Finding Structure in Science and Mathematics by Noson S. Yanofsky

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

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 the universe is chaotic and lacks structure. The reason why we see so much structure is that scientists act like a sieve and pull out only those phenomena that are predictable. They do not take into account all phenomena; rather, they select those phenomena they can deal with."

2. "science predicts predictable phenomena"

3. "Despite these failings of our explanation for the structure, we believe it is the best candidate for being the solution."

4. "in the middle of the 19th century, physicists started using complex numbers to discuss waves. In the 20th century, complex numbers became fundamental for the study of quantum mechanics."

5. "the octonions as fundamental and all the other number systems as just special subsets of octonions. The only number system that really exists is the octonions. To paraphrase Leopold Kronecker, "God made the octonions, all else is the work of man." The octonions contain every number that we will ever need"

6. "This is similar to what we are doing in physics. We do not look at all phenomena. Rather, we pick out those phenomena that satisfy the requirements of symmetry and predictability. In mathematics, we describe the subset with the axiom that describes it. In physics, we describe the selected subset of phenomena with a law of nature."

7. "As physics progresses and we become aware of more and more physical phenomena, larger and larger classes of mathematical structures are needed and we get them by looking at fewer and fewer axioms."

8. With the final concluding sentence... "Rather than looking at the universe, we should look at the way we look at the universe."

Are really excellent.

It leads to a question, while describing some portions of Universe, if some mathematical structure is used, later we find some undefined area or singularities.... We will be left with no alternative except to find those singularities, is it not? Or can we change the structure of mathematics to find a better solution...

Here in Dynamic universe model an attempt was made to find a singularity free tensor mathematics, which provides a solution to many of the present day Physics problems.

Many papers and books were published by the author on unsolved problems of present day Physics, for example 'Absolute Rest frame of reference is not necessary' (1994) , 'Multiple bending of light ray can create many images for one Galaxy: in our dynamic universe', About "SITA" simulations, 'Missing mass in Galaxy is NOT required', "New mathematics tensors without Differential and Integral equations", "Information, Reality and Relics of Cosmic Microwave Background", "Dynamic Universe Model explains the Discrepancies of Very-Long-Baseline Interferometry Observations.", in 2015 'Explaining Formation of Astronomical Jets Using Dynamic Universe Model, 'Explaining Pioneer anomaly', 'Explaining Near luminal velocities in Astronomical jets', 'Observation of super luminal neutrinos', 'Process of quenching in Galaxies due to formation of hole at the center of Galaxy, as its central densemass dries up', "Dynamic Universe Model Predicts the Trajectory of New Horizons Satellite Going to Pluto" etc., are some more papers from the Dynamic Universe model. Four Books also were published. Book1 shows Dynamic Universe Model is singularity free and body to collision free, Book 2, and Book 3 are explanation of equations of Dynamic Universe model. Book 4 deals about prediction and finding of Blue shifted Galaxies in the universe.

With axioms like... No Isotropy; No Homogeneity; No Space-time continuum; Non-uniform density of matter(Universe is lumpy); No singularities; No collisions between bodies; No Blackholes; No warm holes; No Bigbang; No repulsion between distant Galaxies; Non-empty Universe; No imaginary or negative time axis; No imaginary X, Y, Z axes; No differential and Integral Equations mathematically; No General Relativity and Model does not reduce to General Relativity on any condition; No Creation of matter like Bigbang or steady-state models; No many mini Bigbangs; No Missing Mass; No Dark matter; No Dark energy; No Bigbang generated CMB detected; No Multi-verses etc.

Dynamic Universe Model gave many results otherwise difficult to explain

Have a look at my essay on Dynamic Universe Model and I request your esteemed opinion...

Best wishes................

=snp. gupta

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

"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?

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 will be replaced by substitute of abnormal knowledge.

Today humanity is in deep crisis associated with the transition to a new techno-economic paradigm - the knowledge economy. It uses the knowledge to generate tangible and intangible values. This requires abandoning the biblical paradigm based on myths. This paradigm has lost its relevance for the management of large masses of people, as it is based on mythology and distortion of objective knowledge. For example, the relativistic world view does not contradict the Old Testament in which God created the world not from the finished material but created the matter itself. Therefore, all the experimental data that contradict the relativistic worldview are falsified or silenced. Today, the struggle for resources in the modern world of physics is reduced to competition of hypotheses and as a consequence to fight without rules on the basis of clericalism and postpositivism.

I am in more agreement with you, that the job of physics is to describe a function from the collection of observed physical phenomena to mathematical structure. The basis of any science is the experiment that is why the science was called natural philosophy. In mathematics the experiments are not used. It is based on axioms and theorems. So formally it should not be considered as science. Of course, the mathematics is very important for science as well as it allows you to see patterns and to predict new effects, i.e. it is a kind of glasses to the experimenter. So the question is - Are the glasses we choose proper?

So the "elegant" mathematical equations, which are attributed to some physical phenomena, often do not allow us to see the fallacy of the original physical models that are used in mathematical physics, and are essentially metaphysical.

More detailed information on the subject can be found in Galactic Internet and Femtotechnologies

Femtotechnologies Presentation

Quantum_Astronomy_Part_II

My best wishes

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

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

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

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 thoughts i had during the reading.

Firstly, if considering the contest's questions, i think one has to presuppose as an axiom that all that exists does all things the right way. If we drop that assumption, we end up at nihilism. So i presuppose that the universe and its possible causes and all the rest is a consistent whole.

