A prediction. Also, a couple of wishes…

The Prediction:

While the week of the Nobel prizes always has a way to generate a sense of suspense, of excitement, and even of wonderment, as far as I am concerned, the one prize that does that in the real sense to me is, of course, the Physics Nobel. … Nothing compares to it. Chemistry can come close, but not always. [And, Mr. Nobel was a good guy; he instituted no prize for maths! [LOL!]]. …

The Physics Nobel is the King of all awards in all fields, as far as I am concerned.

That’s why, this year, I have this feeling of missing something. … The reason is, this year’s Physics Nobel is already “known”; it will go to Kip Thorne and pals.

[I will not eat crow even if they don’t get it. [… Unless, of course, you know a delicious recipe or two for the same, and also demonstrate it to me, complete with you sampling it first.]]

But yes, Kip Thorne richly deserves it, and he will get it. That’s the prediction. I wanted to slip it in even if only few hours before the announcement arrives.

I will update this post later right today/tonight, after the Physics Nobel is actually announced.

Now let me come to the couple of wishes, as mentioned in the title. I will try to be brief. [Have been too busy these days… OK. Will let you know. We are going in for accreditation, and so, it’s been all heavy documentation-related work for the past few months. Despite all that hard-work, we still have managed to slip a bit on the progress, and so, currently, we are working on all week-ends and on most public holidays, too. [Yes, we came to work yesterday.] So, it’s only somehow that I manage to find some time to slip in this post—which is written absolutely on the fly, with no second thoughts or re-reading before posting. … So excuse me if there is a bit of lack of balance in the presentation, and of course, typos etc.]

Wish # 1:

The first wish is that a Physics Nobel should go, in a combined way, to what actually are two separate, but very intimately related, and two most significant advances in the physical understanding of man: (i) chaos theory (including fractals) and (ii)catastrophe theory.

If you don’t like the idea of two ideas being given a single Nobel, then, well, let me put it this way: the Nobel should be given for achieving the most significant advancements in the field of the differential nonlinearities, for a very substantial progress in the physical understanding of the behaviour of nonlinear physical systems, forging pathways for predictive capacity.

Let me emphasize, this has been one of the most significant advances in physics in the last century. No, saying so is emphatically not a hyperbole.

And, yes, it’s an advance in physics, primarily, and then, also in maths—but only secondarily.

… It’s unfortunate that an advancement which has been this remarkable never did register as such with most of the S&T “manpower”, esp., engineers and practical designers. It’s also unfortunate that the twin advancement arrived on the scene at the time of bad cultural (even epistemological) trends, and so, the advancements got embedded in a fabric of hyperbole, even nonsense.

But regardless of the cultural tones in which the popular presentations of these advancements (esp. of the chaos theory) got couched, taken as a science, the studies of nonlinearity in the physical systems has been a very, very, original, and a very, very creative, advancement. It needs to be recognized as such.

That way, I don’t much care for what it helped produce on the maths side of it. But yes, even a not very extraordinarily talented undergraduate in CS (one with a special interest in deterministic methods in cryptography) would be able to tell you how much light got shone on their discipline because of the catastrophe and chaos theories.

The catastrophe theory has been simply marvellous in one crucial aspect: it actually pushed the boundaries of what is understood by the term: mathematics. The theory has been daring enough to propose, literally for the first time in the entire history of mankind, a well-refined qualitative approach to an infinity of quantitative processes taken as a group.

The distinction between the qualitative and the quantitative had kept philosophers (and laymen) pre-occupied for millenia. But the nonlinear theory has been the first theoretical approach that tells you how to spot and isolate the objective bases for distinguishing what we consider as the qualitative changes.

Remove the understanding given by the nonlinear theory—by the catastrophe-theoretical approach—and, once in the domain of the linear theory, the differences in kind immediately begin to appear as more or less completely arbitrary. There is no place in theory for them—the qualitative distinctions are external to the theory because a linear system always behaves exactly the same with any quantitative changes made, at any scale, to any of the controlling parameters. Since in the linear theory the qualitative changes are not produced from within the theory itself, such distinctions must be imported into it out of some considerations that are in principle external to the theory.

People often confuse such imports with “applications.” No, when it comes to the linear theory, it’s not the considerations of applications which can be said to be driving any divisions of qualitative changes. The qualitative distinctions are basically arbitrary in a linear theory. It is important to realize that that usual question: “Now where do we draw the line?” is basically absolutely superfluous once you are within the domain of the linear systems. There are no objective grounds on the basis of which such distinctions can be made.

Studies of the nonlinear phenomena sure do precede the catastrophe and the chaos theories. Even in the times before these two theories came on the scene, applied physicists would think of certain ideas such as differences of regimes, esp. in the areas like fluid dynamics.

But to understand the illuminating power of the nonlinear theory, just catch hold of an industrial CFD guy (or a good professor of fluid dynamics from a good university [not, you know, from SPPU or similar universities]), and ask him whether there can be any deeper theoretical significance to the procedure of the Buckingham Pi Theorem, to the necessity, in his art (or science) of having to use so many dimensionless numbers. (Every mechanical/allied engineering undergraduate has at least once in life cursed the sheer number of them.) The competent CFD guy (or the good professor) would easily be at a loss. Then, toss a good book on the Catastrophe Theory to him, leave him alone for a couple of weeks or may be a month, return, and raise the same question again. He now may or may not have a very good, “flowy” sort of a verbal answer ready for you. But one look at his face would tell you that it has now begun to reflect a qualitatively different depth of physical understanding even as he tries to tackle that question in his own way. That difference arises only because of the Catastrophe Theory.

As to the Chaos Theory (and I club the fractal theory right in it), more number of people are likely to know about it, and so, I don’t have to wax a lot (whether eloquently or incompetently). But let me tell you one thing.

Feigenbaum’s discovery of the universal constant remains, to my mind, one of the most ingenious advancements in the entire history of physics, even of science. Especially, given the experimental equipment with which he made that discovery—a handheld HP Calculator (not a computer) in the seventies (or may be in the sixties)! … And yes, getting to that universal constant was, if you ask me, an act of discovery, and not of invention. (Invention was very intimately involved in the process; but the overall act and the end-product was one of discovery.)

So, here is a wish that these fundamental studies of the nonlinear systems get their due—the recognition they so well deserve—in the form of a Physics Nobel.

…And, as always, the sooner the better!

Wish # 2:

The second wish I want to put up here is this: I wish there was some commercial/applied artist, well-conversant with the “art” of supplying illustrations for a physics book, who also was available for a long-term project I have in mind.

To share a bit: Years ago (actually, almost two decades ago, in 1998 to be precise), I had made a suggestion that novels by Ayn Rand be put in the form of comics. As far as I was concerned, the idea was novel (i.e. new). I didn’t know at that time that a comics-book version of The Fountainhead had already been conceived of by none other than Ayn Rand herself, and it, in fact, had also been executed. In short, there was a comics-book version of The Fountainhead. … These days, I gather, they are doing something similar for Atlas Shrugged.

If you think about it, my idea was not at all a leap of imagination. Newspapers (even those in India) have been carrying comic strips for decades (right since before my own childhood), and Amar Chitrakatha was coming of age just when I was. (It was founded in 1967 by Mr. Pai.)

Similarly, conceiving of a comics-like book for physics is not at all a very creative act of imagination. In fact, it is not even original. Everyone knows those books by that Japanese linguistics group, the books on topics like the Fourier theory.

So, no claim of originality here.

It’s just that for my new theory of QM, I find that the format of a comics-book would be most suitable. (And what the hell if physicists don’t take me seriously because I put it in this form first. Who cares what they think anyway!)

Indeed, I would even like to write/produce some comics books on maths topics, too. Topics like grads, divs, curls, tensors, etc., eventually. … Guess I will save that part for keeping me preoccupied during my retirement. BTW, my retirement is not all that far away; it’s going to be here pretty soon, right within just five years from now. (Do one thing: Check out what I was writing, say in 2012 on this blog.)

But the one thing I would like write/produce right in the more immediate future is: the comics book on QM, putting forth my new approach.

So, in the closing, here is a request. If you know some artist (or an engineer/physicist with fairly good sketching/computer-drawing skills), and has time at hand, and has the capacity to stay put in a sizeable project, and won’t ask money for it (a fair share in the royalty is a given—provided we manage to find a publisher first, that is), then please do bring this post to his notice.


A Song I Like:

And, finally, here is the Marathi song I had promised you the last time round. It’s a fusion of what to my mind is one of the best tunes Shrinivas Khale ever produced, and the best justice to the words and the tunes by the singer. Imagine any one else in her place, and you will immediately come to know what I mean. … Pushpa Pagdhare easily takes this song to the levels of the very best by the best, including Lata Mangeshkar. [Oh yes, BTW, congrats are due to the selection committe of this year’s Lata Mangeshkar award, for selecting Pushpa Pagdhare.]

(Marathi) “yeuni swapnaat maajhyaa…”
Singer: Pushpa Pagdhare
Music: Shrinivas Khale
Lyrics: Devakinandan Saraswat

[PS: Note: I am going to come back and add an update once this year’s Physics Nobel is announced. At that time (or tonight) I will also try to streamline this post.

