted.

Does nature "work" at all in the same sense as do humans? I would rather postulate causality.

At least I don't feel stunned, shocked or amazed by getting aware that primitive amimals/humans/religions tend to behave irrational as do rabbits, as if unlimited growth was feasible.

When Alfred Nobel did love poetry, this attitude helped him to envision the only rational road to peace.

Because, I did never before hear of Little Jack Horner and Henry David Thoreaut, I prefer more directly understandable arguments in a scientific discussion among unspecialized participants.

Kind regards, Eckard

Quote: "I do not have any particular religion of my own. That would partly close my mind, which I prefer to keep open. I do, however, have a sort of frankly irrational suspicion -- which is akin to faith -- that when we understand the fundamental ways in which nature works we shall be far more stunned, shocked, amazed than even the lyricists, poets, etc. have it in their power to imagine." Unquote.

Reasoning tells me that irrational analogy between e.g. Nemzov and Jean Jaurès is hopefully unwarranted.

Does nature "work" at all in the same sense as do humans? I would rather postulate causality.

At least I don't feel stunned, shocked or amazed by getting aware that primitive amimals/humans/religions tend to behave irrational as do rabbits, as if unlimited growth was feasible.

When Alfred Nobel did love poetry, this attitude helped him to envision the only rational road to peace.

Because, I did never before hear of Little Jack Horner and Henry David Thoreaut, I prefer more directly understandable arguments in a scientific discussion among unspecialized participants.

Kind regards, Eckard

Dear Eckard,

I ask this question, because a modern physical picture of the world very poor in meanings, it semantic incomplete and without ontologic justification. The solution of fundamental problems of physics and mathematics and need of new heuristics demand deep judgment of the philosophical foundations of these two fundamental sign systems. I hope that you will read also my essay to conduct subject discussion on the philosophical bases of physics and mathematics.

Yours faithfully,

Vladimir

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I ask this question, because a modern physical picture of the world very poor in meanings, it semantic incomplete and without ontologic justification. The solution of fundamental problems of physics and mathematics and need of new heuristics demand deep judgment of the philosophical foundations of these two fundamental sign systems. I hope that you will read also my essay to conduct subject discussion on the philosophical bases of physics and mathematics.

Yours faithfully,

Vladimir

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Dear Vladimir,

Your essay guided me to an "Ontology of Mathematical Discourse" by G Gunter in Russian language. Chapter 2 deals with "Interpretation of Existence in Mathematics" and lists concepts by G. Cantor, by Brauer, and by Hilbert. Cantor mentioned the TND. As usual, I cannot accept his ideas, and I prefer reading at best his original papers in German which is difficult enough for me.

I looked in vain for Brauer in the bibliography. Perhaps Richard Brauer (1901-1977) is meant. Can you please confirm this?

Yours faithfully,

Eckard

Your essay guided me to an "Ontology of Mathematical Discourse" by G Gunter in Russian language. Chapter 2 deals with "Interpretation of Existence in Mathematics" and lists concepts by G. Cantor, by Brauer, and by Hilbert. Cantor mentioned the TND. As usual, I cannot accept his ideas, and I prefer reading at best his original papers in German which is difficult enough for me.

I looked in vain for Brauer in the bibliography. Perhaps Richard Brauer (1901-1977) is meant. Can you please confirm this?

Yours faithfully,

Eckard

Dear Eckard,

At the bottom of the article three links Brouwer L.E.J.

65. Brouwer L.E.J. On the foundations of Mathematics // Collected Works. V.1. Philosophy and Foundations of Mathematics. Amsterdam - Oxford - New York, 1975, p.11-101

66. Brouwer L.E.J. Guidelines of Intuitionistic Mathematics // Ibid., P. 477-507

67. Brouwer L.E.J. Historical Background, Principles and Methods of Intuitionism // Ibid., P.508-515

Kind regards,

Vladimir

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At the bottom of the article three links Brouwer L.E.J.

65. Brouwer L.E.J. On the foundations of Mathematics // Collected Works. V.1. Philosophy and Foundations of Mathematics. Amsterdam - Oxford - New York, 1975, p.11-101

66. Brouwer L.E.J. Guidelines of Intuitionistic Mathematics // Ibid., P. 477-507

67. Brouwer L.E.J. Historical Background, Principles and Methods of Intuitionism // Ibid., P.508-515

Kind regards,

Vladimir

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Dear Vladimir,

Thank you for revealing my mistake. When I read "Brauer" I was mislead. Brauer is a frequent German name and means brewer (of beer). Brouwer means the same in Dutch and is indeed pronounced almost like Brauer. If I didn't skip reading the text then I should quickly have realized that Brauer meant Brouwer. While I wondered how Richard Brauer relates to the matter, Brouwer makes more sense.

