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RECENT POSTS IN THIS TOPIC

Noson Yanofsky: on 4/6/17 at 20:26pm UTC, wrote Dear Peter, I am sorry. There is no disrespect. Just time is a precious...

Peter Jackson: on 4/6/17 at 19:46pm UTC, wrote Noson, You didn't respond to my post above and haven't read my essay. Is...

Dizhechko Semyonovich: on 4/6/17 at 14:42pm UTC, wrote Dear Noson S. Yanofsky, Excellent informative essays about the temporal...

George Gantz: on 4/4/17 at 18:04pm UTC, wrote Noson - Thanks for an interesting essay. It's a highly challenging...

Noson Yanofsky: on 4/4/17 at 13:56pm UTC, wrote Dear Edwin, Thank you for the kind words. It would indeed be nice to...

Noson Yanofsky: on 4/4/17 at 13:52pm UTC, wrote Dear Conrad, Thank you for the kind words. I do not think we are in a...

Noson Yanofsky: on 4/4/17 at 13:49pm UTC, wrote Dear Peter, Thank you for the kind words. I do not see the reason why a...

peter wanjohi: on 4/4/17 at 13:36pm UTC, wrote Dear Professor, Your essay is very educative to say the least. However, as...


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FQXi FORUM
September 25, 2017

CATEGORY: Wandering Towards a Goal Essay Contest (2016-2017) [back]
TOPIC: Finding Structure in Science and Mathematics by Noson S. Yanofsky [refresh]
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Author Noson S. Yanofsky wrote on Feb. 21, 2017 @ 15:31 GMT
Essay Abstract

One can view the laws of nature as having goals and intentions to produce the complex structures that we see. But there is another, deeper, way of seeing our world. The universe is full of many chaotic phenomena devoid of any goals and intents. The structure that we see comes from the amazing ability that scientists have to act like a sieve and isolate those phenomena that have certain regularities. By examining such phenomena, scientists formulate laws of nature. There is an analogous situation in mathematics in which researchers choose a subset of structures that satisfy certain axioms. In this paper, we examine the way these two processes work in tandem and show how science and mathematics progress in this way. The paper ends with a speculative note on what might be the logical conclusion of these ideas.

Author Bio

Noson S. Yanofsky has a PhD in mathematics (category theory). He is a professor of computer science in Brooklyn College and The Graduate Center of CUNY. In addition to writing research papers he also co-authored “Quantum Computing for Computer Scientists”(Cambridge University Press, 2008) and is the author of “The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us” (MIT Press 2013). The second book is a popular science book that has been received very well both critically and popularly. He lives in Brooklyn with his wife and four children.

Download Essay PDF File




Steve Dufourny wrote on Feb. 21, 2017 @ 16:34 GMT
Hello Mr Yanofsky,

I loved your general papper.It is one of my favorite.Because your have well generalised about maths.Noether I like also ,she was very relevant.I like the determionism and the objectivity of methods.

I liked also your interpretation of chaos and order.Especialy how you show the harmony in its generality and order by these mathema and symmetries.I like also these...

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Jochen Szangolies wrote on Feb. 22, 2017 @ 13:03 GMT
Dear Noson,

glad to see you entering this contest!

I like your idea that finding (simple) mathematical laws in nature is, in part, due to a certain selection bias. Ultimately, to connect with the contest's topic, one might then speculate that it's not nature working according to mathematical laws that gives rise to goal-directed behavior, but rather, that it's the other way around:...

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Author Noson S. Yanofsky replied on Feb. 26, 2017 @ 10:01 GMT
Dear Jochan,

Thank you for the kind words.

Yes, Wheeler's law without law does come in here. However I always got the impression that he used that as a way of introducing his participatory anthropic principle. While the PAP might be true, it seems to bring in some quantum magic which makes me nervous. I am trying to point to a more general way of picking out laws.

Your point about any stream of bits automatically having structure is very true. It is probably the simplest version of Ramsey theory. This says that as chaotic as you can get, there is always some order that has to show up. This is what I am aiming at. What is needed is some way of quantifying the complexities of observed physical phenomena and show that although we focus on the structured phenomena that we see it is only a small part of all the phenomena that exists.

I look forward to reading your essay today.