Then, I will be gone off the blogging for yet another couple of weeks or so—unless it’s a small little “kutty” post of the “Blog-Filler” kind or two.]



Shaken, because of a stir

We have demonstrably been shaken here on earth, because of a stir in the cosmos.

The measured peak strain was 10^{-21} [^].

For comparison: In our college lab, we typically measure strains of magnitude like 10^{-3} or at the most 10^{-4}. (Google search on “yield strain of mild steel” does not throw up any directly relevant page, but it does tell you that the yield strength of mild steel is 450 MPa, and all mechanical (civil/metallurgical/aero/etc.) engineers know that Young’s modulus for mild steel is 210 GPa. … You get the idea. …)

Einstein got it wrong twice, but at least eventually, he did correct himself.

But other physicists (and popular science writers, and blog-writers), even after getting a full century to think over the issue, still continue to commit blunders. They continue using terms like “distortions of spacetime.” As if, space and time themselves repeatedly “bent” (or, to use a euphemism, got “distorted”) together, to convey the force through “vacuum.”

It’s not a waving of the “spacetime” through a vaccum, stupid! It’s just the splashing of the aether!!

The Indian credit is, at the most, 1.3%.

If it could be taken as 3.7%, then the number of India’s science Nobels would also have to increase dramatically. Har Gobind Singh Khorana, for instance, would have to be included. The IAS-/MPSC-/scientist-bureaucrats “serving” during my childhood-days had made sure to include Khorana’s name in our school-time science text-books, even though Khorana had been born only in (the latter-day) Pakistan, and even if he himself had publicly given up on both Pakistan and India—which, even as children, we knew! Further, from whatever I recall of me and all my classmates (from two different schools), we the (then) children (and, later, teen-agers) were neither inspired nor discouraged even just a tiny bit by either Khorana’s mention or his only too willing renunciation of the Indian citizenship. The whole thing seemed too remote to us. …

Overall, Khorana’s back-ground would be a matter of pride etc. only to those bureaucrats and possibly Delhi intellectuals (and also to politicians, of course, but to a far lesser extent than is routinely supposed). Not to others.

Something similar seems to be happening now. (Something very similar did happen with the moon orbiter; check out the page 1 headlines in the government gazettes like Times of India and Indian Express.)

Conclusion: Some nut-heads continue to run the show from Delhi even today—even under the BJP.

Anyway, the reason I said “at most” 1.3 % is because, even though I lack a knowledge of the field, I do know that there’s a difference between 1976, and, say, 1987. This fact by itself sets a natural upper bound on the strength of the Indian contribution.

BTW, I don’t want to take anything away from Prof. Dhurandhar (and from what I have informally gathered here in Pune, he is a respectable professor doing some good work), but reading through the media reports (about how he was discouraged 30 years ago, and how he has now been vindicated today etc.) made me wonder: Did Dhurandhar go without a job for years because of his intellectual convictions—the way I have been made to go, before, during and after my PhD?

As far as I am concerned, the matter ends there.

At least it should—I mean, this post should end right here. But, OK, let me make an exception, and note a bit about one more point.

The experimental result has thrown the Nobel bookies out of business for this year—at least to a great part.

It is certain that Kip Thorne will get the 2016 Physics Nobel. There is no uncertainty on that count.

It is also nearly as certain that he will only co-win the prize—there will be others to share the credit (and obviously deservingly so). The only question remaining is, will it be just one more person or will it be two more (Nobel rules allow only max 3, I suppose), what will be their prize proportions, and who those other person(s) will be (apart from Thorne). So, as far as the bettors and the bookies are concerned, they are not entirely out of the pleasure and the business, yet.

Anyway, my point here was twofold: (i) The 2016 Physics Nobel will not be given for any other discovery, and (ii) Kip Thorne will be one of the (richly deserving) recipients.



Squeezing in a post before the 2015 gets over…

The first purpose of this post is to own up a few nasty things that I did. Recently I posted some nasty comments on iMechanica. I got as randomly nasty in them as I could.

My overwhelming mental state at that time was to show just a (mild) example of the “received” things, of what I have had to endure, for years. In fact what I had to endure has been far worse than mere comments on the ‘net, but I tried to keep it aside even in that nasty moment. … Yes, that’s right. I have resisted putting out nastiness, in response to that which I have gotten over years (for more than a decade-and-a-half!). I have not succeeded always, and this recent instance is one of that infrequent times I could not.

On the other hand, check the better side of my record at the same forum, I mean iMechanica: Hundreds of comments on more than two hundred threads.

Yes, I do regret my recent “response.” But if you ask me, the issue has gone beyond the considerations of justifiable-ness and otherwise. Not in the sense that moral principles don’t apply for such things (exchanges on the Internet), but in this sense: Let us change the chairs. I mean to say: Even if someone else in my position were to write ten-folds more such comments, and if I on the other hand were to be in a general observer’s position, then: the current state of the world is such that I would no longer have a right to expect any better coming off him. If anything else better were at all to come off him, I may or may not be grateful (it would depend on the specific value of that better thing to me). But I would certainly put it on account of his graciousness.


All the same, I will sure try to improve my own record, and try to avoid such nastiness in future, esp. at iMechanica (a forum that has given me so much of intellectual satisfaction, and has extended so much friendliness). [No, if you ask me, the matter involves such bad context that I won’t include this resolve as a part of my NYR, even though I will, as I said, try even more to observe it.]

I also have been down with a bout of cold and cough for the past 2–3 days, now barely recovering, and therefore don’t expect to join in the New Year’s party anywhere.

My NYR remains as before (namely, to share my newer thoughts on QM). There is an addition in fact.

I have found that I can now resolve the issue: “Stress or strain: which one is more fundamental?” It is one of the most widely read threads at iMechanica (current count: 135,000+), and though a lot of knowledgeable and eminent mechanicians participated in it, at the natural cessation of any further real discussion several years ago, the matter had still remained unresolved [^].

I now have found a logic to take the issue to (what I think is) its definite resolution. I intend to share it in the new year. That’s my NYR no. 2 (the no. 1 being about QM). I am also thinking of writing a journal paper about this stress-strain issue—for no reason other than the fact it has gone unresolved for such a long time, despite such wide publicity. It clearly has gone beyond the stage of an informal discussion, and does deserve, IMO, a place in an archival journal. For the same reason, give me time—months, if I decide to include some simulations, or at least several weeks, if I decide to share only the bare logic, before I come back.

Yes, as usual, you can always ask me in person, and I could give the gist of my answer right on the fly. It’s only the aspect of writing down a proper archival journal paper that takes time.

A Song I Like:

It’s being dropped for this time round.

I cannot pick out which one of the poems of Mangesh Padgaonkar I love better. He passed away just yesterday, at a ripe age of 86.

Just like most any Marathi-knowing person of my age (and so many of other ages as well), I have had a deeply personal kind of an appeal for Mangesh Padgaonkar’s poetry. It’s so rich, so lovely, and yet so simple of language—and so lucid. He somehow had a knack to spot the unusual, the dramatic in a very commonplace circumstance, and bring it out lucidly, using exactly the right shade of some very lyrical words. At other times, he also had the knack to take something very astounding or dramatic but to put it in such simple (almost homely) sort of way, that even a direct dramatic statement would cause no real offence. (I here remember his “salaam.”) And, even if he always was quite modern in terms of some basic attitudes (try putting his “yaa janmaavara” as “nothing but the next” in a series of the poems expressing the received Indian wisdom, or compare his “shraavaNaata ghana neeLaa” with the best of any naturalistic poet), his poetry still somehow remained so deeply rooted in the Marathi culture. Speaking of the latter, yes, though he was modern, one could still very easily put him in the series of “bhaa. raa. taambe,” “baalakavee,” and others. Padgaonkar could very well turn out to be the last authentic exponent of the Marathi Enlightenment.

All in all, at least in my mind, he occupies the same place as that reserved for the likes of V. S. Khandekar and “kusumaagraj.” People like these don’t just point out the possibilities, in some indirect and subtle ways, they actually help you mould your own sense of what words like art and literature mean.

If I were to be my younger self, my only regret would be that he never received the “dynaanapeetha” award. Today, I both (i) know better, and (ii) no longer expect such things to necessarily come to a pass.

Anyway, here is a prayer that may his soul find “sadgati.”

Alright now, let me conclude.

Here is wishing you all the best for a happy and prosperous new year!

[May be another pass, “the next year”…]


The Infosys Prizes, 2015

I realized that it was the end of November the other day, and it somehow struck me that I should check out if there has been any news on the Infosys prizes for this year. I vaguely recalled that they make the yearly announcements sometime in the last quarter of a year.

Turns out that, although academic bloggers whose blogs I usually check out had not highlighted this news, the prizes had already been announced right in mid-November [^].

It also turns out also that, yes, I “know”—i.e., have in-person chatted (exactly once) with—one of the recipients. I mean Professor Dr. Umesh Waghmare, who received this year’s award for Engineering Sciences [^]. I had run into him in an informal conference once, and have written about it in a recent post, here [^].

Dr. Waghmare is a very good choice, if you ask me. His work is very neat—I mean both the ideas which he picks out to work on, and the execution on them.

