Dear Mauro and Peter,

I read your exchange with interest and apologize for not replying sooner -- I've been traveling (a combination of science and music), so things got put off.

I agree that one should not try to use chaos as the "little monster" that can explain everything, especially at this early stage, when things are pretty much empirical and by analogy. Actually, the violations of Bell's inequalities are more related to Bayesian statistics than they are to chaos. The point of attack is on the classical side, for classical nonlinear systems can exhibit correlations (analogous to entanglement) essentially as large as those in quantum mechanics. Thus, the violations of the inequalities are ruling out the lack of correlations (in linear systems?!) rather than classical mechanics per se. (If you look back at the so-called "classical" derivation of, say, the CHSH inequality, which is the most experimentally friendly version and the one commonly used, you will find that there are really no correlations built in -- they are just glossed over, whereas the on the quantum mechanical side one normally starts with a singlet state, which as about as entangled as you can get.) These classical correlations have been studied extensively in systems as diverse as tornados and energy distributions of cosmic rays, and they exhibit so-called nonextensive (Tsallis) entropy. The book "Nonextensive Entropy: Interdisciplinary Applications," put together by Gell-Mann and Tsallis (Ref. [7] in my essay) covers this in a relatively straightforward fashion. Currently, the whole business is mostly experimentally driven, so mathematical derivations are at a minimum, but they have had surprising success with quite diverse systems.

A final word. Perhaps I am naive, but coming from an experimentalist's perspective, I find it odd the way people jump from statistical correlations to individual cases. All of the Bell-type inequalities rely on correlations found in large numbers of data, when "enough events have been recorded to be statistically significant and meaningful." (This is true even for the three-state GHZ correlations, which don't rely on an inequality.) Yet, when it comes to the interpretation, people say such things as, "When the spin direction of Alice's particle is measured as 'up,' this has caused its wave-function (previously assumed to be in entangled limbo) to collapse, and since it came from a singlet state, this causes the wave-function of Bob's particle to collapse INSTANTANEOUSLY into a 'down' state." Experimentally, there has been no analysis of individual particle-particle data -- the correlations are meaningful only after many thousands of events have been collected and compared statistically. Surely this is a weakness in the argument!

Again, thanks for the dialog.

Bill

Dear Sir,

We just happened to read a book written in the 9th Century by Jayant Bhatt titled "Nyaya Manjari", where in the Volume II, 8th Chapter page 294, he has discussed observer created reality to scientifically refute it. The book is in Sanskrit, but its translations in other languages are also available.

He argues: some people say that the objects exist only when we observe them. This implies the existence or non-existence of an object rests on whether we observe it or not. But nonexistence are of various types. There is prior nonexistence of an object before it is transformed from being to becoming (cause and effect). Thereafter, it exists independent of observation or otherwise. This gives rise to number sequence. There is temporary non-existence, which is related to its transformation in space or time independent of the observer. This gives rise to negative numbers. There is destruction or death, which is the opposite of prior nonexistence. Then there is non-commuting nonexistence like position and momentum: a fixed position implies nonexistence of momentum with mobile coordinates and vice versa.Lastly, there is the absolute nonexistence, which means, it is impossible as per physical laws like the horns of a rabbit.

Regards,

basudeba

Dear Antony,

Thank you for your complimentary remarks. I also read your essay, which was quite well written. The idea of a Fibonacci sequence explaining the behavior of black holes is a novel, clever idea, but I wonder about whether or not it really applies to the physical situation. To be sure, it's a clever mathematical construct, but with enough variables, one can fit almost anything. On the other hand, it's just such clever group-theoretical constructs that wound up predicting the omega-minus particle.

The thing one has to worry about is that there are far more mathematical constructs than there are physical applications, and deciding which ones are really relevant is not a trivial task. Can you extend your model to make predictions?

Best wishes,

Bill

Dear Bill,

I can indeed make predictions and I'll reply on my thread.

Best wishes,

Antony

Dear Professor McHarris,

Thank you for your reply and thank you so much for your kind comments on my essay in my blog. I can't relay how much your approval and high rating means to me, coming from a luminary like you.

...and I know exactly what you mean by a writing style "wrapped up in seemingly eloquent yet obscuring philosophical and/or physics-derived jargon" -- I'm afraid some of my ex-countrymen are often guilty of this. I call it "the academic style", and this applies to Russian academics only (I know, because I've read plenty of English scientific literature to compare). I personally cannot read this style and don't, unless I have to. (it's hard to stay awake lol)

And thank you very much for your explanation re captions. I do remember --vaguely-- these diagrams from James Gleick book, soon after it came out, which was a long time ago (yeah, how fast we forget -- I am planning to re-read it now). And so I could guess where that A = 3.82 was but could not be certain -- the question 'what if I'm mistaken?' always looms over my head -- and so I thought a caption would remove that uncertainty. Thank you for your explanation again!