All the best,

Noson




Francis Duane Moore wrote on Feb. 22, 2017 @ 20:33 GMT
Hello Noson, Very nice representation of symmetry structure subsets. If you are interested In the upper and lower limit numbers of a quantum field with subsets described by plane immersion,read my essay "Proton Three Plane Immersion Connection theory" Thanks francis Duane Moore

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Wilhelmus de Wilde wrote on Feb. 23, 2017 @ 16:17 GMT
Dear Professot Yanovsky

Thank you for a very clear explanation of your view points. You are finishing with:

qoute

If the structure that we see is only an illusion, then why do we see this illusion? Instead of looking at the laws of nature that are formulated by scientists, we have to look at scientists and the way they pick out (subsets of phenomena and their concomitant) laws of nature.

unquote

In my essay I called "Illusion" EMERGENT PHENOMENON and I tried to explain my perception on the question you are proposing. It is quite different of course, but the totality of perceptions gives us all the colours of the rainbow.

You can link to my essay here and I hope to hear your opinion :

The Purpose of Life[link]

best regards

Wilhelmus de Wilde

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Joe Fisher wrote on Feb. 23, 2017 @ 16:59 GMT
Dear Professor Yanofsky,

Please excuse me for I have no intention of disparaging in any way any part of your essay.

I merely wish to point out that “Everything should be made as simple as possible, but not simpler. Albert Einstein (1879 - 1955) Physicist & Nobel Laureate.”

Only nature could produce a reality so simple, a single cell amoeba could deal with it.

The real Universe must consist only of one unified visible infinite physical surface occurring in one infinite dimension, that am always illuminated by infinite non-surface light.

A more detailed explanation of natural reality can be found in my essay, SCORE ONE FOR SIMPLICITY. I do hope that you will read my essay and perhaps comment on its merit.

Joe Fisher, Realist

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Author Noson S. Yanofsky replied on Feb. 26, 2017 @ 10:23 GMT
Dear Joe,

What if Einstein was wrong and the universe is not simple?

Also, I am not a surface. "If you prick us, do we not bleed?"

I will look at your essay.

All the best,

Noson




Satyavarapu Naga Parameswara Gupta wrote on Feb. 24, 2017 @ 12:18 GMT
Dear Prof Yanofsky,

Good essay on Structures of the mathematics and number systems required for explaining this Universe or Multiverse…

Your observations like…

1. “Since we have no contact with possible other universes, the question of the existence of the multiverse is essentially metaphysics.” And “Rather than saying that the universe is very structured, say that...

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Author Noson S. Yanofsky replied on Mar. 3, 2017 @ 15:15 GMT
Thank you for looking at my essay. Thank you for the summary of the best lines. I will look at your paper.

All the best,

Noson




Jeff Yee wrote on Feb. 24, 2017 @ 22:35 GMT
Dr. Yanofsky,

Your essay is on point with topic and you've brilliantly summarized the link between physics and mathematics, with relevant examples from history. Another example would have been Newton creating calculus for his works.

If you haven't seen Gary Simpon’s essay, he is another fan of quaternions. Thought you might have an interest in it. Or, you may have an interest in our essay too: (The Relation of Particles Numbers to Atomic Numbers). It's not as similar to yours, but my co-authors and I would certainly appreciate your feedback.

Regards,

Jeff

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Author Noson S. Yanofsky replied on Mar. 3, 2017 @ 15:16 GMT
Hi,

Thank you for the kind words. I will look at those other essays.

All the best,

Noson




David Brown wrote on Feb. 26, 2017 @ 16:57 GMT
"Since we have no contact with possible other universes, the question of the existence of the multiverse is essentially metaphysics." The preceding statement is an interesting hypothesis which might, or might not, be true. Does string theory with the finite nature hypothesis imply MOND and no supersymmetry?