I still remember his presentation at that informal conference (where I chatted with him). He had talked about a (seemingly) very simple idea, related to graphene [^]—its buckling.

Here is my highly dumbed down version of that work by Waghmare and co-authors. (It’s dumbed down a lot—Waghmare et al’s work was on buckling, not bending. But it’s OK; this is just a blog, and guess I have a pretty general sort of a “general readership” here.)

Bending, in general, sets up a combination of tensile and compressive stresses, which results in the setting up of a bending moment within a beam or a plate. All engineers (except possibly for the “soft” branches like CS and IT) study bending quite early in their undergraduate program, typically in the second year. So, I need not explain its analysis in detail. In fact, in this post, I will write only a common-sense level description of the issue. For technical details, look up the Wiki articles on bending [^] and buckling [^] or Prof. Bower’s book [^].

Assuming you are not an engineer, you can always take a longish rubber eraser, hold it so that its longest edge is horizontal, and then bend it with a twist of your fingers. If the bent shape is like an inverted ‘U’, then, the inner (bottom) surface has got compressed, and the outer (top) surface has got stretched. Since compression and tension are opposite in nature, and since the eraser is a continuous body of a finite height, it is easy to see that there has to be a continuous surface within the volume of the eraser, some half-way through its height, where there can be no stresses. That’s because, the stresses change sign in going from the compressive stress at the bottom surface to the tensile stresses on the top surface. For simplicity of mathematics, this problem is modeled as a 1D (line) element, and therefore, in elasticity theory, this actual 2D surface is referred to as the neutral axis (i.e. a line).

The deformation of the eraser is elastic, which means that it remains in the bent state only so long as you are applying a bending “force” to it (actually, it’s a moment of a force).

The classical theory of bending allows you to relate the curvature of the beam, and the bending moment applied to it. Thus, knowing bending moment (or the applied forces), you can tell how much the eraser should bend. Or, knowing how much the eraser has curved, you can tell how big a pair of fforces would have to be applied to its ends. The theory works pretty well; it forms of the basis of how most buildings are designed anyway.

So far, so good. What happens if you bend, not an eraser, but a graphene sheet?

The peculiarity of graphene is that it is a single atom-thick sheet of carbon atoms. Your usual eraser contains billions and billions of layers of atoms through its thickness. In contrast, the thickness of a graphene sheet is entirely accounted for by the finite size of the single layer of atoms. And, it is found that unlike thin paper, the graphen sheet, even if it is the the most extreme case of a thin sheet, actually does offer a good resistance to bending. How do you explain that?

The naive expectation is that something related to the interatomic bonding within this single layer must, somehow, produce both the compressive and tensile stresses—and the systematic variation from the locally tensile to the locally compressive state as we go through this thickness.

Now, at the scale of single atoms, quantum mechanical effects obviously are dominant. Thus, you have to consider those electronic orbitals setting up the bond. A shift in the density of the single layer of orbitals should correspond to the stresses and strains in the classical mechanics of beams and plates.

What Waghmare related at that conference was a very interesting bit.

He calculated the stresses as predicted by (in my words) the changed local density of the orbitals, and found that the forces predicted this way are way smaller than the experimentally reported values for graphene sheets. In other words, the actual graphene is much stiffer than what the naive quantum mechanics-based model shows—even if the model considers those electronic orbitals. What is the source of this additional stiffness?

He then showed a more detailed calculation (i.e. a simulation), and found that the additional stiffness comes from a quantum-mechanical interaction between the portions of the atomic orbitals that go off transverse to the plane of the graphene sheet.

Thus, suppose a graphene sheet is initially held horizontally, and then bent to form an inverted U-like curvature. According to Waghmare and co-authros, you now have to consider not just the orbital cloud between the atoms (i.e. the cloud lying in the same plane as the graphene sheet) but also the orbital “petals” that shoot vertically off the plane of the graphene. Such petals are attached to nucleus of each C atom; they are a part of the electronic (or orbital) structure of the carbon atoms in the graphene sheet.

In other words, the simplest engineering sketch for the graphene sheet, as drawn in the front view, wouldn’t look like a thin horizontal line; it would also have these small vertical “pins” at the site of each carbon atom, overall giving it an appearance rather like a fish-bone.

What happens when you bend the graphene sheet is that on the compression side, the orbital clouds for these vertical petals run into each other. Now, you know that an orbital cloud can be loosely taken as the electronic charge density, and that the like charges (e.g. the negatively charged electrons) repel each other. This inter-electronic repulsive force tends to oppose the bending action. Thus, it is the petals’ contribution which accounts for the additional stiffness of the graphene sheet.

I don’t know whether this result was already known to the scientific community back then in 2010 or not, but in any case, it was a very early analysis of bending of graphene. Further, as far as I could tell, the quality of Waghmare’s calculations and simulations was very definitely superlative. … You work in a field (say computational modeling) for some time, and you just develop a “nose” of sorts, that allows you to “smell” a superlative calculation from an average one. Particularly so, if your own skills on the calculations side are rather on the average, as happens to be the case with me. (My strengths are in conceptual and computational sides, but not on the mathematical side.) …

So, all in all, it’s a very well deserved prize. Congratulations, Dr. Waghmare!


A Song I Like:

(The so-called “fusion” music) “Jaisalmer”
Artists: Rahul Sharma (Santoor) and Richard Clayderman (Piano)
Album: Confluence

[As usual, may be one more editing pass…]


The 2015 Physics Nobel, the neutrino, and the quantum entanglement

Okey dokey, so…. Quite a few important things have happened since I wrote my last post. Let me jot them down here, in the order of the decreasing importance:

  1. The teaching part of our UG term has (finally) ended.
  2. The QM papers mentioning Alice, Bob, entanglement or Bell’s inequalities did not get the Nobel recognition, not even this year—and if you ask me, for a very, very good set of reasons, but more on it later; I am not done with my list yet.
  3. Takaaki Kajita and Arthur McDonald did get the Physics Nobel for this year, “for the discovery of neutrino oscillations, which shows that neutrinos have mass.” The official popular explanation is here [(.PDF) ^]
  4. Youyou Tu got half of the Nobel prize for Physiology or Medicine this year, “for her discoveries concerning a novel therapy against Malaria.” The press release is here [^]. … Is it just me or you too failed to notice any “China-tva-vadi” thumping his chest in “pride” of the ancient Chinese medical system?

OK. Now, a few personal comments, in the reverse order of the list.

Given my interests, the list could have ended at point no. 3 above. It’s just that, given the emphasis that the supposedly ancient “vimaanashaastra” happened to receive in India over the last year, I was compelled me to add the fourth point too.

I don’t understand Kajita and McDonald’s work really well. That’s why the link I have provided above goes only to the popular explanation, not to the advanced information.

However, that doesn’t mean that I knew nothing about it. For instance, I could appreciate the importance of the phrase “mass eigenstates.” … It’s just that I don’t “get” this theory to the same extent that I get, say, Dan Schechtman’s work for his 2011 Chemistry Nobel.

That way, I have known about neutrinos for quite some time, may be for some 25 years or more. In fact, there also is a small personal story about this word that I could share here.

If you are an Indian of my generation, you would know that it would be impossible for you to ever forget the very first radio which your family had got (it probably was the one on which you listened to your Binaca Geetmaalaa every Wednesday evening), the first (and probably the only) bicycle your father bought for you (the one which you were riding in your bell-bottoms, when the thoughts of somehow having to impress that first crush of yours passed you by), the first PC that you bought…

Oh well, I am jumping ahead of myself. Correction. It should be: The first PC whose OS you installed. …

Chances are high that you got to install—nay, you had to re-install—DOS or Windows on your office or lab machine quite a few times, and chances are even higher that you therefore had become an expert of Windows installation way before you could save enough money to buy your first PC…. You can’t forget things like these.

So, in my case, while the first time I ever touched a PC was way back right in 1983 (I was in the EDP department at Mukand back then—a trainee engineer), the first time I got the opportunity to format a HDD and install a fresh OS on it was as late as in the late-July of 1996. (I happened to buy my first PC just a few months later on.) I was already a software engineer back then. The company I then worked with (Frontier Software) was a startup, and so, there were no policies or manuals concerning what names were to be given to an office PC. So, I was free to choose any which name I liked. While some others had chosen names like “koala” or “viper,” or “bramha” or “shiva,” when it came my turn, as the VGA-resolution screen on a small (13”) CRT monitor kept staring at me, the name I ended up choosing in the heat of the moment was: “neutrino.”

“`Neutrino’? Why `neutrino’? What is `neutrino’?”—the colleague who was watching over my shoulder spontaneously wondered aloud. He had been to California on company work some time earlier, and therefore, my guess at that time was that he perhaps could be guessing that “neutrino” could be some Mexican/Spanish/Italian name or expression. I, therefore, hastened to clarify what neutrino really meant (already wondering aloud why this guy had never heard of the term (even if he would maintain that he was into reading popular science books)). … No, he wasn’t thinking Mexican/Spanish/Italian; he was just wondering if I had made up that name. Alright, following my clarification that some billions of these neutrinos were passing through his body every second—even right at that moment, sitting in the comfort of a office, and right while our conversation was going on… Hearing this left him, say, dazed, sort of.