And regarding Dr. Rose, he was telling about the non-reducibility of evolving biological systems for years, but somehow, it finally clicked in my head only when I read your essay. My brain will never be the same, because a very important neuronal connection was made. There are very few such essays, and even books or articles, that make a brain click. You did that for me and I will never forget that. Thank you!

-Marina

Having read so many insightful essays, I am probably not the only one to find that my views have crystallized, and that I can now move forward with growing confidence. I cannot exactly say who in the course of the competition was most inspiring - probably it was the continuous back and forth between so many of us. In this case, we should all be grateful to each other.

If I may, I'd like to express some of my newer conclusions - by themselves, so to speak, and independently of the logic that justifies them; the logic is, of course, outlined in my essay.

I now see the Cosmos as founded upon positive-negative charges: It is a binary structure and process that acquires its most elemental dimensional definition with the appearance of Hydrogen - one proton, one electron.

There is no other interaction so fundamental and all-pervasive as this binary phenomenon: Its continuance produces our elements - which are the array of all possible inorganic variants.

Once there exists a great enough correlation between protons and electrons - that is, once there are a great many Hydrogen atoms, and a great many other types of atoms as well - the continuing Cosmic binary process arranges them all into a new platform: Life.

This phenomenon is quite simply inherent to a Cosmos that has reached a certain volume of particles; and like the Cosmos from which it evolves, life behaves as a binary process.

Life therefore evolves not only by the chance events of natural selection, but also by the chance interactions of its underlying binary elements.

This means that ultimately, DNA behaves as does the atom - each is a particle defined by, and interacting within, its distinct Vortex - or 'platform'.

However, as the cosmic system expands, simple sensory activity is transformed into a third platform, one that is correlated with the Organic and Inorganic phenomena already in existence: This is the Sensory-Cognitive platform.

Most significantly, the development of Sensory-Cognition into a distinct platform, or Vortex, is the event that is responsible for creating (on Earth) the Human Species - in whom the mind has acquired the dexterity to focus upon itself.

Humans affect, and are affected by, the binary field of Sensory-Cognition: We can ask specific questions and enunciate specific answers - and we can also step back and contextualize our conclusions: That is to say, we can move beyond the specific, and create what might be termed 'Unified Binary Fields' - in the same way that the forces acting upon the Cosmos, and holding the whole structure together, simultaneously act upon its individual particles, giving them their motion and structure.

The mind mimics the Cosmos - or more exactly, it is correlated with it.

Thus, it transpires that the role of chance decreases with evolution, because this dual activity (by which we 'particularize' binary elements, while also unifying them into fields) clearly increases our control over the foundational binary process itself.

This in turn signifies that we are evolving, as life in general has always done, towards a new interaction with the Cosmos.

Clearly, the Cosmos is participatory to a far greater degree than Wheeler imagined - with the evolution of the observer continuously re-defining the system.

You might recall the logic by which these conclusions were originally reached in my essay, and the more detailed structure that I also outline there. These elements still hold; the details stated here simply put the paradigm into a sharper focus, I believe.

With many thanks and best wishes,

John

jselye@gmail.com

Dear William

I just read your interesting and novel essay. I think that nonlinear dynamics is gaining acceptation in physics in recent years. In particular, in fluid mechanics, optics, soft and hard condensed matter physics. You mention that nonlinear dynamics may give a different view of quantum mechanics. My question is whether the mysterious phenomena such as entanglement could find a common sense explanation. What are your thoughts on this respect; what would be the interpretation under the nonlinear approach of the two-slit interference and entanglement experiments?

Finally, I'd like to invite you to read my essay and leave some comments. There I discuss about Wheeler's dream and propose a potential way to get out of the present crisis assuming that space is a nonlinear continuum medium.

I'll be looking forward to hearing any comments you may have.

Regards

Israel

Bill,

You're very welcome. Well earned. thanks also for your post on mine. I think we're onto something very important for progress and certainly paradigm changing. Where do we go for one of those? Do they exist any more? It looks to me like they've stopped doing them!?

Peter

(PS. Could be an opening then!)?

Dear Chidi,

Thank you for your kind words. I read your essay with pleasure, too. It's quite fascinating.