Your take on mathematical number systems is fascinating, innovative and thought provoking to me. The progression in the dimensionalities of the mentioned number systems is clearly an expression of logic, it is a kind of algorithm and it has therefore structure. In contrast to this - as you annotated at the end of your essay - one may arrive with such a progression at a level of description of 'all there is' which seems to say that the universe, viewed objectively, is devoid of structure. The interesting question is (and i formulated similar questions at the essay page of Cristinel Stoica) how order and disorder, randomness and information are intertwined.

If the mentioned progression of the dimensionalities of number systems indeed leads to the conclusion that the universe is devoid of structure, this would pose serious questions. For example, does it make sense right from the start to extrapolate a mathematical algorithm like the one for building up ever higher dimensional number systems? Isn't this somewhat similar to Cantors cardinalities, building up ever higher infinities out of a simple algorithm? Surely, your progression should not be infinite but terminate at a certain level where no axioms are left. Although i am not a mathematician and certainly not an expert on octonions and so forth, i ask myself how can such a progression of number systems be able to drop one axiom after the other, until there are no axioms left? But taking it as given, what you arrive at is simply a tautology, namely a 'number system' (although without any axioms) saying that the universe and all the rest is just what it is (without specifying it further). Obviously this is plainly true, indeed the universe and all the rest is just what it is. One does not need a single axiom to conclude this!

The problem only arises when one wants to specify the whole thing due to a certain category. I assume it to be true that our universe has many phenomena which do not have goals and intentions. But this does neither imply that the universe's main characteristic must be termed as 'chaos', nor does it mean that the universe's existence and the many 'mindless' phenomena in it are senseless from a higher point of view. Maybe mindless phenomena serve a higher purpose; surely, this purpose then had to be determined via the construction and rules of the universe and also surely not by some physical mechanisms, but by an entity which has goals and intentions. I see no contradiction that randomness, chaos and disorder cannot support goals and intentions. This may be a hard to swallow statement, but i will explain it further.

As you know, a perfectly random sequence of 0's and 1's follows a certain mathematical law. The digits 0 and 1 should be evenly distributed over the whole pattern. Random in this case means that the occurrence of either of the two digits does not depend on the value of the preceding or following values of such digits. Every event should be totally independent of each other event. Have we catched 'chaos' and 'randomness' with this? In no way. We only catched the extreme case at one end of the continuum of order. 'Randomness' as a nihilistic ontological fact should have other features, i suspect. It should be not catched up with any mathematical description. For example, imagine that you are a kind of Boltzmann brain, but without all the physics needed for it. Just imagine you are aware of something. This something does not reveal any correlations. At one time you see a flash, then you see the flasch forming to a vague kind of bubbeling-up of some melted cheese-like thing, you see all sorts of visual impressions and they do not make any sense to you. 'Randomness' defined as this would be just like a nightmare.

Now, let us elevate the mathematical concept of randomness to perhaps meet what you intended to say in your essay's last paragraphs. Maybe the observed structure of our universe is a lucky fluke within a chain of random events (like the 0's and 1's, randomly encoding some kind of theory of everything). Would this be a convincing scenario to explain the order in our universe and its - assumed - dichotomy to the observed chaos in our universe? I would say no, because it does not answer where the randomness comes from, how and on what existencial features it operates on and why it can be mathematically explored to the point where it produces conscious beings which indeed then mathematically have explored it.

The whole point for me here is to say that behind the concepts of randomness and order, there must be a common fundamental origin of all of this. Alternatively one must conclude that reality is somewhat irrational. Because i am not the kind of Boltzmann brain described above, i conlude that behind the interplay between randomness and order, there is some deeper origin of all there is. As you envisioned with the progressions of number systems, mathematics seems to be able to transcend itself - in the sense that its very limits show us how the universe cannot be. It cannot be infinitely dividable, it cannot be overall deterministic and at the same time be overall consistent, it cannot be overall chaotic and nihilistic in a Boltzmann-brain sense and it cannot capture the whole of existence. All this cries out for an explanation that is metaphysical. It is no wonder that the progression of number systems tends to converge towards a non-axiomatic description of reality. Because mathematics cannot capture all there is due to the nature of it. Its nature is not overall compressible. But this does not mean that for explaining the nature of reality otherwise than with mathematics, one wouldn't need some axioms. My axioms are that there are realms beyond space and time from which our universe originated. It is limited in time, duration and space. At the outer borders (at the microscale) of this universe, quantum mechanics rules and spontaneous collapses occur. These collapses may not have an explanation in terms of physical causality, but i am convinced they have an explanation in terms of purpose and intention. For me, it is no problem to think of a creator that has the power to give some order to his creations to behave spontaneously (although here again, this spontanity is restricted by the rules of QM, also given by this creator). Surely, these considerations are all axioms, choosen by me, they do not arise necessarily from what i have written. But i see no alternatives between a creator and nihilism, the latter in the sense that reality is absurd and logics cannot conclude something logical from the fact that logics has its limits in deducing the ultimate layer of reality. But it surely can *induce* these layers on the basis that logics has realized its own deductive limits. Therefore i tend to say that logics, as an expression of a formal system, is as incomplete in the sense of Gödel's results as every other formal system subject to Gödels results. The main result for me is that the limits of deducability do not necessarily mean that the universe is absurd. It is open for the possibility being not so. This openness is installed even within the very structure of logics, since logics can discriminate between a possibility and a necessity.

I would be happy if you could write what you think about this all.

Best wishes

Stefan Weckbach

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.

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

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

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

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