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RECENT POSTS IN THIS TOPIC

Vesselin Petkov: on 4/20/15 at 20:50pm UTC, wrote Dear Milen, Thank you for the excellent and informative essay. It raises a...

RJ Tang: on 4/12/15 at 20:16pm UTC, wrote Simplicity is a result of long term evolution in a close system. The...

Joe Fisher: on 4/2/15 at 14:52pm UTC, wrote Dear Professor Velev, I thought that your engrossing essay was...

Sylvain Poirier: on 3/16/15 at 9:11am UTC, wrote I don't need to refer to what "World-famous scientists" wrote in...

Milen Velev: on 3/6/15 at 8:23am UTC, wrote Dear Sylvain, I don’t contend that in order for mathematics to be...

Milen Velev: on 3/6/15 at 8:21am UTC, wrote Dear Sujatha, Thanks for reading my essay and for the interesting comment....

Sylvain Poirier: on 3/1/15 at 21:36pm UTC, wrote Hello. You seem to identify the mathematical character with the presence of...

Sujatha Jagannathan: on 2/26/15 at 17:39pm UTC, wrote You've gathered lots of pieces to create a piece within piece which is...


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FQXi FORUM
May 20, 2019

CATEGORY: Trick or Truth Essay Contest (2015) [back]
TOPIC: Trick or Truth: The applicability of the mathematical language in physics and in economics by Milen Velchev Velev [refresh]
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Author Milen Velchev Velev wrote on Feb. 18, 2015 @ 20:31 GMT
Essay Abstract

What is the reason for the unreasonable effectiveness of mathematics in physics and the unreasonable ineffectiveness of mathematics in economics? The bottom line is that the incredible effectiveness of mathematics in describing physical reality is due to the existence of symmetries in nature. And the reason for the existence of these symmetries is that the universe arose from a state characterized by perfect symmetry. Unlike physical phenomena, economic phenomena do not obey symmetries. It is possible to achieve higher effectiveness of the application of mathematics in economics when direct empirical research in the structural properties of the economic system is combined with the development of new appropriate mathematical structures.

Author Bio

Milen Velev is PhD and Assistant Professor at University “Prof. Dr. A. Zlatarov” – Burgas, Bulgaria. He is the author of the paper “Relativistic mechanics in multiple time dimensions” published in Physics Essays 25 (3): 403–438. His research interests include applied mathematics, special and general relativity, quantum mechanics, cosmology, philosophy of science, the nature of space and time, chaos theory, mathematical economics, micro- and macroeconomics.

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Edwin Eugene Klingman wrote on Feb. 19, 2015 @ 05:37 GMT
Dear Milen Velev ,

I enjoyed reading your essay and found your contrast to Wigner's "effectiveness" in science with Velupillai's "ineffectiveness" in economics quite effective. I would suggest that the essential difference is the deterministic nature of most physics, complemented by the statistical 'determinism' of distributions implied by the partition function. Thus even apparently random phenomena are combinatorially predictable by entropic thermodynamics. This is opposed to those economic and social systems whose essential character is human free will. There is no "partition function" to describe distributions whose observations (say of the stock market) give rise to unpredictable (buy/sell) events that are manifestations of free will plus intelligence.

A major theme seems to be that symmetry is the underlying explanation for the effectiveness of mathematics. And I very much agree with you that in all likelihood the universe began as a state of perfect symmetry – until it broke. But, ignoring cosmological lack of perfect symmetry, in particle physics, from proton/neutron iso-symmetry to the failed SUSY symmetry, in which no superpartners are found with mass is equal to their Standard Model partners, there are no exact symmetries. They are all imperfect symmetries, useful, but not ideal. As you note, Noether's theorem implies conservation for every symmetry, but I suspect it is the opposite that is most basic. I propose that every conservation law yields an appropriate symmetry, and that it is conservation, not symmetry, that is at the root. Conservation would appear to be the physical reality, whereas symmetry appears as a mathematical overlay.

I would be interested in your thoughts on this.

I also invite you to read my essay and hope you will comment on my thread.

