Friday, July 28, 2017

New paper explains how to really rule out or allow local realistic theories of nature

There has been great publicity lately about experiments which claim to have ruled out "local realistic" theories of physics. In essence, they assert that there is no such things as objective reality, or, if it exists, the laws of physics must permit action at a distance. These claims are largely inspired by a popular book by J.S. Bell which fails to mention that there is another way to satisfy the requirements of the original theorem and experiments by Clauser, Holt, Shimony and Horne (CHSH): a different way of describing statistics and time at the macroscopic level of human experience.

Because the idea of objective reality (the idea that "existence exists" despite the fact that Robert Mercer has funded Ted Cruz and his mafia to convince us all otherwise, a really serious problem which has led to many, many purges at NSF) is increasingly taboo lately, I decided to post my new paper on this subject at a repository for scientists challenging orthodoxy:  http://vixra.org/abs/1707.0343.

If the two experiments discussed THERE support the Copenhagen theory, THAT is what would probably rule out local realistic theories. But until someone does the experiments, and they are replicated enough to make clear story, we do not know what will happen. Maybe they will rule out local realistic theories, but, because I believe in objective reality, I believe they are more likely to rule out the objections which have been made based on Bell's Theorem. No true scientist would rely too heavily on faith or opinion when simple experiments could tell us the truth.

Luda and I previously published a paper proposing a more definitive but difficult experiment. On this blog, I sketched out another experiment, which would also demonstrate faster than light or backwards time communication. The new paper gives more detail and explanation and theory.

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Beyond that, a few people in the Vedanta Society have objected to this concept of objective reality, the idea that everything which exists might be the emergent outcome of an Einsteinian kind of physics over four dimensional space-time, treating time as just another dimension. My comments to others in that group might also be helpful to others trying to understand the full import of the new paper:

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Me: Thank you for your intelligent questions, Serge!

 Serge: The physics of the phenomenon of light starts with the question "What is "light"? So, the answer is: while propagating, "light" behaves as a wave, and it behaves as a particle while interacting with solid body". So, what is "photon"? Is it an e-m wave or a particle? For me, the very idea of "wave packet" is the dullest and most senseless in all Physics. 

The number one message in this paper is "how to do an experiment which could radically reset the paradigm in real physics and technology." There are universities in India which have the skills and resources to do this, who could get instant global recognition. They could do so even without grasping all the related issues I discuss.

But yes, the 9 page paper also contains a condensed review of the underlying principles related to your questions.

One of the core problems here is that we have to use multiple levels of model and description, because of the practical realities of life. Just this morning, I discussed that problem with my wife in bed, and mentioned how we still use Newton's theory of gravity and Einstein-style general relativity (GR). We know that GR is more true and more basic than Newton's theory, but when you design a satellite orbit on a finite budget you probably don't implement GR on your PC!

The experiment which I propose in this paper falls in the realm of quantum optics. It builds on decades of empirical work with photons. To predict and design these experiments, we need to use quantum electrodynamics (QED). But I believe that QED is in principle just a practical approximation, like Newton's theory of gravity. In all forms of QED, the "photon" is one of the fundamental entities in the theory. It is mathematically well-defined -- but it is not either a particle in the classical sense, or a wave, or even a fuzzy mix of the two; it is a precise type of mathematical object (a dimension of Fock space).

 If we ask "What is a photon beyond the mathematics of QED? Why do photons exist?", that is like the folks who asked : "If radio waves are waves, what is the ether they are waves of?" It makes no sense to try to "explain" what the photons of QED are, EXCEPT by seeking a more fundamental theory. In fact, 'tHooft and I  (and Einstein) agree that we SHOULD be looking for such a more fundamental theory, which DOES include an effort to explain what a "photon" really is.  This new paper focuses on different versions of QED, and how to fix them.. but it also cites a previous open access paper I did on possibilities for a deeper theory. This past month, I have a much more complete idea of how to build and test such a theory, but as a retired person without the right kind of collaborators, I am not sure how to follow up.

But yes, I have long ago figured out my view of  "what a photon really is" in such a theory. Like Willis Lamb (famous for the Lamb shift), I believe that "there is no such thing as a photon, at the deeper level of description." The photon, like the consciousness of the human brain, is an important practical emergent pattern, but not "fundamental" in a physics sense.
It is a quantized flow of energetic force, quantized by the boundary conditions of the moment of its creation and the moment of its annihilation. Controversial as it is, I tend to expect that the same is true for the neutrino, regardless of its spin and the small rest mass people now think it has.