Consider 3 conjectures: (1) Milgrom is the Kepler of contemporary cosmology, and the empirical validity of Milgrom’s MOdified Newtonian Dynamics (MOND) requires a modification of Einstein’s field equations. (2) The Koide formula suggests that there might be a modification of Einstein’s field equations. (3) Lestone’s heuristic string theory suggests that there might be a modification of Einstein’s field equations. Are (2) and (3) sure bets? No. Is (1) a sure bet? I say yes. I suggest that there might be 3 possible modifications of Einstein’s field equations. Consider Einstein’s field equations: R(mu,nu) + (-1/2) * g(mu,nu) * R = - κ * T(mu,nu) - Λ * g(mu,nu) — what might be wrong? Consider the possible correction R(mu,nu) + (-1/2 + dark-matter-compensation-constant) * g(mu,nu) * R * (1 - (R(min) / R)^2)^(1/2) = - κ * (T(mu,nu) / equivalence-principle-failure-factor) - Λ * g(mu,nu), where equivalence-principle-failure-factor = (1 - (T(mu,nu)/T(max))^2)^(1/2) — if dark-matter-compensation-constant = 0, R(min) = 0, and T(max) = +∞ then Einstein’s field equations are recovered. Can gravitons escape from the boundary of the multiverse into the interior of the multiverse? Does Lestone's theory of virtual cross sections suggest a theory of the multiverse in which virtual energy is shared among many different universes and is indirectly measured in every alternate universe in the multiverse?

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Alexander M. Ilyanok wrote on Feb. 27, 2017 @ 14:50 GMT
Dear Professor Noson Yanofsky

You essay is very interesting. You clearly see the problem in modern physics. I also think on the problem “where is the boundary between science and non-science?” If we consider that it is the metaphysics shape public opinion through the media it is a real danger that an adequate conception of science, its methods and ways of existence in the public mind...

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Eckard Blumschein wrote on Feb. 27, 2017 @ 19:00 GMT
Dear Noson Yanowsky,

I am looking for someone with whom I may largely agree on some rather uncommon views while I nonetheless intend to defend my criticism of seemingly mandatory tenets.

Someone who rated my essay 1 did not reveal his reason. I guess he judged me a moron because I am arguing against symmetry as a pillar of reality. You correctly explained symmetry as invariance against shift, rotation, and so on. While I am not familiar with S. Lee I vaguely recall the notion continuous symmetry.

To me, perfect symmetry is rarely a property of nature. I see it rather indicating an artificial mathematical ideal. Don't get me wrong, I don't question the essence of your essay. We are in agreement on that reality needs a sieve. I merely distinguish between what I defined to be reality and what the sieve has been abstracted from it. The symmetry you have in mind belongs to the level of abstracted laws of nature. Nature is not invariant against shift or reversal of time. The invariance is artificial.

I cannot hide that my criterion non-arbitrariness has unwelcome consequences.

Respectfully,

Eckard Blumschein

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George Kirakosyan wrote on Feb. 28, 2017 @ 08:08 GMT
Dear Noson,

I have read your work with big interest as I find some judgments which has excited also my mind with time. Particularly, the matter concerns to your assertion on a priority of representation the calculus with complex numbers as more capable - powerful tool than the ordinary numerical (which may be represented as the trivial case of the first). I am fully agree with you. I can say even that specialists have used complex representations in many important areas that mainly are joined, especially, with the harmonical (and non harmonical) oscillations. But, one amazing thing may be derived from this (from your assertion). It is the formal possibility to interpretation the quantum relations as the derivative from harmonical movement (i.e. from causal relations).

So, I see main merit of your formulation in what I am saying. Moreover, I try even to realize this opportunity in my works that I hope may serve to your attention (see in refs). So, I can only welcome your essay!

I hope to see some your comment on this in my page

Best wishes

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Author Noson S. Yanofsky replied on Mar. 3, 2017 @ 15:19 GMT
Hi,

Thank you.

I will look at your paper.

All the best,

Noson




Gary D. Simpson wrote on Mar. 4, 2017 @ 01:14 GMT
Noson,

This is a very good explanation of the relationships between the Division Algebras ... well done.

The observation that scientists act as sieves is also very appropriate. There is an old saying ... "If you are a carpenter then every problem is a nail". Essentially, people use the tools that they know how to use on everything ... even if it is not the correct tool.

I will offer one small criticism though ... truly ground breaking science is not simply sifting through data and finding order or symmetry. The ground breaking stuff predicts what the order and symmetry will be. That was the case when Paul Dirac predicted the existence of anti-matter as a consequence of his solution to the relativistic wave equation.