Kind regards,

Eckard

Thank you for revealing my mistake. When I read "Brauer" I was mislead. Brauer is a frequent German name and means brewer (of beer). Brouwer means the same in Dutch and is indeed pronounced almost like Brauer. If I didn't skip reading the text then I should quickly have realized that Brauer meant Brouwer. While I wondered how Richard Brauer relates to the matter, Brouwer makes more sense.

Kind regards,

Eckard

Dear Mr. Blumschein

I read with interest your essay and like a few remarks such as “Moreover, they use Heaviside’s trick which tempts to unwarrantedly interpret results of complex calculations”. This is right. He, not Maxwell coined the “Maxwell Equations” with a wrong Ampere’s law and a nonexistent “displacement current”

Another good part is “Leibniz and Newton merely agreed on that acceleration is an absolute quality. Let’s show Newton’s mistake with the metaphor of an unlimited to both sides box [14]. Only if there is a preferred point of reference, it is possible to attribute a position to it. In space, such point is usually missing.” However, I think you are helping the relativists defending their ideology. Newton was perfect in insisting on absolute velocities with reference to space. All astronomers are measuring peculiar motions of stars and galaxies. And we know that we are travelling through space with an absolute velocity of 371000 m/s towards the Virgo cluster. With the CMB zero this discussion is finally closed and relativity is dead.

You also warn about the mindless use of singularities in math. But you fail to mention that these singularities created by illegal divide by zero operations in Levy-Civita’s tensor math have finally led to monstrosities like the big bang and black holes. These are purely mathematical constructs and misled physicists and a wide public to believe in such singular objects. They even claim to be able to imagine such singularities in space and time. Here you mathematicians have strong duty to warn urgently. Nature hates singularities; beware of them!

All the best for your future work

Lutz

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I read with interest your essay and like a few remarks such as “Moreover, they use Heaviside’s trick which tempts to unwarrantedly interpret results of complex calculations”. This is right. He, not Maxwell coined the “Maxwell Equations” with a wrong Ampere’s law and a nonexistent “displacement current”

Another good part is “Leibniz and Newton merely agreed on that acceleration is an absolute quality. Let’s show Newton’s mistake with the metaphor of an unlimited to both sides box [14]. Only if there is a preferred point of reference, it is possible to attribute a position to it. In space, such point is usually missing.” However, I think you are helping the relativists defending their ideology. Newton was perfect in insisting on absolute velocities with reference to space. All astronomers are measuring peculiar motions of stars and galaxies. And we know that we are travelling through space with an absolute velocity of 371000 m/s towards the Virgo cluster. With the CMB zero this discussion is finally closed and relativity is dead.

You also warn about the mindless use of singularities in math. But you fail to mention that these singularities created by illegal divide by zero operations in Levy-Civita’s tensor math have finally led to monstrosities like the big bang and black holes. These are purely mathematical constructs and misled physicists and a wide public to believe in such singular objects. They even claim to be able to imagine such singularities in space and time. Here you mathematicians have strong duty to warn urgently. Nature hates singularities; beware of them!

All the best for your future work

Lutz

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Dear Professor Kayser,

While I appreciate confirming comments like yours, I am even more grateful for frankly uttered criticism. Maybe, you mistook me “helping the relativists defending their ideology.” I neither intended to do so nor do I agree with your lecturing: “Newton was perfect in insisting on absolute velocities with reference to space.”

I am distinguishing by...

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While I appreciate confirming comments like yours, I am even more grateful for frankly uttered criticism. Maybe, you mistook me “helping the relativists defending their ideology.” I neither intended to do so nor do I agree with your lecturing: “Newton was perfect in insisting on absolute velocities with reference to space.”

I am distinguishing by...

view entire post

Dear Lutz,

You asked: "Who has invented symmetrical relativity the first time? Was it Poincare?"

In my previous essay "Peace via Discoveries and Inventions", I expressed between the lines that I see both Henry and Raymond Poincaré tragic historic figures. Science and mankind, respectively, payed high prices for their successes.

Henry P. admired Lorentz and did not just coin the term Lorentz transformation. He also introduced the notion relativity and suggested x^2+y^2+z^2+(ict)^2 already in 1904, i.e. before Einstein's Relativity and Minkowski's spacetime.

We agree at least with Phipps on that unwarranted expectation and interpretation of Michelson's 1881/87 experiment implied Heaviside's variant of Maxwell's equations. The same misinterpretation caused FitzGerald and Lorentz to fabricate length contraction.

Looking for origins of the abstruse symmetry between past and future time, I delved into some much earlier made mistakes concerning how mathematics was founded and interpreted. So far I am not in position to at least skim through all essays. I merely got aware of Akinbo Ojo and Giovanni Prisinzano who dealt with related enigma.

Thank you for the request.

Best,

Eckard

You asked: "Who has invented symmetrical relativity the first time? Was it Poincare?"