Your essay is fairly consistent with the Copenhagen interpretation, and I think this is where we differ. With a nonlinear element in quantum mechanics (implying feedback), we don't have to worry about the distinction between system and observer or where to delineate the locale of separation. Instead, quantum mechanics becomes ontological, and the Uncertainty Principle can be interpreted in its old-fashioned sense in that the observer doesn't cause the wave-function to collapse, but he or she does perturb the system, affecting successive measurements. Thus, feedback is not a phase space but its implications can affect the phase space. I hope I have understood your question and this perhaps starts to answer it.

Best wishes,

Bill

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  • Post #67

Hi,

Thanks for your comments.

I found your essay fascinating, with much to commend it. However, I am curious when you make a fundamental distinction between biology and physics. Although biology is infinitely more complicated than physics, scientists working in nonlinear dynamics are making baby steps toward interpreting it. For example, nonlinear network theory has made considerable progress in explaining how very complicated networks, such as the internet, function. And it is conceivable that simple brains (perhaps at insect level) eventually will be understood on the basis of feedback in networks. We're in a modern position similar to that of organic chemistry in the early 1800's, when it was thought that some sort of "vital" component was present in organic compounds that wasn't necessary for more straightforward inorganic compounds. But then urea was synthesized in the laboratory, disproving the necessity of this vital component -- after all, organic chemistry is simply the chemistry of carbon, which can be considerably more complicated than the chemistry of most other elements, but there's nothing "vital" about it. Something similar is undoubtedly true about biological systems. They may be so complicated that we can never completely fathom them, but there should be no fundamental difference between them and physical systems. (This may well be the situation where "in principal" and "in practice" wind up being being so different that for all practical purposes they are essentially antipodal.)

I look forward to seeing your comments on my essay,

Bill

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  • Post #68

Dear Cristi,

Thanks for your comments. I also read your lovely essay and was very favorably impressed by it. I included a few comments on the thread below your paper.

The link to my paper from the DICE Conference is Chaos and the Quantum. This paper includes a number of references your might find useful, although the idea of nonlinear influences in quantum mechanics is very much in an early, empirical stage.

I think in principle we are saying much of the same thing in that nonlinear equations can be represented by (many, many more) linear equations of higher order. But, of course, this quickly becomes cumbersome. For all practical purposes chaos theory was unknown when the formulators of quantum mechanics were active, so they forced it into a linear format. One of my favorite quotations comes from Mielnik [Phys. Lett. A289, 1 (2001)], when he was worrying about the superluminal signals that ensued when he was working on (weak!) nonlinear effects:

"I cannot help concluding that we do not know truly whether or not QM generates superluminal signals--or perhaps, it resists embedding into too narrow a scheme of tensor products. After all, if the scalar potentials were an obligatory tool to describe the vector fields, some surprising predictions could as well arise! ...the nonlinear theory would be in a peculiar situation of an Orwellian 'thoughtcrime' confined to a language in which it cannot even be expressed. ...A way out, perhaps, could well be a careful revision of all traditional concepts..."

I often wonder what Wheeler himself, had he been working several decades later, would have done with modern chaos theory. (Although it was known more or less outside of meteorology starting in the 1970's and 1980's, it was by no means widely disseminated among most main-stream physicists -- I hesitate to label Wheeler as a "main-stream" physicist! And it was well into the 1990's, with the growth of quantum information theory that anyone started to think seriously about applying it to the basics of quantum mechanics.) Wheeler was so responsive to new, novel ideas that I suspect he might have run with it.

I found your paper so interesting that I have located many of your other papers, and I would like to continue our discussion after I have had time to peruse and understand them more thoroughly.

Best wishes,

Bill

Hi, again,

It seems one gets logged out if he takes too long to formulate an answer, so my post above is listed as "anonymous." But, as you can discern, it's from me. Again, thanks for your comments.

Bill McHarris

Dear Armin,

Thank your for your astute comments.

Yes, sensitive dependence on initial conditions offers the possibility for explaining the two-slit expedient. Classical chaotic scattering can produce patterns that look very much like diffraction patterns. This sort of behavior is discussed in detail in a series of papers in a special issue of "Physics D," introduced by a paper by Bleher, Grebogi, and Ott; a more straightforward discussion is given in the book, "Classical Dynamics: A Contemporary Approach," by José and Salatan; both are listed under Ref. [6] in my essay. The basic idea involves the intimate mixture of chaos and order in various locales of phase space for chaotic systems. This admixture can be very fine, since bifurcation diagrams for such systems tend to be self-affine, mathematically at least, all the way to infinite magnification. If a system finds itself in such a regime, then an almost infinitesimal variation in initial conditions can cause it to move back and forth between ordered (cyclic) and chaotic behavior, which means the difference between a particle's landing in a predictable location and being scattered "unpredictably" (not really fundamentally, but for all practical purposes it might as well be). Hence, the apparent diffraction pattern. This is only one of the so-called paradoxes of the Copenhagen interpretation of quantum mechanics that can more or less be explained by analogy, having a parallel explanation in terms of nonlinear dynamics. Superficially, nonlinear dynamics and its extreme (chaos) can be just as counterintuitive as quantum mechanics, but upon deeper scrutiny, their peculiarities come about more logically.

