How to generate correlations of ANY strength: Linear to Box

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Re: How to generate correlations of ANY strength: Linear to

Postby gill1109 » Mon Mar 10, 2014 10:30 am

That derivation started with an e_0 and a g_0. There is no mention of their probability distribution, but it seems that they are supposed to be statistically independent and uniformly distributed ... except that their domain is not a product space since they have to satisfy some requirement together.

Anyway: tell us the joint probability distribution of e_0 and g_0 (including where it lives). This is the S^3 stuff, the quaternionic stuff. Your model!

Then derive from that, the function f(.) and the law of theta_0; more precisely, derive the joint probability law of e_0 and theta_0.
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Re: How to generate correlations of ANY strength: Linear to

Postby Joy Christian » Mon Mar 10, 2014 11:24 am

gill1109 wrote:That derivation started with an e_0 and a g_0. There is no mention of their probability distribution, but it seems that they are supposed to be statistically independent and uniformly distributed ... except that their domain is not a product space since they have to satisfy some requirement together.

Anyway: tell us the joint probability distribution of e_0 and g_0 (including where it lives). This is the S^3 stuff, the quaternionic stuff. Your model!

Then derive from that, the function f(.) and the law of theta_0; more precisely, derive the joint probability law of e_0 and theta_0.


and are random vectors, uniformly distributed over S^2. In this respect is no different from , apart form the fact that they are statistically independent.

The function has been derived already in this document. The initial state of the system is a pair of quaternions, , in S^3, with the requirement that

,

where is an arbitrary function. No further specification of the physicial system is needed apart from the choice of , where .
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Re: How to generate correlations of ANY strength: Linear to

Postby gill1109 » Mon Mar 10, 2014 11:48 pm

Joy Christian wrote:
gill1109 wrote:That derivation started with an e_0 and a g_0. There is no mention of their probability distribution, but it seems that they are supposed to be statistically independent and uniformly distributed ... except that their domain is not a product space since they have to satisfy some requirement together.

Anyway: tell us the joint probability distribution of e_0 and g_0 (including where it lives). This is the S^3 stuff, the quaternionic stuff. Your model!

Then derive from that, the function f(.) and the law of theta_0; more precisely, derive the joint probability law of e_0 and theta_0.


and are random vectors, uniformly distributed over S^2. In this respect is no different from , apart form the fact that they are statistically independent.

The function has been derived already in this document. The initial state of the system is a pair of quaternions, , in S^3, with the requirement that

,

where is an arbitrary function. No further specification of the physicial system is needed apart from the choice of , where .

Excellent.

e_0 and g_0 are independent uniform random points on S^2.

You need to tell us what is x.

The initial state of the system is two quaternions p_0 and q_0. I suppose e_0 is somehow connected to p_0 and g_0 to q_0, am I right? If so, how?

What is the joint probability distribution of p_0 and q_0? What is x? After that, everything is fixed.

(e_0, theta_0) is a function of (e_0, g_0, x) is a function of (p_0, q_0, x).

The identity of mystery man "x" needs to be revealed!
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Re: How to generate correlations of ANY strength: Linear to

Postby Joy Christian » Tue Mar 11, 2014 4:02 am

is an arbitrary vector in R^3. The derivation I described can be repeated for another vector, say , instead of , and then another one, say , and so on.

In other words,



holds for all vectors in R^3, where the quaternions and in S^3 are defined in terms of , , and in eqs. (3) and (4) of this one-page document.

and are random vectors, uniformly distributed over S^2. In this respect is no different from , apart form the fact that they are statistically independent.

The function has been derived already in this document. The initial state of the system is a pair of quaternions, , in S^3, with the requirement that

,

where is an arbitrary function. No further specification of the physicial system is needed apart from the choice of , where .
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Re: How to generate correlations of ANY strength: Linear to

Postby gill1109 » Tue Mar 11, 2014 5:43 am

According to (3) and (4) in "complete.pdf", two quaternions called p_0 and q_0 are determined by specifying three elements of S^2 called e_0, g_0 and x. So we could proceed as follows: fix x (any you like). Choose e_0 and g_0 independently and uniformly distributed over S^2. Thereby we have defined quaternions p_0 and q_0 which will be statistically independent of one another. I don't think they are uniformly distributed over S^3. Their real parts (which are of course just one of their four components, when seen as points in R^4) have the uniform distribution over the interval [-1, 1]. And that's not the right answer for S^3. Their imaginary parts, when normalized to have length one, do have the uniform distribution on S^2. That part is the right answer. But together, it's the wrong answer. p_0 and q_0 are independent but not uniformly distributed.

