CATEGORY:
Trick or Truth Essay Contest (2015)
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TOPIC:
How Accurately Can Mathematics Describe Nature? by Basem Galal and Mohammed M. Khalil
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Author Mohammed M. Khalil wrote on Mar. 10, 2015 @ 15:41 GMT
Essay AbstractMathematics and physics are different, yet they are closely connected. The effectiveness of mathematics in physics is unparalleled in any other branch of knowledge. In this essay, we try to explain the reason for this effectiveness based on the view that mathematics is invented. We also question the accuracy of mathematics in describing nature, and argue that mathematics does not provide us with the truth about how nature works, but with models that enable us to make predictions about the outcome of observations and experiments.
Author BioBasem and Mohammed are undergraduate students at Alexandria University, Egypt. Basem is interested in doing research in machine learning (theory and application), especially deep learning. Mohammed is interested in theoretical physics. He won third prize in the previous FQXi essay contest, and coauthored 7 research papers http://inspirehep.net/author/profile/M.M.Khalil.1
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John C Hodge wrote on Mar. 11, 2015 @ 02:21 GMT
Great essay.
I think math is discovered. I think you present a very good analysis of the comparison of discovered vs. invented. I’ll spend more time thinking about your `invented’ arguments.
The following addresses your objections to `discovered’ (``Math is a part of nature…”.)
A There is a need to discover the truth of how nature works to advance our survival....
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Great essay.
I think math is discovered. I think you present a very good analysis of the comparison of discovered vs. invented. I’ll spend more time thinking about your `invented’ arguments.
The following addresses your objections to `discovered’ (``Math is a part of nature…”.)
A There is a need to discover the truth of how nature works to advance our survival. There is much more to learn about the universe, math and physics. We don’t have different math formulas for the same physics phenomena. We have different assumptions for the same phenomena. OR, the formulas produce the same predictions with an easier formulation. Liebniz postulated if the different formulas produce the same results, they are the same.
B Even math starts with axioms. So, derivation of principles is not done in physics or math.
C We have many mysteries. Saying they have no solution is inaccurate and misleading. More accurate is we haven’t discovered (or invented) the math yet. For example, Fourier analysis was unknown but the Greeks had `harmony of the spheres’ and circles within circles (Ptolomey).
D Your 4th objection is really the crux of the whole issue. Infinity is not a number. It means unbounded or the increase without limit. Whether the universe is unbounded or not is currently a metaphysical issue. I consider it bounded and flat (see my essay on how). Thanks to the essay by Ojo and conversation with him, I have come to think that division is an unnatural operation. I think irrational numbers are invented and therefore are not natural and not valid math. Its purpose is to be an inverse of multiplication, but multiplication is repetitive addition. Therefore, the inverse of multiplication is repetitive subtraction. It solves Zeno’s paradox. That is, the invented parts of math are invalid and not natural.
Your section on Patterns and Regularities argues for math being a part of nature. Thanks also for the recognition of the fractal nature of the universe.
Statistics may be an invention. I take the nature of physics to be cause and effect. Statistics addresses a situation where a pattern in the data has been noted and no cause-effect model has yet been developed. For example, QM may indicate the type of cause-effect model such as the Bohm Interpretation (I’ve researched this wit a model of photon interference). I suggest Group models are like the periodic table in the 19th century. A pattern was recognized; the table was constructed based on properties, holes in the table predicted new elements and their properties. Further, the early 20th century saw the development of a cause-effect (structure) model of why the periodic table worked. The table itself was invented, but the cause-effect was natural. The same is true of the group model where the holes predicted the properties of undiscovered particles.
I particularily like the `Beautiful but wrong’ section. I suggest all our current models are `wrong’ in the sense of limited.
Your essay is one of the very few that addresses the topic. Well, done!
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Author Mohammed M. Khalil replied on Mar. 11, 2015 @ 16:59 GMT
Dear Mr. Hodge,
Thank you for your comments. I looked at your essay, and I appreciate your arguments for mathematics as a characteristic of the universe.
I will read your essay in more detail and write my comments on it, but here I would like to address your comments about the discovery of mathematics.
A) Different formulations
are equivalent, but they tell us...
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Dear Mr. Hodge,
Thank you for your comments. I looked at your essay, and I appreciate your arguments for mathematics as a characteristic of the universe.