This instance conclusively proves that I have always known about neutrinos.

My “knowledge” about them hasn’t changed much over the past two decades.

… Anyway, my knowledge of QM has…  Two things, and let me end this section about neutrinos.

(i) If they could hunt for just a few (like just tens of) neutrinos out of billions of billions of them, why can’t they build a relatively much less costly equipment to test the hypothesis that the transient dynamics of the far simpler quantum particles—photons and electrons—isn’t quite the same as that put forth by the mainstream QM? [I have made a prediction about photons, and even if my particular published theory turns out to be wrong, any new theory that I replace it with will always have this tiny difference from the mainstream QM, because my theorization is local, whereas the mainstream QM is global.]

(ii) Can photon have mass? … Think about it. It’s not so stupid a suggestion as it may initially sound. (Of course, this point is nowhere as important as the first one concerning the transient dynamics).

Many, many people have been at least anticipating (if not also “predicting,” or “supporting”) a physics Nobel to something related to quantum entanglement. By “quantum entanglement,” I mean things like: Bell’s inequalities, or Clauser/Aspect/ Zeilinger, or Alice and Bob, … you get the idea.

I am happy that none of these ideas/experiments got to get a Nobel, also this time round. [Even if a lot of Americans were rooting for such an outcome!]

No, I have no enmity towards any of them, not even Bob; I never did. In fact, I carry a ton of a respect for them.

My point is: their work (or at least the work they have done so far) doesn’t merit a physics Nobel. Why?

Because, Nobels for the same theoretical framework have been given to many people already, say, to Planck, Einstein, Compton, Bohr, de Broglie, Heisenberg, Schrodinger, Pauli, Dirac, Born, et al. The theoretical framework of QM (and unfortunately, even today, it still remains only a framework, not a theory) as built by these pioneers—and as systematized by John von Neumann—already fully contains the same physics that Bell highlighted.

In other words, Bell’s principle is only a sort of a “corollary” (rather, an implication of the already known physics)—it’s not an independent “theorem” (rather, a discovery of new fact, phenomenon, or principle of physics).

As to the experimentalists working on entanglement, if you take the sum-totality of what they have reported, there is not a single surprise. Forget surprise, there isn’t even an unproved hunch here. For a contrasting example, see what Lubos Motl describes in case of neutrinos, here [^]. Unlike neutrinos, when it comes to quantum entanglement, there literally is nothing new. There has been nothing new, over all these decades—except for the addition of a lot of “press,” esp. in the USA, and esp. in the recent times. [Incidentally, you may want to note that Motl supports string theory—which, IMO, basically has always been, and remains, a post ex facto theory.]

The Nobel committee has once again demonstrated that it has a very solid grasp of what an advance of physics means.

An advance of/in physics is to be contrasted from “mere” deductions of corollaries, no matter how brilliant these may be.

About a century ago, they (the Nobel committee members back then) had shown a very robust sense regarding what the terms like “discovery” and “physics” mean, when they had skipped over the relativity theory even in the act of honoring Einstein—they had instead picked up his work on the photoelectric effect.

The parallels are unmistakable. Relativity theory was “sexy” those days; quantum entanglement is “sexy” today. Relativity theory was only a corollary of James Clerk Maxwell’s synthesis (at least the special relativity certainly was just that); quantum entanglement is just a corollary of the mainstream QM. And, while Maxwell had not pointed out relativity, entanglement indeed was pointed out by Schrodinger himself, and that too as early as before EPR had even thought of writing down their paper. So, the parallels—and the degradation in the American and European cultural standards over time—are quite obvious.

Still, what is to be noted here is the fact that the respective Nobel committees, separated by about a century, in both cases chose not to be taken in by the hype of the day. Congratulations are due to them!

And of course, as far as I am concerned, congratulations are also due to Kajita and McDonald.

BTW, Einstein does not become a lesser physicist because he never got a Nobel for the relativity theory. [And people do argue that he didn’t invent the relativity theory either; cf. Roger Schlafly.] So what? Even if relativity couldn’t possibly have qualified for a Nobel, Einstein sure did. He did a lot of work in quantum mechanics. He explained the photoelectric effect; he explained the temperature dependence of the heat capacity of solids using the quantum hypothesis; he didn’t merely explain but predicted the LASER using the QM decades before they were built (1917, vs. 1947–52). If you ask me, any single one of these achievements would have amply qualified him for a physics Nobel. I don’t say it out of deference to the general physics community. You can see it independently. Just put any of these advances in juxtaposition to some of the other undisputed Nobels, e.g., Jean Perrin’s demonstration of the molecular nature of matter (a work which itself was motivated by Einstein’s analysis of the Brownian motion); or de Broglie’s assertion that matter had a wave character; or Bohr’s “construction” of a model that still went missing on two very obvious and very crucial features: stability of orbits and the nature of quantum transitions. (Come to think of it, Einstein also was the first to assert a spatially finite nature for the photon, a point on which all physicists don’t necessarily agree with Einstein, but I, anyway, do.)

So, to conclude, (i) much of Einstein’s best work wasn’t as “sexy” as E = mc^2 or  the “relativity” theory; (ii) the physics Nobel committee showed enormously good judgment in picking up the photoelectric effect and leaving out relativity theory.

Just the way relativity didn’t deserve a Nobel then, similarly, nothing related to quantum entanglement deserves it now.

It doesn’t mean that Bell wasn’t a genius. It doesn’t mean that the experimental work that Clauser, Aspect, Zeilinger, or others have done wasn’t ingenious or challenging.

What it means is simply this: they have been either (very good/brilliant) engineers or mathematicians, but they have not been discoverers of new physics. Whenever they have been physicists, their work has happened to have remained within the limits of testing a known theory, and finding it to be valid (within the experimental error), again and again. And again. But, somehow, they have not been discoverers of new physics. That’s the bottom line!

To conclude this post, think of the “photogenic” apparatus that helped nail down the issue of the neutrino oscillation (e.g. see here [^]). Then, go back to the point I have made concerning accurately measuring the transient dynamics of QM phenomena (whether involving photons or electrons). Then, think a bit about how relatively modest apparatus could still easily settle that issue. And, how it happens to be a very foundational issue, an issue that takes the decades of mystification of QM head-on.

If someone told you that all local theories of QM are BS, or that all theories of QM lead to the same quantitative predictions, he was wrong, basically wrong. The choice isn’t limited to confirmation of the mainstream QM in experiments on the one hand, and creative affirmations or denials of QM via arm-chair philosophic interpretations (such as MWI) on the other hand. There is a third choice: Verification of quantitative predictions that are different (even if only by a very tiny bit) from those of the mainstream QM. The wrong guy should have told you the right thing. Too bad he didn’t—bad for you, that is.

A Song I Like:
(Marathi) “saavaLe sundara, roopa manohara”
Lyrics: Sant Tukaram
Singer: Pt. Bhimsen Joshi
Music: Shrinivas Khale

[May be one (more) editing pass is due for this post (and also the last post). Done with editing of this post. Will let the last post remain as it is; have to move on. ]




The Bhatnagar prizes 2015

The Bhatnagar prizes [^] for 2015 have been announced [(.PDF) ^]. The selections seem to be, as usual, the “safe” ones. So there can’t be much to comment on, on that count.

So, let me try to squeeze out something interesting and relevant from that bit of the news.

As far as I am concerned, the first interesting bit is this: I “know”—i.e. have run into and exchanged a few words with—one of the awardees. Exactly once, at a conference. The fellow in question is Dr. Mandar Deshmukh (2015, Physical Sciences). From the presentation he made at that conference, it was quite clear (at least to me) that he was doing some neat science. While making his presentation, he had assumed that informal and abstract air which by now has become typical for the relatively younger IIT Bombay graduates. I do like this change in them. Earlier, i.e. in my times and earlier, they used to be far too arrogant, pompous, or self-assuming. Even in their informal presentations. Important to me, Deshmukh carried the same air of informality (of a kind of friendliness, almost) during the in-person chat that I had with him on the side-lines during the buffet lunch. Why, he even casually asked me (as others) to “drop by [his] lab and have a look at the equipment any time,” adding that it was “interesting,” with a glint in his eye. Hmmm… Turns out that he has continued doing “interesting” things. (This conference was in 2009 or 2010.) As far as I am concerned, this selection seems quite right. So, congratulations, Dr. Deshmukh!

The second interesting bit is that Deshmukh was the second person present at that conference with who I had chatted during lunch and who eventually got the Bhatnagar award. The first person was Dr. Umesh Waghmare. (Yet another younger IIT Bombay alumnus.)

To go on to the third interesting bit, let me note that it was not a very “official” kind of a conference. It was just a symposium arranged to honor Professor Dilip Kanhere, on the occasion of his retirement as a Professor of Physics in the (now S. P.) University of Pune. There were no brownie points to be scored from this conference; people got together only out of respect for the retiring professor—and of course, out of the love of the research topics. Important to note: People had dropped by from as far places as the USA, Germany, Sweden, etc. (I came to know Prof. Kanhere through Web searches; he had just founded the Center for Modeling and Simulation; I was interesting in anything combining computation and physics. I approached him; he allowed me to attend his classes and generally roam around in the CMS for a while.)

