Yo—5: Giving thanks to the Fourier transform

Every year, at the time of thanksgiving, the CalTech physicist (and author of popular science books) Sean Carroll picks up a technique, principle, or theory of physics (or mathematics), for giving his thanks. Following this tradition (of some 8 years, I gather), Carroll has, for this year, picked up the Fourier transform as the recipient of his thanks. [^]

That way, it’s quite a good choice, if you ask me. …

…Though, of course, as soon as I began reading Carroll’s post, a certain thing to immediately cross my mind was what someone had said concerning Fourier’s theory.

Fourier’s is the most widely used theory in the entire history of physics, he had said, as well as the most abused one . … The words may not be exact, but that was the sense of what had been said. Someone respectable had said it, though I can’t any longer recall exactly who. (Perhaps, an engineer, not a physicist.)

The Fourier theory has fascinated me for long; I have published not just a paper on it but also quite a few blog posts.

To cut a long story short, I would pick out (i) the Lagrangian program (including what is known as the Lagrangian mechanics as well as the calculus of variations, the stationarity/minimum/maximum/action etc. principles, the Hamiltonian mechanics, etc.) and (ii) the Fourier theory, as the two basic “pillars” over which every modern quantum-mechanical riddle rests.

Yes, including wave-particle duality, quantum entanglement, EPR, Bell’s inequalities,  whatnot….

As I have been pointing out, the biggest good point that both these theories have in common is that they allow us to at all perform at least some kind of a mathematical calculation of the analytical kind—even if, often times, only in a physically approximate sense—in situations where none would otherwise be possible.

The bad point goes with the good point.

The biggest bad point common to both of them is that they both take some physics that actually occurs only locally (say the classical Newtonian mechanics) and smear it onto a supposedly equivalent “world”—an imaginary non-entity serving as a substitute for the actually existing physical world. And, this non-entity, in both theories (Lagrangian and Fourier’s) is global in nature.

The substitution of the global mathematics in place of the local physics is the sin common to the abuse of both the theories.

Think of the brachistochrone problem, for instance [^]. The original Newtonian approach of working with the local forces using \vec{F} = d\vec{p}/dt (including their reactions), is in principle applicable also in this situation. The trouble is, both the gravitational potential field and the constraints are continuous in nature, not discrete. As the bead descends on the curve, it undergoes an infinity of collisions, and so, as far as performing calculations go, the vector approach can’t be put to use in a direct manner here: you can’t possibly calculate an infinity of forces, or reactions to them, or use them to incrementally calculate the changes in velocities that these come to enforce. Thus, it is the complexity of the constraints (or the “boundary conditions”)—though not the inapplicability of the basic governing physical laws—that make Newton’s original approach impracticable in situations like the brachistochrone. The Lagrangian approach allows us to approach the same problem in a mathematically far simpler manner. [Newton himself was one of the very first to solve this problem using this alternative approach which, later on, to be formalized by Lagrange. (Look up the “lion’s paws” story.)]

Something similar happens also with the Fourier analysis. Even if a phenomenon is decidedly local, like diffusion of the physically distinct material particles (or parcels) from one place to another, the Fourier theory takes these distinct (spatially definite) particles, and then replaces them by positing a global non-entity that is spread everywhere in the universe, but with some peak coinciding with where the actual particles physically are. The so-smeared non-entity is the place-holder [!] for the spatially delimited particles, in Fourier’s theory. The globally spread-out entity is not just an abstraction, but, really speaking, also an approximation—a mathematical approximation. And as far as the inaccuracies in the calculations go, it turns out, this approximation does work out very well in practice. (The reason is not mystical. It is simply that the diffusing particles (atoms/molecules) are so small and so numerous in the physically existing universe.) But if you therefore commit the error of substituting this approximate mathematical abstraction in place of the exact physical reality, you directly end up having the riddles of QM.

If you are interested in pursuing this matter further, you should see my conference paper, first. (Drop me a line if you haven’t already downloaded it when it was available off my Web site, or can’t locate it any other way.) … Though I have also written quite a few posts on the topic, they don’t make for the best material—they are far too informally written (meaning: written completely on the fly and without any previously thought out structure at all). They also too lengthy, and often dwell on technical aspects that are too detailed.

And, that way, they don’t have much mathematical depth, anyway.

But since I seem to be the only person in the entire world who has ever thought along these lines (and one who continues to care), you may want to have a look at myQ detailed musings, too: [^] [^] [^][^].

(… And, no, as far as this issue goes, by no means am I done. I would continue exploring this topic further in my research, also in the future. Though, let me wind it all up for now… This was supposed to be a short and sweet post—a “Yo” post!)

