Imagination and the Unreasonable Effectiveness of Mathematics by Armin Nikkhah Shirazi

Dear Vladimir,

Thank you for your comments. It is too bad that you got lost after the word "modal", if anything I would have expected that as an artist you might actually appreciate it because there is a neat analogy to color and painting:

Working within classical logic is like being able to paint only using black and white as available colors. But because the only limit on finding interpretations for modalities is one's imagination, working within modal logic is like painting using many more different colors. The fact that modalities capture subtle nuances in meaning is like having access to a rich palette of colors to paint subtle nuances that you see in your mind's eye.

"I also empathized with your words "pseudo-nonlocality" because in BU angular momentum is transmitted node to ether node as in a slippery gear train and nothing is lost or hidden"

Well, the "pseudo" in pseudo-nonlocality in my theory comes out of something that most opponents of non-locality would probably not find palatable, namely a radical non-realism according to which there is "nothing" (i.e. no spacetime object) in between quantum measurements. This ensures that there are no "beables" in Bell's sense (The absence of a "beable" is what marks the ontological significance of the incomplete spacetime vector), and so there is nothing that could receive a non-local influence. In my view, Bell's arguments for non-locality are in and of themselves correct, but they simply fail to apply because they require "beables" in order to do so.

"Did you read Klingman's essay debunking Bell's theorem in this contest?"

Yes, I read his essay and found that he did no such thing. What he did is to point out the possibility that a particular experiment (the SG experiment) that could be used to test (really, I should say check its applicability to) Bell's theorem might not be appropriately modeled by Bell's theorem. While I doubt that he is correct I don't think it is impossible, but even if he is right then this has nothing to do with the correctness of Bell's theorem, because the theorem stands independently of any experiment.

Bell's theorem is a mathematical theorem, and trying to debunk it is like trying to debunk the theorem that the product of the number 1 and the number -1 is something other than -1. The only way this could be done is by changing some axioms in the foundations of mathematics, but that would have the highly unwelcome side effect that a whole host of other intuitive commonsense results would become mathematically invalid.

Also, I am a bit disturbed by how quickly you were willing to jump on his "debunking" claim, presumably because it agrees with your metaphysical preferences. Let me just mention that the mark of good science is applying one's skepticism to new claims equally and without regard to whether they agree with one's philosophical predilections or not. Few people may achieve perfection in this regard, but it is a goal that should be aspired to.

"You lost me in your next section about the path integral because you take quantum probability as a given, which I think is only a mathematical analogy."

It's too bad that I lost you in section 6 because that is the heart of my paper. It shows directly, by means of a theorem, the connection between the novel objects definable under an expanded foundation for mathematics and quantum mechanics.

Also, it is not the case that I took probability as a given. Rather, I showed (although omitting a lot of details) that the concept of probability is one of the thing that arises from the the application of axiom D, and then applied the example at the end of section 3, which pertains to an incomplete space vector, in section 6 to an incomplete spacetime vector, thereby setting the stage for deriving the Feynman path integral.

"Time to listen to music- I hope you are still composing!"

Well, thank you, yes as a matter of fact I still am. Last year I composed nearly 25 new pieces, so that my total is now up to almost 140. This year, I have not taken the time to compose because I am trying to focus filling in all the details of my theory.

Thank you again for your comments, I will read your essay shortly and leave some comments.

All the best,

Armin

Dear Akinbo,

I suppose nothing I say is going to change your perception that I am desperately clinging to SR in the face of puzzles like the existence paradox (and even the other ones I pointed out in my existence of photons paper), which should have dissuaded me from accepting the theory.

But, being the optimist that I am, let me just emphasize one last time that the reason I accept the special theory of relativity is that I find the totality of evidence compelling, and the reason that these puzzles do not only weaken my acceptance of SR but actually strengthen it is because I see these as fundamental implications of the theory which have at present not been noticed to give clues about how to understand reality at a more fundamental level and how special relativity can be derived from a common framework that also leads to quantum theory. These implications of SR, being consistent with a picture of quantum theory according to which quantum objects really "come into existence" only when they are measured point to a picture in which spacetime itself, our repository of existence, emerges from something more fundamental. I don't know if you know of my prior work on the dimensional theory, but that "something more fundamental" is, I believe, a 2+1 analog of spacetime which I call areatime. Once you understand this, then (coupled with an understanding of the dual role of metric intervals as "distance" and as "proper time" in spacetimes with Lorentzian metrics) these puzzles make perfect sense. There really is no reason for me to take these puzzles as difficulties for the theory.