So, the interesting bit is the knack that Prof. Kanhere evidently has to gather together some talented (and/or interesting) people. [I don’t mean to refer to me here.] I don’t know why not every professor succeeds doing that. But some professors do have this knack. Talented folks somehow “smell” such people and almost as if “by default” gather around them. Consider Kanhere’s PhD students (or research associates), and compare them to any randomly selected PhD from any department at the S. P. University of Pune during the same time; Kanhere’s students (and associates) stand out. The current director of CMS, Anjali Kshirsagar, is his PhD student; many others have had post-docs at good institutes abroad, which, incidentally, is a good benchmark for Indian universities (other than the IIXs). This point is important.

Even while working within the “parameters” of this third-class university (I mean the S. P. University of Pune), Kanhere managed to inculcate the right kind of intellectual spirit, and culture in his group, why, even some simple manners and rules of etiquette that researchers from the first-world almost always follow, and a normal guy in the S. P. University of Pune is blissfully (or more likely: arrogantly) unaware of. (Ditto for almost any other Indian university.) At least as far as I am concerned, if I know that if someone has been a student or post-doc with Prof. Kanhere, I immediately know that my emails will not only be read but also replied—and more important, its contents would be thought about before the reply is made (and perhaps also afterwards). It’s something like the atmosphere at iMechanica that Prof. Zhigang Suo has managed to create and maintain. How do some professors succeed doing such a thing regardless of the environment surrounding them? [Compare other blogging fora and iMechanica, on this count: the overall and general civility of the interaction present at iMechanica, combined with the informality. The fact that iMechanica is based at Harvard must have helped to a great extent, but this one factor alone doesn’t explain the outcome.]

So, how is a better atmosphere created? I have no idea. But the point especially relevant to us Indians is: it requires almost no money, almost no hard-work. (Well at least, not the futilely draining kind of a hard-work). And yet, only a few professors ever manage to accomplish that. It’s not everyone’s cup of tea. [As a professor myself, I am too new to know if I could manage to do that. But my point is: I would like to at least try.]

There is a value in such things. Kanhere’s students (and the people who had gathered for his retirement symposium) happened to be more or less the only people who (i) did not laugh at me when I said I am trying to derive a new view of QM, (ii) did not advise me to go read text-books within the first 5 minutes of my mentioning my published paper (or in the first email (if at all a reply came forth)), and (iii) did not try to avoid me the next time we ran into each other. Indeed, as far as the in-person interaction goes, the only people who have ever thoughtfully and informally commented on my QM ideas were Kanhere’s students. One of his students (then a professor himself) emphasized the complex number nature of the \Psi wave-function, and also brought home the fact that the name random variable is a misnomer, it actually being a function. Another student of his (again himself a professor) emphasized the conjugate nature of energy and time, not just of the momentum and position; see John Baez’ coverage here [^]. He also pointed out quantum chemistry to me; I didn’t know about it (“just substitute it in place of t; you will get it”). This, while people were busy saying to me that they won’t read a paper if it was about QM and written in MS Word, and that I should send the paper to a journal. (If they themselves couldn’t bother to even read the paper, why would they think that a journal could accept it? Blank-out. As far as they were concerned, the fact was that I myself had approached them, and so in that very act, I myself had put them in a higher, advising, position; they would therefore be generous in dispensing advice; the matter ended there as far as they were concerned.)

Reading the post in the plain, it’s impossible to convey what value mere “emphases” can be, because the issues are so generally well known. The point is: within the context of that particular discussion, within the context of that particular cluster of ideas, it’s just this one word emphasis that really gives you the clue. … It’s been more than five years since these comments, and I still marvel at how they got me out of my conceptual difficult spots with these off-hand but thoughtful remarks. (Their clarifications and even casually expressed emphases continue to help me, including during my recent-most brain-storming that I noted just yesterday in the previous post.) Why would only Kanhere’s students do that, despite the individual differences between them?

Thus, to use a cliche, some people manage to bring people together in such a way that 1 and 1 does not become 2; it becomes 11. How do they manage to do that? I have no idea.

How was it that Bohr managed to attract so many talented people to his institute? It is especially relevant to point out to Indians that this “institute,” when it was founded, had only one professor—Bohr himself—and a couple of other support staff. The visitors (like Heisenberg) would be lodged in a top-floor “room” (one having a low slanted roof), in the same building. Why, even as recently as in the late 1990s, the “University Department” at Utrecht had a faculty strength of less than 10—that’s roughly the time when Professor Gerard ‘t Hooft got his Nobel. The “Department” was that small; yet he would manage to attract talented folks from all over the world, i.e., even before the time that he got his Nobel. Sommerfeld had this same knack; look at the list of the PhDs he graduated and the post-docs he nurtured. For an example of the more recent times and from the US, look at the list of John Wheeler’s PhD students and post-docs: Richard Feynman and Kip Thorne count among his PhD students. Kip Thorne himself has been attracting an incredibly large pool of PhD students, post-docs and research associates.

Why do some people succeed attracting talent? Are there any lessons we can draw and learn? Let us not focus only on the Nobel laureates. Really speaking, winners of the Nobel prizes, or their mentors, do not make for a good, fitting example for us Indians. It cannot. Precisely because the achievement in question is so great, the difference in the perceived levels so large, that we Indians actually end up doing is to silently dismiss such instances away without any actual consideration. We cannot draw any lessons from them, for the simple reason that the very possibility of building the super-high-end intellectual hubs is completely surreal to us. [And, our friends and kins in the USA, esp. those in the San Francisco Bay Area, specialize in continually reminding us of the impossibility.]

So, let’s lower our bar a bit. I don’t mind doing that. But lowering the bar doesn’t mean we stop attempting. We can—and must—ask: is it possible to replicate, say, Professor Kanhere’s success, even if Wheeler’s example would be completely surreal to us? Is it possible to create an environment in which a prior PhD failure, esp. the one in engineering (and that too from a US university) runs into a physics professor, and says something using some stupid halting words which effectively convey: he wants to reformulate the foundations of QM. He says that, and still the physics professor doesn’t laugh it away right then and there? Is it possible to create this kind of an environment? Not just at an IIX, but also within the lowly S. P. University of Pune? Yes, it is possible; it has happened. … Is it possible that future Bhatnagar recipients flock together for what basically is just a “send-off” function of a non-IIX professor? Yes, it is possible; it has happened.

And, if such things are possible, then, the next question is: what precisely does it take to make it happen? to replicate it? I would like to know.

Over to you all.

[And, in the meanwhile, congratulations to the fresh Bhatnagar awardees once again, esp. Dr. Deshmukh.]

A Song I Like:
(Hindi) “yeh dil aur un ki nigahon ke saaye”
Music: Jaidev
Lyrics: Jan Nisar Akhtar
Singer: Lata Mangeshkar




Yo—4: The 2014 Physics Nobel

The physics Nobel for this year has gone to Isamu Akasaki, Hiroshi Amano and Shuji Nakamura, for the invention of the blue LED. Check out the official Nobel prize page to see the huge cost savings the invention implies [^]. Very, very, very well deserved!

Congratulations to all the winners.

Their invention has already begun transforming our lives, and, definitely, much more is slated to come. Just to name two: (i) flexible LEDs, (ii) lost-cost designer walls smartly emitting diffuse light (so that the light (in the sense lamp) is not different from the wall, the wall itself is light)… The possibilities are just astounding… For instance, think how it might affect (i) buildings architecture and interior designing, (ii) lighting inside tunnels/underground transportation…. You couldn’t wish for more…

Or, may be, you could! (Hey, this is science and this is life… There is always scope for more!) … If you ask me to single out just one thing, as far as these light- and energy-related matters go, I would choose: cost-effective (i.e. scalable and high energy-density) artificial photo-synthesis. … But then, that is strictly for another day.

As of today, do pause to note here that the realization of the blue LED also took something like three decades! Enormous achievement, that!!

Congratulations to the winners, once again!

* * * * *   * * * * *   * * * * *

A Song I Like:
(Hindi) “pyaar baanTate chalo…”
Singer: Kishore Kumar
Music: Laxmikant Pyarelal
Lyrics: Asad Bhopali
[BTW, if some of you don’t like some part of the lyrics, or of the video, then that can be OK by me, I can understand. Just don’t let it spoil this song itself for you, though. [And, also avoid the cynical temptation to associate this song with the money-distribution that does often go on, at the time of elections.] Instead, just take this song as a song, and appreciate that joyous sense which it carries, the sense of innocence and benevolence which comes so abundantly overflowing from it.]



The Other Clay Maths Problem

[Major updates to this post are now all complete. 2014.08.31 12:10 PM.]

Everybody knows about The Clay Maths Problem. There are claims, and then there are counter-claims. … First, there are some claims regarding The Clay Maths Problem. Then there are some claims going counter to them… And then, there also are claims about the claims about The Clay Maths Problem. Here is an example of a claim of the third kind.

If what Prof. Scott Aaronson often writes on his blog [^] about this issue is to be taken even semi-seriously, then he routinely receives something like [the particular estimates being mine] 2^{n^n} emails per week, all seeking his opinion about what he thinks of the 2^n arXiv article submissions per week claiming to have proved the P-vs-NP problem one way or the other, where n is a very, very large number; who knows, it might even be approaching \infty.