Talk about "wave packets" was important in the early history of quantum mechanics, but now it is basically just a heuristic way of trying to understand what the Maxwell-Dirac equations predict. Neither of us want to focus a lot of energy on wave packets right now.

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What does the phrase "speed of light" mean? For me, it should mean the speed with which the front of e-m wave propagates in all radial directions in reference to the source.

In the new paper, at the QED level, the speed of light is not a great mystery. The experiments involve propagation of photons through the air (or in the full version of the final experiment, an optical fiber). The mainstream version is totally consistent with what you just said. But the final experiment is designed to show propagation of information faster than light, and even backwards through time. 
The experiment does not play with the speed of light, but with the speed of propagation of information. 
 
Another unanswerable question (at least, for me) is as follows. Time is continuous. Time is not discrete. It means that the events may happen as close in time to each other as possible, or without any restrictions. So, if the Sun emits different e-m waves, it emits them continuously at the moments as close to each other in time as possible, but not discretely -- it does not emit all the possible e-m waves at the same moment of time and periodically. Then, why we have a frequency of e-m wave? We have this frequency AS IF the Sun is one single source of e-m waves -- a point emitter.

No great mystery here yet. The sun contains a huge number of atoms, each of which often emits a photon at a frequency described by basic quantum mechanics. Light from the sun is not one big wave, but rather a mix of light at different colors and frequencies. Still, it does have a certain degree of coherence. Natural sources of light do have a "coherence length" (which is probably explained in Scully great book on quantum optics) important to how they work. There has been a lot of work on coherence lengths, but I have often wished for a more complete picture. 

The only rational explanation for me is that "frequency" is a characteristic of space itself which, in such a way, reacts on the activity of Sun or any other continuous source of e-m waves.

No, just a  mix of a lot of frequencies from the sun. That's what white light is.

Second. What does it mean "to be informed"? What does it mean "to communicate information"?

Sometimes a simple example is better than an abstract statement.

Suppose that two entangled photons are emitted from the point x=0, one sent to detectors at x=-1 and another to a system at x=+5. Suppose that they are travelling at the speed of light, such that the photon on the left arrives at the detectors  1 nanosecond after the pair is created,  while the photon on the right arrives 5 nanoseconds after pair creation.

Suppose that we can flip a switch on the right, 5 nanoseconds after the pair is created, in such a way that we can flip which of the detectors on the left goes off. If we have total choice on the right, this clearly lets us send a bit of information from the time 5 nanoseconds back to 1 nanosecond, 4 nanoseconds back in time. 

People once thought that the quantum delay eraser system (by shih, Scully, etc, PRL January 2000) should allow such signalling, but it doesn't, because of technical constraints discussed in j.s. Bell's classic book. But this new system is different, and it really offers this kind of direct connection.
Furthermore, once it is shown for 4 nanoseconds,  changing the assumptions about physics, it then is relatively straightforward engineering to extend the delay to milliseconds to minutes and generate other applications, as in what I cited.

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Question: what is the speed of changing the overall entropic state?

Certainly the concepts of entropy, information and energy are important to understanding and designing the more complex systems which the new paradigm allows. But one step at a time. We have to make it real first.. and for myself, I am not sure which of the many important needs should get priority.

So, if instead of the "speed of light" we will consider the "speed of changing the entropic state of the complex system", then we can easily account for the effect of nonlocal entanglement.

I hear you asking "what is entanglement, really?" That's like your earlier question "What is a photon really?" As with the photon, it is not really a mystery within QED, but we can try to develop a more fundamental theory. At arxiv.org, I have given my view of it: a kind of statistical correlation of the field in one place with the field in another, specified mathematically by my new extension of the Glauber-Sudarshan P mapping.

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Thanks for the summary here, and also for other contributions reflecting your extensive knowledge. 

So many specific points to consider; I'll just respond generally by suggesting the distinction of the phenomenal objective level of nature, the phenomenal level of subjectivity (levels of mind), and pure 'subjectivity,' the level of consciousness itself--within which from a holistic (Vedant darshana) rather than reductive view, objective and subjective levels exist. In that holistic view, wholeness creates the parts.