* * * * *   * * * * *   * * * * *

A Song I Like:

(Marathi) “ekaTyaane ekaTe gardeet chaalaave”
Singer: Avadhoot Gupte
Lyrics: Mangesh Padgaonkar
Music: Shreedhar Phadake

[May be I should post a translation of this song some time later. … Also, of that another Marathi song which I have run just a few posts ago, viz., “man pisaaT majhe…” As to that song (“man pisaaT”) I know for a fact that a lot of Marathi-“knowing” people have never bothered to carefully go through the actual words, they have never tried to put them in some kind of a context, and thus, paying only a fragmentary attention here and there, they have come to associate something of a too abstract and weird (or “artsy”) kind of a sense to it. Their appreciation of that song rests mostly on the musical tune and the singer’s rendition, but their sense of the lyrics seems to be quite off the mark. The actual song isn’t of a meaningless “artsy” kind, and I hope to bring out what I think is the original sense of that song, too. And, as far as the present song goes, there isn’t just an  innovative sort of tune and a wonderful rendering by the singer. There also is a very beautiful piece of poetry lying underneath. … It’s a young new song (it came out only in 2010), but with an obvious touch of class to it. The original CD is just Rs. 100. … Enjoy…. More, later]



Errors in Physics-Related Public Presentations + Ethics of Researchers from/at Elite American Universities (Like MIT/Stanford) and the Indians’ Typical F***ed Up Response to It

QM-Related Errors, Part I:

Actually, this part was highlighted right the last time. In my previous blog post, I had asked you to check out a post by Dr. Sean Carroll (PhD: Harvard, Current Employers: CalTech), here [^]. As noted by him, the whole controversy began with a presentation by Dr. Brian Cox (PhD: Victoria University of Manchester (now Uni. of Manchester), Current Employers: University of Manchester and CERN (the same folks who rejected my paper without assigning any reason [^])).

IMO, the best among the huge responses this small controversy generated (made via any avenues: posts, comments, videos, twitter, etc.) was this one [^], made by Dr. Jonathan Butterworth (PhD: Oxford, Current Employer: University College, London).

As I said in my previous post, I had no desire to comment at any of their blogs. … But that still leaves open an issue: Does that mean that I could have provided the right answer? (IMO, the right answer is the one given by Prof. Butterworth.)

My answer to that question is: no. But let me explain.

Of course, I knew about issues and ideas like: quantum state in general vs. energy eigenstate, the universe as a single wavefunction, propagation of the characteristics at c as advocated by the relativity theory, etc.

However, I must still say that my knowledge is still not sufficiently “gelled” or crystallized so well together that I could have come up with the right answer, right on the fly.

I could easily sense the quantum state vs the energy state issue right on the first reading. However, Carroll (and others) had raised so many other, related issues that I kindaa got sidetracked in thinking how I might answer those so many other issues using my approach.

Now, as you know, my approach is still under development, and one reason why my knowledge of QM is not yet crystallized so well is because I find myself keeping on doing this to-and-fro between my approach and the mainstream QM: the physics of what my approach leads to (and what they all miss, so easily!) Hence, I couldn’t have got that answer so easily.

There also is another reason. Carroll himself, as well as the folks replying there (and at other blog posts/threads) really made it more complicated than was necessary—and I am sure that was a very honest thing on (many among) their part (Carroll certainly included among the honest ones). …You see, the mainstream QM doesn’t—in fact, cannot—provide you with a neat physical picture. This deficiency of the mainstream QM leads to a significant handicap. Notice the number of years of QM the debaters have had, and then, notice also the kind of this small, almost a QM 101 issue they still are left grappling with. So, what happens is, any time any basic issue of QM is opened for discussion, there is too much of digression. Which, in a way, feeds into my reformulation thoughts, and, so, I too get digressed.

QM-Related Errors, Part II, + Ethics Etc.:

Anyway, here is another presentation that I came across just yesterday. First, “a” word about the presenter.

The presentation is by Dr. Ramesh Raskar (XII MS Board Rank: 1st, BE E&TC (not Metallurgy) from COEP, PhD in CS (not Metallurgy, Materials Science/Engg, or Mechanical) from Uni. North Carolina Chapel Hill; Current Employers: Massachusetts Institute of Technology, Cambridge, MA, USA (not jobless); also check out the awards he has been bestowed with, at his MIT page here: [^]). “A” word is over. Many more will now follow. That is to say, before going to the presentation proper, let me make something public, here.

As you know, I have been on the lookout for any possibility of any experimental validation of my new approach in QM. I have contacted people from all leading universities in the world. Most of them did not bother to reply back—not even a regret email—with barely one or two honorable exceptions (notably, that of Prof. Lyman Page of Princeton).