"I get the impression that we reach some form of agreement that 'detection times', 'observed frequency', 'observed period' or 'observed light arrival times' can be influenced by the relative velocity. This if you crosscheck is against the principle of Lorentz invariance, according to which the velocity of the observer towards or away from the source has no effect on these observed parameters."

Well, I gave the derivation of the relativistic doppler shift in frequency earlier, what do you think is wrong with it? Or better yet, what do you think the correct expression for the relativistic doppler shift should be?

"Now what is the v in the equation? If it is relative velocity between source and receiver/observer, then in the Michelson-Morley interferometer since this is zero, then no length contraction or time dilation mechanism should occur or be applicable to explain the null findings."

I don't understand this assertion, it seems to me that you are mixing the length contraction phenomenon with the relativistic doppler shift. They are separate phenomena.

"On the other hand, if v is the observer's velocity in space towards the incoming light travelling at speed, c, then there is a dilemma of which velocities of the earthly observer in space to apply. v could simultaneously have three different velocities as it moves in space towards the light. In the M-M experiment, the v considered was the orbital velocity 30km/s about the sun. However, today, we now know that the sun as well as the Milky Way are moving with the result that in the Lorentz factor, the magnitude of v for a moving earth in space can be 30km/s, 225km/s (solar system motion in space) or 370km/s (earth motion relative to CMB). So which v applies in the Lorentz factor during the M-M experiment?"

It seems to me that you are arguing from a point of view which assumes that there is such a thing as an absolute velocity. From that point of view, I agree, that the fact that the LT could change depending on the fact that earth is moving at different velocities relative to different objects seems egregiously wrong.

But, the central lesson of special relativity is *there is no absolute frame*. All three velocities are on an equal footing, and which v you use depends on which frame is relevant for the problem you are trying to solve. So if you accept the central lesson of relativity, there is no problem at all.

"What is the - sign in the Lorentz factor? If it applies to the direction of the observer relative to the incoming light, then it means we can also have length dilation for a + sign and time contraction for a + sign apart from the contradiction that the observer's frame of motion then becomes capable of influencing whether it is contraction or dilation that happens."

No, you have misunderstood the significance of the sign. It cannot refer to the direction of relative motion because the sign stands in front of a squared quantity, so whether the quantity itself is positive or negative, the square will always be positive. If you want to understand the fundamental significance of the minus sign, I can only refer you to my old paper in which I derived the invariance of the speed of light.

http://deepblue.lib.umich.edu/handle/2027.42/83152

Look at Axiom I and divide by c. What you should hopefully realize is that the significance of the minus sign is that every spacetime object is associated with c, which depending on the frame is distributed over motion in space and "motion in time", better known as "aging".

To sum up, what I perceive here is negative feedback loop. There are aspects of SR that are distasteful to your philosophical prejudices, and which prevent you from understanding what the theory is really saying. This leads to misunderstandings which in turn seem to confirm your prior prejudices. I really don't know how this cycle can be broken except if you really take the time to really understand the theory, even if only for the sake of trying to mount stronger arguments against it.

Hope this helps.

Best,

Armin

Thank you for letting me know, I will leave a comment there shortly. Also, please note: My last name is Nikkhah Shirazi, not Shirazi.

Thanks,

Armin

Dear Harry,

Thank you for your comments. I am a bit surprised about your comments about special relativity because it was barely mentioned in my paper. In fact, the main result, the theorem on page 8 is expressly in the non-relativistic limit. You are correct that I did not define inconsistency; the reason was that I thought it would be reasonable to expect the reader to know this. If the reader doesn't know what an inconsistency is, then there is little hope they will understand the rest of my essay.

"It seems anyone with a high school math background can see that relativity is mathematically inconsistent while experts can not recognize this fact at all and insist that the theory is not inconsistent.

Well, why do you think it seems that way? Could it be because there is a grand conspiracy among physicists, mathematicians and nuclear engineers worldwide to impose on the rest an obviously false theory, presumably fudging all the technological innovations and experiments based on it, like nuclear reactors, atomic bombs, astrophysical observations, particle accelerators, GPS devices, not to mention all the physics labs so that each new generation of physicists gets brainwashed to join the grand conspiracy? Or could it be because if someone with a high school background misunderstands relativity and, in best Dunning-Kruger form, blames the theory and everyone who uses it for his misunderstanding?