But maybe you don't really want this uniform distribution, anyway. It is true that the final definition of the joint probability distribution of p_0 and q_0 is no longer dependent on which x we chose to start with.

What you do want, is to restrict your pair of quaternions to a particular subset. You demand a certain condition, (8), to hold for all x. Unfortunately, condition (8) leads on to (10) which is impossible to satisfy for all x simultaneously.

I conclude that the model is "empty". This is consistent with what we find from the mathematical link with the Pearle model. The restriction of hidden variables to those satisfying a certain condition for particular a and b, does not result in the condition being satisfied for all other a' and all other b' as well. This follows from Bell's theorem, which as a piece of pure mathematics (or pure probability theory) can certainly be applied to the "conspiracy loophole" variant of Pearle's model (by which I mean that the outcomes "0" aren't interpreted as "no detection but the state was there", but as "no state was there in the first place").
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Re: How to generate correlations of ANY strength: Linear to

Postby Joy Christian » Tue Mar 11, 2014 5:57 am

What is empty is Bell's so-called theorem. It has been proven wrong by me many times over. It is as wrong as 2+2=5 is wrong. 2+2=5 and Bell's so-called theorem are mathematical statements that have no relevance to physics. To understand Bell's naïve mistakes, you may have to read at least the introductory parts of my book:

Image http://libertesphilosophica.info/blog/
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Re: How to generate correlations of ANY strength: Linear to

Postby gill1109 » Tue Mar 11, 2014 6:11 am

Joy Christian wrote:What is empty is Bell's so-called theorem. It has been proven wrong by me many times over. It is as wrong as 2+2=5 is wrong. 2+2=5 and Bell's so-called theorem are mathematical statements that have no relevance to physics. To understand Bell's naïve mistakes, you may have to read at least the introductory parts of my book:

I think your representation of Bell is very naive. I just started a new topic which is related to this issue,
http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=30.

I want to isolate a true mathematical kernel from the big topic of Bell's theorem. You may or may not find it relevant, but I hope we will all be able to agree on some facts from elementary (discrete) mathematical probability theory. (You will find these facts irrelevant, because you circumvent Bell by changing the "background" assumptions. I am not going to change the conventional assumptions. You may call them naive if you like. It doesn't matter)

If we are able to agree on these elementary mathematical facts, then I would like to discuss their possible implication for computer simulation models such as the Michel Fodje ("epr-simple")/Caroline Thompson/Phil Pearle models. Now this could be interesting for you. If you want to somehow represent your model in a computer simulation, then it can be useful to know what such simulations can do, and what they can't do.

If we are able to agree on some mathematical statements about the limitations of such computer simulation models, then there is hope we might have a contentful discussion on physics and on metaphysics. On the relation between mathematical models of reality, and reality itself. The reason that going to computer simulation models is fruitful, is because computer simulation models can themselves be seen as instantiations of mathematical models. I find that physicists often find it hard to separate mathematical models of reality, from reality itself. This is because, for them, mathematics is "just" the language with which they describe nature. But for a mathematician, mathematical models have their own abstract existence, independence of whatever physical situations they might be used to describe. I think that physicists are more able to comprehend the distinction (between reality, and a mathematical model for part of it) when we look instead at the difference between reality and a computer simulation of part of reality. Everyone can comprehend that distinction.

Also we could branch out and discuss coincidence loophole models (Michel's "epr-clocked"). We could branch out and discuss QRC (the quantum Randi challenge).

However I'm not prepared to discuss the computer simulation models, and even less, the physical and metaphysical implications, till after we have been through the first step. Can we agree on some facts from elementary (discrete) mathematical probability theory? A mundane first step, for sure. Classical discrete probability. Pure mathematics. No physics. Possibly irrelevant... whether or not it is relevant is a different question, which I insist on postponing. In order to communicate at all we need a common platform of agreed facts. Part of that common platform has to be "elementary facts from elementary mathematics".