I will read your essay in more detail and write my comments on it, but here I would like to address your comments about the discovery of mathematics.
A) Different formulations
are equivalent, but they tell us different stories about how nature works. If mathematics is discovered and it is part of nature, shouldn't we expect it to reveal the reality of how nature works?
B) Mathematical axioms are more intuitive than the principles of physics. And I think those principles should be derivable if mathematics is part of nature.
C) I agree that we might invent the mathematics needed to address those currently unsolved problems, and we speculate on that near the end of the essay. However, we cannot know that for sure. Some problems might never have analytical solutions, but we could only find approximate or numerical solutions.
D) The fourth objection is not just about infinity. Many mathematical constructs have no correspondence in nature, which might mean mathematics is not part of nature. Mathematics seeks generalization and abstraction.
Finally, I would like to thank you for your other comments, and I agree with your opinion about statistics.
Best regards,
Mohammed
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Alan M. Kadin wrote on Mar. 11, 2015 @ 02:33 GMT
Dear Mr. Galal and Mr. Khalil:
Your essay is very well written and insightful. Are you really both undergraduate students?
Given that your essay focuses on the role of mathematics in providing models for physical systems, you might be interested in my essay, "Remove the Blinders: How Mathematics Distorted the Development of Quantum Theory". I argue that contrary to universal...
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Dear Mr. Galal and Mr. Khalil:
Your essay is very well written and insightful. Are you really both undergraduate students?
Given that your essay focuses on the role of mathematics in providing models for physical systems, you might be interested in my essay,
"Remove the Blinders: How Mathematics Distorted the Development of Quantum Theory". I argue that contrary to universal belief, a simple realistic picture of the microworld is possible, completely avoiding the paradoxes that plague orthodox quantum mechanics. QM is not a universal theory of matter; it is rather a mechanism for distributed vector fields to self-organize into spin-quantized coherent domains similar to solitons. This requires nonlinear mathematics that is not present in the standard Hilbert-space formalism. This also makes directly testable experimental predictions, based on little more than Stern-Gerlach measurements. Remarkably, these simple experiments have never been done.
So while mathematics can provide important insights into physics, an incorrect mathematical model that becomes established may be seen as virtually religious dogma which is not to be questioned. That prevents further progress.
Alan Kadin
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Author Mohammed M. Khalil replied on Mar. 11, 2015 @ 17:03 GMT
Dear Dr. Kadin,
Thank you for your interesting post. I am glad you liked our essay. I agree with you that mathematics provides models for nature. Some models might accelerate the progress of physics, while others might hinder it.
Your model for quantum mechanics seems interesting. I will read it in more detail soon.
Best,
Mohammed
James Lee Hoover wrote on Mar. 11, 2015 @ 22:11 GMT
Basem and Mohammed,
I salute you for your cogent and straightforward argument that math is invented.
I also believe that it is an effective invention to represent and model the natural world, providing all the advantages you mention. My views are similar in my essay, "Connections: math, physics and the mind"
Regards,
Jim
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Author Mohammed M. Khalil replied on Mar. 12, 2015 @ 20:22 GMT
Dear Jim,
Thank you for your kind comments. I am glad we agree that mathematics is an effective invention. I looked at your essay and I also salute your well-written arguments. I enjoyed your analogy with the Euler’s identity and the connection between math, physics, and the brain.
Best regards,
Mohammed
Ed Unverricht wrote on Mar. 12, 2015 @ 01:04 GMT
Dear Basem Galal and Mohammed M. Khalil,
Very interesting and thought provoking essay. Your initial premise that mathematics is invented leading to its effectiveness, is followed up by a very solid argument "we argue that the usefulness of mathematics in discovering new theories is limited, and that it does not provide us with a real picture of the world, but with models useful as calculational tools for making predictions.".
Your statement "Our theories are models of nature. Some models are more useful than others." is the lead in to the geometric models in my essay
here of the particles of the standard model. Hope you get a chance to read and comment on it.
Great essay, best of luck in the contest.
Regards, Ed Unverricht
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Author Mohammed M. Khalil replied on Mar. 12, 2015 @ 20:31 GMT
Dear Ed Unverricht,
Thank you for the kind and interesting comments. I looked at your essay, and I am glad we agree that mathematics provides useful models for nature. I enjoyed very much your beautiful images, and I could only wonder at the amazing usefulness of mathematical models.