Best Regards and Good Luck,

Gary Simpson

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Author Noson S. Yanofsky replied on Mar. 5, 2017 @ 05:22 GMT
Dear Gary,

Thank you for taking an interest in my paper.

As to your example about predicting symmetry: many people make such predictions. The ones that are true are recorded. The ones that fail are not recorded. Dirac was one of the best sieves around. : )

All the best,

Noson




Stefan Weckbach wrote on Mar. 5, 2017 @ 07:44 GMT
Dear Noson,

i now read your essay in detail. It is written in clear language, simple to understand and the lines of reasoning can be traced very easily. Good work.

You contrast order with disorder, structure with chaos. You seem to have a rather pessimistic view on things like goals and intentions. But nonetheless, you argue your case very well and stringently. Let me annotate some...

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Author Noson S. Yanofsky replied on Mar. 26, 2017 @ 23:09 GMT
Thank you for the long post. I agree with most of what you say. But I am not a nihilist... : )

I commented on your nice essay.

All the best,

Noson




Ines Samengo wrote on Mar. 11, 2017 @ 20:57 GMT
Hi, Noson, thanks for the good read, I specially appreciated the analogy with mathematics, which was original and (at least for me) instructive. I share also the view that "intention is in the eye of the beholder". You have focused in the role of symmetry, I chose to focus in predictability: humans design their seives in order to be able to predict the future. Regarding your question "What is it about human beings that renders us so good at being sieves?", I believe there are good evolutionary arguments to become good seives, which I mention briefly in my essay. Given the similiarity of our approaches, I would appreciate your comments - if you have any.

Thanks again!

inés.

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Willy K wrote on Mar. 14, 2017 @ 05:57 GMT
Dear Yanofsky

A great introduction into the fascinating land of quaternions and octonions. I honestly had no idea that such mathematics existed and that they were promising candidates for future scientific developments. Having read your essay, I am now convinced that they have a role to play in future discoveries. The analogies that you pointed out from the past development in physics are just too powerful to be ignored. You may want to check out the essays of Dickau and van Leunen. They areboth talking in terms of the number system that you are advocating. All the best!

Warm Regards, Willy

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Stefan Keppeler wrote on Mar. 18, 2017 @ 21:46 GMT
Dear Noson, I like how you contrast selecting subsets with taking quotients. I rather focused on taking quotients in my contribution but I have to admit that selecting subsets may be equally important when discussing emergent phenomena. Cheers, Stefan

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Jonathan J. Dickau wrote on Mar. 21, 2017 @ 04:49 GMT
Greetings Noson,

Your essay complements mine well, in terms of telling the other side of the story I tell. I once wrote about the value of the octonions, and in the same paper said I thought the sedenions were unlikely to have uses in Physics. And then I learned geometrically the sedenions are truly aimless like a blank slate, having no preferred direction, but heir decompositions via fibration yields only the C, H, and O algebras. So they give us only the set of algebras useful to Physics.

I must find fault in your chosen sieve criterion, after more than 30 years of research into the possible applications for Physics of the Mandelbrot Set, which is maximally asymmetric. I had a few phone conversations with Ben Mandelbrot, and published a brief letter in the 80s, before setting it aside, but the theory of gravitation I presented last year at GR21 is an outgrowth of that work. Ergo; I have serious doubts about the hypothesis that symmetry is the feature that characterizes genuine Physics.

I will send a PDF of what I presented at GR21 by e-mail, if you like. But I had to grapple for many years with the subject of asymmetry in Physics, as a result of my finding parallels to Cosmology in M, or rather its family of related figures, years ago. My algorithms reveal the trends in iteration, where coloring in monotonically diminishing iterands shows basins of attraction near the Misiurewicz points.

Theories of entropic or emergent gravitation, like those of Jacobson, Verlinde, and Padmanabhan, are well modeled by M, but Mandelbrot gravitation most closely resembles DGP gravity, where the 5-d black hole into 4-d spacetime idea of Pourhasan, Afshordi, and Mann is exactly modeled at (-0.75, 0i, in M, when it is embedded in the octonions. This spot is also a precise replication of Cartan's rolling-ball model of G2 - which is what creates the bubble we inhabit- so symmetry does emerge victorious in the end.