There has been SO MUCH of a firehose of words debating which is more fundamental, consciousness or objective reality!!!! In my view, a sincere workable resolution is not something so trivial as cheering for one side or the other. I proposed a more complete picture in a paper published in Russia a few years back, posted at www.werbos.com/Mind_in_Time.pdf.

A few quick thoughts, trying again to explain.

For our personal, intelligent consciousness, we start in a way with key questions: is it possible to understand anything at all about our flow of experience? Is it so hard to understand that we have no choice (or desire?) but to lie back, revel at the incomprehensibility of it all and sincerely try to enjoy the pain and confusion which result? Or do we give in to our natural inner desire to understand better what is in this flow of experience, what comes to us -- to understand as well as possible? In my case, I do not give up trying to understand the flow of experience as completely as I can, because I have learned that persistence and discipline do make it possible to learn better. The most complete well-specified description of dynamic experience is what we call "mathematical" (simply a discipline of trying to be coherent and as complete as possible), and I see no reason as yet to give up on the hope of attaining that highest level of understanding (meaningful of course only if we know how to connect mathematics with other dimensions of life and experience).

To put it another way, mathematics is the only language on earth likely to be used elsewhere in our huge cosmos beyond the simple, relatively backward planet we live on. For me, it is a challenge to psychiatry to try to understand why a villager in an obscure isolated place should assume: 'Of course the God of the cosmos is just like me, speaking my own language, as stupid and unable to understand mathematics as I am. And of course the words I emit subject to these constraints must be the holy infallible scriptures of the cosmos." Even as he know there does exist another village on either side, equally reverent to other scriptures totally contradictory, with justification no better and no worse.

As a next step, people like Heisenberg start in the same place, and dedicate their lives to mathematical prediction of the flow of their experience, rejecting the concept that experience may be generated by a fundamental objective reality.
But realism IS NOT reductionist!!! Assuming such an equivalence.. is logically like racism, and like the people who say 'If you believe in climate change, you must be a Communist infiltrator trying to destroy democracy." We cannot really see truth unless we work hard to discipline away such knee-jerk behavior even in our own minds.

Unlike Heisenberg, I have had the additional experience from recent experiments and new mathematics, to see that the idea of objective reality is still possible. In time, having been open-minded both about paranormal experience and about objective reality, I am more and more convinced that both are real, and that both can be reconciled with each other. 

Based on that experience, I now believe that our consciousness and objective mathematical reality ( essentially just 'the law of everything" in mathematical physics) are BOTH absolutely fundamental, but in different ways. I see an image of the worm ouroboros, with the head inside the tail and the tail inside the head, in a way. I remember form pure mathematics how the even integers are a ;proper subset of all integers, under a homomorphism, BUT ALSO VICE-VERSA! Both viewpoints, objective and subjective, are valid, and consistent (or reconcileable) with each other.

In Mind_in_Time, I define first order "sanity" or 'zhengqi" as those states of a human brain or higher level intelligence, in which  there is full respect both for the primacy of the subjective viewpoint and for the primacy of the objective viewpoint, and effective integration of the two.

Many Chinese mystics say they demand body disciplines as first step on path to enlightenment, NOT because body discipline leads to enlightenment, but because it is essential to survival of the body after enlightenment. Gopi Krishna wrote a book on the great challenge of how to keep his body alive after he succeeded in raising kundalini, and I found it very helpful to my own survival in 1971/1972 after I did the same. But keeping the brain alive and functional is just as important as keeping the body alive, and I really wish the discipline of sanity were a key starting point of any really effective mystical development.

Of course, I have known for a very long time what varieties of hermeneutics exist in ever so many cultures, both spiritual and scientific, all over the world, and how they are usually biased somewhat by the nature tendency of human brains, before discipline, to construct stories which glorify their self-image by easy stereotypes of others. that is such an old story!!! Also, how people often look for excuses to avoid painful experience-based reality testing, and to retreat to the comfort of images they create in their own mind and they inherit from whatever culture they belong to. (Again, I highly recommend the article "Are we a nation of mystics?" by Greeley and McCready in Goleman's book Consciousness, which has empirical data on how this psychology plays out even in PhDs without the relevant type of training. Why not buy this important book used for $1+$3 for shipping from Amazon, as I did? It includes so many important viewpoints..)