Best wishes,

Bill

Dear William,

We are at the end of this essay contest.

In conclusion, at the question to know if Information is more fundamental than Matter, there is a good reason to answer that Matter is made of an amazing mixture of eInfo and eEnergy, at the same time.

Matter is thus eInfo made with eEnergy rather than answer it is made with eEnergy and eInfo ; because eInfo is eEnergy, and the one does not go without the other one.

eEnergy and eInfo are the two basic Principles of the eUniverse. Nothing can exist if it is not eEnergy, and any object is eInfo, and therefore eEnergy.

And consequently our eReality is eInfo made with eEnergy. And the final verdict is : eReality is virtual, and virtuality is our fundamental eReality.

Good luck to the winners,

And see you soon, with good news on this topic, and the Theory of Everything.

Amazigh H.

I rated your essay.

Please visit My essay.

Hello Bill - I'm a seventy yr old lady so I can call you that !!!!

I love it that you question 'mainstream' & are looking for alternatives such as might be found in non-linear processes with their concatenating feedback - & feedforward - loops.

My own investigations have led me to conclude that 'information' is NOT digits - no kind nor amount of them (including any that can be extracted from quantum phenomena!), nor how algorithmically-well they may be massaged & shunted through any device that uses them.

Nor whether they are processed non-linearly !!

Unequivocally they - digits - make for wonderful COUNTING & CALCULATING assistants, witness our own now many & various, most excellent, counting, calculating devices BUT according to my investigations real thinking is an entirely different phenomenon from mere counting, calculating & computing.

For which phenomenon - real thinking - real information is required.

My own investigations led me to discover what I have come to believe real information is & as it so transpires it turns out to be an especially innocuous - not to omit almost entirely overlooked & massively understudied - phenomenon, none other than the sum total of geometrical objects otherwise quite really & quite properly present here in our universe. Not digits.

One grade (the secondary one) of geometrical-cum-informational objects lavishly present here in our cosmos, is comprised of all the countless trillions & trillions of left-over bump-marks still remaining on all previously impacted solid objects here in our universe - that is to say, all of the left-over dents, scratches, scars, vibrations & residues (just the shapes of residues - not their content!) (really) existing here in the universe.

Examples of some real geometrical objects of this secondary class in their native state are all of the craters on the Moon. Note that these craters are - in & of themselves - just shapes - just geometrical objects. And the reason they are, also one & at the same time, informational objects too, can be seen by the fact that each 'tells a story' - each advertises (literally) some items of information on its back - each relates a tale of not only what created it but when, where & how fast & from what angle the impacting object descended onto the Moon's surface. Again, each literally carries some information on its back. (Note : Not a digit in sight !!)

How we actually think - rather than just count, calculate & compute - with these strictly non-digital entities, specifically these geometrical-cum-informational objects, in precisely the way we do, please see my essay.

Yes, geometrical-cum-informational-objects do, indeed, get processed non-digitally by our brains - & I'm quite sure that many of these processes are thoroughly non-linear - with massive amounts of feedback/feedforward loops, but which processorial work results in 'collations' - not in SOLUTIONS TO 'algorithms' or arithmetical or algebraic calculations - just collations - just 'regroupings' of select geometrical objects according to pre-established re-grouping (collating) protocols !!!!!

I did not make the distinction between computing with digits & real thinking with real information, sufficiently strongly in my essay.

This contest is such a wonderful 'sharing' - Wow - & open to amateurs like myself - Wow. How great is that !!! Thank you Foundational Questions Institute!!! What a great pleasure it has been to participate. What a joy to read, share & discuss with other entrants !!!

Margriet O'Regan

    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 William,

    Now is last day to completing somewhat our discuss and conversations.

    I has find your work interesting for me, I have read it and has invited you to discussion (see my post above.) I did not get answer however. I think you was busy, just tired or with some other reason. Anyway, I must give my rating to your essay as really one good work, presented in contest that I have do.

    Regards,

    George Kirakosyan