When I came to know of Prof. Raskar’s research in the high-speed cameras and all, I thought that the experimental generated by this research might provide for at least some indirect data towards having my theory validated. So, I wrote to him an email. (There also was another background to it. While working in the SF Bay Area in late 1990s, I had commented on a Web page on COEP alumni that Raskar maintained. I am not sure if I had mentioned this connection. I certainly had mentioned the commonality of COEP, also education from Nasik, to him.)

As expected, the email went unanswered. A few months later, I again wrote an email. This time, it was to take objection to a line that one of his MS students had written in his MS thesis. Essentially, I wanted to point out that I already had a publication on QM modeling of light and diffraction/interference, and that my precedence should be acknowledged. There also was this matter about a paper that Raskar had co-authored with a guy from West-coast (I no longer recall his name, but will look up and supply the details in a next blog post).

No reply from Raskar.

Yet another reminder.

No reply.

Then I thought of the situation in exactly those terms in which most any COEP alumnus would have. The difference was, I expressed my thoughts in an email, explicitly using exactly those words (i.e. expletives), and even sent that email to him.

At this stage, I knew I should either not get any reply at all, or, it will be a very direct (if not friendly) kind of an interaction. Raskar wrote one line asking me for my phone so he could call me. I gave him that, adding also something to the effect that now that the possibility of having at least some communication is there, I would approach things differently.

Then, I pointed out that MS thesis thing to him. —namely, that my research had precedence, and that his student had written that one line wrongly. (This MS student of Raskar’s is a JPBTI (JEE Pass BTech IITian). Naturally, it was known that the bastard wouldn’t reply someone like me—esp. now that he had gone to MIT, and I had a PhD from COEP, University of Pune.)

Raskar didn’t address the issue directly. This much is what I now gather vaguely. It’s been more than a year, and I will have to look up my emails—perhaps made from SoftTech’s account, and thus no longer accessible to me. But doing that is not really necessary. I know for sure that if Raskar were to address the issue directly, honestly, without the airs of being at MIT, he would have written it in a different way—and this difference would have been tremendous enough that I surely would have remembered it very distinctly.

So, there. The story doesn’t end here, though.

There is a JPBTI by name Dr. Naveen Kabra (BTech in CS (not Metallurgy) at IIT Bombay (not COEP), PhD in CS (neither Mechanical nor Metallurgy) from University of Wisconsin at Madison (not COEP, University of Pune); only today I got to know that, like me and Raskar, he too attended schooling in Nasik [^]). I had got to know him via a Hindi songs site he used to maintain (or perhaps still does). I had sent him an email enquiring about an old Hindi film song. I took a chance, but had a feeling that since he was a JPBTI in CS, he wouldn’t write back. Dr. Kabra turned out to have been true to his JPBTI color—he didn’t reply back.

Story forward. This guy Kabra now runs an online forum called PuneTech. I don’t visit them often, but by luck (or whatever), one day I happened to notice at PuneTech that Raskar would be delivering a lecture in IISER/NCL.

I immediately took this opportunity by writing Raskar an email that I would be attending the event. (I didn’t want to throw him off-guard. His being a COEP junior is just one of the two main reasons. (The other is: my knowledge of his relative but certain incompetence in that area in which our interests seem to overlap.))

I did attend the event. And, as covered in the emails, went up to talk to him after the lecture. (The lecture itself was not on an area of my interest; it was on that NETRA technology developed by him—the thing to do with using mobile phone camera as a low-cost medical instrument for checking eye conditions.) I made sure that he recognized me as the guy who had used expletives; then duly offered a formal apology though, in the heart of my hearts, I knew—and still know—that any apology was neither necessary nor sufficient to get him to change his ways.

As expected, he seemed deliberately following on continuing to harbor that feeling of having been unjustly offended, despite my, definitely formal, apology.

“I receive so many emails a day” was the sort of explanation he had, for not replying my initial emails. I pointed out a few examples of the opposite kind; the examples included, a Physics Nobel nominee (Thomson Reuter Hall etc.), an von Neumann awardee (who has publicly noted that he gets more than a 100 emails a day (leaving aside spams) and tries to reply all of them), etc.

Then, he said it, with dripping sarcasm clearly evident on his contorted face, “Yes, Ajit, you are ahead of us! You are a genius!” My spontaneous reaction, clearly, was unexpected by him. I told him that I didn’t care about being described a genius, and that, yes, I, indeed, have been ahead of them.