I also recall the old Sufi story about an old student who has made no real progress towards authentic paranormal experience, who complained about it to his teacher. "I have studied for so many years. How can that youngster do things I cannot." Teacher: "because you lack desire." "Desire? But I have worked so hard for so long... done my best..!"
Teacher: "Let me show you what kind of desire I mean.' He puts the student's head under water almost to the point of death. Student: "Why did you do that?' Teacher:'Remember that feeling. When you desire the feelings of enlightenment as sincerely as you felt desire for air, then you might start to make real progress, and not just empty words you are so proud of."

Some aspirants to power in Islam interpret that story as justification for abusing students or being mean, but that is not the intent. If we can imagine what that experience would really feel like, using the natural power of empathy (mirror neurons) of our brain and the natural resonance between brain and soul, we can open the door to something real and far more important than empty purely verbal discourse. Though of course it requires more than just focus on the nonverbal flow of experience; it requires a kind of acceptance of peripheral vision, an ability to play a bit with "irrelevant" feelings different from what we expect or hope for looking forward. It is very important that we learn to work together to better teach this kind of whole-person development, building on sanity and reality testing and exploiting that as the basis for progress.

I also owe extreme thanks to my wife for her help in making sure I do not neglect intense reality testing myself. 
It is not always easy, but it is one important part of why I married her. 

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Luda and I returned late Monday from six months traveling mostly like students from Barcelona to the Arctic Ocean (two weeks on a Norwegian ship) and back to Rome, an incredibly rich and diverse set of experiences, only a few shown so far in my pictures on facebook. In mid August, thanks to the Ramanujan Foundation, I fly to Nepal (but sadly without Luda or my younger son Chris, who will stay here) to give a talk on how to reconcile science and spiritual reality, doing full justice to what we learn both from physics labs and from uncanny experience which humans have been puzzled by for ages and ages. Perhaps I will post that paper too somewhere, or publish it, after I learn more about the preferences and constraints of the people who invited the paper and pay for the travel.



Tuesday, July 25, 2017

Back to reality: review of book by lead physicist


Many of you know that theoretical physics is still mainly dominated by the school of thought pioneered by Heisenberg, who argued that the concept of objective reality is no longer tenable; we should not even try to understand how reality works, he argued, since our mind is all that is real to us, and all we need to be concerned with is making probabilistic predictions of experiments. That makes life a bit tricky for folks who want to be in touch with reality and to stick with the most established version of mainstream physics, both at the same time. Does anyone even remember the phrase “existence exists?”

A new book on this issue – available free on the web – has appeared, written by Gerard ‘tHooft, one of the key developers of the most mainstream theory of physics, the Standard Model of Physics, which is an example of two quantum field theories (QFT) glued together. Weinberg, Salam and ‘tHooft created EWT, the half which replaces Maxwell’s Laws and which has been tested over more experiments than any other physics theory in history. Just as Dyson developed the math needed to make Feynmann’s earlier work precise enough to be useful, ‘tHooft developed the math needed to convert the ideas of Weiner and Salam into something well-defined enough to meet the standards of physicists.

To download his book, just go to http:arxiv.org and search on his name (looking for cellular automaton interpretation in recent years). But I hope some of my comments will be understandable to people who do not understand everything in his book:
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First I thank the person who alerted us to the new book by 'tHooft explaining why he believes that objective reality (without the action at a distance assumed in many world's theories and in recent versions of Bohmianism) is still a tenable possibility in physics. 'tHooft is a brilliant and creative man, rightly recognized as one of the world leaders in the field.

I agree with 'tHooft that local realism is still possible and worth aiming at, despite the huge mass of misinformation out there in mainstream physics about this subject. 'tHooft supports local realism in the new book, just as he did many years ago. At that time, I was excited to find someone else in an excellent position to fight the popular misconceptions, but when I contacted him,  it turned out that he had additional conservative biases such that he may be REDUCING our chances of a "return to reality." The new book does not change that basic fact.

The bias which is a problem here is NOT his opposition to paranormal and spiritual ideas of all kinds. New breakthrough papers in physics do not require that the authors agree on everything else in the world!

The problem is his refusal to really face up to the problems posed by the "Bell's Theorem" experiments. He has a whole chapter on that issue in his book, but it seems to say "Well, I could be right, and this theorem/experiments could be right, so we need to check it further. Maybe my new mathematical theory could be local and realistic, so maybe the theorem somehow doesn't work."