My very best regards,

Edwin Eugene Klingman

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Author Milen Velchev Velev replied on Feb. 25, 2015 @ 16:48 GMT
Dear Edwin Klingman,

Thank you very much for reading my text carefully. I’ll be very interested in reading your essay. There is a high probability that the universe started out in a condition of perfect symmetry but at present we observe imperfect, broken and hidden symmetry in nature. In my opinion, symmetry is a more general and fundamental notion compared to the concept of conservation. Symmetry is defined as a physical or mathematical feature of the system which is preserved or remains unchanged under some transformation. The conservation laws only apply to a particular measurable physical property which does not change in an isolated physical system. For example, the law of conservation of mass-energy, the laws of conservation of linear and angular momentum and the CPT theorem follow from the validity of Lorentz invariance symmetry.

Best regards,

Milen Velev

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John C Hodge wrote on Feb. 19, 2015 @ 23:09 GMT
I think you got something. The reason math is less effective in economics or social sciences is the definition of terms and postulates is too vague.

But why is that? Do you have a suggestion as to why?

I suggest it is because the goals of these ranches of knowledge are to support a political model. The politics don’t like the answers that match predictions. Therefore, the science gets diverted into vague relms that fail to make good predictions. My 2014 contest paper notes the Friedman economic (monetarist) model did make predictions. But the competing Keynesian model is accepted because it produces a politically accepted view but fails to predict observations. The difficulty caused by complexity is compounded by marginalizing knowledge that has successfully predicted events, but is politically awkward. For example, predicted stagflation that Keynesian derived doctrine said could not happen, predicted the collapse of the soviet system that Keynesian derived doctrine praised, and predicted negative results of big government. The Keynesian derived doctrine of big government has repeatedly been falsified. Friedman argued for a small national government, which the politicians vote against.

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Author Milen Velchev Velev replied on Feb. 25, 2015 @ 16:52 GMT
Dear John,

Thanks for the interesting question. I will read your essay carefully. I agree with your opinion that the politicians don’t like the answers that match predictions. The choice of one macroeconomic policy or another could be dictated by a desired political effect. But the influence of the political factor is just one of a whole host of problems in this area. For example, in macroeconomics the concepts of potential aggregate output and natural rate of unemployment (NAIRU) are of great significance. The effectiveness of the applied macroeconomic policy depends on the correct determination of the values of these factors. But the problem of calculating them is difficult and not that clear. They can’t be measured directly. There are a lot of differences and difficulties in determining these quantities. They can be evaluated by using various methods and means and each one would produce approximate, expert results. Another important issue is the time lag in implementing a macroeconomic policy. It takes a while between the time corrections are made to the macroeconomic policy and the time when it shows its effects, a period during which the economic conditions might change and the measures undertaken might prove inadequate. When a certain macroeconomic policy is implemented, the secondary effects that arise should also be considered. That’s why economists often use the “Ceteris paribus” assumption.



Best regards,

Milen

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basudeba mishra wrote on Feb. 21, 2015 @ 13:14 GMT
Dear Sir,

You have raised and brilliantly discussed several important aspects that provide food for thought for extending those lines. We thoroughly enjoyed your essay.

Mathematics is not independent of human experience, as numbers are perceived as a property of objects by which we differentiate between similars. If there are no similars, it is one. If there are similars, it is...

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Author Milen Velchev Velev replied on Feb. 25, 2015 @ 16:57 GMT
Dear Basudeba,

Thanks for reading and commenting on my essay. I agree with you that in a way mathematics is not entirely independent of human experience. Elementary arithmetic, Euclidean geometry, etc. can be given as examples. But some mathematical conceptions were introduced into mathematics without any relation to human experience, long before they were applied in physics (for example, imaginary numbers). Some mathematical conceptions are so abstract that initially, it wasn’t clear where they could find any practical application (for example, Calabi–Yau manifold). Other conceptions have no analogues whatsoever in the physical reality (transfinite cardinal and ordinal numbers, the continuum hypothesis, etc.). Maybe at some point in the future they will find some practical application. So, it can be asserted that the development of mathematics is comparatively independent of the first-hand human experience.

Best regards,

Milen

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Sujatha Jagannathan wrote on Feb. 26, 2015 @ 17:39 GMT
You've gathered lots of pieces to create a piece within piece which is symmetrically inclined.