Then, I challenged him point-blank: “Could you make that statement publicly, tomorrow—that, in QM, in your opinion, I am ahead of you?” At that time, he started muttering things like: “It’s not my field,” and began looking around at the organizers, who, by now, were already getting into the hero’s side-kick-rescuing-the-hero mode. (These people included a certain woman. I recently saw her profile at a matrimonials site. Looking at her profile, this entire incidence also came back to my mind, apart from the QM mistake Dr. Raskar has committed, and then, I decided to blog about it.)

Ok. To cut the long story short. In the ensuing brief discussion (ultimately cut short by the sidekicks—and the whole thing hadn’t even lasted some 3–4 minutes), Raskar did not ever say that not citing my research was an oversight. No. He knew the line he was going to adopt.

Raskar managed to keep his face straight while, in answer, asking me to get in touch with his co-authors (one of them being a PhD from Stanford, Current Employer: University of California, Santa Cruz). I told Raskar that I had already written emails to them, but they were not responding. Since Raskar was a co-author, and since we were already physically standing face to face, why couldn’t he at least begin to address the issue, as would be expected by ethics in science? Or was the fact of my using those expletives, out of exasperation, now only to be very smartly used as a cover?

I would have liked to leave you to think about things like that—the things of snobbishness and of ethics—at this stage. However, I happened to have promised you something else. So, here we go:

Check out Raskar’s video here [^]. Though not necessary, also check out the material here [^]. Raskar reveals a very definitely mistaken understanding of the physics in his presentation here. The task for you is to identify it.

And, coming back to the Raskar episode. To be fair to him, even as the hero’s sidekicks were almost on the edge of shoving me out, he did manage to say that he (“we”) could consider giving email replies, that he (“we”) could help, that he (“we”) could even consider collaboration, but nothing can come out if that kind of a language was being used. I include this bit while saying: “to be fair to him.” The reason is, he could at least utter words such as “we could consider collaboration.” Though, he made sure that I wouldn’t go for it.

As I said above, if I can get access to those emails, I will surely write another post mentioning the priority matter, that Stanford PhD bastard coauthor of Raskar’s, and, as you now know, the definitely not-a-bastard Raskar. (Not only these words, but even the emphasis in italics is mine).

I wonder how come those Nobel laureates at MIT let their professional (i.e. paid) colleagues (i.e. guys and gals employed by MIT) get away betraying such a poor understanding of physics.

But then, what the hell do those (Nobel-laureate) certainly-not-bastards care—they got their Nobels, right? Right, Frank Wilczek? What do you care if some Indian guy claims to have resolved the wave particle duality and sends his thesis to you. Right?

And, what do American fuckers care? … Well, on second thoughts, they actually do!! American Fuckers!!!

One final comment, now to Rama Bijapurkar (re. her recent column in that unnecessary Sunday supplement that Indian Express sends out): I do maintain what I said in my comment at Abi’s blog, viz., that Dr. Scott Aaronson does not show sufficient clarity. However, the sense in which you seem to value clarity—and the sense in which I do—seems to a bit at odds. And, I am confident that I am right. So, get the matter clarified on your own, or, if that’s not possible, from someone competent—is that clear? Anyone else from that BJP+Israeli lobby maintaining the same/similar position: ditto.

Last point: I remain jobless. Keep that in mind.

[May be I will streamline this whole thing a bit, esp. the II part, esp. related to the precedence/priority-related matters regarding Raskar’s MS student, his Stanford-PhD-coauthor, and my QM research. I hope to find those email copies stored somewhere or so, though I can’t be very sure—some of them were sent using SoftTech’s office email address, and those emails would have been deleted by now.]


An Important Comment I Just Made at iMechanica—And, (Much) More!

0. The title says it all!

Go, check out this comment I just made at iMechanica: [^].

1. Now, on to the “more” part of the title. Noted below are a few more things about my research.

2. My Researches on QM:

2.1 Since the publication of my QM-related results, I have moved on considerably further. As mentioned earlier on this blog, I have since then realized that my approach—the way I thought about it, as in contrast to what I (happened to have) published—always could handle the vector field equations of electromagnetism, including those for light. That is, including the angular momentum part of the EM fields. (Paddy, Suku, are you listening?) … However, I decided against publishing something in more detail to cover this aspect. A good decision, now it seems in retrospect.

(Yes, Jayant, you may now try your best to prod me towards publishing, including emphasizing how unpublished research is non-existent research. Just try it! Any which way you wish. … Precisely just the way I don’t give a damn to wannabe physicists turning JPBTIs turning entrepreneurs, I also don’t give a damn to the Statism-entrenching advices coming off the Statism-entrenching scientists, esp so if they also are the State-revered ones. So, just try it!! Also others, like, say, Sunil!!!)