I think I have a good idea which one you think is more likely.

Best,

Armin

Hi Jon,

"Am I the only one who thinks maybe HAL could be looked at in a positive light?"

No, I'm sure all the peers of HAL would also look at his actions in a positive light, presumably because they would be sufficiently advanced to have something like empathy for HAL, but the not the astronauts.

"But if the axioms are enumerable, couldn't a computer just systematically go through them, computing say the first 1000 "theorems" of each. If the goal of physics is to compress complex physical phenomenon into simple equations, then if you were to take this idea to the extreme, could you just systematically (without imagination) just looking through the space of all simple axiom systems (with simple updating rules/rules of inference) with some romantic hope that our universe might happen to be describable with a very simple system/program? Do you think that this is a worthwhile endeavor or just some pipe-dream?"

I think being able to answer these questions intelligently requires a background in both complexity theory and in computability theory, neither of which I posses, unfortunately. I would like to clarify that by using imagination in this sort of situation I had in mind something like the following: You pick some axiom system and think about what requirements it fails to satisfy, then use your imagination to add/subtract or modify the axioms and now you can take advantage of the ability to have computer system check the thousands of theorems that follow from the tweaked system.

"If equations didn't have closed-formed solutions that harnessed infinities and we saw things as a computation do you think the concept of time would stand out more in the equations/programs? Could time just be where you are in the calculation?"

I have a hard time understanding what it means for something physical to be a computation, so I am afraid I can't really answer that question. However, I suspect that computation conceptualized broadly in this way pre-supposes the existence of time, and if that it is true, then you cannot just say that time is defined by where you are in the calculation on risk of circularity.

"Do you think nature, evolution, or the universe is creating this way, with some high-level purpose in mind?"

No, I do not think there is such a high-level purpose. In my view, whatever adaptions you see are the result of environmental constraints, which though obeying regular patterns, do not serve to advance any particular purpose.

"How do I know that the truncated version of the one you provided is some particular noncomputable real and not another? How do you even know which one you had in mind that you are approximating?"

I would say that if you have to ask these questions, then you have not yet approximated the number to sufficient precision and need to approximate further. It seems doubtful to me that you would run into a realistic situation in which you need an arbitrary uncomputable number to infinite precision. What would you do with it? Any manipulation involving it to infinite precision is also going to be uncomputable, unless it happens to be expressible in simple form like e and pi.

"In the case of you flipping a coin, we could say that the outcome has already been logically determined, but we just don't know what the outcome is because the universe hasn't done the computation yet. In certain situations the calculation might be compressible, and these would be the cases in which we can make precise predictions. In the cases where the computation the universe is doing isn't compressible, we would resort to probabilities."

Again, because I have a hard time wrapping my mind around the idea of physical processes as computations, I'm afraid I can't say much. But if what you are saying is right, it seems that this would imply a novel interpretation of probability.

"...maybe some of Chaitin's youtube lectures might interest you if the Wikipedia page didn't offer too much insight on his Omega constant."

Thank you for the suggestion, I'll look into it.

I hope I was able to at least answer some of your questions, though I felt that they were somewhat outside of what I consider to be my area of knowledge.

Best,

Armin

Dear Akinbo,

"To form an all encompassing opinion, and to know where any conspiracy could be coming from..."

Are you seriously considering the possibility of such a worldwide conspiracy?!?

All those physicists working on the Manhattan project generations before GPS must have done an outstanding job not only maintaining the secrecy of the conspiracy but of giving terrifying fake evidence that the theory works.

Or wait...maybe you think Hiroshima and Nagasaki was not A-bombed, either?

My point is that if your really believe such things, then it seems that such beliefs, in order to be consistent with other beliefs, entail beliefs which become ever more absurd. And citing one person in one particular field is not going to help much.

I see that Ronald Hatch has written a lot of critical material on SR. I find it curious that, at least upon a cursory search, I was not able to find any critique of his work except for one particular blog.

"By any stretch of imagination going by his Bio above, Ron Hatch cannot be said to be someone with a high school background who misunderstands relativity. Why, my friend Armin would feel such a person should be disregarded along with other references like Prof. Herbert Dingle is what looks more like conspiracy, probably unintentional or well meaning, I can't really say."

