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Abhishek Majhi

Dear Vladimir

聽 聽 聽 Since you wanted me to make some critical comments on you essay, I am here to write. I did not write this earlier because, as I had already mentioned, I am not a professional philosopher. For the same reason, when I tried to go through your essay, I found many remarks based on several references which I could not follow. Therefore, I could not find an actual application of what your ideas are. I apologize for my incompetence. However, I do strongly agree with you that dialectics (I call contradictions) are necessary to be thought about because, according to me, we use those everyday without understanding -- I would rather say that contradiction is what prevails, decisions are the limits. I hope you may have already got my view while you read my essay. Nonetheless, I shall take this opportunity to express my views regarding the article by C. Rovelli that you referred to. Being from a physics background, I would focus on the following two quotes: ``Philosophy is dead'' -- Hawking, ``Philosophy is useless'' -- Weinberg. I do not agree with Carlo's judgments, where he called these two people ``anti-philosophers'' to push forward his arguments for necessity of philosophy and physics for each other. Hawking and Weinberg opposed philosophy for different reasons and which were based on their personal expectations. Let me take Hawking first and Weinberg second.

聽 聽 聽 Hawking's quote was followed by the sentence: ``Philosophy has not kept up with modern developments in science, particularly physics.'' I absolutely agree with this comment because I have not seen any contribution from a philosopher to solve some longstanding problem in physics. I do not think modern philosophy deals with the questions regarding the foundations physics like what Berkeley did by questioning the foundations of calculus in `The Analyst' or Mach did by questioning the concept of ``mass'' in `Science of Mechanics' or Poincare did by pointing out that mathematical science might be an insoluble contradiction in `Science and Hypothesis'. Even after that, what is necessary is an end product and practical application. This is the single most reason why Newton and Einstein are more famous than the above phenomenal thinkers. Therefore, the question is about the practicality of philosophy. This is what Hawking could not find from modern philosophy. However, that does not mean that I agree with all of Hawking's views later in that book referred to by Rovelli.

聽 聽 聽 聽Weinberg's case is different. He has a personal dream of a unified theory and he considers philosophy to be useless because he questions ``Can philosophy give us any guidance toward a final theory?''聽 I do not know what is a final theory and I do not care about somebody's personal dream. Therefore, I consider such anti-philosophical聽 attitude to be meaningless.聽 It appears to me that he can not find his philosophical thoughts leading him to some final theory which he seeks and then puts that burden on philosophers. That is unacceptable for me.聽 聽 聽 聽 Therefore, as far as Rovelli's article is concerned, I did not find it of much use other than a good popular article because I could not find a discussion about in what way we can actually apply philosophy to do physics and apply scientific theories to answer philosophical queries.聽 To do that one needs to think of physics and mathematics in a collective fashion as ``mathematical science'' and that needs to be founded on measurements or relation between observed and the observers.聽 If I suggest somebody to read about philosophical writings about physics and why both need to go hand in hand, I would suggest reading Berkeley, Poincare, Mach, etc.聽聽 聽 聽 聽

Further, I聽find it strange Rovelli only writes about Western half of the world when it comes to philosophy, while the two fathers of quantum mechanics, namely, Schroedinger and Heisenberg found their thoughts akin to the philosophy embedded in a聽culture on the other half of the world. Such strangeness only increases when I learn that the father of relativity, Einstein, said to Tagore, a poet from a country on that other half of the world, that聽 ``Then I am more religious than you are!'' while discussing about science, truth, reality, etc.聽

聽 聽 聽I wish you luck with your essay.

Regards

Abhishek

Dear Flavio

I came here to comment by seeing the popularity of your essay and by reading the abstract I understood your view point at least (I guess). Then, going through the successive posts I encountered your comment: ``the whole point of my view is that there is ALWAYS an element of genuine randomness. If you accept my alternative interpretation, even the length of a metal rod would not be fully determined.'' I appreciate your attitude and your thought is in the right direction (in my personal opinion). I wrote this obviously because it somewhat matches with mine. However, I may humbly opine that you have assumed a lot and then expressed your view.

I believe you could have got to the crux of the problem by asking much more elementary questions related to you probably learnt in your school. It is about units, measurements and calculus. Have you ever wondered, when your write, following Cauchy, ``infinitely small quantity'' in the definition of derivative, if this phrase makes sense at all or it only makes sense when you write ``infinitely small quantity with respect to another quantity''. Think about it.

Consider your metal rod. Can you tell me whether it is ``long or short''? Yes, my question is meaningless and you can not answer because you need to know ``with respect to what''. So, comparison of two lengths (or similar physical quantities) only provide a number and with this number you do mathematics and draw inference. However, as you say, there is ALWAYS a randomness, or as I say ``inexactness'' in measurement. Einstein himself ignored this fact by writing that this problem can be overcome by choosing sub divided rods (smaller units). If you don't believe me, I can give you the reference.