[Since this is a problem from theoretical computer science, for all estimates, the base has to be `2′; any thing else would be unacceptable. Aaronson is usually silent on precisely where the partition lies: whether the number of claims proving P = NP is statistically equal to those proving P != NP. However, he seems to hint that the two are equal. If so, then the CS-favorite number 2 would slip in once again, now as a divisor.]

The P-vs-NP problem is, thus, THE well-known Clay Maths Problem. Everyone knows about it.

Few people also know that there also is/was one more Clay Maths problem. … For example, they know that some decidedly crazy guy fooled them all—first, the mathematicians, and then, also himself. They—the mathematicians—accepted his solution, but he declined to accept the award, even the $1 million prize money that goes with it [^]. [Since the definition of a proper solution for the award is acceptance by mathematicians, it is easily conceivable that someone manages to fool them for two years and collects the prize.]

Relatively fewer people still know that as many as seven such million dollar problems were announced by the Clay Institute at the turn of the millennium.

As to the other problems, still fewer people ever bother to get past talking about the Yang-Mills problem. Even when it comes to this problem, as usual, they do not entertain any hope about seeing its resolution in the near future, where the “near” is left unquantified. But they all agree that it is a problem from mathematics—not physics.

What theoreticians agree on is always more interesting than what they disagree on. And, guess it was Ayn Rand who said it: also more dangerous.

Then, there are even fewer people who at all know anything about the Navier-Stokes problem—the mathematical version of it.

And, from my Web searches yesterday, there are very, very, very few people, at most a handful, who do something serious about it. This post is about them.

* * * * *  * * * * *   * * * * *

The first gentleman who purportedly continues to remain concerned about this Navier-Stokes problem is: Prof. Charles Fefferman. He should have no choice in the matter, I suppose, because it was he who wrote the official problem statement for Mr. Clay in the first place. Prof. Fefferman is an American mathematician [^].

The second man person to stay worried about this problem for as long a period as one entire month, was one maths professor from Lehigh, one Ms. Penny Smith [^]. She—an American—soon later retracted her solution [^]. Judging by the dates of the v1 and v5 versions on abstract page of her arXiv paper, the retraction took about half a month. (The number two, again!) Most of the ‘net discussions regarding her solution seem to have since then undergone a process of typographical mistake-making [^], or of plain vaporization [^]. Peter Woit, an American professor of Mathematics Physics Mathematics at Columbia, often better known on the ‘net for his proclivity to arbitrarily delete others’ replies on his blog even after having first having allowed their publication there, however, tenaciously holds on to some of that discussion [^]. (Here, I read only the first and the last still-published comments.)

The third person to stay sufficiently bothered about this problem so as to go to the extent of  writing a significant paper on it, seems to have been Prof. Mukhtarbay Otelbayev of Kazakhstan [^].

The first guy to venture discussing Otelbayev’s solution on the Mathematics StackExchange forum, chose to do so anonymously [^]. There must be something about the character of this problem that makes even people from Berlin, Germany, behave this way—writing anonymously—even on the Mathematics part of the StackExchange forum. Indeed, the question to strike this “Unknown” Berlin-based guy wasn’t the correctness or otherwise of Otelbayev’s solution; it was: Did Otelbayev solve the same problem as was posed by the Clay Institute? [^].

There were other follow-up discussions, but soon enough [within a month, of course] the author admitted that there was a mistake in his proof. The ‘net discussion on his proposal is still available [^]. [Professor Otelbayev is not an American.]

To my utter and great surprise, I also found (during an Internet search right this week) that in the meanwhile, there also has been none other than Terry Tao himself jumping into the frey issue. (No one calls him Professor Terence Tao. That’s exactly like how very, very few people, if any one, anywhere, ever, calls Prof. Aaronson by his last name and/or profession.)

My surprise was not entirely baseless. Terry Tao is a Fields medallist [^]. It was plain inconceivable that someone who already is a Fields medallist, would directly take on a(ny) million [American-] dollar problem.

That, indeed, turns out to have been the actual case. Terry Tao didn’t directly tackle the Clay Maths problem itself. See the Simons Foundation’s original coverage here [^], or the San Francisco-based Scientific American’s copy-paste job, here [^]. What Terry instead did is to pose a similar, and related, problem, and then solved it [^].

The “Unknown” Berlin-er mentioned above, was absolutely on the right track. It’s one thing to pose a problem. It’s another thing to pose it well.

That’s the light in which you might want to examine both the Clay Institute’s formulation of the problem and Tao’s recent efforts concerning it.  Realize, Terry didn’t solve the original problem. He solved another, well-posed, problem. And, as to the well-posed-ness of the original Clay Maths problem, there has been another notable effort.

Challenging the well posed-ness of the Clay Maths NS problem seems to have been the track adopted by Prof. Claes Johnson [^] for quite some time by now—several years or so.

Johnson is not a pure mathematician, but a fluid dynamicist. In fact, he is a computational fluid dynamicist, who has actually worked on some practical fluid dynamical problems [^][^]. He seems to be an interesting fellow. Despite having an h-Index of 52 [^], he has written against the climate-warming alarmism [(.pptx) ^][^]. Also see his response after having been selected for the Prandtl medal [^].

There is no Simons Foundation coverage on Johnson’s work. Naturally, any coverage by the Scientific American is plain inconceivable—especially if Johnson is going to write about his positions in springs and summers.

Johnson raises the issue of whether the Clay Maths formulation is well-posed or not. In simple words, can it at all be solved (by any one, ever) or not—whether the problem is in principle amenable to a solution or not. In case you don’t know, the “well-posed-ness” is a technical concept from mathematics [^].

Yes, that way, the issue of whether a problem is well-posed or not, does mean something like: “do you yourself know what you are asking, or not,” but the sense in which Hadamard meant it was certainly a bit more refined.

The distinction of the well-posed vs. ill-posed applies specifically to the solution of differential equations, and it means something like the following:

If you are going to throw a ball so as to hit a distant target (i.e., technically, a two-point BV problem for the second-order differential equation i.e. Newton’s 2nd law), you have the following choice: within appropriate limits, you can select the initial angle for the parabolic trajectory of the ball, in which case you have no choice about its initial speed—the horizontal distance to cover, together with the initial angle, would fix the value of the initial speed with which the ball must be thrown if it is to hit the target. (It would fix how tall the parabola should be, given the initial slope and a fixed horizontal distance.) Alternatively, you can choose the initial speed for the ball, in which case you have no longer have a choice about the initial angle. If hitting the target is your objective, you cannot arbitrarily specify both the auxiliary conditions: the initial angle and the initial speed, at the initial point. The nature of the differential equation is such that specifying both the auxiliary conditions at the same time at the same point renders this differential equation problem ill-posed. That, probably, is the simplest conceivable example of what it means for a problem to be ill-posed or well-posed.

As Hadamard pointed out, a differential equation problem, to be well-posed, must fulfill three conditions: (a) a solution must exist, (b) the solution must be unique, (c) the solution must change continuously with data (i.e., auxiliary conditions, i.e., the boundary and initial conditions).

Sometimes, the solution exists, but is not unique. For example, the diffusion equation problem is well-posed in the forward time direction but not in the reverse, in general. The diffusion process tends to smoothen out any initial sharpness. For example, if you place a drop of ink in the shape of a square on a blotting paper, it soon spreads and becomes a big, thin blot, growing ever rounder and rounder in shape as time passes by. Therefore, the information about the initial shape of the blot gets smeared all over the domain in such a way that starting from this later, bigger and roundish shape, and then going back in time following the diffusion equation, you cannot uniquely recover the initial shape of the blot. Whether the initial ink blot is square or hexagon, they both become round during diffusion. The resulting round shape doesn’t hold enough clue as to the number and locations of the sharp corners in the initial shape. In other words, the information about the initial sharpness is immediately lost during the diffusion process. And so, you can’t uniquely say whether it was a square or a hexagon: both (and infinity of other shapes) are possibilities. [As an aside, I do have some objections to this logic of the diffusion equation, but more on it, in a separate blog post, some time later.] So, the forward diffusion problem is well-posed, but the reverse one is not—no unique solution exists for the latter.

There also are other considerations for well-posed and ill-posed problems, which are more complicated. They refer to the continuous dependence of the solution to the auxiliary data. The auxiliary data, for the time-marching problems like diffusion and fluid flow, crucially means: the initial data.

Thus, the additional relevant consideration concerning the NS system has to do with the smoothness or otherwise of the initial velocity field. Johnson and a colleague rightly point in a paper [(.PDF) ^], that:

“If a vanishingly small perturbation can have a major effect on a solution, then the solution (or problem) is illposed [in the Hadamard sense], and in this case the solution may not carry any meaningful information and thus may be meaningless from both mathematical and applications points of view.

In this perspective it is remarkable that the issue of wellposedness does not appear in the formulation of the Millenium Problem. The purpose of this note is to seek an explanation of this fact, which threatens to make the problem formulation itself illposed in the sense that a resolution is either trivial or impossible.”

I agree. Do see the paper in original.

