Classical Spheres, Division Algebras, and the Illusion of Quantum Non-locality:

Thomas Ray

"Any mathematical formulation ought to be classically computable."

Then tell me the value of Chaitin's Omega number.

Thomas Ray

"Algorithms are products of the brain-mind, but that doesn't mean the physical processes of the brain-mind are themselves algorithmic."

Come again? You suggest that algorithms -- which are essentially recipes for functions -- mystically emerge from brain minds. No wonder you and quantum mechanics are so confused.

Thomas Ray

"Go ahead, simulate the physical space as S^3, not as R^3! Nobody has done it yet. Nobody knows how to do it. Christian is not giving us any clue. Tom H Ray is not giving us any clue. I suspect it cannot be done without networking a whole lot of computers through a Möbius-band-like randomly parity reversing wormhole through some black holes into alternative universes."

Richard apparently can't read the clues. In the very beginning, I asked whether the simulation of a continuous function is a continuous function. It turns out that the multitude of simulations that represent Joy's function on classical computers aren't good enough for Bell believers who said that couldn't be done. Richard is like Bishop Berkley snorting "ghosts of departed quantities!" at Newton, whose success at the calculus overshadowed the method.

If the simulation of a continuous function is a continuous function, a distributed computer network might be able to emulate or replicate -- rather than simulate -- Joy's function with a reversible algorithm that continues the function analytically. A simulation, though, is a programmed representation of a function, and the Bell believers got exactly what they asked for.

Another clue I dropped -- the missing theorem that allows 1 to 1 correspondence between every classical observation to at least 1 quantum state. That's local realism, without collapse of the wave function and without entanglement. The wave function is continuous, and the physics is covariant -- just as Joy has it.

Richard Gill

Peter: "If anyone in the field wishes to run a computer model they're welcome to your £500. I'm sure it wouldn't be difficult as I can do it with cosine tables.

Did you understand what the blue pivoting quadrant did? I think it's cleverer than you noticed. A number of others have so I'm sure you're able. I've improved at A4 'Kit' with more cosines added in the right places to show how they should be read off."

No I didn't understand. I also made a typing error. The offer is 5000 not 500. But Euros not pounds or dollars.

So, great that so many people understand it. Now they can program it, show how it can run on a network of computers connected to as to respect locality and causality, and not only win 5000 Euro from me but also the Nobel prize.

No one has yet performed a successful loophole free Bell-CHSH test experiment. They might succeed in about five years from now, some people think. So not only would the lucky winner be the first to perform a successful loophole free Bell-CHSH test experiment, they would also actually do it using only classical physical systems (I mean of course: using only physical systems for which classical physics gives a perfectly adequate, "local realistic", description).

Now don't tell me that a computer uses quantum physics because it has transistors in it or whatever they use nowadays. You can replace the machine on your desk with a scribe and an abacus and a papyrus roll, if you like. It's just another Turing machine, for present purposes.

Now don't tell me that quantum physics makes our brains work like they do and create the illusion of consciousness because of QM, either.

The point is that a classical physical description would adequately represent the phenomenon being studied here. Alice and Bob tossing coins to choose settings on a machine by pressing buttons marked "H" and "T". Alice and Bob's machines receive some kind of message or transmission from another machine. After this has happened Alice and Bob's machine starts flashing a green or red lights. The machines are black boxes. There could be a PC in the box, or a scribe; the transmissions could be by email, or by pigeon post.

Write three computer programs (one for a PC inside Alice's box, one for a PC inside Bob's box, and one for a PC standing for the source). You know which communications are allowed, when, and in which sequence. All others are forbidden.

Simulate a violation of the CHSH inequality and become world famous.

Thomas Ray

For the benefit of those who don't understand why Nick's pontifications on computer science are irrelevant to cutting edge computability research, consider that Chaitin's Omega number is algorithmically compressible and uncomputable.

So when Nick makes his logically contradictory statement that all mathematical functions should be computable, he betrays an innocence of the mathematical fact that most numbers are uncomputable -- as applied to physical models, then, no discrete numerical implementation of a model is identical to the model. Trivial? Yes -- except that Nick (and Richard et al) would have us believe that Joy Christian's simulations aren't 'real' simulations because his model exists in a different space than the computer lives in. Yet they will also turn around and say the computer is indifferent to what space it is computing in! Heads I win, tails you lose.

Richard's personal putdowns and Nick's pontifications, however, do not reach the level of serious criticism required to explain why computer simulations of conventional quantum mechanical models -- complete with interpretations of superposition and nonlocality -- are physically real, while the simulation of a continuous measurement function without the superfluous assumptions is not.

One will always find it exceedingly easy to prove what one assumes in the first place.

Tom

Thomas Ray

"Write three computer programs (one for a PC inside Alice's box, one for a PC inside Bob's box, and one for a PC standing for the source). You know which communications are allowed, when, and in which sequence. All others are forbidden."

A perfectly coherent example of proving what one assumes. The correlation function of A,B is random relative to the source whose choice is random.