To be honest, that is just sad. The theorem is a theorem, and there is no evidence that his new theory is local/realistic. To escape the consequences of a real mathematical theorem, it is essential to pay focused attention on the REQUIRED CONDITIONS of the theorem which 'tHooft has resisted doing, because of his emotional attachments/distractions which get in the way of seeking a local realistic model.

My 2009 paper in IJTP (open access, easily located via scholar.google.com) goes into detail on the three conditions in the CHSH theorem, and on what is LOGICALLY NECESSARY in order to construct a local realistic theory of physics consistent with the Bell's Theorem experiments. One simply MUST change the PARTICULAR MATHEMATICAL FORMULATION OF "CAUSALITY" assumed in the CHSH theorem.

In the new book, 'tHooft rightly points to constraints on human experimenters as a kind of cause of the Bell's theorem paradox. But he does not work out the IMPLICATIONS of those constraints. The most important implication is that a deterministic underlying theory results in more time-symmetric statistics than what CHSH causality assumes. Thus is what logically makes local realism possible.  But 'tHooft has a kind of phobia about time symmetry which gets in the way of what he wants to do.

In fact, while 'tHooft talks in hypothetical terms about the possibility of a local realistic models able to replicate the success of orthodox quantum mechanics in predicting the Bell's Theorem experiments, I have already constructed such local realistic models in concrete terms, in a series papers posted at arxiv.org, and in my 2015 paper with Dolmatova reviewing those results and going further.

It is ever so frustrating to hear people debate in abstract terms whether such a local realistic models is possible, when in fact it already exists. And no, it's not just a bunch of words; it is math, and testable math at that.

However, there is a very important caveat here. Nature is not always trivial to understand,  when we need to use multiple levels of approximation.

'tHooft rightly notes that canonical QED (KQED) gets a lot of popularity, rightfully, from its relative simplicity. When we assume first simplicity that electric transfer and protons and other simple charged particles all have a radius of zero, that simplifies the task of calculation and prediction. After studying this in much greater depth than 'tHooft has, I do conclude, regretfully, that a local realistic model which maintains that approximation and which fits the main database of QED Experiments is not possible. My 2015 paper with Dolmatova  (QIP, also posted at www.werbos.com/ triphoton.pdf) gives a basic description of MQED, which is not local/realistic any more than KQED is. However, MQED,  unlike KQED, is consistent with the key idea which Einstein, 'tHooft and I all emphasize: the idea that a relatively accurate quantum field theory  (like MQED) can be derived as the emergent statistical outcome of something like deterministic PDE operating at a more fundamental level. We can never show that, until we actually have that kind of quantum theory!

Another barnacle limiting 'tHooft's progress in establishing local realism is his insistence that "no predictions must change. The Born law must not be touched." That would be like refusing to touch the ether assumption and doing the Michelson-Morely Experiment!

I actually have made a lot of progress lately on the type of underlying deterministic model which could fill the gap, concretely. But if the political nonsense is too intense even to allow the trivial new to step of testing alternatives to Born (as in our QIP paper and in a simple new possibility I have discussed), should I even say More? Should I try to teach calculus to people who go psychotic when simple arithmetic comes up? (And when technological applications of "calculus" are riskier than those of "arithmetic ".) And no, I am not thinking of ‘tHooft as I say this.
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I wrote that in the Rome airport, in the hours waiting my flight home yesterday, on my Samsung tablet, using my wife’s Google FI phone as a mobile hotspot.
There are of course many technical points which should and could be spelled out in more detail, if a proper venue appears. Will it ever? I don’t know. For example, ‘tHooft seems to understand clearly at times that statistical mixtures of possible true states of the underlying real world  (what HE calls beables) are expressed as density matrices, not wave functions. For bosons at least, there is good reason to believe that these are NOT orthogonal! That math I have worked out, and Scully was excited.. until I also started to present the additional new work demonstrating local realistic models, which totally terrifies the Heisenberg set.

Friday, July 21, 2017

What happens to you and me when we die?

This week I witnessed an intense debate for and against the idea of afterlife. I proposed a view quite different from the usual extremes:
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Actually, as I near 70th birthday, a year after cancer surgery, I experience a more practical reason to be more concrete about how I view death in my personal planning.
Most people fall into the usual trap of a bias towards black or white thinking on the issue.
I really like Connie Willis's  inspired novel Passages on the issue of life after death, from a more sensitive and less formal black and white viewpoint. She does not endorse the Mickey mouse mundane view that "nothing at all survives death ever" but deeply and sensitively disputes the naive idea that we are the same after death, that we appear as our normal selves in some Bardo or other, to be judged where to walk with our normal two legs.