While Johnson and colleague’s technical paper may be out of the reach of many people—and in any case, at many places in the later half, it certainly is beyond my reach—the first half of the paper as well as Johnson’s blog entries are simple and clear enough to be understood even by any graduate engineer. See the series of his blog posts on this topic, here [^]. For ease of reference, the Clay Maths official problem description is here [(.PDF) ^].

[In this update of my blog post, I have edited a lot around here—from the meaning of the well-posed-ness, to what constitutes Johnson’s position. Some of my writing in the very first version of this post simply was some draft in (very rapid) progress, and so didn’t summarize Johnson’s position well. But then, I had noted that I was going to come back and edit this whole post. In particular, in the following couple of updates, I have deleted the line to the effect that Johnson meant that a blow-up won’t occur in the NS, as if this were to be his final, unqualified position, which, of course, it is not. ]

So,  in summary, Johnson has been repeatedly pointing out some important considerations regarding this problem, for a long time. A summary post could be this one, his latest [^].

And then, tarries along Terry Tao, correctly poses and seemingly correctly solves a problem that is teasingly near the original Clay Maths problem. He shows that a blow-up does occur—but only in his system, not necessarily in the NS system.

Terry, obviously, is interested in only teasing his reader, but not yet quite willing to jump into the… [Ahem.] … You see, otherwise, he could have easily dressed up the same result in different terms [say, in fuller clothes] without making any reference to the Clay Institute or its problem. But he does.

So, that’s what Terry Tao does. He wants to be seen as both addressing and not addressing the Clay Maths Problem. [He is an American.]

And, of course, even though Terry Tao responds at his blog to many, many people, he curiously doesn’t at all respond to a well-established European professor with definitely impressive credentials, like Johnson [^]. [Interestingly, though, Tao also does not delete Johnson’s replies once he publishes them. [Tao also is an Australian—he is a dual citizen.]] But the lack of response in such a context takes the matter closer to “tantalizing” than plain “teasing.” At least to someone like me, it does.

The issue is not whether the particular arguments that Prof. Johnson forwards are in themselves general or powerful enough to settle by themselves the Clay Maths Problem, or not.

The real issue is: the broader, valid and extremely relevant point regarding well-posed-ness which he repeatedly raises. Professor Tao should have responded to that. … You simply can’t go on beating [dancing] around the bush [pole], you know! [Professor Tao works in California, USA.]

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Ok, enough of “cross-referencing.”

But if you ask me what my take on this whole issue is, let me stick my neck out and say (at least) this much:

I think that:

(i) Prof. Johnson’s broader point, regarding the well-posed-ness is absolutely relevant, and unless it is addressed in a forthright manner by the Clay Institute, this Millenium problem essentially remains muddy, and

(ii)  Prof. Tao’s line of thought—the idea of fluid logic gates and machines to be built out of the ideal fluid, and the fluid computer, etc., etc., etc.—would eventually be regarded as not at all relevant to the very core of resolving the NS issue. Tao at best clarifies some abstract part of the nature of the problem, and this part, IMO, isn’t going to be relevant—not to the NS problem itself. His best contribution concerns the energy cascade across the scales, but he offers absolutely no insight as to how that cascade might respond in the actual NS problem settings.

Let me put the second point in a round-about and enormously hand-waving kind of way: If Tao’s current work is at all relevant to the NS problem, then it means that the mathematical community’s standards are sufficiently lax that a solution to the P-vs-NP problem could also be had without the mathematical community first coming to agree with some new and explicit clarity about some of the particular details about how the continuum hypothesis is to be interpreted in that context. But the second is not going to happen, simply because it is THE Clay Maths Problem. Ergo, Tao’s current work… QED.

On the other hand, to repeat, the points that Johnson raises are relevant, and they will stay relevant.

And, of course, all that is quite apart from another, “related” issue: even if there is or isn’t a blow-up in the NS system (and even if the Clay prize gets awarded for “proving” it either way (i.e. for someone getting the mathematicians to agree with him for two consecutive years)), the real issue would still remain: whether the Navier-Stokes system happens to be a good model for real fluids or not.

Just for the starters, as every one knows, at appropriate Knudsen numbers, the no-slip condition is no good. If you are going to complicate the auxiliary conditions to such an extent that the complexity of their effects exceeds that of the basic governing differential equation, then, you sure gotta ask of what good use your basic differential equation is, in the first place. In physics and engineering, we adopt the differential equation paradigm only because it has an epistemological value: it helps reduce cognitive load. If the bells and whistles are going to weigh a ton, how do you expect a cart powered by a toy-spring (or a 12 V 0.4 A Watt stepper motor) to get off to any start?

Or, for another matter, if what happens at the small, local, scale is extraordinarily different from what happens at the large, global, scale, or if pathological connections exists between the two scales, then, you have gotta ask some time: Why elevate some scale-based parameters that only give kicks to the mathematicians but does not make life any simpler to anyone else? Why stick to this continuum-based description for all the scales, in the first place? After all, even simplest phenomena like droplet formation or coalescence are in any case beyond the reach of this “basic,” “fundamental,” etc. etc. Navier-Stokes formalism anyway. Why elevate a theory of such obvious flaws to such a high pedestal? Why keep such a narrow mind that it can’t even deal with some of the simplest phenomena of nature? And, if you must do that, then why not take just one more step and declare another million dollar prize for some latest parlour game? What ultimately does distinguish mathematics as we know it, from the parlour games?

But, of course, we need not go all that far, really speaking. In many ways, the NS system is of enormous practical importance. All that we need to do is to bring some astute observations regarding differential equations, into the problem formulation.

Absent that one, no one has proved either a blow-up, or its absence, in the NS system, thus far. Not even Terry Tao. And, he must know that that’s because of the ill-posed-ness of the problem formulation itself. That’s why he must be choosing to remain silent to Johnson’s query, here [^]. Remember, he both works and does not work on the Clay Maths problem?

The current situation, in many, many ways, is something like this:

Suppose that mathematicians are busy building castles out of thin air (say, debating endlessly about whether the d’Almbert paradox is mathematically consistent or not). Suppose that the working epistemology of the culture has reached such a low level that no one can tell if the theories of thermodynamics and EM are consistent within themselves, let alone with each other. So, a rich guy steps in and declares a big mathematical prize for someone proving whether the Rayleigh-Jean blow-up really follows from the Maxwell system or not. Predictably, there is a flurry of activity, and thus there follow a few mathematicians who can’t get it right. And then, there steps in a young, brilliant mathematician, and declares that he can prove that a blow-up cannot occur but that his proof is limited only to a subcategory of the classical EM fields: the ones that are averaged in some sense. And then comes along some industrial physicist (i.e. actually a theoretical engineer, who has got a job declaring himself an applied mathematician). The industrial physicist points out that the mathematician’s argument can also be taken to imply the exactly opposite conclusion: namely, that these average fields must necessarily lead to the ultraviolet catastrophe. The mathematician chooses not to respond. The audience claps for the mathematician, and falls dead silent for the industrial physicist.

And, no one thinks of instituting a new prize that would reward such efforts as of building a new theory of physics which shows how to prevent the blow-up, even if doing so would involve breaking away from the clutches of some deeply held assumptions about the physical nature of reality, even if such a break-away is only a desperate last measure.

Sure, the situation is not exactly analogous. But if you go through the history of QM, and see how no physicist (or mathematician) ever left others’ valid queries unanswered—if you see how, on the contrary, they rapidly and openly communicated if not collaborated with each other—and then, if you see the kind of hype and blogging practices currently going on in our times, you will begin to see some pattern, and if not that, then at least some semblance, somewhere.

And, you will dearly feel something like—what? wistfulness?—about the good old times now so distant from ours: the times when the rational culture of science had already taken strong roots and it still was mostly a free, application-driven enterprise (the studies of cavity radiation, leading to the first physics Nobel, were sponsored precisely so as to help produce brighter bulbs more cheaply, for better business profits); the times when the state control of science was barely in its nascent stages or altogether absent. (Check out the history of Income Tax on Google, for instance. And, remember, that one—the Income Tax—is only for the starters, as far as the means of the state control of science goes.)

Guess I have made the most important two points which I had.

[Guess my major editing is over, except perhaps for a typo here and there. This long week-end for the Ganesh Chaturthee ends today, and from tomorrow, I will be back to my heavy class-room teaching duties—i.e. away from blogging. (In fact, factoring in the preparations for lectures, I would be into my heavy teaching duty starting right this afternoon.) So, bye for now.]

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A Song I Like:
(Hindi) “purvaiyya leke chali…”
Music: Ravindra Jain
Singers: Lata Mangeshkar and Shailendra Singh
Lyrics: ? (Ravindra Jain?)


My comments at other blogs—part 3: They don’t like you if…

They don’t like you rate you down if you ask them what they were calculating. That’s the takeaway a month later.

Here, the first “they” refers to the readers [and possibly writers] of the CalTech blog: “Quantum Frontiers”. The second “they” refers to the potential winners of the Fundamental Physics Prize. The term “them” includes both. CalTech, of course, is in California [^].

The prize money, here, is $300 k for the runner-ups. [Or is it runners-up?] Yes, they will get that much money. Not just that, the runner-ups here will get also a separate prize, called the “Physics Frontiers” prize. The topper, however, will get $3 million, and the “Fundamental Physics Prize.” The prizes are sponsored by a Russian [^].