General covariance as explained in Joy's measurement framework falsifies the notion that the choice function is invested in random detector settings -- the correlation function C_a,b is a pair of dichotomic variables that evolve covariantly as determined from the initial condition, conveniently chosen by random toss of a fair coin, which is a deterministic function. The extra degree of freedom required for covariant evolution is built into the structure of the real spacetime in which we measure, not an unconstrained probability space of discrete measurement functions.

pjackson

Richard,

Your playing field isn't level. A classical experiment does the task perfectly well. You may like writing computer programmes but you're in the the minority. Your description of a valid EPR experimental protocal is also unrecognisable. Why do Alice and Bob need to press buttons market H and T? They should have no input to the random H/T state which represents spin 'up/down'.

The H/T state is generated by the single independent (Stern-Gerlach etc) splitter creating the two so called 'singlet state' particles which represent H and T, then sent a (preferably great) distance in opposite directions.

All Alice and Bob do is independently select an angle each time. Then, on arrival of the (H/T) state and 'detection/measurement', the red or green light flashes.

We then have two data sets; We can thus analyse EACH before putting them together for correlation. Consistent with past experiments I've shown that each of them has their own LOCAL unequal distribution using absolute angles. i.e. when they chose say 180^o the flashes are 100% red, when choosing 0^o 100% green, and at 60^o they both find 75% red and 25% Green.

Now in stage 2 we put them together and correlate (compare) them using RELATIVE angles (weak measurement statistical analysis). Now you mistook the sand v sand (90^o) correlation for stage 1, where they both find 50%. In fact it's NOW just one of many 'same setting' cases. Penny dropped? In ALL such cases their findings are identical. What the 'pivoting quadrant' does is allow the relative findings to be compared for all cases;

i.e. whatever the H/T case; 30^o and 120^o = 90^o difference. Alice 30^o (lime) was 97% green, and Bob's 120^o (buff) was 77% red. But we're not comparing just those! The reciprocal case of Bob 30^o and Alice 90^o is in the SAME set. All results in that set then balance out, giving the 50:50 correlation!

On that bombshell... I'll leave you to ponder.

Peter

pjackson

Tom,

Please take more care. Your last post was almost comprehensible and appeared to agree with my experiment, theory and pedagogical explanation (though any consistencies with Joys supermathegeometopologimatial approach are as I always suspected).

Best wishes

Peter

John Merryman

Tom,

"One will always find it exceedingly easy to prove what one assumes in the first place."

I assume this applies to spacetime being physically real as well.

It seems to me there is a deeper issue going on here, that is generating all the rancor and emotional static and that has to do with how knowledge, models, terms, descriptions, etc. are constructed out of an editing process, because the whole is not discrete and therefore not computable. We still have this sense of some objective state of knowledge, even though all we learn keeps telling us that the very process of thought creates bias. Even physicists are subject to their points of view. So it seems likely this conflict will continue until everyone is exhausted and then the psychologists and philosophers will pick through the battlefield for clues, as fights over the multiverses and non-locality continue in the geriatric wards.

Regards,

John M

Nick Mann

"Then tell me the value of Chaitin's Omega number."

I don't know how this relates to anything I said, but here's 64 digits of an Omega:

0000001000000100000110001000011010001111110010111011101000010000.

https://www.cs.auckland.ac.nz/~cristian/Calude361_370.pdf

Been around for over a decade. You need to keep up.

John Cox

Back to what I understand to be Dr. Christian's opening argument; ie. simply that Bell assumed correlation of points on a plane to points on a sphere would be the same as correlation spatially as points on a bounded surface to points on another bounded surface. The argument therefore going to; a sphere being an unbounded surface, it could spatially continuously roll on a bounded planar surface and thereby perform a mechanical function where uniformly distributed points on a sphere would continually contact equivalently spaced points on the plane, thus producing (at least) as many correlations of point pairs as predicted by a QM model.

That goes to Nick's argument that it should therefore be macroscopically demonstrable, and to Richards contention that to do so means in a computer program if one instruction is followed, another has to be changed. Obviously there is a bug.

I don't know computers well at all but I know hyper text mark-up language when I see it, and here is what looks like a spider to me. On April 5 Joy posted a comment which included a link consisting of one underlined word 'here', and if you read down you'll see the instruction line saying; ##Uniform random points on sphere generated using 'trig method' (method 3) , which is followed with specs as to the program code used. Now, I'm not certain but that trig method 3 might refer to one of seven regular forms of geometric shapes to project points and is probably that of an equilateral triangle with the three points defining the equatorial plane, which then can be rotated omni-directionally. So far, so good. BUT, if you take a hexagonal pattern of six triangles on a plane and replicate them to fill a planar surface , then wrap them into a spherical surface, you have to loose one of those triangles in enough hex regions so the plane will negatively warp. Typically in Thompson Problem projections this results in a non-homogeneous pattern on the sphere surface such that; there will be simply connected triangles in a hex pattern with simply connected edges to others, until you reach a node where there is a region of five triangles in a pentagonal arrangement. In the program code using (method 3) this might result in those pentagons having common vertices at the three points of the equatorial triangle. Hence the rolling ball would fail to have correlation to the hexagonal packing on the planes surface.