In spite of such practical inexactness, equations in physics are written as if they are exact. Starting from Newton to Cauchy and other great men of science, including Einstein, have treated science as exact, at least in writing (may be not in the attitude). Otherwise, science could have been very different, without having any singularity problems or the difficulties regarding the classical-quantum distinction.

Anyways, I do not want to bore you more with my childish comments, because I have already written a childish essay posted here. I would rather conclude by wishing you luck for winning this essay contest (which I think you are the most probable one).

Regards

Abhishek Majhi

Dear Gopal

Thank you very much for making this comment. I fully agree with you, except that I want to replace ``always might not get back'' with ``never get back without making a fatal contradiction''.

Thanks for the wishes.

Regards

Abhishek

Abhishek Majhi re-uploaded the file Majhi_FQXIESS.pdf for the essay entitled "Contradictions, mathematical science and incompleteness" on 2020-04-24 05:20:08 UTC.

Dear Vladimir,

聽 聽 聽 聽Thank you very much for reading my essay and providing some valuable feedback. I am glad that you found the essay ``very interesting'' and ``deep''. However, the essence goes beyond ``Cartesian doubt''. A bit of reading Descartes gave me the impression that he used to consider `extensions' as the essence of existence. Although, I agree to some extent with Descartes, however, I do not know whether he considered ``relational existence'' and actually found a way to do mathematical science based on such philosophy (my view is akin to certain aspects of Indian philosophy, see end note).聽 Furthermore, unlike Descartes, I have not only raised ``doubts'', but I have actually shown how to clear those doubts in terms of mathematical expressions leading to fruitful results i.e. philosophy having a practical impact. I have never read the books of the people you have mentioned,聽but thanks for mentioning them anyways. However, the words聽 ``coincidence of the opposites'' looks very much like what I have called ``middle-way'' (borrowed from Nagarjuna, see end note). 聽 As far as the word ``truth'' is concerned, for me its ``relational'' and not ``absolute'' (Sunyata, see end note). As far as pure mathematical thoughts like numbers and geometry are concerned, I consider them to be ideal realizations of the mind which can only be used in practice with approximations.聽 Considering all these views, I may point out that this essay is a practical essay which does not stop at some philosophical discussion but shows how to apply philosophical thoughts through mathematics to solve, or at least lay the ground to solve, one of the hardest problems in physics called asymptotic safety, which I strongly believe is related to the problem of confinement. It is unfortunate for me that the simple (high school level) mathematics that I have shown towards the end of the essay, does not appear to the reader appreciable.聽聽As far as your ideas are concerned, I shall try to have a look at it if I can understand with my poor knowledge of mainstream philosophy.

Regards

Abhishek

The current status of physics stands on the firm belief of an ultimate reality and a theory of everything. This stems from the thought that there is a notion of reality independent of human thoughts and scientific queries. However, basic knowledge of mathematical science regarding units and measurements is suggestive of relational existence and therefore, no ultimate reality i.e. the perception of reality is based on how we perceive or choose to perceive. This leads to singularity resolution in gravity, results in a well behaved ``small distance'' theory of gravity. The two body interaction given by an infinite series expansion in G-inverse i.e. gravity is asymptotically safe. The mathematics is so easy that it can be taught to an undergraduate student. I have explained it in detail in an essay named ``Contradictions, mathematical science and incompleteness'' posted in the essay competition on 7th April, 2020. I have attached a copy of that essay here also. Any feedback from anybody is appreciated. However, since it is an essay, it contains a bit of dramatic writing that should be taken by the reader personally.Attachment #1: FQXIESS_arxiv.pdf

Dear Heinz,

I am glad that you have enjoyed my essay. However, I am not capable of understanding in what way you superposed my parents' views. Rather, it seems that it is my misfortune or incapability that I have not been able to convey my message through my writing. I think so because of the following reasons.

While you write F=ma, that involves a definition of acceleration in terms of standard derivative. I shall be glad to know if you have enjoyed reading my critiques of calculus. Because, I have discussed in what way standard calculus, as applied in physics (where units are involved), is based on incomplete statements. The word ``vector'' that you have used is explained on the basis of such incomplete statements. The word ``black hole'' that you have used is also explained with a theory (differential geometry) that is based on such calculus.

By the way, if you have enjoyed reading the later section on non-singular gravity, then you should have seen that the so called singularity problem has been resolved by showing that gravity is asymptotically safe. The math is simple -- just series expansions. The picture that was snapped last year, was that of the asymptotic safe region where motion could not be realized giving the appearance of black.