2.2 I had also resolved the entanglement issue, and have chosen not to publish about it. As I stated earlier here [^], Louisa Guilder reports that Bell’s inequality paper has garnered the highest number of citations in physics literature so far, an astounding 2,500. The paper # 2,501 (or greater, as of today) must have concluded that the entanglement issue cannot be resolved—possibly out of the position/conviction that there was nothing to be resolved.

So, basically, I have resolved what an enormous number of misguided (and, possibly outright stupid) people could cite but not resolve.

Aside: Of the hundreds of papers on this topic I have come across, I know of Dr. Joy Christian’s position to be most reasonable—and in my knowledge, only his. Now, there are some minor differences between what he says and what I have always known and never published. But these differences are, in a sense, minor. The important part—and aren’t we concerned only with the important things here?—is that I knew about it, and have deliberately chosen not to publish about it. (If holding this position makes it possible to tick me off via certain lists such those maintained by a John Baez or a Scott Aaronson, I couldn’t care less about it—and both (and all) of them, I suppose, should know/could get to know, how (I care so less about those lists).)

BTW, as a matter of progression in time, I had thought that the issue would have to be first resolved in the context of photons, not of electrons. I am not very sure about it, though. In any case, that was the sequence in which I did it. First, photons; then, electrons.

Go, try your best to prod me towards publishing something on it! Just try it!! … BTW, my resolution had happened years before I had publicly offered an Indian PhD physicist on a “LinkedIn” group that I could explain my results if she (or anyone else) could meet me in person at Pune. This public offer of mine has just ended, right now!…. So, go ahead! Just try it!!!

3. My Researches on Other Topics

3.1 I have had some definite ideas for research on other topics from computational science and engineering and allied fields (including a numerics). I have kept these aside for the time being, because many of these are well-suited for guiding PhDs. Which brings me to the last couple of points for today (or at least, as of now, in the first version of this post).

3.2 As to student projects, I have decided not to accept anyone unless he is remarkably bright, and hard-working. (For those who seek to do truly independent PhD research, I cannot make myself available as a guide, as of now. Also see the point 3.3 below.) Roughly speaking, this means that rough level as would be understood by one or more of the following: GRE (V+Q) scores of at least 1350; GATE score of 95+P; throughout distinction class (or in at least 5 semesters out of 8) in BE of University of Pune (or equivalent).

3.3 The University of Pune has a stupid requirement for becoming a PhD guide: you (i.e. a fresh PhD graduate) must wait for at least 3 years after his own (successful) defense before he can become a PhD guide himself. The three years, in my case, end on September 20, 2012. (They—the Indian government(s)—probably arranged the date to numerically coincide with the date on which I first entered USA: 2nd September, 1990. Yes, the same government that whispered the UK government to give Rahul Gandhi’s brother-in-law all security clearance at UK airports, on par with the President and Prime Minister of India.)

Recently, someone reminded me a further requirement that I had forgotten. You also need to have two publications in those three years, before you can become a guide. Since I have mentioned the Gandhi’s and the defence-date here, I am sure that they would now interpret the sufficiently vague rules to imply that those two must be journal articles—peer-reviewed conference proceedings won’t do.

I, therefore, have decided to try to publish two journal articles in the near future of a few months. (Hey Elsevier, take notice!)

At least one, and probably both of these two articles would be on CFD.

Those of you who know me, would know that once I get going, I get going. I don’t disappoint (these of) you, not this time around at least: I have already installed Ubuntu 11.10 (natty) inside Oracle’s VirtualBox running on top of Windows (32 bit XP and 64-bit 7), and have already installed OpenFOAM v. 2.0.1 in that Ubuntu (32-bit, as of now). I also have installed other software. I have shortlisted the niche problems I could work on. I have contacted a couple of IIT Bombay professors, not for collaboration, but merely for sounding out. I knew that being employed by the IIT Bombay, there would be no collaboration, though a collaboration could have been perfectly OK by me. I also knew that once I wrote an email to them, it would get trapped (as all my emails are), and then, even the sounding things out over a 30 minute session would soon become impossible. And, that the impossibility would never be communicated explicitly via any means, esp. via an email. This  supposition of mine has indeed come to pass. (Congratulate me for being a good judge of the IIT Bombay, of the Indian government(s)—all of them, today’s and those of the past under the BJP regime as well, of Indians, and of humanity in general.) I knew all that, right in advance, and had prepared myself mentally for it. And, thought of plans B and C as well. I am executing on these.