Good luck to you too.
Best regards,
Mohammed
Edward Michael MacKinnon wrote on Mar. 12, 2015 @ 04:30 GMT
I think that this is a remarkable essay for two undergraduates. It should signal a great future for both. Since my contribution takes a very similar position, but develops it historically, I really have no adverse comments. However, I find the claim that nature is symmetric a bit ambiguous. We use symmetry principles in developing theories especially the standard model of particle physics. Then we have to add qualifications because what we find are broken symmetries.
Ed MacKinnon
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Author Mohammed M. Khalil replied on Mar. 12, 2015 @ 20:46 GMT
Dear Ed MacKinnon,
Thank you for your kind comments. Your essay is interesting, and you gave well-written arguments for the coevolution of physics and mathematics. I am glad we agree on some points.
By "nature is symmetric", we mean that the laws of physics are invariant under specific transformations, such as translation in space and motion at constant velocity. If not for this property, describing nature would be very difficult indeed.
Best regards,
Mohammed
Joe Fisher wrote on Mar. 17, 2015 @ 16:42 GMT
Dear Mssrs. Galal and Khalil,
You wrote: “A theory can have support from its theoretical foundation and solid mathematics,
but until it can produce predictions that can be compared with experiment, we must not evaluate it as the only truth. We should always consider alternative approaches even if they are less developed.”
Please behold my alternative approach: This is my...
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Dear Mssrs. Galal and Khalil,
You wrote: “A theory can have support from its theoretical foundation and solid mathematics,
but until it can produce predictions that can be compared with experiment, we must not evaluate it as the only truth. We should always consider alternative approaches even if they are less developed.”
Please behold my alternative approach: This is my single unified theorem of how the real Universe is occurring: Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of abstract NOTHING. Proof exists that every real astronomer looking through a real telescope has failed to notice that each of the real galaxies he has observed is unique as to its structure and its perceived distance from all other real galaxies. Each real star is unique as to its structure and its perceived distance apart from all other real stars. Every real scientist who has peered at real snowflakes through a real microscope has concluded that each real snowflake is unique as to its structure. Real structure is unique, once. Unique, once does not consist of abstract amounts of abstract quanta. Based on one’s normal observation, one must conclude that all of the stars, all of the planets, all of the asteroids, all of the comets, all of the meteors, all of the specks of astral dust and all real objects have only one real thing in common. Each real object has a real material surface that seems to be attached to a material sub-surface. All surfaces, no matter the apparent degree of separation, must travel at the same constant speed. No matter in which direction one looks, one will only ever see a plethora of real surfaces and those surfaces must all be traveling at the same constant speed or else it would be physically impossible for one to observe them instantly and simultaneously. Real surfaces are easy to spot because they are well lighted. Real light does not travel far from its source as can be confirmed by looking at the real stars, or a real lightning bolt. Reflected light needs to adhere to a surface in order for it to be observed, which means that real light cannot have a surface of its own. Real light must be the only stationary substance in the real Universe. The stars remain in place due to astral radiation. The planets orbit because of atmospheric accumulation. There is no space.
Warm regards,
Joe Fisher
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Author Mohammed M. Khalil replied on Mar. 17, 2015 @ 18:35 GMT
Dear Mr. Fisher,
Thank you for your comment, and for sharing your views.
Best regards,
Mohammed
adel sadeq wrote on Mar. 22, 2015 @ 17:23 GMT
Hi Mohammed,
Thank you for reading my essay. You have written a very well essay although you probably know that our philosophies are different.
I have seen that you have co authored with Das and Faraj, that is very impressive. How did you do that? Is it possible to show my idea to Faraj and also get Basem to run the simple simulation(at the end of each section written "program link") to confirm the results.
Thanks and good luck.
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Author Mohammed M. Khalil replied on Mar. 22, 2015 @ 21:59 GMT
Dear Adel,
Thank you for your kind comments. I suggest you send Dr. Farag an email yourself, because you will be able to explain the idea better than me, and I am sure you will find him very cooperative.
Best regards,
Mohammed
Rick Searle wrote on Mar. 22, 2015 @ 21:05 GMT
Dear Basem Galal and Mohammed M. Khalil,
This is by far the best essay to argue that mathematics is invented which I have read, and, believe me, in researching for this contest, I read a lot of them!
