It from qubit: how to draw quantum contextuality by Michel Dr Planat

Dear Torsten,

Thanks for your careful reading.

1) It is not straight to see the contradiction in the dessin of Fig. 3b, I failed to see it in general (for other contexts). Also there is not a single dessin leading to Mermin's square but many, why is it so? More work is necessary. This non-bijection is general for most geometries I have tried to reconstruct from the n-simplices to projective configurations such as Desargues, Cremona-Richmund (i.e. the doily W(2) of two-qubit commutatitivity) and others.

2) You are right that transitive action may not be a necessary condition. The geometry is constructed by having recourse to the stabilizer of each point in the permutation group relevant to the dessin.

3) Last remark, the geometry is of the projective type not the dessin. Here you have to refer to the theory that is well explained, for example in Lando and Zvonkin (my ref. [6]).

Torsten, please check that you vote was recorded.

Thanks Michel for your message on my blog. My arguments are from a philosophical and classical perspective. It is possible that when viewed from your perspective we may well be saying something similar. I am not expert on the math involved in quantum theory.

Following additional insights gained from interacting with FQXi community members, perhaps you will find the the judgement in the case of Atomistic Enterprises Inc. vs. Plato & Ors, delivered on Jul. 28, 2013 @ 11:39 GMT easier to understand my thinking.

Best regards,

Akinbo

*I have already rated your essay so you may do likewise.

Greetings Michel,

I enjoyed the last comments left on my essay space, and I eagerly await the next chapter on Hopf fibrations - which are already a subject of interest.

It appears the 'infection' has spread, but Dr. Planat is in!

Have Fun,

Jonathan

Hi Michel,

So it appears that the FQXI database has been reset and my comments have disappeared... I will add them back in. As I said before:

Your very interesting essay, taking us right to the foundations, raises some questions. You wrote:

> This implies the non-existence of the Belyi map and puts three-qubit contextuality on a qualitatively different footing when compared with the two-qubit case.

It seems that your quest to model 3-qubit contextuality has an unhappy ending in your essay. Do you thus conclude that (some? all?) mechanisms that explain contextuality for 2-qubit systems will not explain it for 3-qubit systems?

What avenues are you now taking to explore 3-qubit contextuality? (Yes, yes I know I should read your recent papers... after the contest, please...) I am hoping there is another chapter to come in your story... with finally, a happy ending. I do like the idea that you mention of lifting the Riemann sphere to S3 via the inverse Hopf Fibration. I will put some more comments about this on my blog.

> To find the corresponding Belyi map seems to be a challenging math problem.

My thought was there might be a possibility of easier results if we restrict white and black points to lie at k-rational points:

Consider Q(phi), the algebraic extension of the rationals by the golden ratio. These numbers are able to provide cartesian coordinates for all the vertices of Platonic solids, and many other polytopes besides. These could be considered as k-rational points within larger fields, but also as a field on their own. (For such fields, Falting's Theorem should apply and might possibly be useful.) But I was mainly wondering if anyone had looked at the techniques you describe with such k-rational points and fields in mind.

Anyway, if they prove useful, I imagined that such diagrams (living in S3?) might be called "Dessins d'Or"... and eventually lead to a happy ending. Next year's essay, perhaps?

Hugh

I also saved a copy of your response, so I add it here:

--------------------------------------

Dear Hugh,

"different footing"

it is a matter of perspective, the pentagram possesses the same graph than the Desargues configuration that can be drawn in several ways. The non-bijection between drawings and geometries here (and elswhere) is something I am currently working at.

"avenues"

yes, our recent papers pointing out G2(2) and octonions (several comments in this blog) and more to come, including (with you?) the lift to S3.

"k-rational points"

excellent, we are preciselt talking about algebraic curves on the Riemann sphere (S2 say), after the lift we should keep the algebraic property.

"Dessins d'Or"

a lift to Orland circles, or Urland knots.

My kind regards,

Michel

Hi Michel,

Your very interesting essay, taking us right to the foundations, raises some questions. You wrote:

> This implies the non-existence of the Belyi map and puts three-qubit contextuality on a qualitatively different footing when compared with the two-qubit case.

It seems that your quest to model 3-qubit contextuality has an unhappy ending in your essay. Do you thus conclude that (some? all?) mechanisms that explain contextuality for 2-qubit systems will not explain it for 3-qubit systems?

What avenues are you now taking to explore 3-qubit contextuality? (Yes, yes, I know I should read your recent papers... after the contest, please...) I am hoping there is another chapter to come in your story... with finally, a happy ending. I very much like the idea that you mention of lifting the Riemann sphere to S3 via the inverse Hopf Fibration. I will put some more comments about this on my blog.