In my previous essay "Peace via Discoveries and Inventions", I expressed between the lines that I see both Henry and Raymond Poincaré tragic historic figures. Science and mankind, respectively, payed high prices for their successes.

Henry P. admired Lorentz and did not just coin the term Lorentz transformation. He also introduced the notion relativity and suggested x^2+y^2+z^2+(ict)^2 already in 1904, i.e. before Einstein's Relativity and Minkowski's spacetime.

We agree at least with Phipps on that unwarranted expectation and interpretation of Michelson's 1881/87 experiment implied Heaviside's variant of Maxwell's equations. The same misinterpretation caused FitzGerald and Lorentz to fabricate length contraction.

Looking for origins of the abstruse symmetry between past and future time, I delved into some much earlier made mistakes concerning how mathematics was founded and interpreted. So far I am not in position to at least skim through all essays. I merely got aware of Akinbo Ojo and Giovanni Prisinzano who dealt with related enigma.

Thank you for the request.

Best,

Eckard

Dear Eckard,

the more I read from you the better I understand you and your superb knowledge.

Please forgive me. I did not intend to lecture you, Maybe I fell back to my bad professorial habit.

I see from your comments, that you have deeper doubts on the math problems of Relativity than I was able to deduce from your essay. I think in a FQXI contest it is permissible to deviate a bit from the mainstream physics ideology.

Let us take for example the Einstein vector addition, invented by E. in order to "fit" the relative light speed invariance. This even flies in the face of high school algebra. But where are the mathematicians attacking or even discussing it?

This is what I meant with: "We should all be a little braver"

With your Dedekind remark I agree completely.

It is interesting you mention the "Minkovski space-time bubble". It is totally contradictory to the "relative light velocity constancy".

Can I read more from you concerning Relativity?

In case you can spare the time please read my paper

https://www.academia.edu/10256811/Falsification_of_Eins

tein_Theories_of_Relativity

I am thankful for all critical comments

Best

Lutz

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the more I read from you the better I understand you and your superb knowledge.

Please forgive me. I did not intend to lecture you, Maybe I fell back to my bad professorial habit.

I see from your comments, that you have deeper doubts on the math problems of Relativity than I was able to deduce from your essay. I think in a FQXI contest it is permissible to deviate a bit from the mainstream physics ideology.

Let us take for example the Einstein vector addition, invented by E. in order to "fit" the relative light speed invariance. This even flies in the face of high school algebra. But where are the mathematicians attacking or even discussing it?

This is what I meant with: "We should all be a little braver"

With your Dedekind remark I agree completely.

It is interesting you mention the "Minkovski space-time bubble". It is totally contradictory to the "relative light velocity constancy".

Can I read more from you concerning Relativity?

In case you can spare the time please read my paper

https://www.academia.edu/10256811/Falsification_of_Eins

tein_Theories_of_Relativity

I am thankful for all critical comments

Best

Lutz

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Eckard,

I love your historical approach here. Much is gained from seeing how the present has been arrived at regardless of a science or how to sweep the kitchen. I have grievances with patchwork done for the sake of consistency. It just seems dishonest to work out anomalies instead of asking what they are clues to, what new understaning would better take account of them. Sorely, history is recorded in a way of strict progression of this leading to that advance. this way of categorizing also has lots of the story missing. Finally but what i want to say most is that it is not just math and science that are subject to interpretation errors. Anything that a human can see or even imagine is only there interpretation. Good writing.

best of luck,

william amos

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I love your historical approach here. Much is gained from seeing how the present has been arrived at regardless of a science or how to sweep the kitchen. I have grievances with patchwork done for the sake of consistency. It just seems dishonest to work out anomalies instead of asking what they are clues to, what new understaning would better take account of them. Sorely, history is recorded in a way of strict progression of this leading to that advance. this way of categorizing also has lots of the story missing. Finally but what i want to say most is that it is not just math and science that are subject to interpretation errors. Anything that a human can see or even imagine is only there interpretation. Good writing.

best of luck,

william amos

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Hi William Amos,

I noticed that you followed the instructions given by fqxi and the formulation of the topic almost as closely as did Noson Yanofsky with perhaps more success in the contest. I don't agree with those like Yanofsky who consider symmetry a mystic basic principle behind physics. My essays intend to reveal the reasons, not just the historical but also the logical ones, that led to such unwarranted belief.

What about reality vs. interpretation, as an old engineer, I consider the conjecture of reproducibly confirmed and logically consistent reality in contrast to mere imagination a reasonable distinction.

Best of luck in your life,

Eckard

I noticed that you followed the instructions given by fqxi and the formulation of the topic almost as closely as did Noson Yanofsky with perhaps more success in the contest. I don't agree with those like Yanofsky who consider symmetry a mystic basic principle behind physics. My essays intend to reveal the reasons, not just the historical but also the logical ones, that led to such unwarranted belief.