Please take the time to check out and vote on my own essay:
http://fqxi.org/community/forum/topic/2391
Best of luck in the contest!
Rick Searle
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Author Mohammed M. Khalil replied on Mar. 22, 2015 @ 21:58 GMT
Dear Rick,
Thank you for your kind comments. I really liked your essay; I rated it and wrote you a comment there.
Best regards,
Mohammed
Thomas Howard Ray wrote on Mar. 23, 2015 @ 14:46 GMT
Mohammed (& Basem),
Thanks for commenting in my forum. I am at a loss, however, to know why you think our ideas are opposed -- I found your excellent essay to reflect an entirely rationalist view of science, as does mine.
I want to point out something to you: You quote Einstein on mathematics as a human invention:
“How is it possible that mathematics, a product of human...
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Mohammed (& Basem),
Thanks for commenting in my forum. I am at a loss, however, to know why you think our ideas are opposed -- I found your excellent essay to reflect an entirely rationalist view of science, as does mine.
I want to point out something to you: You quote Einstein on mathematics as a human invention:
“How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” (from *Sidelights in Relativity* 1922)
In my youth, I studied Einstein's and Leopold Infeld's popular book, *The Evolution of Physics* (1938) the way some people study religious texts. They write:
"Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world. In our endeavor to understand reality we are somewhat like a man trying to understand the mechanism of a closed watch. He sees the face and the moving hands, even hears its ticking, but he has no way of opening the case. If he is ingenious he may form some picture of a mechanism which could be responsible for all the things he observes, but he may never be quite sure his picture is the only one which could explain his observations. He will never be able to compare his picture with the real mechanism and he cannot even imagine the possibility or the meaning of such a comparison."
So regardless of whether mathematics is discovered or invented, it is only the rational correspondence of the mathematical language to experience and experiment, that gives us rational knowledge of the world.
Your concluding statement begins, "Mathematics and physics are different; mathematics is a useful human construct, and physics tries to describe the laws of nature. Yet, mathematics is very effective in physics. It enables us to make accurate predictions about the outcome of experiments and even predict undiscovered phenomena."
How could you think that this view differs from mine? I hope you return to my essay with new comments.
All best,
Tom
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Author Mohammed M. Khalil replied on Mar. 23, 2015 @ 18:27 GMT
Dear Tom,
Thank you for your comments. I really like that quote of Einstein; his closed watch analogy agrees well with our essays.
I admit that our essays have some similar views. However, I think that mathematics is invented, and hence, there is no preexisting correspondence between mathematics and the physical world. Mathematics is effective because it was invented to describe patterns and regularities in nature. Mathematics provides models that describe nature, and most of those models are not exact, i.e. they do not correspond exactly to the phenomena they describe. This view is different from that of the mathematical universe hypothesis which your essay supports.
All the best,
Mohammed
Thomas Howard Ray replied on Mar. 24, 2015 @ 00:54 GMT
Mohammed, I'm afraid you still miss the point. I don't support the mathematical universe hypothesis a priori. The philosophical question of whether mathematics is invented or discovered has *nothing* to do with the correspondence of mathematics to physics, i.e., the corresponding truth content of their respective models.
You wouldn't say that natural language has truth content independent of physics, would you? In other words, the string of symbols C-A-T is true if, and only if, there is a physical counterpart to the symbols. That is what Einstein was saying -- e.g., he favored the introduction of extra dimensional models, even in his day, " ... if there exist good physical reasons to do so."
The MUH is based on physical probability, not mathematical philosophy.
Best,
Tom
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Author Mohammed M. Khalil replied on Mar. 25, 2015 @ 14:27 GMT
Dear Tom,
Thank you for your comment and for the explanation. I think I see your point now.
Best,
Mohammed
Jose P. Koshy wrote on Mar. 24, 2015 @ 06:21 GMT
Dear Galal & Khalil,
You have tried to give a logical picture how mathematics has become effective in physics, and suggest the need for new mathematical inventions to solve the hitherto unsolved problems. You say correctly, “A great mystery about nature is that we can describe the same phenomenon with different mathematical formulations”. Have you thought of the reverse possibility? A...
