GENESIS OF A PYTHAGOREAN UNIVERSE by Alexey and Lev Burov

I just thought of something that may cause confusion about voting, if it's based on looking at comment times (may or may not be relevant to the above worries in particular.) The comment times are shown in GMT, which someone looking may forget to take into account (like, when trying to compare favorable comment with rating change.) Just passing it on FWIW. Actually, I want to see some kind of post-verification so voters can be more sure, and that's something political voters need more of too.

Dear Alexey and Lev,

I found great depth in your essay and good argumentation. It's a very interesting idea that the source of order in the universe cannot be limited to the fine tuning of the constants but must be extended to a "right choice of the fundamental principles of physical laws". Another striking point that you make is the distinction between the types of observers and the theoretizability of the world. My main take away from your essay is the uniqueness of the laws. Another very interesting exercise you make is the deduction of the consequences of noise in a universe with semi-stable laws of nature.

Cheers,

Cristi

Dear Alexey and Lev,

An absolutely brilliant essay. I agree with you in many points such as your opinion on Tegmark's hypothesis. I especially liked the section "The condition of Elegance". Your essay deserves the highest rating. I would be glad to take your opinion in my essay.

Best regards and good luck in the contest.

Mohammed

Dear Alexey and Lev,

Your essay presents a very intriguing philosophical argument backed by empirical considerations and I appreciate that. I like how you went deeper into the analysis of the anthropic principle and ascertained tests for MUH (Mathematical Universe Hypothesis) using the fine tuning and accuracy of fundamental constants. My essay, though focusing on other topics, also discusses checks on MUH in light self-referential considerations. Your narrative is very well written, and I also appreciated the historical context. I particularly liked the balance you formulated in developing the Cosmic Anthropic Principle "to allow life and consciousness,... To satisfy both conditions, the laws must be just right. The laws of nature are fine-tuned not only with respect to the anthropic principle but to be discoverable as well." I also discuss anthropic ideas relating causality and consciousness. I've seen different perspectives on these issues, and your essay is an excellent contribution to this very interesting forum topic. I rate it very highly.

Please take a moment to read and rate my essay as well. Although are focuses may be different, I think we both overlap in ways that are supportive.

Best regards,

Steve Sax

Dear Burovs,

While I don't feel obliged to comment on mysticism, I would just like to ask you whether the following utterance is correct:

"all great theories, from Copernicus, Kepler and Newton to Einstein and Dirac happened as guesses on the grounds of some fundamentally simple ideas like symmetry, conserva:on, or equivalence."

I am rather aware of the Church having caused Copernicus to revise the calendar which led him to reinvent an ancient observation, etc.

The Pythagorean guess "anything is number" has proven wrong by the discovery of incommensurables.

For such reasons, I would like to defend the role of observation and reasoning instead of putting unwarranted questions that didn't prove useful. Engineers have first to look for a relevant problem and then to describe the elements of how their invention may solve it. What problem do those like you intend solving, and is there any idea how to succeed?

Of course, Otto de Guericke dealt speculatively with the problem of what is holding the world together. Steam engine and electricity arose from the experiments that he created.

Can you tell me likewise convincing results from the belief in purpose and soul?

Darwin's approach didn't rest on religious belief in a mystic purpose.

While the consistency of theories in physics can be checked to some extent by experiments, guesses in mathematics may be confirmed if they are logically flawless and useful. I consider set theory failing both.

Sincerely,

Eckard Blumschein

Dear Eckard,

Of course we must accept what observation shows us, but meanwhile: we need a guiding intuition about what to look for, how to look, what to expect etc. These intuitions might be wrong and needing of later revision, but there's nothing wrong with trying them out.

Purpose and soul: "Purpose" is hard to get a handle on, but thinking the universe is geared to the development and usability of intelligence, motivates even thinking it is lawful in the first place, etc. And soul? It's IMHO not not a religious concept. If there is something more "whole" about a person than momentary fluctuations and passing on of memories and typical patterns of though, then we can more easily justify the basic rational philosophy of choices based on "your self" still being there in the future. My brain changes around, my mental contents do too, what then persists into successive years, to validate ordinary economic-type utilitarian reasoning? We take that for granted, but study of philosophical paradoxes about Star-Trek style duplications (what if the original is not destroyed, who is "the real you" etc?) shows that we need a deeper concept of self than just sheer continuity of process in a body.

I am not saying that process violates physical law or should be taken as it is revealed in religious claims (and they conflict yet claim to be absolutes to be taken for granted - neither science nor rational philosophies can work like that) - but nature then, has to make some kind of more-than-sum-of-parts out of us, for our future planning to be intelligible. And yes, quantum issues of wholeness and interrelation could well play a role in that (especially after the find that it does play a role in photosynthesis and even the sense of smell.)

As I said I appreciate the general ideas of your essay, as a logical argument against some widespread conceptions, but still I have remarks. That is, what does the landscape of logically possible laws of physics, look like. Of course as you explained we can abstractly consider any ugly arbitrary law as a "possible law", and in this vast chaotic landscape of "possible laws", find many possibilities of biological evolution similar to what happened on Earth, with the difference that the fundamental laws would not be intelligible. However it seems to me (and maybe I read from other sources) that, among all "possible laws" able of biological evolution, our particular laws (quantum field theory, the standard model) differ from the rest of this landscape not just by their intelligibility, but also in other ways : something like, apart from modifying the values of physical constants, they are not so much modifiable in the small details of their consequences without destroying all their mathematical coherence.