What about reality vs. interpretation, as an old engineer, I consider the conjecture of reproducibly confirmed and logically consistent reality in contrast to mere imagination a reasonable distinction.

Best of luck in your life,

Eckard

My reply to Matt Visser tries to once again explain my suspicion that theoretical physics might use complex calculus not as proper as required.

Dear Matt,

You got me and perhaps may essay repeatedly wrong. I am not David Garfinkle, and I hope you will not go on getting me wrong concerning complex calculus. While complex calculus is an application of complex numbers, theorists like...

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Dear Matt,

You got me and perhaps may essay repeatedly wrong. I am not David Garfinkle, and I hope you will not go on getting me wrong concerning complex calculus. While complex calculus is an application of complex numbers, theorists like...

view entire post

Dear Eckard,

I read your beautiful essay with a lot of pleasure, getting from it several fruiful suggestions and informations. Your knowledge of the historical background of mathematical and physical theories from ancient Greece until today is admirable!

I share your view that the continuum cannot be seen merely as a set of adimensional euclidean points. Euclidean points are indistinguishable from each other and no set of them – no matter if countably or uncountably infinite – is able to afford any physical extension. Therefore these points can hardly have a physical meaning. On the contrary real numbers (wich are not indistinguishable from each other) can effectively produce, from my point of view, the spatial and temporal continuum. Nevertheless the euclidean right line can be still used – as done by Dedekind and others – as a geometrical representation of the set of real numbers, with the caveat that it is not identical with the latter.

Now I would like to ask you a question (which is maybe typical of a philosopher lacking of practality). It seems that you are inclined to think that ideal models generally fail to grasp reality. That is probably true. But we don't have much more than these models at our disposal. How could we explain the world without them?

I heartily whish you all the best,

Giovanni

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I read your beautiful essay with a lot of pleasure, getting from it several fruiful suggestions and informations. Your knowledge of the historical background of mathematical and physical theories from ancient Greece until today is admirable!

I share your view that the continuum cannot be seen merely as a set of adimensional euclidean points. Euclidean points are indistinguishable from each other and no set of them – no matter if countably or uncountably infinite – is able to afford any physical extension. Therefore these points can hardly have a physical meaning. On the contrary real numbers (wich are not indistinguishable from each other) can effectively produce, from my point of view, the spatial and temporal continuum. Nevertheless the euclidean right line can be still used – as done by Dedekind and others – as a geometrical representation of the set of real numbers, with the caveat that it is not identical with the latter.

Now I would like to ask you a question (which is maybe typical of a philosopher lacking of practality). It seems that you are inclined to think that ideal models generally fail to grasp reality. That is probably true. But we don't have much more than these models at our disposal. How could we explain the world without them?

I heartily whish you all the best,

Giovanni

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Dear Giovanni,

Let me first try and answer your question. Mister moon was imagined male, lady Luna female; this more or less ideal model of a pretty old point mass in space is not the only one that was repeatedly changed, corrected, explored, and even exploited.

What about rational vs. real numbers, I largely agree with G. Cantor on that rational numbers are discrete, i.e. numerically distinguishable. Real numbers are not altogether numerically distinguishable. Stiefel spoke of a fog, Weyl of a the sauce of continuum. While I would with pleasure call this continuum of real numbers the mathematical one, set theory occupied and mystified the notion mathematical continuum. Therefore I am calling the continuum of the liquid of measures the Peirce continuum or the logical one, something every part of which has parts.

Are there spacial and temporal continua? The attribution of continuity to space or time is reasonable guesswork. I see a more serious problem in the persistently denied fact that elapsed and future times denote essentially different scales. That's why I see spacetime belonging to speculation and Phipps providing light at the end of the tunnel.

With right line you did perhaps mean straight line?

Thank you very much for your good wishes,

Eckard

Let me first try and answer your question. Mister moon was imagined male, lady Luna female; this more or less ideal model of a pretty old point mass in space is not the only one that was repeatedly changed, corrected, explored, and even exploited.

What about rational vs. real numbers, I largely agree with G. Cantor on that rational numbers are discrete, i.e. numerically distinguishable. Real numbers are not altogether numerically distinguishable. Stiefel spoke of a fog, Weyl of a the sauce of continuum. While I would with pleasure call this continuum of real numbers the mathematical one, set theory occupied and mystified the notion mathematical continuum. Therefore I am calling the continuum of the liquid of measures the Peirce continuum or the logical one, something every part of which has parts.

Are there spacial and temporal continua? The attribution of continuity to space or time is reasonable guesswork. I see a more serious problem in the persistently denied fact that elapsed and future times denote essentially different scales. That's why I see spacetime belonging to speculation and Phipps providing light at the end of the tunnel.

With right line you did perhaps mean straight line?