There might be a fix, however. I found a recent arXiv paper, 1403.3851v1 submitted 15 March 2014 by Cheng Guan Koay of the University of Wisconsin School of Medicine, titled Distributing points uniformly on the unit sphere under a mirror reflection symmetry constraint. This projection uses a quaternion, and achieves symmetry across the equatorial plane on all but three runs (rotation orientations) out of 400, and those three need only a slight fudge and thus might be of utility in establishing the orthogonals in Joy's topological framework ( not model, but more like the wire armature a sculptor might use to support the clay in forming a model).

Don't know if this would be helpful, somebody that knows Joy's framework well enough, and computer program language well enough, might be able to say at a glance. jrc

Thomas Ray

Oh, I know the result, Nick. I'm an avid reader of Chaitin. Being up to date on one's references doesn't guarantee one's knowledge, however. For instance, knowing the difference between calculating and computing.

Thomas Ray

No, John, it does not apply to spacetime. Spacetime is precisely described in closed form mathematics (Minkowski space) which is completely independent of, yet correspondent to, the well tested physical phenomena of special and general relativity.

Please, take it to another thread.

Nick Mann

"Oh, I know the result, Nick. I'm an avid reader of Chaitin."

Chaitin didn't write the paper. Cris Calude et alii wrote the paper. Chaitin held their hand, spoke encouragement and apparently granted his imprimatur.

Since you're an avid reader of GC maybe you can cite where he discusses "Computing a Glimpse of Randomness." Undoubtedly he does somewhere or other. Maybe he says the title ought to have been "Calculating a Glimpse of Randomness."

Thomas Ray

You're talking yourself into a hole of your own digging, Nick. Do the words "universal Turing machine" ring a bell?

Nick Mann

Marcus Chown seems to use "compute" and "calculate" interchangeably here, but then what does he know? Anyway, I'm answering my question which Tom seems unable to deal with, to wit, how does Greg Chaitin feel about "Computing a Glimpse of Randomness?":

"Determining all the digits of Omega is clearly an impossibility for lowly human beings. The number in its entirety is really knowable only by God. Incredibly, however, Calude has managed to calculate the first 64 digits of Omega -- or at least an Omega. Those digits are the ones shown at the beginning of this chapter.

"Calude was able to calculate 64 bits of a nominally uncomputable number because, contrary to everything that has been said up to now, the computing barrier discovered by Turing can actually be broken. This is because Turing dened the halting problem for a classical Turing machine -- a familiar general-purpose computer. However, nature permits types of machines that Turing did not anticipate such as quantum computers. These are 'accelerated Turing machines'. It may be possible to use them solve the halting problem and compute other apparently uncomputable things. Calude himself used ingenious mathematical tricks to partially circumvent the Turing barrier and compute 64 bits of Omega -- a feat even Chaitin, the inventor of Omega, had believed impossible.

"Calude's demonstration that it is possible to know at least some of the digits of Omega has left a strong impression on Chaitin. He has gone so far as to suggest that knowledge of Omega could be used to characterise the level of development of human civilisation. Chaitin points out that, in the 17th-century, the mathematician Gottfried Leibniz observed that, at any particular time, we may know all the interesting mathematical theorems with proofs of up to any given size, and that this knowledge could be used to measure human progress. 'Instead, I would propose that human progress -- purely intellectual not moral -- be measured by the number of bits of Omega that we have been able to determine,' says Chaitin."

http://ondoc.logand.com/d/1777/pdf (pp. 330-1)

Nick Mann

Sloppy cut-and-paste job there. Paragraph 3. Should read: "Turing defined the halting problem".

[deleted]

A mathematical calculation is always a definite numerical result. Most numbers, on the other hand, are uncomputable.

One can usually compute a function, however, which is why most mathematicians and computer scientists do use the terms interchangeably.

In Chaitin's case, the numerical result is calculable, yet the function is uncomputable. The arithmetic has a built in uncertainty.

In Joy's research as well as Chaitin's, the function is independent of its numerical implementation. The structure of the space has a built in certainty: strong quantum correlations.

Thomas Ray

Last was mine.

Nick Mann

Calude maintains that most of the interesting mathematical problems can be written as halting problems. This blurs the distinction, and you see its inspiration in Gödel's letter to John von Neumann as well as in Chaitin. In a P=NP universe (probably not ours) there'd be no work for mathematicians.

Your concern about algorithmic formulations appearing "mystically" is unfounded. They're emergent, like all mental constructs. That's what the what the whole supervenience and downward causation debate has been about lo these many decades. George Ellis' contest paper is an interesting recent example -- and he cleverly uses hierarchy theory to buttress macrorealism. A guy called Russ Abbott works along more strictly computationalist lines on a less highfalutin' level (his baby is "downward entailment"). Since you're a fan of complexity theory you must dig hierarchy theory, one would think. Is it mysticism?

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