And, no, I couldn’t care a hoot for how many freaking citations those two journal papers generate. As far as I am concerned, these two papers would allow me to fulfill the stupid requirements whereby I can become a PhD guide. And whereby, a slim chance does exist that I might get some good guy (gals included) for PhD supervision. (Chances are, it could be someone I already knew as a friend—numerically speaking, most of my friends are without PhDs.)

So, there. For the next few months, that’s the sort of research I am going to do—in my spare time, of course. Hey Elsevier, take notice (once again!!). As to others: If you consider yourself my friend, help me publish it in an easy and timely manner, ASAP.

That’s all for today. For this first version, anyway. As always, I might come back and correct or add a few things. …. Might as well add a few political comments right here.

4. A Few Comments on Politics and All:

Just noting down a few comments on politics (i.e. that politics which is “larger” than the one in S&T fields) in passing (and I will take liberties to pass comments on people without alerting them):

To ObjectivistMantra and Others:

Tavleen Singh’s article on the slap to Mr. Pawar was the best. However, it fell short on the count of completeness. On this count of completeness, she does far, far better (actually excellent) with her next article in the Indian Express’ Fifth Column. Why I say she fell short. In an entrenched mixed economy such as ours (i.e. India’s as in the past and as of today, and of USA’s in near future), the whole system has already become so statist, so mangling of individual rights, that it is impossible to systematically assign blame on any one systemic part of it. In my twenties and early thirty’s (i.e. 15–25 years ago), having known this, I used to argue that it would be impossible for the Indian army (i.e. defence services in general) or the Indian courts to be singled out as being clean. Time proved me right. Indeed, it’s at least since my X standard (i.e. for ~35 years now) that I have argued that you can’t blame politicians—indeed that far too many politicians, from the village through the national level enjoyed much more of esteem in my opinion than what salaried class (say, my “Brahmin” friends) would allow them. Sometime while I was in SF Bay Area, I further realized that the trend to say: “It’s all polltishuns; common people and businessmen are clean” had originated not in India, but in the middle-east and Pakistan etc., and that our Punjabi’s, Gujarathi’s etc. settled in the USA and UK (e.g. Kanwal Rehi, Vinod Khosla and their friends there and here) had been simply rubbing the characterization (actually applicable in the middle-east and Pakistan etc.), expectedly witlessly, on to India’s scene. Since Shobha Dey makes many frequent visits to Dubai, she was expected to have picked it up, too. And, she has shown over the years  that she has. Her latest column springs from that faulty position as regards India. Tavleen Singh is better. (That’s one basic reason why a link to her columns features in the my blogroll here.) Singh did stop short of stretching on that line. However, she did get overwhelmed by the dominant presence of that erroneous idea in our present culture. That’s why, she couldn’t think of a single example on the following lines: Taking a symmetrical case, should I be allowed to put a slap on the face of a Kanwal Rekhi or a Vinod Khosla, for not giving me a job in SF Bay Area in late 2000/early 2001, so that my green-card processing could have been completed? Should I be permitted—morally, even if not legally—to land a (Marathi) “saNsaNit thappaD” (nearest English: a resounding slap) on the face of a Ratan Tata, not just for never giving a job in his company (in Ratan’s case, Tatas) but even allowing my harassment (e.g. as stated on a LinkedIn thread re. VSNL/Tata Indicom Broadband)? Would it be morally justifiable? Why, Ms Tavleen, speak of the emotions of common man but refuse to discuss the issue on more clearly and more on specifically moral terms? So, you see, even if Ms. Singh is far better—and here I thankfully recall all her wonderful articles in the recent past, esp. the courage she has shown in taking on the urban twittering “middle” classes in the “Gandhian” Anna Hazaare “movement”—it is obvious that she overlooked something. Mind you, it’s just plain omission (and as far as I am concerned, it seems to be a very honest one). But still, an error is an error. On omission is an omission. Since I enjoy and admire her columns as much as you do, I hope that she addresses the moral aspects of the emotional issues rather than emotions. In any case, what she wrote was otherwise far better, far superior to what I could have written. This is exactly like Swapan Dasgupta’s recent article. Except for that one error, the rest of the article is excellent! But, hey, you don’t design or manufacture 99 components of an engine well, and leave 1 component out of either good design process or actual testing. As to Ms. Dey, I think I am going to stop reading her now. Some time ago, she was wondering when certain people had kissed last, in the context of—and who else: Indian “poltishun”s. (In case someone finds it intriguing, realize that she is a daughter of an Indian central bureucrat, and as far as I can make it out, has had no explicit rational philosophy to guide her writings, though she is a lady of enormous culture and composure in her own right too. Oh well, even explicit rational ideas do make a difference—think what a whole rational philosophy can do!)