Of course, regarding the first pages of your book, I think there are some howlers of mathematical errors in those first pages of your book. We have been through all that before. I think we've agreed not to talk about this particular issue any more. You know my opinion, I know yours. I just mention my opinion for the benefit of any new "neutral bystanders", any newcomers. They can find my documentation of support for my opinion elsewhere, easily; and they can find your "refutation" of it, too. And judge for themselves.
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Re: How to generate correlations of ANY strength: Linear to

Postby Joy Christian » Tue Mar 11, 2014 7:55 am

There are indeed many mathematical and logical howlers in your uninformed and dishonest argument. I myself, as well as many others, have exposed your howlers many times over: http://arxiv.org/abs/1203.2529.

My physics and mathematics, on the other hand, are of highest calibre. I am sorry that you are unable to understand my argument, but that is not really my problem.
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Re: How to generate correlations of ANY strength: Linear to

Postby gill1109 » Wed Mar 12, 2014 12:19 am

Joy Christian wrote:There are indeed many mathematical and logical howlers in your uninformed and dishonest argument. I myself, as well as many others, have exposed your howlers many times over: http://arxiv.org/abs/1203.2529.

My physics and mathematics, on the other hand, are of highest calibre. I am sorry that you are unable to understand my argument, but that is not really my problem.

I think you should delete the word "dishonest". That is a personal attack, an attack on my scientific integrity.

You are welcome to your high opinion of your mathematics, and low opinion of mine. I have no problem with that.
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Re: How to generate correlations of ANY strength: Linear to

Postby Joy Christian » Wed Mar 12, 2014 12:25 am

gill1109 wrote:
Joy Christian wrote:There are indeed many mathematical and logical howlers in your uninformed and dishonest argument. I myself, as well as many others, have exposed your howlers many times over: http://arxiv.org/abs/1203.2529.

My physics and mathematics, on the other hand, are of highest calibre. I am sorry that you are unable to understand my argument, but that is not really my problem.

I think you should delete the word "dishonest". That is a personal attack, an attack on my scientific integrity.

You are welcome to your high opinion of your mathematics, and low opinion of mine. I have no problem with that.


It is not a personal attack. Your argument IS dishonest, as explained in the linked video. Please watch the video to appreciate how dishonest your argument really is.
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Re: How to generate correlations of ANY strength: Linear to

Postby gill1109 » Wed Mar 12, 2014 12:44 am

Joy Christian wrote:It is not a personal attack. Your argument IS dishonest, as explained in the linked video. Please watch the video to appreciate how dishonest your argument really is.

My argument would be dishonest, if (a) it really was a "straw man" argument, and (b) it was knowingly a straw-man argument.

You may believe (a) if you want to (I believe you would be wrong). But even if you know my argument is a straw man argument, you cannot know (b) that I was fully aware of that. Please withdraw the word "dishonest". It has no place here. You may attack my scientific competence indirectly, through attacking my arguments, but not my scientific integrity.
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Re: How to generate correlations of ANY strength: Linear to

Postby Joy Christian » Wed Mar 12, 2014 1:17 am

gill1109 wrote:
Joy Christian wrote:It is not a personal attack. Your argument IS dishonest, as explained in the linked video. Please watch the video to appreciate how dishonest your argument really is.

My argument would be dishonest, if (a) it really was a "straw man" argument, and (b) it was knowingly a straw-man argument.

You may believe (a) if you want to (I believe you would be wrong). But even if you know my argument is a straw man argument, you cannot know (b) that I was fully aware of that. Please withdraw the word "dishonest". It has no place here. You may attack my scientific competence indirectly, through attacking my arguments, but not my scientific integrity.


The dishonesty of (b)-kind started to occur in your argument when you continued to use your incorrect argument even after your errors were pointed out to you by several people, at least 85 times, to be exact. For example, it was pointed out to you that you have inserted an error in your equation (2), and then falsely claimed that your erroneous equation (2) is actually my equation. That is deliberate deception, according to the video I have linked above. What is more, it is not only I who has pointed out to you that your equation (2) is not my equation, but also Fred and Edwin Klingman, among several others---at least 85 times, to be exact. And yet you continue to insist that your erroneous equation (2) is actually my equation. Can you explain to us why that is not deliberate dishonesty in your modus operandi?
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Re: How to generate correlations of ANY strength: Linear to

Postby gill1109 » Wed Mar 12, 2014 3:08 am

Joy Christian wrote:
gill1109 wrote:
Joy Christian wrote:It is not a personal attack. Your argument IS dishonest, as explained in the linked video. Please watch the video to appreciate how dishonest your argument really is.