Thank you very much for your good wishes,

Eckard

Let's benefit from comparisons; this is Robert McEachern's comment on my essay:

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Quote/ Eckard, I think the title of your essay hits the nail on the head. It is indeed the unwarranted interpretations, slapped onto the equations of mathematical physics, that cause all the problems in understanding the nature of reality.

Where we differ, seems to be that you believe...

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Quote/ Eckard, I think the title of your essay hits the nail on the head. It is indeed the unwarranted interpretations, slapped onto the equations of mathematical physics, that cause all the problems in understanding the nature of reality.

Where we differ, seems to be that you believe...

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Dear Dr. Blumschein,

I thought that your engrossing essay was exceptionally well written and I do hope that it fares well in the competition.

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 thought that your engrossing essay was exceptionally well written and I do hope that it fares well in the competition.

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 Joe Fisher,

My essay does neither address gravity nor Hawking. What about spacetime, I prefer attributing it to Poincaré 1904 and Minkowski, and I see its root in a unwarranted guess by Maxwell, Michelson, Lorentz, and others, cf. Phipps. I don't guess that we need dealing e.g. with the GZK paradox in order to question SR.

I agree with you on that reality "is not mathematical". In particular modern mathematics lost connection to common sense.

I am arguing that there is an ignored paradox: Mathematics putatively demands using complex Fourier transformation for frequency analysis, i.e. integration over time from -oo to +oo. Perhaps one must be self-taught like you, just a user of MP3, or a physiologist in order to admit that a real-valued cosine transformation, i.e. integration only over elapsed time, yields the same result except for an unnecessary arbitrarily chosen reference.

I enjoy Leifer's cut between useful and in principle aviodable mathematics.

Eckard Blumschein

My essay does neither address gravity nor Hawking. What about spacetime, I prefer attributing it to Poincaré 1904 and Minkowski, and I see its root in a unwarranted guess by Maxwell, Michelson, Lorentz, and others, cf. Phipps. I don't guess that we need dealing e.g. with the GZK paradox in order to question SR.

I agree with you on that reality "is not mathematical". In particular modern mathematics lost connection to common sense.

I am arguing that there is an ignored paradox: Mathematics putatively demands using complex Fourier transformation for frequency analysis, i.e. integration over time from -oo to +oo. Perhaps one must be self-taught like you, just a user of MP3, or a physiologist in order to admit that a real-valued cosine transformation, i.e. integration only over elapsed time, yields the same result except for an unnecessary arbitrarily chosen reference.

I enjoy Leifer's cut between useful and in principle aviodable mathematics.

Eckard Blumschein

Dear Eckard,

I totally agree with the first sentence of your abstract "Some seemingly mysterious interpretations of mathematics by physicists are just unwarranted" and much of what you are writing afterwards. My longstanding interest is to recognize and possibly expand the right mathematics appropriate to a seemingly paradoxal subject. I did it by using number theory for explaining the non-orthodox statistics one find in the so-called 1/f noise that you may know because you worked in signal processing. I do it now by using group concepts for understanding the deep nature of quantum paradoxes such as EPR.

I like that you put the development of mathematics in an historic perspective on p.2 and afterwards and criticize the false ideas that have appeared and have been corrected by the appropriate maths.

I disagree with "physics must be fully consistent with the premise of only one causally connected real world", where this requirement (that reminds the requirement of the preexistence of a space-time) comes from? For example, quantum theory don't need space-time and is acausal.

Finally, I enjoyed reading you and I hope you take the time to read my essay as well.

Best,

Michel

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I totally agree with the first sentence of your abstract "Some seemingly mysterious interpretations of mathematics by physicists are just unwarranted" and much of what you are writing afterwards. My longstanding interest is to recognize and possibly expand the right mathematics appropriate to a seemingly paradoxal subject. I did it by using number theory for explaining the non-orthodox statistics one find in the so-called 1/f noise that you may know because you worked in signal processing. I do it now by using group concepts for understanding the deep nature of quantum paradoxes such as EPR.

I like that you put the development of mathematics in an historic perspective on p.2 and afterwards and criticize the false ideas that have appeared and have been corrected by the appropriate maths.

I disagree with "physics must be fully consistent with the premise of only one causally connected real world", where this requirement (that reminds the requirement of the preexistence of a space-time) comes from? For example, quantum theory don't need space-time and is acausal.

Finally, I enjoyed reading you and I hope you take the time to read my essay as well.

Best,

Michel

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Dear Michel,

Thank you in particular for pointing me to pink noise and disagreeing with ubiquitous causality.

I am distinguishing between ubiquitous causality and its only logical alternative of resorting in something supra-natural. This implies to also distinguish between conjectured causality and a naive determinism as exemplified in La Mettrie's "L'Homme machine". Well, there is perhaps no reason why nature shouldn't play dice, but this doesn't contradict to ubiquitous causality.

Having often used non-causal signal processing myself, I feel aware of this as pragmatic sinning against consequent logical correctness.