More later,

Jonathan

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Jonathan J. Dickau replied on Mar. 21, 2017 @ 05:00 GMT
By the way..

Seeing the value of this work, and especially seeing it is ranked well below that value, I gave it an honest rating of 8 out of 10, which should boost your score a bit. I am discouraged to be in the 90th %-ile myself, and be highly regarded, and yet still have such a low score (below the median of 5.5). It is even more tragic when an essay like yours gets pushed down in the pack so far where it can easily be lost.

Good luck. I may want to continue this conversation further.

All the Best,

Jonathan

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Jonathan J. Dickau replied on Mar. 21, 2017 @ 05:21 GMT
I wanted to comment further..

What the Mandelbrot Set seems to teach us is that Physics is about how exact local symmetries are bounded by global asymmetry. So this is my proposal for a more realistic sieve condition. For the record; the Mandelbrot Set admits the Multiverse hypothesis but denies the possibility that the range is endless, and instead spells out specific spectral ranges where bubble universes can form.

All the Best,

Jonathan

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Jonathan J. Dickau replied on Mar. 21, 2017 @ 14:35 GMT
I also wanted to thank you..

Your bottom-up explanation and discussion of the octonions was especially lucid, and I will probably refer other contestants to your essay for its value in clarifying what I leave out. I think this contest is a learning experience for many of us, and is especially valuable for seeing the ways different ideas fit together or relate, to give us a better perspective on the whole truth of the matter we are examining.

All the Best,

Jonathan

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Alan M. Kadin wrote on Mar. 21, 2017 @ 12:45 GMT
Dear Prof. Yanofsky,

Your very interesting essay asks two important questions: Why are there structures, and why do we see structures?

I think that the answer to both of these questions lies in the biological concept of evolutionary adaptation. Particularly on a macro scale, only ordered structures can be maintained. Secondly, our tendency to see structure and agency all around us is itself a successful adaption to perceiving and acting in the real world.

I address the issue of adaptation in my own essay, “No Ghost in the Machine”. I argue that recognition of self, other agents, and a causal narrative are built into specific evolved brain structures, based on neural networks, which create a sense of consciousness as part of a dynamic model of the environment. The reason that this is such a difficult problem is that we are being misled by the subjective perceptions of our own minds.

Alan Kadin

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Member Rick Searle wrote on Mar. 27, 2017 @ 01:04 GMT
Hello Noson,

I greatly enjoyed your essay. I think it actually would have been perfect for earlier FQXi contest "Trick or Truth" about the relationship between mathematics and the laws of physics. What I am less sure of is how you're addressing the question of the current contest which is the emergence of goals and intentions from mathematical laws.

What is your view?

Thanks,

Rick Searle

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Author Noson S. Yanofsky replied on Mar. 27, 2017 @ 01:11 GMT
Hi,

The two questions are related.

I did post in Trick or Truth essay contest and won a fourth prize.

Here it is: http://fqxi.org/data/essay-contest-files/Yanofsky_Why_Mathem
atics_Wo_1.pdf

Please comment.

All the best,

Noson




George Kirakosyan wrote on Mar. 27, 2017 @ 04:47 GMT
Thank you dear professor, for answering my post and favorable words on my work. This important for me as a opinion of one deeply thinker specialist. Unfortunately our approach on the role and significance of math are some different from opinions of many important bosses in present science. However, we can thinking as we see it correct.

Maybe I have not enough level to say this, but I think your clear approach to a relation between facts with math may induce a lot of perspectives, therefore I am going to rate your work!

Best regards

George K.

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Anonymous replied on Mar. 27, 2017 @ 22:49 GMT
Dear George,

Thank you for the nice rating.

All the best,

Noson

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Conrad Dale Johnson wrote on Mar. 27, 2017 @ 13:59 GMT
Dear Noson,

I can’t agree with your argument quite as you put it, but I think you’re on the right track. I like the premise “that the universe is chaotic and lacks structure,” and that something “acts like a sieve” to pull out only the very small subset of phenomena we actually observe. But as you note, it hardly seems reasonable to make scientists the primary agency of the...

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Author Noson S. Yanofsky replied on Apr. 4, 2017 @ 13:52 GMT
Dear Conrad,

Thank you for the kind words.