My argument would be dishonest, if (a) it really was a "straw man" argument, and (b) it was knowingly a straw-man argument.

You may believe (a) if you want to (I believe you would be wrong). But even if you know my argument is a straw man argument, you cannot know (b) that I was fully aware of that. Please withdraw the word "dishonest". It has no place here. You may attack my scientific competence indirectly, through attacking my arguments, but not my scientific integrity.


The dishonesty of (b)-kind started to occur in your argument when you continued to use your incorrect argument even after your errors were pointed out to you by several people, at least 85 times, to be exact. For example, it was pointed out to you that you have inserted an error in your equation (2), and then falsely claimed that your erroneous equation (2) is actually my equation. That is deliberate deception, according to the video I have linked above. What is more, it is not only I who has pointed out to you that your equation (2) is not my equation, but also Fred and Edwin Klingman, among several others---at least 85 times, to be exact. And yet you continue to insist that your erroneous equation (2) is actually my equation. Can you explain to us why that is not deliberate dishonesty in your modus operandi?


Yes I know that you, Fred and others claimed that my analysis was false and pointed out alleged errors numerous times. I could not make any sense of any of their criticisms. On the other hand, a lot of other people agreed with my analysis (Lucien Hardy, Scott Aaronson, Adrian Kent, Florin Moldoveanu, David Hestenes, Manfried Faber, Azhar Iqbal, Bryan Sanctuary, to name but a few. Some of whom actually had a strong interest in hoping that you were right, and some of whom are far more competent in this particular branch of algebra than you or I).

So I do not think my persistence in claiming that my analysis was *not* a straw-man attack does not constitute any kind of dishonesty. Your criticasters read what you write. They discover inconsistencies. They are forced to "reconstruct" what you probably meant, since what you actually wrote appears to them clearly to be plain nonsense. Garbled text? Typos? Missing definitions? They might be wrong in their reconstructions, since obviously you are the sole person who knows what the intended "sense" of what appears nonsense to others, might be. I did not find Edwin's or Fred's explanations of any help at all. In fact from their "explanations" I got the impression they were a good deal less competent in algebra than you or I are. I have plenty of good reasons to believe that no scientific "sense" can be made of your models at all. It's just poetry. Science Fantasy. It could also be a fantastic new long-running Sokal-like hoax.

I'm interested in the limits of local realist simulation models for EPR-B experiments, and I'm interested in science outreach. I have yet to meet a science journalist who had a clue what Bell was all about. Many experimenters do fantastic experiments but actually are also rather shaky in the "metaphysical" implications of what they are doing. A famous Leiden colleague of mine in quantum optics published, in one of the top journals, an experimental violation of the Tsirelson inequality, without anyone noticing that QM had thereby been destroyed (unless there was a mistake in the experiment. There was.) Another famous Leiden colleague of mine in quantum optics told journalists that his GHZ experiment proved with onlhy finitely many runs, just by a logical deduction, that local realism was impossible. His own experiment did not actually reproduce the GHZ predictions exactly so his own logic would have destroyed his own paper! There has been a conspiracy of silence around the famous loopholes. It is only now that the experimenters suddenly see a loophole free experiment in reach, that it has become politically correct to discuss them seriously. Caroline Thompson did wonderful work and was shamelessly treated by the establishment. They are now silently adopting many of her suggestions and at last trying to take account of her criticisms, but you won't hear them mention her name or publications.

http://freespace.virgin.net/ch.thompson1/Papers/The%20Record/TheRecord.htm
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Re: How to generate correlations of ANY strength: Linear to

Postby Joy Christian » Wed Mar 12, 2014 4:15 am

gill1109 wrote:Yes I know that you, Fred and others claimed that my analysis was false and pointed out alleged errors numerous times. I could not make any sense of any of their criticisms.


Let me then point out your errors to you once again, especially because you confessed in this post that you are "algebraically challenged." Here is the paper where I systematically list all of your algebraic errors, misrepresentations, and confusions: http://arxiv.org/abs/1203.2529. I hope that it finally helps you to see your errors.

gill1109 wrote:On the other hand, a lot of other people agreed with my analysis (Lucien Hardy, Scott Aaronson, Adrian Kent, Florin Moldoveanu, David Hestenes, Manfried Faber, Azhar Iqbal, Bryan Sanctuary, to name but a few).