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Dear Galal & Khalil,
You have tried to give a logical picture how mathematics has become effective in physics, and suggest the need for new mathematical inventions to solve the hitherto unsolved problems. You say correctly, “A great mystery about nature is that we can describe the same phenomenon with different mathematical formulations”. Have you thought of the reverse possibility? A unique mathematical equation can have different physical interpretations. Refer my essay:
A physicalist interpretation of the relation between Physics and Mathematics.
Are there any mathematical laws? Or are there only mathematical structures? I would answer that both exist, and there should be a clear distinction between the two: mathematical laws are discovered; but mathematical structures are invented. The laws are fundamental and eternal, that even an omnipotent creator cannot defy the laws. The structures depend on axioms, which are nothing but 'assigned properties'. But the evolution of the structure follows the eternal mathematical laws.
The same thing is true for the physical world. The physical world has certain properties; but its evolution (the series of changes) depends solely on mathematical laws, and this leads to structures that are mathematically explainable. We try to explain the physical world based on axioms (assigned properties). To arrive at these properties, we depend on 'mathematical relations' based on the observable natural structures. However, this can be tricky. My essay deals with this. If the assigned properties are correct, we will be able to explain everything.
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Author Mohammed M. Khalil replied on Mar. 25, 2015 @ 14:33 GMT
Dear Jose,
Thank you for your comment. I think mathematics is invented in the sense that we define/invent a set of rules (axioms) and then discover certain relations based on them (theorems).
Best,
Mohammed
Janko Kokosar wrote on Apr. 4, 2015 @ 13:09 GMT
Dear Basem and Mohammed
I agree with your that mathematics is not enough to describe physics. Thus, that many mathematical theories predicted something in mathematics, but predictions were wrong. My opinion is that math is only an abstract language, which tell more simple what happening in physics. (Torsten Asselmeyer-Maluga used the best words: ''' abstraction is necessary concept for...
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Dear Basem and Mohammed
I agree with your that mathematics is not enough to describe physics. Thus, that many mathematical theories predicted something in mathematics, but predictions were wrong. My opinion is that math is only an abstract language, which tell more simple what happening in physics. (Torsten Asselmeyer-Maluga used the best words: '''
abstraction is necessary concept for our species: we have a limited memory in our brain and a limited number of sensors to sense the world. Therefore, we have to simplify many relations in the world to understand them. But abstraction is also the root of mathematics: numbers as an abstract count of objects was the beginning. ') But fundamental physics should be simple, thus I hope that quantum gravity should be simple.
Thus, your approach is naturalistic (also Smolin) what is closer to me. Although you find good examples where only mathematics gave wrong predictions, I wrote one example where mathematics gave good predictions: Units kg, meter and second needs matematization and simplification, thus Planck found how to eliminate them, thus he showed how physics can become closer to mathematics. But my example with rectangular triangle shows how that euclidean geometry is a consequence of physics.
What do you think if I change one your sentence: ''
U(1) gauge theory was an extension of general relativity that naturaly leads to electromagnetism. ''
But, I disagree that our theories are only models of nature. Math is a true goal of physics, but it is not everything.
My essayBest regards,
Janko Kokosar
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Author Mohammed M. Khalil replied on Apr. 7, 2015 @ 16:35 GMT
Dear Janko,
Thank you for your interesting comments. We seem to agree about the limitations of mathematics but disagree about the accuracy of theories in describing nature.
Best regards,
Mohammed
Cristinel Stoica wrote on Apr. 5, 2015 @ 17:07 GMT
Dear Basem and Mohammed,
I liked reading your essay. It is very well written, and you explain very well the role of mathematical models, and how they can turn out to be inadequate to describe the physical world. I also like that you let open the possibility that a mathematical theory well suited to describe the universe may exist, although we will never be sure it is the true one.
Best wishes,
Cristi
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Author Mohammed M. Khalil replied on Apr. 7, 2015 @ 16:14 GMT
Dear Cristi,
Thank you for reading our essay and for your kind and encouraging comments.
Best regards,
Mohammed
Jacek Safuta wrote on Apr. 10, 2015 @ 10:06 GMT
Dear Basem and Mohammed,
You have presented one of the best essays in the contest. Very clear, modest and not intrusive like many others. You deserve very high rating what you will observe in a minute. However I want to address some issues.
You present important objections to the view No. “2. Mathematics is discovered because it is part of nature just like physics.” I agree with...
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Dear Basem and Mohammed,
You have presented one of the best essays in the contest. Very clear, modest and not intrusive like many others. You deserve very high rating what you will observe in a minute. However I want to address some issues.