One of the past winners includes an Indian “physicist” who got the prize for the output published while being employed in India: Ashoke Sen  [^]. On receiving the prize, Sen had notably said that he “is happy to pay the tax that is due,” and that “…in theoretical physics one can in principle work from any place as long as one has a computer and internet connection,” and that, for that reason, he does not “find any disadvantage of being in Allahabad” [^].

Padma Bhushan Professor Dr. Ashoke Sen does not, however, write any blog, and so, the question of publicly raising this concern—expressed in the first line of this post—to him, cannot arise, ordinarily. Hence the Californian blog. But, yes, this co-winner of the prize right in its inaugural edition had also said that “Indian science has a bright future” [ibid].

My rated-down [or is it down-rated?] comment is here [^].

At the current rating of -13, mine seems to be the most down-rated comment on that quantum physics frontiers-related blog, at least since the time I began reading it some time ago. From the general impression which I get from my rapid browsing of the comments on that blog, usually, the down-rated comments go down to a rating like -2 or -3 or so, but not into the [negative] double-digits and all, though I could easily be wrong here.

They should call out the worst down-rated comments such as mine on that blog, don’t you think? I mean to say, they should have a feature to properly highlight the comments that were allowed publication even after moderation, but which, subsequently, were rated down the most by their readership. … No, I wouldn’t at all mind if they were also to highlight the comments most up-rated there! … But they could have this feature, couldn’t they? What do you think? If done this way, wouldn’t it be, say, rather symmetric?

And, what do you think of the fact that these days, the “physicists,” or the folks concerned with fundamental “physics” [or at least, the folks concerned with quantum frontiers, whatever that means] un-like/dislike/don’t like you, or rate you down, if you ask them what they were calculating?

Or is it that you, too, think that when it comes to physics, the what isn’t (or shouldn’t be) a matter of concern?

[PS: I usually blog to express my own ideas or viewpoints. In that sense, this post still does not fully represent a resumption of my blogging.]


I am not participating in this FQXi competition

Actually, I had more or less reached this decision right by the middle of this month, but still, just because there was some time in hand, kept on indulging in aimless, useless, baseless, energy-less vacillations about it. Until it was the evening of August 31st, anyway.  … Yes, yes, I know there still is some more time in hand, even if only because India is ahead of USA in terms of the time of the time-zone. The time still in hand (about 15 hours) is enough to write a mere nine-page essay anyway. However, read on to get to know why I would still not be writing. …

The reason, ultimately, turns out to be grounded in the competition topic itself, viz., the question: “Which of our basic physical assumptions are wrong?”

Loosely speaking, the nature of this question makes it a “negative” topic, not a “positive” one. … That could take some explanation. …

OK. No. I am not a New Age idiot. So, I don’t mean to say that the reason I decided to keep away from this competition is because the topic invites some of kind of a criticism of others. That’s not what I mean by the adjective “negative” here.

What I mean by “negative,” here, is: the (logical) compliment of “the positive.” And, by “positive,” what I mean is: a direct existential kind of a statement. … More detailed explanation is called for.

OK. For example: “The Sun exists” is a positive statement. It directly captures a fact of reality. Another example: “The Sun shines brightly,” again, is a positive statement. Not primarily because the word “brightness” has a connotation of clarity, efficacy, joy, happiness, etc., all supposedly positive things, but simply because the adjective “brightly” does not logically negate the sense of the basic truth contained in the rest of that sentence.  On these lines, the statement: “A black hole sucks in everything, even light” also is a positive statement. Its purpose is to identify the nature of an existent rather than to deny, qualify, or question one.

In Ayn Rand’s way of putting it: The positive statements are of the kind: Existence is identity. Or: A is A. They are not concerned with what possibly might belong in the non-A. They are not concerned with the logical complement of A.

Alright. … What’s that to do with not participating in the essay competition?

I think I have already ended up hinting at this aspect, right during my last post.

The FQXi competition question does not ask: “What new, foundational thing have you got right?” It asks: Where did physicists got it wrong?

Answering the first question is always easier; the second one is not.

Physics is a science. It establishes its truth via a laborious process, one that proceeds through observations, analysis, hypotheses, experimentation, analysis of data, validation, integration, etc. And, it’s a cyclic or iterative process; the parts of it are interdependent. You don’t begin thinking of integration only after conducting the experiments; considerations of integration are part of the context of analysis and hypothesis generation as well. You don’t do analysis only before experimentation; you need it right during validation, too. So on and so forth. All in all, establishing a new truth requires a whole lot of real, hard, work. Naturally, the progress is slow. Naturally, therefore, there is very little to show in any annual/biennial essay contest, if at all one has produced anything in that time period. Naturally, therefore, it is very easy to identify what one does have to show, if one has it.

However, precisely due to the nature and extent of the hard-work involved, it is very difficult to even summarize what all things one does not have.

In a way, it’s a matter of teleology—and the crow-principle of epistemology. The goals are few. But they lead to a whole big “tree” of issues, factors, possibilities and considerations to manage. It’s always possible to tell the goals—and it’s even easier to tell the actually achieved goals from among them  (which are even fewer than the goals). But it’s always too complex to even indicate the extent and scope of the “tree”s directly involved in it: the teleological one, and the epistemological one (by which, here, I mean: the “tree” arising out of the basic meanings of the concepts, generalizations or issues at hand).

Beyond these complex trees, there also is that biggest of all considerations, when it comes to all matters concerning knowledge, viz., the consideration of integration. Integration of the new knowledge with the sum total of all of the rest of the knowledge.

Statements of goals and achievements are easier to make. But since the process of knowledge creation is so intricate, difficult and laborious, statements of what went wrong are far more difficult to make. The “A” is easy enough to identify if it involves the goals and the achievements; the “non-A” is far too voluminous for the mind to separately deal with.

That’s the basic reason why mere polemics never succeeds. Even if a polemics (the non-A) is objectively valid, and even if it’s done very neatly or sharply, the listener’s mind still is simply unable to hold on to much of it, unless the positive part—the “A” of it—is not explicitly identified.

So, you get the idea of why I couldn’t get much past that question.

Of course, as I stated in my last post, I could still have written something on some one important issue and simply dumped it. I did try. … As it so happens, I was participating in a LinkedIn discussion on the nature of randomness (“Is anything truly random?”). I wrote a lot there, and also got misunderstood—at least some, if not a lot. (Expectedly so.) So, it seemed like a good topic on which to write the FQXi essay. I did try along this direction.

However, as soon as I finished my initial take on the “outline” part of it, I realized the essential dissonance. What I was addressing was an identification of the basic nature of randomness. But what I was supposed to be addressing was a survey of the physical assumptions that are not only wrong but also obvious enough in their wrongness as to be ripe to be acknowledged by the (astro)physicist community (at MIT) as indeed being wrong. Too much of a chasm in there. Too much of dissonance.

The essay indeed would have carried some (what I think are) good contents. Indeed,  I should sincerely try to bring it all together, give it some good, additional touches—specifically, the scholarly kind of touches (doing a real serious lit search etc.). And, then, submit it to a suitable journal (e.g. Foundations of Physics/AJP/The Physics Teacher/Whatever; not Nature/Science/PRL). However, just the fact that it can make for a good essay, doesn’t mean that it makes for a good essay for this competition.

Could anyone have written a good essay to address that particular question?

For the reasons indicated above, I don’t think anyone could have. There is just too much that is bad with the present-day physics. The situation is so (or such) bad that, as mentioned in my last post, in one’s attempts to condense it all, the first things to strike one happen to be all philosophic in nature. And, rational philosophic principles are not always well-known to people. So, you also have to face the issue of having to explain even simpler among the terms, as you go along.

Further, things have gone bad to such extent that not just the Platonic intrinsicism but even classical subjectivism looks brightly rational in comparison. For example, in the so-called Many Worlds Interpretation, originated in an American’s 1950’s PhD at Princeton, people don’t just create their own reality, as a classical subjectivist would have you believe. The Many Worlds Interpretation’s point is that no people are basically necessary to create world, not even a creator god (the idea of it). Physical processes, occurring in the universe, by themselves, are enough to spawn infinity of universes. Yes, you read it right. That’s the actual thesis. (And, idiots at places like Princeton, Berkeley, MIT, etc., have by now developed a tradition of taking such nonsense seriously.) So, in short, there indeed is a lot of nonsense out there. (It’s precisely because the situation is so bad philosophically that it also is so bad quantitatively.)

But there still is that nine page limit. So, you can’t possibly both write well and comprehensively enough to actually address the essay question. There are objective principles because of which an essay of the kind that the competition question demands, is impossible to write.

So, no, I don’t think that anyone else could possibly have a good essay that also actually addresses the actually posed question. They may have good essays that don’t address the question or bad essays that do. But they can’t possibly have both. Now, that’s something that looks like modern physics, doesn’t it, FQXi?

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No “A Song I Like” section, once again. I still go jobless. Keep that in mind.

[This is initial draft, published on August 31, 2012, 6:31 PM, IST. May be I will make some minor corrections/updates later on]