Thanks a lot for reading my essay.

Regards

Abhishek

Thank you Daniel for reading my essay in the first place and for the compliments. However, I would like to clarify that a vital message of this essay is the inexactness of practical expressions of the ideal thoughts of pure mathematics. Please note that ``number line'' is the geometric representation of the thought of real numbers. While the thought is ideal and arbitrarily accurate, the expression is not. When you draw a line with your pencil, your expression is only accurate up to the extension of your pencil tip. But, only with that inaccuracy of the object of expression that you can express. Same is the case for measurement or comparison e.g. if you do not see the cross-wire of the eye piece you can not make measurements in a physics lab, although the thickness of the cross-wire, that lets you see, itself serves as the basic irremovable error -- the immeasurable lets you measure. If you do not accept this limitation of the accuracy in the expression (or measurement), you can not express (or measure). The same is the case for language as well -- you and me can communicate only up to the limitation of our knowledge in English -- if you use a word that I do not understand, then communication fails. And, without expression you can not use your thought in for practical purpose e.g. if I have not written this essay to express my thoughts, you would not be reading this. This, interestingly leads to the other crucial issue i.e. relational existence. This essay does not exist if you do not read it, it does not have a value unless you find a value in it. Even if you find value in it, it is subject to the way you interpret it or relate to my expressions of thought, where the premises are English language, mathematics and symbols.

So, I may write that, if I have favored some viewpoint in this essay, it is practical reasoning that incorporates inaccuracy of expressions and inexact measurement. This is why I have talked about `practical' numbers. Have you thought what or how you count when you say `I have five fingers'. I see immense confusion in this statement if I want give formal reasoning and try to do exact mathematics, because each one of my fingers are different from each other (e.g. by virtue lengths, breadths, fingerprints, wrinkles on the skin, etc.). It seems to me that I am adding like

[math] $1_a+1_b+1_c+1_d+1_e.$ [/math]

But I do not know how to make sense of this. For me, in practice, I use the fact that the fingers are both identical and different (contradiction!) according to need. I perceive of the fingers as different, but express their counting as being identical so as to do arithmetic (sum) by disregarding information on purpose e.g. something like

[math]$1+\delta_a+1+\delta_b+1+\delta_c+1+\delta_d+1+\delta_e=5+\delta~\ni \delta=\sum_{i=a}^e\delta_i$[/math]

where $delta$ is simply ignored for practical purpose. Looking into those different $delta$-s serves a different practical purpose i.e. if one chooses or decides to ask what does a finger look like and starts investigating what is the meaning of a finger.

In a nutshell, the aim of this essay is to convey the role of contradictions in practice and in mathematical science (e.g. how the issue of seeing a point leads to some interesting consequences from standard geometric calculus that is plagued with incomplete statements made by Cauchy).

Essay Abstract

Do you believe that science is based on contradictions? Let me consider the common experience of seeing a dot of the pencil on a paper. If I call the dot ``zero length dimension'' or ``zero extension'', then certainly I have seen `nothing'. But, if I have seen `nothing', I wonder how I can refer to `nothing', let alone naming `nothing' as ``a point''. Therefore, the expression ``zero length dimension'' is a contradiction. Mathematical science, as of now, is based on this contradiction that results from the attitude of exactness, because exact ``zero'' is non-referable and inexpressible. Such attitude leads to incomplete statements like ``infinitesimal quantities'' which never mention ``with respect to'' what. Consequently, as I find, science becomes fraught with singularity and the definition of `field' seems either circular or incomplete in reasoning. I avoid this contradiction, by accepting my inability to do exact science. Therefore, I consider the dot as of ``negligible length dimension''. It is a practical statement rather than a sacrosanct axiom. The practicality serves the purpose of drawing geometry, that becomes impossible if I decide or choose to look at the dot through a magnifying glass. It then answers a different practical question, namely, what the dot is made up of. Certainly, reality of the dot depends on how I choose or decide to observe it. This is the essence of ``relational existence''. On the contrary, modern mathematical science is founded upon belief of ``independent existence''(invariant). My belief in inexact mathematical science and relational existence needs the introduction of an undecidable length unit to do arithmetic and leads to non-singular gravity. Further, the quest for justification of my choice or decision leads to my incompleteness -- ``I''-- the undecidable premise beyond science, the expression of which is a (useful) contradiction in itself as ``I'' is inexpressible.

Author Bio

I got a degree called ``Doctor of Philosophy'' in Science without understanding Philosophy of Science and used to chase a theory of ``everything'' without understanding the subtlety of a ``thing'' and the underlying contradictions of exact mathematical science. Now, I try to understand the value of philosophy and reasoning in the foundations of mathematical science. I am on my own and love to be on my own.

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