You present important objections to the view No. “2. Mathematics is discovered because it is part of nature just like physics.” I agree with all objections if we define math as an abstract language of equations. Then the answer is No.3. The mathematics is invented as an abstract, platonic language used to describe reality and also for many other purposes. But pure geometry, in the meaning of shape and its dynamics and not equations or human language, is discovered in the sense that we perceive shapes and its dynamical changes. I think we need an universal, visual language, based on that geometry. It would be comprehensible to future supercomputers, aliens and maybe children as well. So far we have to use equations as our deficient language.
You claim: “…Mathematics is structured as theorems based on axioms. Axioms are the premise or starting point on which we build theorems” As you probably know, there were many attempts to formulate axioms also in physics (D. Hilbert, J. von Neumann, L. Nordheim, H. Weyl, E. Schrödinger, P. Dirac, E. P. Wigner and others). All these efforts failed. That is a pity, however a deductive system can consist not only of axioms but also other, already established theorems. So far theorems were reserved exclusively for mathematics. That means that we can use these established theorems only if we accept that the reality is isomorphic to mathematical structures. You argue that it is not the case and I agree. But we can use geometrical structures instead general notion of mathematical ones. Then we could try e.g. with the geometrization conjecture, proved by Perelman (so it is a theorem). And it generates testable predictions what you demand in conclusions. We have the set of 8 Thurston geometries. We can treat them as a space-like, totally geodesic submanifolds of a 3+1 dimensional spacetime. Then we use the correspondence rule to assign interactions and matter to the proper geometries. It seems to be oversimplified but you can find some technicalities in e.g. Torsten Asselmeyer-Maluga and Helge Rose’s publications (arxiv.org/abs/1006.2230, arxiv.org/abs/1006.2230v6). In details it is really complicated.
If you are interested you can take a look at my
essay.
I would appreciate your comments however I would understand if you were tired with the contest.
Jacek
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Author Mohammed M. Khalil replied on Apr. 10, 2015 @ 21:46 GMT
Dear Jacek,
Thank you very much for your kind comments and for the rating.
I am glad you agree with our objections to the discovery of mathematics if we define math as an abstract language of equations. However, I also think that geometry is invented not discovered. In the real world there are no straight lines extending to infinity, or perfect circles that exactly lead to pi when...
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Dear Jacek,
Thank you very much for your kind comments and for the rating.
I am glad you agree with our objections to the discovery of mathematics if we define math as an abstract language of equations. However, I also think that geometry is invented not discovered. In the real world there are no straight lines extending to infinity, or perfect circles that exactly lead to pi when you divide the circumference by the diameter. All these geometrical structures are idealizations of similar structures in the real world. The axioms of Euclidean geometry is based on those idealized structures, and hence the theorems based on them are also idealizations that describe the real world only approximately.
The idea of the geometrical universe seems elegant, but I am not familiar with the work of Torsten Asselmeyer-Maluga and Helge Rose. I will read your essay and the mentioned papers soon, and I will comment on them.
Kind regards,
Mohammed
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Jacek Safuta replied on Apr. 11, 2015 @ 07:35 GMT
Dear Mohammed,
The principle of minimum energy (really the second law of thermodynamics) states that for a closed system, with constant external parameters and entropy, the internal energy will decrease and approach a minimum value at equilibrium. It means that every object/structure shall deform to the shape that minimizes the total potential energy. That shape is an ideal shape. But the system cannot approach that ideal shape.
I am not a Platonist. Obviously, in nature we cannot find ideal shapes. As I have mentioned, the geometry is about shapes that we perceive in real world and not equations. However it is not practical or possible to make calculus on real shapes. To make predictions we need calculus. That is the reason we need idealizations (approximations) of real complexity. In my opinion, the lack of ideal shapes in nature is not an intrinsic feature of real objects (the second law) but the outcome of complexity , interactions and dynamics of interacting objects.
Best regards
Jacek
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Vladimir F. Tamari wrote on Apr. 14, 2015 @ 01:19 GMT
Dear Basem and Mohammed
Congratulations on an exceptionally thought-out and well-written essay. It helped me appreciate it that I agree in my own essay with many (but not all) of the points you made. For example you mention symmetry and universality as explanation of the effectiveness of mathematics. I go much further and speculate that at the deepest level mind, mathematics and nature...