Namely, while we can conceive of possible variants (such as was hypothesized as alternatives to the Higgs boson, some supersymmetric models now refuted, etc), they are not so many (if we want to restrict the study to simple ones, thought the motivation for this restriction may be questioned, e.g. for its links to intelligibility). For example, there are not so many conceivable kinds of particles that are mathematically coherent in quantum field theory. The Higgs boson was predicted because there are not many logical possibilities of what may give a mass to particles. We may see it as a beauty of mathematics (a restriction on the number of possibilities, and some of the most elegant ones are actually realized).

More importantly, there are not many logically conceivable alternatives to quantum physics that behave in a roughly similar manner. It is even doubtful whether there is such a logical possibility at all. An important search for such things is the spontaneous collapse theories, however usual attempts of such theories violate both relativistic invariance and the conservation laws, even if very slightly. But a violation of conservation laws, even a very slight one, is something that (when formulated in proper terms) General Relativity dismisses as absolutely impossible. Thus, when trying to conceive logical alternatives that would also lead to a biological evolution, they may have to either be very different from how things go in our universe (very different chemistry, etc), or be of the form "These laws do not always apply, they are sometimes broken", but still in ways that do not result in breaking the whole Universe apart (as "breaking conservation laws" would logically imply), that would be... very odd kinds of laws.

But what I see remarkable about the trouble in trying to locate our laws of physics in a landscape of logical possibilities, is not only the lack of phenomenologically similar possibilities (beyond variations of the values of physical constants) but also that it is questionable whether the laws we found of our universe (quantum physics) may meaningfully be considered as a logical possibility at all. Because if we strictly look at them as a logical possibility, then it logically drives us to the Many-worlds interpretation. But, how can a many-worlds universe be considered as a real universe at all ? It does not look like one ; it is questionable (and a metaphysical question) whether we can make sense of "probabilities" in it, unlike the effective role of probabilities (the Born's rule) in our physical reality.

And, in connection with what I explained in my essay, I see all this as not a trouble, but as the simple consequence of the fact that the whole discussion, as followed by Tedmark and other scientific circles, is usually expressed in the wrong terms. Because if the question is about the possibilities of real universes, then it has to involve an ingredient of "reality" beyond mathematical existence, i.e. beyond pure logic, and this ingredient is consciousness. Since, due to its non-mathematical nature, this ingredient cannot be located in any mathematical landscape of possibilities, the very expression of "logical possibility" is not applicable to it.

For more details, see my notes on spontaneous collapse and the Many-worlds.

On your reply to 1. I agree that your argument on the infinite variability of the laws seems perfectly logical and even necessary, but only from the viewpoint of those who reason like science philosophers (who discuss and understand science like children understand war by playing with plastic soldiers) developing their naive expectations about the panorama of logically conceivable laws of physics, having some notions of classical physics of course (being introduced to the seemingly arbitrary formulas expressing macroscopic laws of classical physics), but without deep enough understanding of the known laws of modern physics (General Relativity, quantum field theory, gauge theories). For example if the laws of physics looked like an arbitrary computer program (as the laws of biology actually look like, and as is the ordinary conceptual framework for the naturalist conception of the development of consciousness as emerging from biological evolution) then of course there would be no logical difficulty in considering the possibility to modify this program by arbitrary modifications of the instructions, adding of terms to formulas, etc.

However I maintain that all these natural expectations fall down when trying to apply them to the specific laws that we found in modern physics. Namely, while (as I expressed in my essay) I do believe that the fundamental laws should be algorithmically expressible in a sense, it is however not an arbitrary algorithm that may receive arbitrary modifications, but a very remarkable one (for its way of defining probabilities, the dissociation of the time of its possible computations from physical time...) ; but I understand that this very statement itself seems absurd for those who don't actually know these laws, as this is a very incredible property of a law indeed, the property of being almost not modifiable in logically consistent manners. Therefore, I see no sense of arguing further that this property may hold in principle, but the meaningful question will instead be the following : how well do you actually understand General Relativity and the Standard Model of particle physics, so as to be entitled to make claims about what is logically conceivable around them ? Among essays, Aldo Filomeno is trying to argue on your side, but I think he overrates his points, and already what he could bring there as a panorama of possibilities does not look as vast as what you seem to assume. For example we can say there is an infinity of possible Lie groups to serve for gauge invariance, however only a finite number of them have dimension lower than any given finite number.

Now let us focus on a very specific point, to make the argument precise: General Relativity and the conservation laws. You wrote "all the fundamental principles are considered as variable (...) All of them are under question, and an attempt to answer by invoking conservation laws, symmetry, General Relativity, or some other specific principle would be a logical mistake, namely, circular logic. ". I'm sorry for you but this view is just wrong in the case of General Relativity and conservation laws: if defined properly, we can find that conservation laws are not an assumption but a theorem of curved geometry (in curved space-time), so that any violation of them is a logical impossibility. Your way to dismiss this idea, suggests to me that you are actually ignorant about General Relativity. Aren't you ?

And for another point that I already mentioned : the difficulty of finding a possible formula (law) of spontaneous collapse that respects the conservation of energy. If you think that it should be easy to invent "logically possible laws of physics" by arbitrarily making up formulas with additional correction terms so as to roughly behave similar to a given phenomenon, then you are welcome to provide your help to the community of physicists who try to conceive models of spontaneous collapse, by making up a candidate formula for spontaneous collapse that would be logically coherent, does not break any mathematical theorem such as the geometric theorem of conservation I just mentioned about curved space-time so as to not bring plain logical contradictions between quantum physics and general relativity as approximate descriptions of aspects of a common universe, and compatible with what is known. I think it will make you famous.