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RECENT POSTS IN THIS TOPIC

Vladimir Rogozhin: on 5/4/20 at 17:19pm UTC, wrote Thanks a lot, Abhishek! I appreciate your detailed explanatory answer. I...

Abhishek Majhi: on 4/24/20 at 10:36am UTC, wrote Dear Gopal Thank you very much for making this comment. I fully agree...

Abhishek Majhi: on 4/24/20 at 5:20am UTC, wrote Abhishek Majhi re-uploaded the file Majhi_FQXIESS.pdf for the essay...

Gopal Sardar: on 4/20/20 at 18:00pm UTC, wrote Dear Dr. Majhi, Thank you very much for the writing an essay on very...

Abhishek Majhi: on 4/15/20 at 2:38am UTC, wrote Dear Vladimir,        Thank you very much for reading my essay and...

Vladimir Rogozhin: on 4/14/20 at 18:35pm UTC, wrote Dear Abhishek, A very interesting and deep essay in the spirit of the...

Abhishek Majhi: on 4/8/20 at 2:31am UTC, wrote Dear Heinz, I am glad that you have enjoyed my essay. However, I am...

Abhishek Majhi: on 4/8/20 at 1:50am UTC, wrote Thank you Daniel for reading my essay in the first place and for the...


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FQXi FORUM
September 17, 2021

CATEGORY: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) [back]
TOPIC: Contradictions, mathematical science and incompleteness by Abhishek Majhi [refresh]
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Author Abhishek Majhi wrote on Apr. 7, 2020 @ 14:53 GMT
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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Note: This Essay PDF was replaced on 2020-04-24 05:20:08 UTC.

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Daniel Thomas Hawkley wrote on Apr. 7, 2020 @ 18:38 GMT
This is an excellent essay, especially in terms of using a minimal number of generic antonyms like "never" (see below). Similar to neurosurgeon Christof Koch's writing style before his book "The Feeling of Life Itself", Abhishek's lengthy appeal sto biography are somewhat thermo-dramatic but "on point" here:

"However, now I find no shame in confessing that I have never really understood the definition of derivative in standard calculus [2], although I applied such tools, quite comfortably, in physics so as to build a career in a discipline of science, based on such acceptance and belief. "

When the essay dials in on "points" and "pointing out" it seems to favor classical number lines (for the sake of complexity?); I believe this could be edited by appealing to predictions and observations (like doctors without borders): "for the sake of non-fiction":

"I may emphasize that I am considering only positive numbers here for the sake of simplicity"

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Author Abhishek Majhi replied on Apr. 8, 2020 @ 01:50 GMT
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...

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H.H.J. Luediger wrote on Apr. 7, 2020 @ 19:45 GMT
Dear Abhishek Majhi,

enjoyed reading your essay! I would, however, opt for a superposition of your father's and mother's advices as follows.

Take, for example, Newton's

F=ma

On the left hand side we have a force, already known to club-swinging Neanderthal man, i.e. a phenomenon. At the same time F is a vector having magnitude and direction. On the right hand side we have two virtual or ideal quantities, mass and acelleration, not represented in natural language and thus acting as 'enablers' or 'jokers' warranting that the mathematical result of the equation does't CONTRADICT the associated phenomenon, with which it obviously cannot be identical. My point is this: math is very precise - provided it has been arrived at in the presence of phenomena. Whether F=ma holds near black holes or at the Planck scale - how could we know? The return path from math to the phenomena is blocked by the NOT-FALSE relation between math and the phenomena. Blindly following theory (here:earth sphericity) made already Colombo falsely believe he had arrived in India...

In sharp contrast to Newton (randomly picked example):

|ΨS⟩ = c[{sj}]|{sj}⟩

Does it speak of the efficiency of angels' wings in vacuum?

good luck for essay,

Heinz

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Author Abhishek Majhi replied on Apr. 8, 2020 @ 02:31 GMT
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

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Vladimir Rogozhin wrote on Apr. 14, 2020 @ 18:35 GMT
Dear Abhishek,

A very interesting and deep essay in the spirit of the Cartesian doubt. It pushes thinking toward the centenary problem No. 1 for fundamental science and cognition as a whole - the justifcation (substantification, “foundations”) of mathematics, which can more accurately be defined as the problem of the ontological basification of mathematics (knowledge). Overcoming the crisis of understanding in the philosophical basis of fundamental science (mathematics, physics, cosmology) is possible only on the basis of breakthrough ontological and dialectical ideas, first of all developing the ideas of Kuzansky - "coincidence of opposites", as well as ideas of the process metaphysics of Whitehead. One of the main reasons for “trouble with physics” (Lee Smolin “Trouble with Physics)”, “loss of certainty” in mathematics (Morris Kline “Mathematics: Loss of Certainty”) is the unsolved problem of the “foundations of mathematics” (justification + substantification = basification). As the doctor of physical and mathematical sciences, Alexander Zenkin, noted in SCIENTIFIC COUNTER-REVOLUTION IN MATHEMATICS: “the truth should be drawn ...”. And I completely agree with him.

Leopold Kronecker: "God made the integers, all else is the work of man" / Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk». ...If it is good to observe Nature, for example, how the vineyard sprouts from grape seed, then a slightly different conclusion can be made: God created the Universum only from the Absolute Forms of matter. Numbers are the work of man... Please also see my ideas on the problem of the philosophical basis of knowledge (framework, carcass, foundation).

I wish you success, Vladimir

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Author Abhishek Majhi replied on Apr. 15, 2020 @ 02:38 GMT
Dear Vladimir,

       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...

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Vladimir Rogozhin replied on May. 4, 2020 @ 17:19 GMT
Thanks a lot, Abhishek! I appreciate your detailed explanatory answer. I believe that today, when fundamental theoretical physics is in a deep crisis of understanding, many researchers will agree with Carlo Rovelli: Physics Needs Philosophy / Philosophy Needs Physics ... I am also waiting for your critical comments on my ontological ideas .

With kind regards,

Vladimir

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Gopal Sardar wrote on Apr. 20, 2020 @ 18:00 GMT
Dear Dr. Majhi,

Thank you very much for the writing an essay on very foundational-level. It is very interesting that you bring the approximation in measurement (not "exactness") at very beginning which we do in practice. However, I have a different view regarding the use of the word "contradiction". If you consider the approximation at very beginning, you always might not get back the same results from considering "exactness".

Good luck for essay,

Gopal Sardar

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Author Abhishek Majhi replied on Apr. 24, 2020 @ 10:36 GMT
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

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Author Abhishek Majhi wrote on Apr. 24, 2020 @ 05:20 GMT
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.

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