> To find the corresponding Belyi map seems to be a challenging math problem.

My thought was there might be a possibility of easier results if we restrict white and black points to lie at k-rational points: Consider Q(phi), the algebraic extension of the rationals by the golden ratio. These numbers are able to provide cartesian coordinates for all the vertices of Platonic solids, and many other polytopes besides. These could be considered as k-rational points within larger fields, but also as a field on their own. (For such fields, Falting's Theorem should apply and might possibly be useful.) But I was mainly wondering if anyone had looked at the techniques you describe with such k-rational points and fields in mind.

Anyway, if they prove useful, I imagined that such diagrams (living in S3?) you could call "Dessins d'Or"... and that they could lead you to a happy ending. A topic for next year's essay, perhaps?

Hugh

This test is the best that I have read and analyzed in this contest.Explains Dr Planat efficiently and deep map the graph theory applied to information processing, in quantum theory. In this analysis, both logically well argued, as mathematically demonstrated the clear and inevitable connection with the theory of graphs and maps permutations, with information theory.Certainly, from my humble point of view, a clear candidate to receive recognition for this contest.

Rate it all!!

Thanks Dr Planat

Dear Michel,

I rated already your sophisticatedly serious essay on August 1st. Somehow, my comment accompanied with my vote is lost or not posted. I definitely agree that all interpretations must be contextual in its nature. Excellent work!

If I may say, KQID proposes contextuality through KQID Ouroboros Equations of Existence that combines Newton, Maxwell, Planck, Boltzmann, Lorentz,Einstein, Laundauer, Wheeler , Feynman, Ssusskind, Hooft, Wilczek, Bousso and others. The Ouroboros Equations mean each interpretation involves every beginning to every ending. Similarly, everything we do involve the Ouroboros action or totality of any action. Nature is such unbelievable phenomena that we are just now starting to peek into its secret that is shockingly simple in the beginning but infinitely complex in the ending that per KQID every absolute digital time ≤ 10^-1000seconds. Interestingly, the mechanism is also simple. See my essay Child of Qbit in time.

All the Best,

Leo KoGuan

Dear Michel - It took three readings of your paper before I understood it. However, I think it was worthwhile. There are some extraordinarily provocative ideas here, and as soon as the contest is over I plan to follow up and read your other publications.

I particularly enjoyed your recognition of bipartite graphs being at the heart of reality (a two-player) two qubit setup.

Introducing Grothendieck's dessin d'enfant was a stroke of genius. A wonderful tool to cut to the heart of the matter and expose the underlying simplicity of our universe.

I was somewhat taken aback by the appearance of what appeared to be a random integer without reference in many places in your essay (e.g 12096 guys), until I realized that you were using the Magma software.

There may be an unfortunate spelling error in the first paragraph under 3.3. Mermin's pentagram: If I am not mistaken "Peceptual" should be "Perceptual". At first I thought it was some new word or concept in in projective geometry I was unfamiliar with, but then discovered I could not find the word in a web search.

All in all this is a great essay and I gave it very high marks. I look forward to following up on your other publications at a later time.

Good luck in the contest.

Kind regards, Paul

Dear Michael,

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.

Late-in-the-Day Thoughts about the Essays I've Read

I am sending to you the following thoughts because I found your essay particularly well stated, insightful, and helpful, even though in certain respects we may significantly diverge in our viewpoints. Thank you! Lumping and sorting is a dangerous adventure; let me apologize in advance if I have significantly misread or misrepresented your essay in what follows.

Of the nearly two hundred essays submitted to the competition, there seems to be a preponderance of sentiment for the 'Bit-from-It" standpoint, though many excellent essays argue against this stance or advocate for a wider perspective on the whole issue. Joseph Brenner provided an excellent analysis of the various positions that might be taken with the topic, which he subsumes under the categories of 'It-from-Bit', 'Bit-from-It', and 'It-and-Bit'.

Brenner himself supports the 'Bit-from-It' position of Julian Barbour as stated in his 2011 essay that gave impetus to the present competition. Others such as James Beichler, Sundance Bilson-Thompson, Agung Budiyono, and Olaf Dreyer have presented well-stated arguments that generally align with a 'Bit-from-It' position.