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Dear Basem and Mohammed
Congratulations on an exceptionally thought-out and well-written essay. It helped me appreciate it that I agree in my own essay with many (but not all) of the points you made. For example you mention symmetry and universality as explanation of the effectiveness of mathematics. I go much further and speculate that at the deepest level mind, mathematics and nature share the same 'building blocks'. One idea I particularly liked is that you stress the power of abstraction in mathematics. As for the Kaluza-Klein theory the mathematics pointed to what I consider the solution to the problems of physics: adoption of a universal absolute ether matrix or lattice - the fifth dimension being the ether nodes. This corresponds to my own
Beautiful Universe Theory so I am a bit biased to it! As you point out the K-K theory does not sit well with dynamic relativity, and I think relativity itself is just a mathematical re-formulation of an absolute universe with variable speed of light and Lorentz transformations.
و الله اعلم
Again congratulations for an excellent essay. Good luck with your studies.
Vladimir
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Author Mohammed M. Khalil replied on Apr. 14, 2015 @ 22:44 GMT
Dear Vladimir,
Thank you for your kind comments, and good luck in the contest.
Mohammed
Torsten Asselmeyer-Maluga wrote on Apr. 15, 2015 @ 08:14 GMT
Dear Mohammed,
thanks for reading my essay. As I see we are agreeing in many points. But more importantly, I also think that math is an invention. Thanks for bringing your essay to my attention.I rate your essay high.
Best
Torsten
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Author Mohammed M. Khalil replied on Apr. 15, 2015 @ 17:52 GMT
Dear Torsten,
Thank you very much for the kind comment and for the rating.
Best,
Mohammed
Michel Planat wrote on Apr. 15, 2015 @ 09:05 GMT
Dear Basem and Mohammed,
Your point is very well argued and reasonable, very close to the one by the great mathematician, physicist and thinker Henri Poincaré in Science and Hypothesis
http://www.gutenberg.org/files/37157/37157-pdf.pdf
"Rôle of Hypothesis.—Every generalisation is a hypothesis. Hypothesis therefore plays a necessary rôle, which no one has ever...
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Dear Basem and Mohammed,
Your point is very well argued and reasonable, very close to the one by the great mathematician, physicist and thinker Henri Poincaré in Science and Hypothesis
http://www.gutenberg.org/files/37157/37157-pdf.pdf
"Rôle of Hypothesis.—Every generalisation is a hypothesis. Hypothesis therefore plays a necessary rôle, which no one has ever contested. Only, it should always be as soon as possible submitted to verification. It goes without saying that, if it cannot stand this test, it must be abandoned without any hesitation."
I am impressed by Poincaré's insight. In our time, physics is much more mathematical. I think that it is the result of a collective cognitive effort, may be an adaptation of our specie to an ever changing environment. I like the view of Vincent Douzal in this respect.
I had a pleasant reading and give you now my best appreciation.
If you have time, I created a dialogue about a topic of interest for mathematical physicists. I am curious to see if you will like it.
Best regards,
Michel
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Author Mohammed M. Khalil replied on Apr. 15, 2015 @ 17:49 GMT
Dear Michel,
Thank you for your kind comments. I wasn't aware of Poincaré's book, but it seems very interesting, and I am glad our essay agrees with his ideas. I think that currently the main problem with theoretical physics is the wide gap between hypothesis and verification.
I have read your essay and I find it very interesting.
Best regards,
Mohammed
Michel Planat replied on Apr. 15, 2015 @ 18:01 GMT
Dear Mohammed,
Congratulations, you are on the right way already gussing what matters, soon being involved in a great chapter of science.
All the best,
Michel
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Member Noson S. Yanofsky wrote on Apr. 17, 2015 @ 15:54 GMT
Hi,
You wrote me that you looked at my paper and I am very appreciative. I read your paper and I like it.
I wish you would work out some more of your idea that simplicity and beauty in physical theories can be understood from the computational complexity point of view. Has anyone else talked about this?
Thanks again!
All the best,
Noson Yanofsky
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Basem Galal Ahmed replied on Apr. 18, 2015 @ 13:35 GMT
Dear Noson,
Thank you for reading our essay
In our article we suggest that we can use computational complexity as a measure of simplicity because we use computers today for almost all physical computations and simulations .Hence , it's reasonable to choose measure of simplicity relative to computers, I am not sure if anyone else talked about that.