Best regards,

Miss. Sujatha Jagannathan

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Author Milen Velchev Velev replied on Mar. 6, 2015 @ 08:21 GMT
Dear Sujatha,

Thanks for reading my essay and for the interesting comment.

Best regards,

Milen

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Sylvain Poirier wrote on Mar. 1, 2015 @ 21:36 GMT
Hello. You seem to identify the mathematical character with the presence of symmetries. I agree to see a connection between both, but not as much as you do. One way is clear : a symmetry means an exact correspondence between parts, and such an exactness is characteristic of the mathematical nature of a system. However the converse is not true: a system can be mathematical but still not...

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Author Milen Velchev Velev replied on Mar. 6, 2015 @ 08:23 GMT
Dear Sylvain,

I don’t contend that in order for mathematics to be effective in describing a given system, this system has to possess symmetries. As you have rightly noted, mathematics has branches that aren’t based on the ideas of symmetries. In those cases symmetries, if applicable at all, just make things simpler and easier, but nothing more. There are probably certain criteria which...

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Sylvain Poirier replied on Mar. 16, 2015 @ 09:11 GMT
I don't need to refer to what "World-famous scientists" wrote in popularization books to discover how things go because I perfectly understand General Relativity myself, so I know very well what I'm talking about. The "disagreement" between us purely comes from the fact that you are yourself ignorant in General Relativity so that you did not understand what I meant, and your only way of replying is to refer to popularization books in guise of an argument. Please know that scientific knowledge in highly mathematical theories is not properly expressed in the language of popularization. So when scientists write popularization books, they may put together some words to look like it means something, but it cannot properly express what the theory really means. In particular the fact is that the expression "total energy of the universe" is basically senseless in General Relativity, so it may be possible to metaphorically use this expression to mean something or something else, but whenever you read it, even from "world-famous scientists", be warned that, due to the fundamental senselessness of this expression, it cannot be meant to be taken seriously anyway. This is metaphor, not science. Several physicists can use a same English expression in popularization books to mean different things when this expression does not have a natural meaning in the theory, so an ignorant reader may have the illusion that they disagree, but in fact they don't. So I'm sure these "world-famous scientists" would agree with me if you ask them.

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Joe Fisher wrote on Apr. 2, 2015 @ 14:52 GMT
Dear Professor Velev,

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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RJ Tang wrote on Apr. 12, 2015 @ 20:16 GMT
Simplicity is a result of long term evolution in a close system. The resulting equilibrium gives rise to simplicity. The infinite possibilities of any member of the system have been largely reduced to a highly confined options. Most of the possibilities are prohibited due to forces that have long been cancelled out during the long evolution. Because of this simplicity, there appears to be causal effect. In other words, causal effect is a direct product of simplicity. Take our universe as an example, the universe is in equilibrium by and large. Only a handful forces remain. Because there are relatively few forces and laws, the universe appears to be orderly and thereby allows mathematics to even exist and work. Mathematics owes its existence to the equilibrium of the universe. Equilibrium brings orderliness and slowness to change. Just imagine, if one puts one stone by another stone, and because the stones decay so fast, by the end of this action of moving them together, one counts zero stone. The law of addition will be forever different from what we know today. In this sense, math and physics have ‘this worldliness’ feature, and is a localized knowledge to this universe at this phase of equilibrium. It could be vastly different in other possible states of the universe or other universes.

One notable exception to the simplicity in universe is the complexity in bio-sphere. Because the bio-sphere is inherently expansive and interactive, we cannot reduce the theories to a few laws and mathematics models. The bio-sphere is NOT an equilibrium system. Therefore it is very hard to apply causal effect to explain human society for instance. It is very hard to generalize theories or apply mathematics in bio-sphere or human society, as we are able to in cosmology.

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Vesselin Petkov wrote on Apr. 20, 2015 @ 20:50 GMT
Dear Milen,

Thank you for the excellent and informative essay. It raises a lot of questions and I hope to come back with some specific comments.

Regarding "Roger Penrose thinks that mathematical ideas exist in a separate “Platonic” world", I wonder whether his view fully reflects Bertrand Russell's view on the same issue. In fact, this is not really a question to you - I myself am interested in answering it.

Best wishes,

Vesselin Petkov

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