I think I will stop here, and add possibly add other points via other blog posts. For the time being, as far as politics goes, I am enjoying (“loving it”) watching the BJP more than anyone else in the opposition/government, as far as the issue of retail FDI goes.  However, I am not going to support Walmart for the simple reasons that (i) their country has unreasonably failed me in the PhD and unreasonably denied me green-card/citizenship, (ii) they are too big to need my support anyway, and (iii) supporting a big company against government—Microsoft, in the DoJ case—was one among many things that got me a heart condition, I know. (How do I know? Well, it’s the same guy who has known how to resolve the QM wave-particle duality in the context of light, and about angular momentum in EM, and then, a resolution of the riddles of quantum entanglement, as well as many other unpublished, even un-discussed topics.)

One final point, again going back towards research. For the past several years I could not fathom the reason why people might be so unenthusiastic about my approach—I mean, honest people (apart from all the dirty things and “political” issues I have mentioned/indicated above.) Well, it was while reading Sean Carroll’s blog at Discovery magazine that I happened to realize one important (technical) reason why this might be (or must be) so! Hmmm…. Nice to know. It’s always great to know. Though, I am not going to divulge here what that thing was—or how it not only doesn’t contradict my approach but rather helps me be even more confident about my approach (if I ever needed such help, in this context!) And, as you know, I am not going to discuss it or publish about it either. Try to get me to do otherwise. … Just try!
Ok. Enough is enough. As usual, to be edited/streamlined later—perhaps!

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A Song I Like:
[RIP, Dev Anand!]
(Hindi) “gaataa rahe, meraa dil…”
Music: S. D. Burman (perhaps with R.D. looking after the orchestra (??) if not also the tune. (I have read somewhere that he was involved in “Aaraadhanaa,” but have no such idea when it comes to “Guide”)
Singers: Kishore Kumar, Lata Mangeshkar
Lyrics: Shailendra


How to supply a visualization for the displacement gradient tensor

[This post was initially posted at iMechanica. After posting it, I realized there was some inconsistency with it, and I noted so at the thread at iMechanica. What I am posting below is a slightly modified version.]

It all began with a paper that I proposed for an upcoming conference in India. The extended abstract got accepted, of course, but my work is still in progress, and today I am quite sure that I cannot meet the deadline. So, I am going to withdraw it, and then submit a longer version of it to a journal, later.

Anyway, here is a gist of the idea behind the paper. I am building a very small pedagogical software called “toyDNS.” DNS stands for Displacement, straiN, and streSs, and the order of the letters in the acronymn emphasizes what I (now) believe is the correct hierarchical order for the three concepts. Anyway, let’s keep the hierarchical order aside and look into what the software does—which I guess could be more interesting.

The sofware is very very small and simple. It begins by showing the user a regular 2D grid (i.e. squares). The user distorts the grid using the mouse, which is somewhat similar to the action of an image-warping software. The software, then, immediately (i.e. in real time, without using menus etc.) computes and shows the following fields in the adjacent windows: (i) the displacement vector field, (ii) the displacement gradient tensor field, (iii) the rotation field, (iv) the strain field, (v) and the stress field. The software assumes plane-stress, linear elasticity, and uses static configuration data for material properties like nu and E. The software also shows the boundary tractions (forces) that would be required to maintain the displacement field that the user has specified.

Basically, the idea is that the beginning undergraduate student encountering the mechanics of materials for the first time, gets to see the importance of the rotation field (which is usually not emphasized in textbooks or courses), and thereby is able to directly appreciate the reason why an arbitrary displacement field uniquely determines the corresponding strain and stress fields but why the converse is not true—why an arbitrary stress/strain field cannot uniquely determine a corresponding displacement field. To illustrate this point (call it the compatibility issue if you wish) is the whole rationale behind this toy software.

Now, when it comes to visualizing the fields, I can always use arrows for showing the vector fields of displacements and forces. For strains and stresses, I can use Lame’s ellipse (this being a 2D space). In fact, since the strain and stress fields are symmetric, in 2D, they each have only 3 components, which means that the symmetric tensor object taken as a whole can directly map onto an RGB (or HLS) color-space, and so, I can also show a single, full-color field plot for the strain (or stress) field.

Ok. So far, so good.

The problem is with the displacement gradient tensor (DG for short here). Since the displacement field is arbitrary, there is no symmetry to the DG tensor. Hence, even in 2D, there are 4 independent components to it—i.e. one component too many than what can be accomodated in the three-component color-space. So, a direct depiction of the tensor object taken as a whole is not possible, and something else has to be done. So, I thought of the following idea.