What about the corner frequency between pink and white noise, I did never deal with this question. So a suspicion of mine might be wrong: I just got aware that the white (higher frequency) part looks irregular as to be expected while the pink (LF) part looks smooth. Maybe, the latter is an artifact of windowing?

Having tried twice to understand your glittering essay, I felt being perhaps too old and also to less familiar with the details as to always get what you meant. When someone else used the expression "lighthearted" I asked him why he hided himself behind humor, and he frankly explained it to me. Why did you invoke moonshine?

Indeed, Schrödinger managed to explained the Hydrogen spectrum without Relativity, and non-Relativistic quantum theory is accepted as serious.

Accordingly I am capitalizing Relativity.

Best,

Eckard

Thank you in particular for pointing me to pink noise and disagreeing with ubiquitous causality.

I am distinguishing between ubiquitous causality and its only logical alternative of resorting in something supra-natural. This implies to also distinguish between conjectured causality and a naive determinism as exemplified in La Mettrie's "L'Homme machine". Well, there is perhaps no reason why nature shouldn't play dice, but this doesn't contradict to ubiquitous causality.

Having often used non-causal signal processing myself, I feel aware of this as pragmatic sinning against consequent logical correctness.

What about the corner frequency between pink and white noise, I did never deal with this question. So a suspicion of mine might be wrong: I just got aware that the white (higher frequency) part looks irregular as to be expected while the pink (LF) part looks smooth. Maybe, the latter is an artifact of windowing?

Having tried twice to understand your glittering essay, I felt being perhaps too old and also to less familiar with the details as to always get what you meant. When someone else used the expression "lighthearted" I asked him why he hided himself behind humor, and he frankly explained it to me. Why did you invoke moonshine?

Indeed, Schrödinger managed to explained the Hydrogen spectrum without Relativity, and non-Relativistic quantum theory is accepted as serious.

Accordingly I am capitalizing Relativity.

Best,

Eckard

Dear Eckard,

Thank you for answering my questions about your view about causality. These are deep thoughts.

Why I arrived to the moonshine topic? I introduced Grothendieck's dessins d'enfants in the field of QM paradoxes at the 2013 contest and since that time I did significant progress that starts to be recognized. In a nutshell, dessins arise from a two-letter (a and b) free group F [there is just the relation that an element u times its inverse u^-1 is the identity element (p. 6 top)]. The group F and its subgroups is a kind of factory for particular permutation groups P.

I found that not only these P's have a topological and algebraic character (over the rationals) as advocated by Grothendieck in his "Esquisse d'un programme" [11] but also stabilize finite geometries that are precisely those involved in QM. The biggest finite group, the Monster group M and most of the sporadic groups can be built from F. Many of them have the extra relation b^2=a^3=1 and are thus also subgroups of the modular group that leads to the moonshine phenomenon by T. Gannon [25]. This is the very reason why I look at the connection between dessins and moonshine. But even without the modular group relations my equations for B and W in Sec. 3 makes sense.

I was fortunate that while writing the essay I found a connection between the moonshine group Gamma_O^(2) of the Baby Monster group and the physics of Bell's theorem. To summarize, I expect that the structure of M has much to say about quantum physics as it is already known that it has much to do with string theory.

I hope you can now grasp my motivation. I regret that my dialogue is not so much for 'pedestrians' but closer to a real dialogue between a mathematician and a theoretical physicist.

I will write another post for the 1/f noise (or pink noise) topic.

Best,

Michel

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Thank you for answering my questions about your view about causality. These are deep thoughts.

Why I arrived to the moonshine topic? I introduced Grothendieck's dessins d'enfants in the field of QM paradoxes at the 2013 contest and since that time I did significant progress that starts to be recognized. In a nutshell, dessins arise from a two-letter (a and b) free group F [there is just the relation that an element u times its inverse u^-1 is the identity element (p. 6 top)]. The group F and its subgroups is a kind of factory for particular permutation groups P.

I found that not only these P's have a topological and algebraic character (over the rationals) as advocated by Grothendieck in his "Esquisse d'un programme" [11] but also stabilize finite geometries that are precisely those involved in QM. The biggest finite group, the Monster group M and most of the sporadic groups can be built from F. Many of them have the extra relation b^2=a^3=1 and are thus also subgroups of the modular group that leads to the moonshine phenomenon by T. Gannon [25]. This is the very reason why I look at the connection between dessins and moonshine. But even without the modular group relations my equations for B and W in Sec. 3 makes sense.

I was fortunate that while writing the essay I found a connection between the moonshine group Gamma_O^(2) of the Baby Monster group and the physics of Bell's theorem. To summarize, I expect that the structure of M has much to say about quantum physics as it is already known that it has much to do with string theory.

I hope you can now grasp my motivation. I regret that my dialogue is not so much for 'pedestrians' but closer to a real dialogue between a mathematician and a theoretical physicist.