Various renderings of the contrary position, 'It-from-Bit', have received well-reasoned support from Stephen Anastasi, Paul Borrill, Luigi Foschini, Akinbo Ojo, and Jochen Szangolies. An allied category that was not included in Brenner's analysis is 'It-from-Qubit', and valuable explorations of this general position were undertaken by Giacomo D'Ariano, Philip Gibbs, Michel Planat and Armin Shirazi.

The category of 'It-and-Bit' displays a great diversity of approaches which can be seen in the works of Mikalai Birukou, Kevin Knuth, Willard Mittelman, Georgina Parry, and Cristinel Stoica,.

It seems useful to discriminate among the various approaches to 'It-and-Bit' a subcategory that perhaps could be identified as 'meaning circuits', in a sense loosely associated with the phrase by J.A. Wheeler. Essays that reveal aspects of 'meaning circuits' are those of Howard Barnum, Hugh Matlock, Georgina Parry, Armin Shirazi, and in especially that of Alexei Grinbaum.

Proceeding from a phenomenological stance as developed by Husserl, Grinbaum asserts that the choice to be made of either 'It from Bit' or 'Bit from It' can be supplemented by considering 'It from Bit' and 'Bit from It'. To do this, he presents an 'epistemic loop' by which physics and information are cyclically connected, essentially the same 'loop' as that which Wheeler represented with his 'meaning circuit'. Depending on where one 'cuts' the loop, antecedent and precedent conditions are obtained which support an 'It from Bit' interpretation, or a 'Bit from It' interpretation, or, though not mentioned by Grinbaum, even an 'It from Qubit' interpretation. I'll also point out that depending on where the cut is made, it can be seen as a 'Cartesian cut' between res extensa and res cogitans or as a 'Heisenberg cut' between the quantum system and the observer. The implications of this perspective are enormous for the present It/Bit debate! To quote Grinbaum: "The key to understanding the opposition between IT and BIT is in choosing a vantage point from which OR looks as good as AND. Then this opposition becomes unnecessary: the loop view simply dissolves it." Grinbaum then goes on to point out that this epistemologically circular structure "...is not a logical disaster, rather it is a well-documented property of all foundational studies."

However, Grinbaum maintains that it is mandatory to cut the loop; he claims that it is "...a logical necessity: it is logically impossible to describe the loop as a whole within one theory." I will argue that in fact it is vital to preserve the loop as a whole and to revise our expectations of what we wish to accomplish by making the cut. In fact, the ongoing It/Bit debate has been sustained for decades by our inability to recognize the consequences that result from making such a cut. As a result, we have been unable to take up the task of studying the properties inherent in the circularity of the loop. Helpful in this regard would be an examination of the role of relations between various elements and aspects of the loop. To a certain extent the importance of the role of relations has already been well stated in the essays of Kevin Knuth, Carlo Rovelli, Cristinel Stoica, and Jochen Szangolies although without application to aspects that clearly arise from 'circularity'. Gary Miller's discussion of the role of patterns, drawn from various historical precedents in mathematics, philosophy, and psychology, provides the clearest hints of all competition submissions on how the holistic analysis of this essential circular structure might be able to proceed.

In my paper, I outlined Susan Carey's assertion that a 'conceptual leap' is often required in the construction of a new scientific theory. Perhaps moving from a 'linearized' perspective of the structure of a scientific theory to one that is 'circularized' is just one further example of this kind of conceptual change.

Hello Michel from Margriet O'Regan from DownUnder !

My research over the years has led me to believe that there are very few geometricians around ! So it's been great to encounter a few here in this essay arena - including Akinbo Ojo & you.

But it has confirmed my belief that few if any persons lay or expert alike, recognise & acknowledge REAL common, ordinary, everyday, garden variety geometrical objects lying all around (& in) us everywhere - rather than the abstract or hypothetical ones which exist only inside mathematicians & theoretical physicists' heads & textbooks !

My claim is not only that 'information' is the full set of geometrical objects present here in our universe but that they are all of the properly real ones present here.

My investigations have led me to believe that there are not any of these real geometrical objects in certain specific places or realms or domains. One of these domains in which no geometrical objects exist is the sub-sub-atomic realm down at the quantum level. I make this conclusion because geometrical objects are strictly 'surface dwelling' entities & do not, because they cannot, exist anywhere but on the surface of some one or another solid object. Whatever it is down there at the quantum level it has no surfaces - therefore no real information.

Space is another place where none of 'my' real geometrical objects exist. I do not believe that space-time itself is curved or warped. I believe that the light that is bent (lensed) around the sun is bent as it is due to the fact that it is passing through the Sun's heliopause & not responding to (non-existent) space-times curvature at all. Einstein did not know of such things as heliopauses or even our own Earth's magnetosphere - which does the same thing (bends light - just a little). The two spacecraft which are currently exiting our Solar system also have been affected by transitting the boundaries of the Sun's gigantic heliopause.