If in reality we as individuals are a symbiosis or "alchemical marriage" of mundane body and "soul" (which is easier for me to fit with science and with experience both), then of course after death we are missing something quite serious. How serious? It varies from person to person. As Bennett says, in his book popularizing Gurdjieff, which I translate as: "If you have important data to save, put it on hard disk."

For this blog, I should go further on a few obvious questions.

First, I never joined any of the various Gurdjieff schools or groups. At Harvard graduate school, I had two very close friends who did – one a fellow graduate student in the El primo scholarship based in France, set up by ouspensky, and another an undergraduate in the number two group based on Bennett in England. I did read all three of Gurdjieff’s books, and one by Bennett and ouspensky each.

Second, what can I say about the specific methods they propose for “putting your data (and other key information) on hard disk, more permanent storage”? Those schools had their own incredible personality issues and distractions and red herrings; I do not endorse all of that. Above all, in discussing ethics or the meaning of life, gurdjieff suggested  (as a very rough generalization) that people go through three levels of spiritual motivation as they mature: “to know, to do, to be.”
Yes, a lot of folks get frozen out as they pursue dry academic “knowledge” about life beyond the mundane. After a period of intense exploration by experiment (“to do”), they settle down to what matters objectively here (to be?). But in fact, it is usually not natural for a creature evolved from natural selection (on earth or in a larger ecology) to care only about prolongation of its own personal existence.
(E.O.Wilson’s book Sociobiology has some important gaps but deserves a lot more respect than the ideologues would allow it.) Thus is why I hesitate to say much more about the two core serious subgoals gurdjieff presents, the most reliable part of his approach: (1) “crystallization,” simply raising intelligence and knowledge in “the soul” based on mental challenges overlapping with the challenges we use to improve our brains; and (2) connection, in which we, like neurons within a brain, develop strong and energetic connections with other souls of the earth, ideally the earth as a whole.
Maybe these two are not so risky, if one remembers that they both require a high degree of honesty and altruism, higher emotional intelligence, without which many types of catastrophic breakdown can occur.

To that list I posted a few more details in another context:

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I am depressed that anyone on this list would reassure us with absolute total conviction  that paranormal connections exist only in a tiny fraction of humanity, somewhere less than .01%. Work in Dean's community, and in western mystical disciplines, suggests that this is false. Priest kings following the tradition of ancient Sumeria have used that lie, and claims of their divinity, to control and repress both brains and souls, for millennia -- most recently support by a follower of Ayn Rand, Mercer, of Ted Cruz, as a cynical way to subvert democracy. (Just search Google news!) As with mathematics ability, another discipline of the mind, DNA does matter, but training (intensity and quality) matters more, and the abilities aren't so strictly personal as the priest kings seem to imagine.

Once again, I highly recommend the article "Are we a nation of mystics?" by Greeley and McCready (sp?), reprinted in Goleman anthology Consciousness, which everyone on this list should own. (I bought it for  $1 used on amazon.)
From what I have seen, paranormal abilities have some analogy to mathematical abilities.  Dean rightly notes that only a small fraction of the people who come to him for testing show dramatic and reliable results, though 30% show something memorable. The classic book Mind Race by Puthoff and Targ sounds similar, and highlights two very special subjects, Swann and Price.

But what if Dean were testing for understanding of the mathematics of general relativity? The percentage of reasonable understanding would be even less -- but would be very much a function of education. Many people who COULD understand the basics of general relativity never do, because their education and motivation does not lead them there. Education in basic mathematics and general relativity is far more available than education in how to use inner powers of mind.  Yoga, AND people like Dean and Julia, have the potential to help close the gap. In truth, I wish for a world where both types of education are more prevalent and effective-- and I believe they support each other because discipline of the mind works best in am integrated way.

I have also been recently near the places of Carl Jung, and people who spoke about the synergy of music, Mathematics and mysticism. 

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Later I noticed a funny typo in the label of this post! "die" versus "due." (Lately such shifts are often done by google...) It reminds me of when my father had a few months left to live. "Just another drop dead deadline," he said. "I've been talking about them for years, and now it is just literal.."