I will write another post for the 1/f noise (or pink noise) topic.

Best,

Michel

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Dear Michel,

Grothendieck's "Esquisse d'un programme" relates to point-set topology, something that my essay puts in question because General topology cannot even perform a symmetrical cut. I am arguing that the distinction between open and closed intervals of real numbers is only justified in the paradise by Cantor and Dedekind. Maybe, Grothendieck disappeared when he got aware of related inconsistencies.

Already Cantor got insane. While I see other possible victims too, I as a pedestrian didn't get aware of tangible practical results of point-set theory so far.

Best,

Eckard

Best,

Eckard

Grothendieck's "Esquisse d'un programme" relates to point-set topology, something that my essay puts in question because General topology cannot even perform a symmetrical cut. I am arguing that the distinction between open and closed intervals of real numbers is only justified in the paradise by Cantor and Dedekind. Maybe, Grothendieck disappeared when he got aware of related inconsistencies.

Already Cantor got insane. While I see other possible victims too, I as a pedestrian didn't get aware of tangible practical results of point-set theory so far.

Best,

Eckard

Best,

Eckard

Dear Eckard,

The topology in question is not that of a point-set (it may have its merit) but that of a Riemann surface (in my table g is the number of holes, g=1: torus...) and there are three punctures denoted 0 (black points), 1 (white points) and infinity (the center of faces). The points belong to a graph (dessin d'enfant) drawn on the Riemann surface. The parenty is Riemann and Klein, not at all Cantor.

Point-set topology may has inconsistencies, I don't know.

Michel

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The topology in question is not that of a point-set (it may have its merit) but that of a Riemann surface (in my table g is the number of holes, g=1: torus...) and there are three punctures denoted 0 (black points), 1 (white points) and infinity (the center of faces). The points belong to a graph (dessin d'enfant) drawn on the Riemann surface. The parenty is Riemann and Klein, not at all Cantor.

Point-set topology may has inconsistencies, I don't know.

Michel

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Dear Michel Planat, dear Tim Maudlin,

I hope to manage making my essay a bit more understandable to experts:

What happened to mathematics? Part 1

Georg Cantor’s naïve transfinite cardinalities have not by chance proved useless despite of evidence that was more or less accepted in 1873 and 1890.

Let’s understand the ideal continuum as a directed measure every part...

view entire post

I hope to manage making my essay a bit more understandable to experts:

What happened to mathematics? Part 1

Georg Cantor’s naïve transfinite cardinalities have not by chance proved useless despite of evidence that was more or less accepted in 1873 and 1890.

Let’s understand the ideal continuum as a directed measure every part...

view entire post

Dear Eckard,

You are perfectly right, from my knowledge of the noise in highly stable oscillators, there is a white noise as predicted by standard thermal physics. The 1/f noise cross the floor at some corner in log/log scales. As I have written above, I arrived at the conclusion that the "smooth" low frequency part is an artefact of the fast Fourier transfom. If one uses another (number theoretical based) signal processing as Ramanujan sum signal processing the 1/f noise acquires structure as explained in this paper "Ramanujan sums analysis of long-period sequences and 1/f noise", EPL, 85 (2009) 40005 (also 0812.2170 [math-ph] ).

Best,

Michel

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You are perfectly right, from my knowledge of the noise in highly stable oscillators, there is a white noise as predicted by standard thermal physics. The 1/f noise cross the floor at some corner in log/log scales. As I have written above, I arrived at the conclusion that the "smooth" low frequency part is an artefact of the fast Fourier transfom. If one uses another (number theoretical based) signal processing as Ramanujan sum signal processing the 1/f noise acquires structure as explained in this paper "Ramanujan sums analysis of long-period sequences and 1/f noise", EPL, 85 (2009) 40005 (also 0812.2170 [math-ph] ).

Best,

Michel

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Eckard,

Having a somewhat primitive grasp of math, I am challenged, but catch pearls here and there. I like your beginning with basic clarifications. I do agree that physics is not identical with math, and I am impressed with your grasp of math's evolution through history. Just to look at weather predictions using math models indicates the folly of generalizing models. Even California weather has complexities and multiple variables (not single points) models can't seem to handle.

Speculative theories are perhaps akin to economic theories with an agenda.

My connections: http://fqxi.org/community/forum/topic/2345 accepts a partnership of math, physics and the mind in bringing about stellar achievements in quantum biology, DNA mapping and BB simulation.

Jim

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Having a somewhat primitive grasp of math, I am challenged, but catch pearls here and there. I like your beginning with basic clarifications. I do agree that physics is not identical with math, and I am impressed with your grasp of math's evolution through history. Just to look at weather predictions using math models indicates the folly of generalizing models. Even California weather has complexities and multiple variables (not single points) models can't seem to handle.

Speculative theories are perhaps akin to economic theories with an agenda.