I do not think we are in a disagreement. I like what you wrote.

All the best,

Noson




James Lee Hoover wrote on Mar. 27, 2017 @ 17:28 GMT
Noson,

Things that need to be said: Rather than looking at the universe, we should look at the way we look at the universe.

In my essay I speculate about discovering dark matter in a dynamic galactic network of complex actions and interactions of normal matter with the various forces -- gravitational, EM, weak and strong interacting with orbits around SMBH. I propose that researchers wiggle free of labs and lab assumptions and static models.

As you suggest, static models are based on "static mathematical functions." and "phenomena with certain symmetry."

Your essay is instructive.

Jim Hoover

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Edwin Eugene Klingman wrote on Mar. 27, 2017 @ 21:33 GMT
Dear Noson Yanofsky,

I enjoyed your essay, and found fascinating the idea of thinking of octonions as fundamental and all other number systems as subsets of the octonions. I very much like your statement: "All the axioms that one wants satisfied are found "sitting inside" the octonions."

You rightly focus on symmetry in physics. While much of particle physics is based on...

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Author Noson S. Yanofsky replied on Apr. 4, 2017 @ 13:56 GMT
Dear Edwin,

Thank you for the kind words. It would indeed be nice to formulate a program to come up with laws of physics. I look forward to reading your essay.

All the best,

Noson




Natesh Ganesh wrote on Mar. 27, 2017 @ 22:53 GMT
Professor Yanofsky,

That was an extremely interesting essay to read. The idea of us being sieves I felt was very insightful. I also enjoyed the journey you took us in a simple manner through the different hierarchies of the number system (I definitely have to look into quaternions in more detail), as well as drawing the corresponding parallels over the course of research in physics.

"One possible conclusion would be that if we look at the universe in

totality and not bracket any subset of phenomena, the mathematics we would need would have no axioms at all"--- I would be very pleasantly surprised if that truly happens to be the case.

While I agree that your essay provides an interesting new perspective, I personally am interested in why we are sieves in the first place? Can we only be sieves in this universe? I would be interested in your thoughts on my submission "Information is Physical", where I talk about the use of some thermodynamic constraints to explain the emergence of learning and intelligence in physical systems. Thanks.

Natesh

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Peter Jackson wrote on Apr. 1, 2017 @ 17:17 GMT
Dear Noson,

That was a somewhat deja-vu experience. A brilliant essay, and great shame we seemed not to read each others last year. We have parallels, and mine was scored highest & yours won a prize. I hope you'll do so this year as I'd value your response to what may be a big advancement in understanding, leading to a real physical sequence of interactions 'classically' reproducing QM's predictions (and rather more besides). Last year I analysed 'brackets' in terms of quantum or 'propositional dynamic' logic (PDL) which hierarchical architecture I employ this year, but describing real physical phenomena rather than just the abstract descriptions of them.

I agree with just about all you wrote. OK it may be a touch off topic and incomplete, but all essays are, and it's fundamental insight surpasses almost all. I certainly agree we; "do not take into account all phenomena", and indeed suggest we miss much, including consistent application of things which may reveal certain more complex or fundamental symmetries.

I'm not a mathematician (maybe why I missed yours last year!), so you did loose me a little for a while (though I knew what you meant) but I've consciously refined, over decades, a more physical (and geometrically dynamic) way of looking at the universe.

At the end you suggest; the universe in totality is devoid of structure and needs no axioms. There are just plain sets without structure. Have you thought a hierachy may have a larger 'elephant in the room' structure? or that your concept may be very close to Einsteins final 1953 inertial systems as; "spaces in motion within spaces", with only the same local rules, but 'transformable' (physically!) in a fundamental Lorentzian way?

Very best

Peter

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Colin Walker wrote on Apr. 4, 2017 @ 00:00 GMT
Dear Noson,

I struggled a bit with your essay at first, then came up with examples.

Consider a differential equation commonly used to model mechanical or electrical resonance. The model takes as input random noise and amplifies a narrow band of frequencies. If the bandwidth is narrow enough, the output is practically indistinguishable from a pure sine wave. We notice the (nearly) predictable sine wave, but it is the noise doing the actual physical work. To describe a realization of the process, the noise is an essential part.