My belief in real geometrical objects gives me the personal advantage of not having to know the maths of 'deep' physics & even though I have read Penrose's 'The Road to Reality : A Complete Guide to the Laws of the Universe' I kind of let the equations 'wash through me' rather than working each out in detail.

And there was for me a very big reward at the end of his book as he confessed after more than one thousand pages of hard work, to not having found 'the answer' at all - not even close !! & that we'd not only better keep looking for it, but do so in significantly different directions from those we have previously taken.

Here is what he said :

On page 1025 in his last chapter 'Where lies the road to reality ?'

'It is certainly possible that there are many clues to Nature's ways hidden in such (modern experimental) data even if we do not properly read them yet. Recall that Einstein's general relativity was crucially based on his insight (the principle of equivalence) which had been implicit in observational data that had been around since (and before) the time of Galileo, but not full appreciated. The may well be other clues hidden in the immeasurably more extensive modern observations. Perhaps there are even 'obvious' ones, before our very eyes, that need to be twisted round and viewed from a different angle, so that a fundamentally new perspective may be obtained concerning the nature of physical reality.

Page 1027 and following.

What is reality ?

As the reader will gather from all this, I do not believe that we have yet found the true 'road to reality', despite the extraordinary progress that has been made over two and one half millennia, particularly in the last few centuries. Some fundamentally new insights are certainly needed, Yet, some readers may well still take the view that the road itself may be a mirage. True - so the might argue - we have been fortunate enough to stumble upon mathematical schemes that accord with Nature in remarkable ways, but the unity of Nature as a whole with some mathematical scheme can be no more than a 'pipe dream'. Others might take the view that the very notion of a 'physical reality' with a truly objective nature, independent of how we might choose to look at it, is itself a pipe dream. . . . .

This is a question that has been posed for thousands of years . . . . .

On page 1045 Mr Penrose's very last paragraph reads :

The spacetime singularities lying at cores of black holes are among the known (or presumed) objects in the universe about which the most profound mysteries remain - and which our present-day theories are powerless to describe. As we have seen ....... There are other deeply mysterious issues about which we have very little comprehension. It is quite likely that the 21st century will reveal even more wonderful insights than those that we have been blessed with in the 20th. But for this to happen, we shall need powerful new ideas, which will take us in directions significiantly different from those currently being pursued. Perhaps what we mainly need is some subtle change in perspective - something that we all have missed . . . .

Mr Penrose did not even mention real geometrical objects let alone consider them to be the (one & only) purveyors of information. So real geometrical objects are at least one of the things that he has 'missed' - nevertheless they are things that are 'before our very eyes' & it will take a rather significant change in perspective if mainstream physics is ever to acknowledge them !!!?

And yes, I can't help repeating what David Deutsch said :

'I'm speaking to you now : Information starts as some kind of electrochemical signals in my brain, and then it gets converted into other signals in my nerves and then into sound waves and then into the vibrations of a microphone, mechanical vibrations, then into electricity and so on, and presumably will eventually go on the Internet, this something has been instantiated in radically different physical objects that obey different laws of physics. Yet in order to describe this process you have to refer to the thing that has remained unchanged through out the process, which is only the information rather than any obviously physical thing like energy or momentum.'

Answer : David Deutsch's elusive 'thing' is geometric objects plain & simple.

Geometric objects are the only phenomena that can be & routinely are copied / transferred on to consecutive sequences of widely different physical objects - from medium to radically different physical medium to radically different physical medium to radically different physical medium - & yet retain their shape - at least this obtains as to certain mediums as on many others they fade quickly away. Which is why we ourselves choose our mediums with a very careful eye to their ability to carry information (in its native that is geometric form) on themselves with optimum stability.

I know it's late but here are my closing remarks !!!! Thank you for your patience !!! I make them because because I want to emphasize a distinction I did not sufficiently clarify in my essay.

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.

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.

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

Some fascinating ideas in here, and I much appreciated your reference to the Hunting of the Snark!

"We have clues, clues most of all in the writings of Bohr, but not

answer ... Are billions upon billions of acts of observer-participancy the foundation of everything? We are about as fas as we can today from knowing enough about the deeper machinery of the universe to answer this question. Increasing knowledge about detail has brought an increasing ignorance about the plan.."

And then are we back at the question as to what is an observation? :)

Cheers!

Jennifer