My connections: http://fqxi.org/community/forum/topic/2345 accepts a partnership of math, physics and the mind in bringing about stellar achievements in quantum biology, DNA mapping and BB simulation.

Jim

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Dear Eckard Blumschein,

While not flashy, I feel that your essays and your approach, aimed basically at keeping math honest and maximally relevant to reality, have great worth.

Edwin Eugene Klingman

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While not flashy, I feel that your essays and your approach, aimed basically at keeping math honest and maximally relevant to reality, have great worth.

Edwin Eugene Klingman

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Dear Edwin Eugene Klingman,

Thank you for your warm words. I added some corrections to part one of "What happened to mathematics? Part 1" and will add Part 2 soon.

Eckard

Thank you for your warm words. I added some corrections to part one of "What happened to mathematics? Part 1" and will add Part 2 soon.

Eckard

Part 2

At the time of Cauchy and Gauss in the middle of 19th century, the plurality of those who were teaching mathematics grew rapidly. Why did Abel see mathematics in a mess? Abel meant its lacking rigorous foundation. While the irrational numbers were well known to be different from the rational ones, it was common practice to ignore this trifle. When Riemann suggested his surfaces...

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At the time of Cauchy and Gauss in the middle of 19th century, the plurality of those who were teaching mathematics grew rapidly. Why did Abel see mathematics in a mess? Abel meant its lacking rigorous foundation. While the irrational numbers were well known to be different from the rational ones, it was common practice to ignore this trifle. When Riemann suggested his surfaces...

view entire post

Part 3

A mathematics that is relevant for physics should be free of arbitrariness. When I first came across to the criticism that modern mathematics was made rigorous by means of an iron bar, I felt inspired to ask what this meant. Among many other other examples, the definition sign(0)=0 proved unwarranted and in practice misleading.

It is commonly accepted that the division by zero is not defined and therefore forbidden. Natural mathematics does not define and forbid. At least I am not aware of any reason to forbid the conclusion that division by zero results in an infinite result. There is merely no logical justification for subsequently calculating with the property oo as if it was a number. This follows from basic and obvious to everybody axiom by Archimedes: To every number n there is a larger one n+1.

G. Cantor's largest finite number oo does not by chance look like omega. His "überabzählbare" (more than countable) numbers contradict to this axiom. That's why his set theory was obviously naive. As Fraenkel admitted, axiomatic set theories replaced this flawed belief by postulating in the last axiom of ZFC the property of endlessness to a set: "There is an endless set". Already the first axiom of ZFC used the notion set in algebraic, i.e., finite sense. The maneuver managed to hide the logical split.

Eckard

A mathematics that is relevant for physics should be free of arbitrariness. When I first came across to the criticism that modern mathematics was made rigorous by means of an iron bar, I felt inspired to ask what this meant. Among many other other examples, the definition sign(0)=0 proved unwarranted and in practice misleading.

It is commonly accepted that the division by zero is not defined and therefore forbidden. Natural mathematics does not define and forbid. At least I am not aware of any reason to forbid the conclusion that division by zero results in an infinite result. There is merely no logical justification for subsequently calculating with the property oo as if it was a number. This follows from basic and obvious to everybody axiom by Archimedes: To every number n there is a larger one n+1.

G. Cantor's largest finite number oo does not by chance look like omega. His "überabzählbare" (more than countable) numbers contradict to this axiom. That's why his set theory was obviously naive. As Fraenkel admitted, axiomatic set theories replaced this flawed belief by postulating in the last axiom of ZFC the property of endlessness to a set: "There is an endless set". Already the first axiom of ZFC used the notion set in algebraic, i.e., finite sense. The maneuver managed to hide the logical split.

Eckard

Eckard,

Shark time as they pull you down, so I am revisiting essays I’ve read to assure I’ve rated them. I find that I rated yours on 4/17, rating it as one I could immediately relate to. I hope you get a chance to look at mine: http://fqxi.org/community/forum/topic/2345

Jim

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Shark time as they pull you down, so I am revisiting essays I’ve read to assure I’ve rated them. I find that I rated yours on 4/17, rating it as one I could immediately relate to. I hope you get a chance to look at mine: http://fqxi.org/community/forum/topic/2345

Jim

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Aldo Filomeno replied on Apr. 30, 2015 @ 18:28 GMT

... Your essay looks interesting and original... I'm curious to see how you argue that (A), i.e. that the world displays spatiotemporal patterns, is hardly indisputable. How could it be disputed? I took it as a premise of my argument ... (By the way I don't understand your last observation!)

In parentheses he referred to my claim:...

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... Your essay looks interesting and original... I'm curious to see how you argue that (A), i.e. that the world displays spatiotemporal patterns, is hardly indisputable. How could it be disputed? I took it as a premise of my argument ... (By the way I don't understand your last observation!)

In parentheses he referred to my claim:...

view entire post

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