Quantum mechanics seems to have a noisy aspect. For example, the position of the next photon (or particle) to show up in a diffraction pattern is unpredictable. As your essay proposes, the necessity to account exactly for unpredictable events leads to the conclusion that, when used to describe the physical universe, mathematics becomes a collection of sets without structure.

On the other hand, it is the differential equation which models resonance that seems to belong in "Plato’s little treasure chest of exact ideals". Because the noise itself can be idealized as having a uniform amplitude spectrum, it belongs as an archetype even if it is not, strictly speaking, exact. Or perhaps there is another chest with inexact ideals.

I think you would be interested in my essay, "Seeking the Analytic Quaternion". Shared symmetry plays a major role in guiding the selection of quaternion derivatives involved in determining the analyticity of a function of a quaternion variable. I find two varieties of analytic functions, and two anti-analytic. My speculation is that these are related to complementarity in quantum mechanics.

Best regards,

Colin

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peter wamai wanjohi wrote on Apr. 4, 2017 @ 13:36 GMT
Dear Professor,

Your essay is very educative to say the least. However, as a follow-up to your logic,the geometric increase in mathematical ( dimensional) structure and the decreasing axiomatic scaffolding can only reach zero axiom ,and therefore lack structure,aims and intentions in an infinite universe. Am i right?

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Author Noson S. Yanofsky replied on Apr. 4, 2017 @ 13:49 GMT
Dear Peter,

Thank you for the kind words.

I do not see the reason why a finite set demands structure. Maybe the universe is finite.

All the best,

Noson




George Gantz wrote on Apr. 4, 2017 @ 18:04 GMT
Noson -

Thanks for an interesting essay. It's a highly challenging notion to conceptualize mathematics without axioms and a physics of perfect, unbroken symmetry. The unity of the indistinguishable void - timeless, motionless, and yet recursively related to the infinity of all potential and all time and place. Great stuff! I put some thought into these question in my last FQXi essay The Hole at The Center of Creation.

I am left wth a question - how does it all get started? I know first causes are a problematic issue - the responses ranging between nothing and God, but I do think it is relevant to the contest. If the beginning is pure symmetry and no distinctions - what gets the ball rolling? My sense is there is of necessity some form of intentionality and direction (whether from divine agency or otherwise).

Sincere Regards - George Gantz (The How and The Why of Emergence and Intention).

I tried to do that in my last FQXi essay

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Dizhechko Boris Semyonovich wrote on Apr. 6, 2017 @ 14:42 GMT
Dear Noson S. Yanofsky,

Excellent informative essays about the temporal and spatial symmetry, about complex numbers, quaternions, etc., written in good academic style. It would be nice if you would consider tensors, which Einstein coded their theories from prying eyes.

I inform all the participants that use the online translator, therefore, my essay is written badly. I participate in the contest to familiarize English-speaking scientists with New Cartesian Physic, the basis of which the principle of identity of space and matter. Combining space and matter into a single essence, the New Cartesian Physic is able to integrate modern physics into a single theory.

Don't let the New Cartesian Physic disappear! Do not ask for himself, but for Descartes.

New Cartesian Physic has great potential in understanding the world. To show potential in this essay I risked give "The way of The materialist explanation of the paranormal and the supernatural" - Is the name of my essay.

Visit my essay and you will find something in it about New Cartesian Physic. After you give a post in my topic, I shall do the same in your theme.

Sincerely,

Dizhechko Boris

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Peter Jackson wrote on Apr. 6, 2017 @ 19:46 GMT
Noson,

You didn't respond to my post above and haven't read my essay. Is there a reason or just pressure of time. I'd hoped we may discuss, including some consistencies, also with my last years (top scored) offering perhaps helping shed some light on; "This idea that we only see structure because we are focusing on a subset of phenomena is novel and hard to wrap one’s head around"

Very best

Peter

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Author Noson S. Yanofsky replied on Apr. 6, 2017 @ 20:26 GMT
Dear Peter,

I am sorry. There is no disrespect. Just time is a precious commodity around here. I will try to look at it and comment. Feel free to send me a personal email.

Again, I sincerely apologize.

All the best,

Noson




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