First, the notation. Assume that the DG tensor is being described thus:

DG11 DG12
DG21 DG22


du/dx du/dy
dv/dx dv/dy

where DGij are the components of the DG tensor, u and v are the x- and y-components of the displacement field, and the d’s represent the partial differentation. (Also imagine as if the square brackets of the matrix notation are placed around the components listing above.)

Consider that DGij can be taken to represent a component of a vector that refers to the i-th face and j-th direction. Understanding this scheme is easier to do for the stress tensor. For the stress tensor, Sij is the component of the traction vector acting across the i-the face and pointing in the j-th direction. For instance, in fig. 2.3 here: http://en.wikipedia.org/wiki/Stress_(mechanics) , T^{e_1} is the vector acting across the face normal to the 1-axis.

Even if the DG tensor is not symmetric, the basic idea would still apply, wouldn’t it?

Thus, each row in the DG tensor represents a vector: the first row is a vector acting on the face normal to the x-axis, and the second is another vector (which, for DG, is completely indpendent of the first) acting on the face normal to the y-axis. For 2D, substitute “line” in place of “face.”

If I now show these two vectors, they would completely describe the DG tensor. This representation would be somewhat similar to the “cross-bars” visualization commonly used in engineering software for the stress tensor, wherein the tensor field is shown using periodically arranged cross-bars—very convenient if the grid is regular and uniform and has square elements.

Notice a salient difference, however. Since the DG tensor is asymmetric, the two vectors will not in general lie at right-angles to each other. The latter is the case only with the symmetric tensors such as the strain and stress tensors. [Correction added while posting this entry at this blog here: Here, for the strain and stress vectors, I have already assumed that the two vectors are aligned along the principal axes. Notice that for the DG tensor, my description assumes that the reference faces or lines are aligned with the global xy reference frame that is attached to the domain. This introduces the inconsistency that I later noted at the iMechanica blog.]

My question is this: Do you see any issues with this kind of visualization for the DG tensor? Is there any loss of generality by following this scheme of visualization? I mean, I read some literature on visualization of asymmetric tensors, and noticed that they sometimes worry about the eigenvalues being complex, not real. I think that complex eigenvalues would not be a consideration for the above kind of depiction of the DG tensor—the rotation part will be separately shown in a separate window anyway. But, still, I wanted to have the generality aspect cross-checked. Hence this post. Am I missing something? assuming too much? What are the other things, if any, that I need to consider? Also: Would you be “intuitively” comfortable with this scheme? Can you think of or suggest any alternatives?

Comments are welcome.

Addenda (while now posting this entry at this blog here, on Oct. 28, 2010):

At iMechanica, Biswajit Banerjee provided a very helpful link to notes on Mohr’s circle by Prof. Rebecca Brannon (Uni. Utah). Then I also found a few papers by her. Dr. Phillips Wallstedt also provided a helpful pointer. I still have to go through all this material, esp. the paper suggested by Wallstedt. Anyhow, let me reiterate my point: Lame’s ellipse is a superior visualization as compared to Mohr’s circle. Brannon’s notes are truly helpful in that they directly show how to use Mohr’s circle for asymmetric tensors as well. Much of the material regarding asymmetric tensors in her notes was not at all known to me, and I am really grateful to her for having posted it online (and to Biswajit for pointing it out to me). Yet, I am going to try and see what(ever) that can be done along the cross-bars and/or Lame’s ellipse side. One solution now obvious to me (after Brannon’s notes—which I have merely browsed not read through) is what she has already shown in her notes: show the eigenvectors in reference to the non-rectangular stress element—even if she adds an “arghh” to the idea :). I think it is not at all a bad idea. Indeed, the more I think about it, the better I like it. At least, it will be consistent with the cross-bars visualization for the symmetric tensors.  … And, oh, BTW, it reminds me of a point that I have wanted to make for a long time, viz., the possibly misleading nature of the stress element they usually always use in showing stress tensor definition. … Next post!

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A Song I Like:

[Initially I thought of skipping this section just for this post, but then changed my mind. … This song is dedicated to the fond memory of a certain relative of ours who passed away yesterday, at a ripe age of 85+. It was my sister’s mother-in-law—but she never let us feel that “in-law” part of it. She was an almost completely unlettered lady who lived all her life in a village, herself working in farms. She was a lifelong “warkari,” and more: a soul of a very rare kind of simplicity and beauty.]

(Marathi) “saavaLyaa viThhalaa, tujhyaa daari aale”
Singer: Suman Kalyanpur
Music: Dashrath Pujari
Lyrics: R. N. Pawar