GENESIS OF A PYTHAGOREAN UNIVERSE by Alexey and Lev Burov

Dear Alexey and Lev,

I think the three points which we are discussing here are related. I find particularly insightful your criticism of indifference or chaos as the ultimate ground for existence. The way you formulate the issue is helpful to me, and I tend to believe your opinions and arguments are correct. As you state, many contemporary writers maintain in one way or another that chaos is the ontological foundation. Until I read your discussion, I had not interpreted Tegmark's theory this way, but you are right about his position. More importantly, I think you are also right that the chaosogenesis or primal-indifference view contradicts current knowledge in physics. On this comments page for your essay, you include a link to some of your presentations at the Fermi Society of Philosophy. I have not studied that material yet, but I look forward to following your work there and perhaps in other writings and presentations also.

Sincerely,

Laurence Hitterdale

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

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.

As for the question whether the known laws constitute a logical possibility at all, there is for example in Tim Maudlin's interview (that I quoted in my review): "Properly speaking, there is no such thing as "quantum theory" (...) What is called "interpreting quantum theory" is really a matter of constructing clear and precise physical theories that return these same predictions, or nearly the same". So it is not as if there were many known logical possibilities that roughly look like what we observe; rather, it is doubtful whether there is such a logical possibility at all. At least we could not explicitly find anyone yet. What we have instead, quantum field theory, is some very successful almost-mathematical concepts that play in practice the role of a theory, but somehow aren't one in a strict logical sense. And it is remarkable that, even though quantum theory is only a non-theory and mathematically ill-defined, it is still very elegant mathematically, and probably much more mathematically elegant than anything that can be genuinely called a "logical possibility" behaving roughly the same.

So, your arguments do apply, not so well to anything near the laws of physics as they were actually found to be, if we can ever find such possibilities, but rather to the abstract framework of some range of "all logical possibilities" which naturalists usually assume as if our physical universe was inside this range, though it actually isn't. Namely, if a "range of possibilities" was found that admits a multitude of expressible mathematically coherent alternatives which behave roughly the same in practice, then in between these many expressible coherent alternatives there would also be some non-intelligible possibilities (such as obtained as the limit of a series of more and more complex versions). But the real problem which physicists face is not any excess of logically coherent candidates between which we have troubles to discern the right one, but the lack of any coherent nearby logical possibility at all.

I was rather puzzled at some time when I attended a seminar of philosophy of science, discussing the theoretical possibility of determinism, focusing the arguments not on any logical verification of what may be compatible with our effectively found laws (quantum physics), but, instead, on a certain "range of all possible laws" to wonder what kind of law, assumed to be expressed by some kinds of equations (such as differential equations), may turn out to be deterministic or not. For example, he pointed out that some differential equations may have non-deterministic consequences depending on their regularity class. Somehow I understand the necessity to adopt such a line of research, precisely because the found laws of quantum physics do not look like laws of physics at all, so that it is hard to reason on this seemingly incoherent basis. Like the story of the man looking for his keys below the lamp not because he lost them there but because he sees there more clearly... However, while such kinds of reasoning may superficially look rational and open-minded to a wide range of possibilities, if this "wide range of all possibilities" cannot include any possibility anywhere near what was actually found to be the case, then the relevance of the whole discussion about such a range remains dubious.

I have neither circular logic nor wrong attitude, I just bring some precise and rigorous remarks to the topic, however, since you are deciding to dismiss the remarks without any proper reply, and calling something "circular logic" when I rigorously explain to you why it is not so, thus refusing any progress to the understanding of the topic, then you are the one having the wrong attitude, so that you are obliging me to remove my support to you.