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Jonathan Dickau: on 3/21/17 at 14:35pm UTC, wrote I also wanted to thank you.. Your bottom-up explanation and discussion of...

Alan Kadin: on 3/21/17 at 12:45pm UTC, wrote Dear Prof. Yanofsky, Your very interesting essay asks two important...

Jonathan Dickau: on 3/21/17 at 5:21am UTC, wrote I wanted to comment further.. What the Mandelbrot Set seems to teach us is...

Jonathan Dickau: on 3/21/17 at 5:00am UTC, wrote By the way.. Seeing the value of this work, and especially seeing it is...

Jonathan Dickau: on 3/21/17 at 4:49am UTC, wrote Greetings Noson, Your essay complements mine well, in terms of telling the...

Stefan Keppeler: on 3/18/17 at 21:46pm UTC, wrote Dear Noson, I like how you contrast selecting subsets with taking...

Willy K: on 3/14/17 at 5:57am UTC, wrote Dear Yanofsky A great introduction into the fascinating land of...

Ines Samengo: on 3/11/17 at 20:57pm UTC, wrote Hi, Noson, thanks for the good read, I specially appreciated the analogy...


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March 23, 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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This essay's rating: Community = 4.8; Public = 2.0

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.

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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,


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:


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.


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,


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,


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.



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

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

All the best,


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.


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

Thank you.

I will look at your paper.

All the best,


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

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,


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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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!


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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,


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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,


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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,


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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,


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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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