This is a patently false claim. No one apart form Mr. Moldoveanu agrees with your "analysis." In particular, Lucien Hardy, David Hestenes, Manfried Faber, Azhar Iqbal, Bryan Sanctuary, and many other competent physicists and mathematicians fully agree with my algebraic arguments and clearly see where you have blundered.

Lucien Hardy, in particular, reproduced the correlation derived in my one-page paper in explicit details, with his considerable theoretical and mathematical talents.

Even the computer tutor Scott Aaronson and the nonlocalist Adrian Kent now realize that they were misled about my work by your erroneous and confused arguments.

That leaves Mr. Moldoveanu, who is an unqualified individual without any academic attachment, and who has never been able to publish a single paper in any journal in his entire lifetime. Moreover he demonstrably lacks intellectual capacity and mathematical competence to understand arguments as physically and mathematically sophisticated as those presented in my papers. Therefore his opinion about my work is not worth a penny. He was also forced to apologize to me publicly by both the FQXi and arXiv administrations for falsely accusing me and my work of various unspeakable things.

gill1109 wrote:So I do not think my persistence in claiming that my analysis was *not* a straw-man attack does not constitute any kind of dishonesty.


I recognize a straw-man argument when I see one.

I recognize a mathematical fallacy when I see one.

I recognize a logical fallacy when I see one.

I recognize dishonesty when I see one.

I recognize a rant when I see one.
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Re: How to generate correlations of ANY strength: Linear to

Postby Heinera » Wed Mar 12, 2014 4:59 am

Joy Christian wrote:Even the computer tutor Scott Aaronson and the nonlocalist Adrian Kent now realize that they were misled about my work by your erroneous and confused arguments.


Has Scott Aaronson said anything about your work since this?
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Re: How to generate correlations of ANY strength: Linear to

Postby Joy Christian » Wed Mar 12, 2014 5:30 am

Heinera wrote:
Joy Christian wrote:Even the computer tutor Scott Aaronson and the nonlocalist Adrian Kent now realize that they were misled about my work by your erroneous and confused arguments.


Has Scott Aaronson said anything about your work since this?


Yes, he has.
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Re: How to generate correlations of ANY strength: Linear to

Postby Heinera » Wed Mar 12, 2014 5:37 am

Joy Christian wrote:
Heinera wrote:
Joy Christian wrote:Even the computer tutor Scott Aaronson and the nonlocalist Adrian Kent now realize that they were misled about my work by your erroneous and confused arguments.


Has Scott Aaronson said anything about your work since this?


Yes, he has.


Interesting. Could you elaborate a bit on that, e.g. give a link or something?
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Re: How to generate correlations of ANY strength: Linear to

Postby Joy Christian » Wed Mar 12, 2014 5:50 am

Heinera wrote:Interesting. Could you elaborate a bit on that, e.g. give a link or something?


Why don't you ask him yourself? You seem to have had no difficulty finding the other link.
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Re: How to generate correlations of ANY strength: Linear to

Postby gill1109 » Wed Mar 12, 2014 10:23 am

Joy Christian wrote:In particular, Lucien Hardy, David Hestenes, Manfried Faber, Azhar Iqbal, Bryan Sanctuary, and many other competent physicists and mathematicians fully agree with my algebraic arguments and clearly see where you have blundered.

Splendid. We look forward to their own publications citing your work and building further on your contributions.
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Re: How to generate correlations of ANY strength: Linear to

Postby Joy Christian » Wed Mar 12, 2014 10:53 am

gill1109 wrote:
Joy Christian wrote:In particular, Lucien Hardy, David Hestenes, Manfried Faber, Azhar Iqbal, Bryan Sanctuary, and many other competent physicists and mathematicians fully agree with my algebraic arguments and clearly see where you have blundered.

Splendid. We look forward to their own publications citing your work and building further on your contributions.


No need to wait. Here is but one example of a paper citing some of my work on the subject: http://arxiv.org/abs/1101.3619 ; cf. Refs. 31 and 32.

There are plenty more citations to my papers, which can be easily found by searching in http://adsabs.harvard.edu/index.html. So splendid, indeed.
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