This is called a straw-man, a fallacy which only further undermines your credibility. Anyone reading my comment knows that my "high school background" comment was a reference to Harry's claim that "anyone with a high school math background can see that relativity is mathematically inconsistent".

It is quite obvious to me that your reason for holding your physics beliefs is not because you are guided by evidence to your beliefs, but because you have already decided what you want to believe. This leads you to grasp every straw you can find, regardless of its merits, to support the position which you already had decided beforehand you wanted to hold. This became especially clear with the articles you cited on the purported invalidity of the Heisenberg uncertainty principle, all of which, except for the one in which the author himself suffered a misunderstanding, contradicted your position.

I have not investigated Hatch and Dingle's works, and so I cannot judge their merits. However, based on my understanding of special relativity and my own research in it, I think if their findings were so revolutionary, we would have heard of it by now. Until that happens, it is much more reasonable to work with the theory for which there are mountains of evidence.

Best,

Armin

Dear Marcel,

Thank you for your comments. As for scientific publication, yes that is a goal, but I omitted a lot of details that still need to be filled in.

Best wishes,

Armin

Dear Lloyd,

Thank you for your kind remarks.

Yes, as you can see, most essays here try to explain the relationship between physics and mathematics solely in terms of those fields (and perhaps some philosophy). But it is easy to ignore the fact that we do both activities in our minds, and therefore its role on the connection is less likely to be appreciated. My essay was in part an effort to bring attention to an important factor that might be easily overlooked.

Best wishes,

Armin

Dear Jon,

"Seth Lloyd has a view of the universe being a quantum computer, ..."

First, whenever you have someone proclaiming that the universe "is" a giant version of some contemporary piece of technology, you should always take that with (more than) a grain of salt . As you may know, a couple centuries ago, during the enlightenment, people proclaimed the universe to be a giant clock, and who knows what people will proclaim the universe is in a couple centuries. To me, the universe is just the universe.

I watched the short video and found Seth LLoyd to be a bit fast and loose with words (For example, he claimed that we already have quantum computers, but I am more skeptical (My view is informed by Scott Aaronson's blog posts on the subject matter).

"...which may be a little more appealing to you..."

No, you know (I think) enough about my ideas to understand that in my view our contemporary conception of the universe, which equates it with spacetime, is too undifferentiated.

If you want to talk just about spacetime, then I definitely disagree with him, because I conceive of quantum theory (well QM, QED, and EW interactions) as the physics of spacetime objects emerging out of areatime. If you already have spacetime to begin with (which is the reasonable interpretation of his use of "universe"), then the appropriate theory is Einstein's General Relativity, not quantum theory.

"Stephen Wolfram, Ed Fredkin, Jurgen Schmidhuber, and some other scientists talk about the universe being a (classical) computation, but these ideas aren't quite as accepted."

Do they give concrete examples for how some physical process can be reframed as a computation?

"From a purely theoretical perspective, no matter how far an uncomputable real number is specified, it will always be ambiguous, since there are an infinite number of real numbers that start with the specified sequence of numbers, and there is no way to refer to or conceive of one specific uncomputable real since they have an infinite amount of information that can't be compressed into a formula like those that represent/generate pi or e. If you don't think this point is relevant when it comes to physics and your ideas regarding ZFCD, then that's probably a slightly different discussion."

Yes, I interpreted you previous question as a physicist, from the point of view of mathematics I agree. Yes, I am uncertain about the relevance of AC. The only reason at this point that I chose ZFCD vs. ZFD (not to be confused with Zermelo-Fraenkel with axiom of Determinacy) is that ZFC is the standard set theory. This does not mean that subtle deep connections may not be there, in fact, more likely than not, I think there may well be.

"I don't think computation broadly defined pre-supposes time, although I do think it would imply a sequential relationship...which I think is slightly different."

You may be right. As mentioned, the notion of a physical process as a computation is not intuitive to me, so my intuitions are more likely to lead me astray than in other areas.

"I tried to raise the question that maybe some of the statistical laws of physics are actually modeling pseudorandom processes, as opposed to truly random processes. If the computation that the universe was doing was too complex, a statistical approach analogous to the PNT might be are only practical approach to making predictions. "

Can you tell me which statistical laws of physics you had in mind?

"I hope some of this made sense."

Rest assured that you did:)

Best,

Armin