All the best,
Basem
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Alma Ionescu wrote on Apr. 19, 2015 @ 19:23 GMT
Dear Mohammed, Basem,
It is a well established fact that people will mostly speak of things that impress them, either good or bad. I couldn't agree more with your point that Wigner's speech is not shedding light on theories that have not worked as hoped. For every successful theory like relativity or quantum mechanics, there is a bunch of other theories that we know are wrong, like N=4 super Yang Mills or your SU(5) example. I like your idea of quantifying the elegance of a theory through the number of dependent variables and the relations between variables. It sounds like the most compact network model possible. Your arguments do a very good job getting the point across as well as your clear and enjoyable writing style.
Warm regards,
Alma
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Author Mohammed M. Khalil replied on Apr. 20, 2015 @ 22:47 GMT
Dear Alma,
Thank you very much for your kind and encouraging words. I agree with you about wrong theories like N=4 super Yang Mills. We suggested using computational complexity as a measure of simplicity because we use computers today for almost all physical computations and simulations. Hence, it's reasonable to choose measure of simplicity relative to computations.
Kind regards,
Mohammed
William T. Parsons wrote on Apr. 20, 2015 @ 19:39 GMT
Hi Mohammed and Basem--
An absolutely brilliant essay. I concur fully with your analysis. In fact, your essay is so good that I'm glad I didn't write on your precise topic. You would have put me to shame. And, needless-to-say, I certainly agree with your last bullet on page 3.
I can't believe you two are only undergraduates. Your professors are lucky to have you. I predict shining futures for both of you. Keep up the good work!
Best regards and best of luck in the contest,
Bill.
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Author Mohammed M. Khalil replied on Apr. 20, 2015 @ 22:51 GMT
Dear William,
Thank you very much for your kind and encouraging words. I am glad you liked our essay. From your essay, I am sure you would have done a better job if you wrote about that topic.
All the best,
Mohammed
Armin Nikkhah Shirazi wrote on Apr. 20, 2015 @ 22:29 GMT
Dear Basem and Mohammed,
Though I disagree with your instrumentalist perspective on physics and your antiplatonist view of mathematics, I am genuinely impressed by your eloquent defense of your positions. It is all the more impressive considering that, if I infer correctly, you are not even native English Speakers.
Despite our philosophical differences, there is much in your essay that I do concur with, especially the notion that observation and experiment trumps any other consideration in science.
Your ideas about quantifying aesthetic notions like beauty are interesting and deserve more detailed treatment.Finally, I could not agree more with your last paragraph as my own research effort is geared precisely to developing new mathematics that helps us model and especially understand fundamental aspects of reality.
Overall, you did a great job
Best wishes,
Armin
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Author Mohammed M. Khalil replied on Apr. 20, 2015 @ 22:59 GMT
Dear Armin,
Thank you very much for your interesting comments. I respect your opinion about the Platonist view, and I am glad you concur with other points.
Indeed the importance of experiments and observations in science cannot be overstressed. I think that currently the main problem with theoretical physics is the wide gap between theory and experiment.
Finally, I am glad to...
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Dear Armin,
Thank you very much for your interesting comments. I respect your opinion about the Platonist view, and I am glad you concur with other points.
Indeed the importance of experiments and observations in science cannot be overstressed. I think that currently the main problem with theoretical physics is the wide gap between theory and experiment.
Finally, I am glad to know that you are working on developing new mathematics for better modelling reality.
Best wishes,
Mohammed
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Steven P Sax wrote on Apr. 23, 2015 @ 01:06 GMT
Dear Mohammed,
Thank you for your kind remarks on my essay and I enjoyed reading yours as well. As you know, we agree on many points. It's very true that many theories which were considered beautiful or simple ended up failing to explain observations and experimental data. I liked your discussion on simplicity and computational complexity, and on how the same phenomenon can be described with different mathematical formulations. You present throughout a very interesting essay, and I rate it highly.
Kind regards,
Steve Sax
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Author Mohammed M. Khalil replied on Apr. 24, 2015 @ 11:01 GMT
Dear Steven,
Thank you for your kind words on our essay. I am glad you enjoyed reading it, and that you agree with us in many points.
Best regards,
Mohammed
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