It from Bit from It from Bit... Nature and Nonlinear Logic by William C. McHarris

Dear Prof. Knuth,

Thank you very much for your comments. I read your essay, and I was overwhelmed by the beauty of it! Imagine being able to come up with relativistic space-time symmetries from a different but straightforward and logical approach. Not being all that familiar with ordering theory, I had to take most of the derivations on faith, accepting the physical analogies as stated, since they seem quite reasonable and not at all forced. I downloaded your arXiv paper, "The Physics of Events," and I'll study it thoroughly during the next month, so perhaps I can have more astute questions and/or comments after that.

I'll also download your other paper, "Origin of Complex Quantum Amplitudes," and work on it. My comments above to Stoica make a start to answering the linearity vs nonlinearity compatibility problem. But, from an experimentalist's physical aspect, I think that your ideas of influence and response indicate a fundamental feedback, a sure sign of nonlinearity. And the influence-response picture fits in with the original interpretations of the Uncertainty Principle, which fell out of favor with the rise of the Copenhagen interpretation. Maybe we can have a more cogent discussion this autumn.

I also wonder why Cvitanovic's work didn't attract more attention. Perhaps he was simply ahead of this time. His 1987 Physical Review Letter came before the quantum information burst and before most people were really aware of chaos theory. Perhaps now is time for a revival of applying periodic orbital theory to "simple" systems such as the He atom or the H molecule-ion. (With good numerical agreement, I think chemists would welcome this sort of analysis.)

And it's amazing to find someone else who generated fractal ferns on an Amiga! (Another promising platform that didn't survive.) As an extension of this sort of thing, the time is ripe to explore electrons in the two-slit experiment using chaotic scattering. I think the two-slit experiment is a prime example of using an overly-simplified model to reach questionable conclusions. Most of the analyses use pictures where the dimensions are far, far greater than the actual wavelengths, where the experiments would show nothing. Performing a detailed microscopic analysis, with the electrons indeed interacting with the individual atoms forming the slits could well produce a situation for chaotic scattering, with its resulting quasi-diffraction patterns. I hope you find this a worthwhile endeavor.

Again, congratulations on an impressive essay. I made a few remarks on its thread.

Cheers,

Bill McHarris

Dear Vladimir,

Yes, I rated your essay a week or so ago. I thought it was a terrific essay.

Best wishes,

Bill

Dear Richard,

Thank your for your observations. Yes, the interplay between observation and system makes for feedback, which can easily generate nonlinear behavior. I enjoyed reading your essay, which covered many of the same sort of ideas. It's all to the good that we are now able to question the strait-jacketed, forced Copenhagen patterns.

Best wishes,

Bill

Dear Dipak,

Thank you for your kind words. Yes, chicken and egg, rather observer and observed, are in a sense inseparable, which leads to feedback and nonlinear behavior. I read your essay with pleasure -- it's a neat, fresh approach to the question from a more philosophical approach. My biggest question concerns how we can discern an analog vs a digital Nature. If our detection (sensory) system happens to be digital, we cannot distinguish between analog signals and digital signals on a much finer scale than our system's scale; similarly, if our detection system were analog, Nature probably requires much higher resolution than we possess in order for us to discern the difference. Could you comment on this?

Thanks,

Bill

Dear George,

Thanks for your comments. I was late is getting started with my answers and have simply become overwhelmed. I did read your essay and rated it very highly. I'll respond more fully to your above comments in a day or two.

Best wishes,

Bill

Dear Margriet,

THank you very much for your lovely comments. I truly appreciate them. And I must say your are very astute and have a lot of common sense -- it gives a breath of life to this contest.

I read your lovely essay, and I agree with your views. (I also rated it highly.) As you gleaned from my essay, I am strongly in favor of an ontological, realistic view of Nature -- I come down strongly on the side of Einstein in his debates with Bohr. And if quantum mechanics were to contain significant nonlinearities, it could well do away with the distinction between it and classical mechanics, which (almost!) all of us agree is ontological. Because time is short and the FQXi server seems to be slowing down, I'll reserve further comments both your your letter and to your essay until things have quieted down. (I think we can still make comments after the voting has ended.)

If by Antipodean you mean Australian, I spent a marvelous month there last fall, traveling to Sydney, Melbourne, Adelaide, and Port Douglas for the solar eclipse. A marvelous, beautiful -- and friendly -- country!

Best wishes,

Bill

I received the following e-mail message from Dr. Klingman on 8 August:

*Dear Bill McHarris,

*I made the mistake of waiting until I had read your other papers before commenting on your essay. This put me near the end of the comments on your page. After you returned and began diligently answering each comment, I watched daily for you to reach mine. But we ran out of time.

*I am therefore using email to say that I very much enjoyed your essay and found it stimulating. I hope you are correct in your suppositions. I also believe that you will find my own essay very interesting. I have recently developed a technique for non-linearizing Einsteins' linearized (weak field) equations. While this may sound nuts, it actually does two things: It makes it possible to actually solve the equations, and it allows one to use the analogy with Maxwell's equations in intuitive fashion (which intuition simply does not exist for the full field equations).

*For this reason I still invite you to read my essay, and I would still appreciate your comments, either on my essay page or by return email.

*http://www.fqxi.org/community/forum/topic/1779

*Thanks for participating in the contest, for so diligently answering the comments, and for the decades you have spent attempting to educate physicists about the implications of non-linearity.

*My best regards,

*Ed

And here I take the opportunity to reply:

Dear Ed,

Thank you for your very kind words. Unfortunately, I ran out of time before answering you properly, but I hope this belated response will partially make up for it.

I read your essay, and I was overwhelmed with it -- especially the first part, "Why Do Physicists 'Believe' Current Theories"! You eloquently and succinctly sum up many of my own thoughts on the subject, so I fully agree with you. Physicists are human like anyone else, so they are not impervious to allowing themselves to be swept along by current fashion. Besides, many of the far-out ideas are far "sexier" than more prosaic explanations, such as nonlinearity. (I never thought I would refer to any aspect of chaos theory as "prosaic," but I guess, compared with string theory and interactions at the Planck scale or the Many-Universes Theory, it doe sound less far out and exciting.) The semi-popular press aids and abets these tendencies. For example, the latest issue of "Scientific American" contains an article, "Quantum Physics: What Is Real?" that makes all sorts of speculations without much hard physical basis.

Not being much of an expert on General Relativity, I must admit that I couldn't follow much of your reasoning -- I'm sure the condensed, "nine pages" also contributed to this. But the interplay of linearity and nonlinearity seems well worth pursuing. I make a few more comments under your thread.

Again, thank for your remarks and for your e-mail.

Best wishes,

Bill