# Some suggested time-pass (including ideas for Python scripts involving vectors and tensors)

Actually, I am busy writing down some notes on scalars, vectors and tensors, which I will share once they are complete. No, nothing great or very systematic; these are just a few notings here and there taken down mainly for myself. More like a formulae cheat-sheet, but the topic is complicated enough that it was necessary that I have them in one place. Once ready, I will share them. (They may get distributed as extra material on my upcoming FDP (faculty development program) on CFD, too.)

While I remain busy in this activity, and thus stay away from blogging, you can do a few things:

1.

Think about it: You can always build a unique tensor field from any given vector field, say by taking its gradient. (Or, you can build yet another unique tensor field, by taking the Kronecker product of the vector field variable with itself. Or, yet another one by taking the Kronecker product with some other vector field, even just the position field!). And, of course, as you know, you can always build a unique vector field from any scalar field, say by taking its gradient.

So, you can write a Python script to load a B&W image file (or load a color .PNG/.BMP/even .JPEG, and convert it into a gray-scale image). You can then interpret the gray-scale intensities of the individual pixels as the local scalar field values existing at the centers of cells of a structured (squares) mesh, and numerically compute the corresponding gradient vector and tensor fields.

Alternatively, you can also interpret the RGB (or HSL/HSV) values of a color image as the x-, y-, and z-components of a vector field, and then proceed to calculate the corresponding gradient tensor field.

Write the output in XML format.

2.

Think about it: You can always build a unique vector field from a given tensor field, say by taking its divergence. Similarly, you can always build a unique scalar field from a vector field, say by taking its divergence.

So, you can write a Python script to load a color image, and interpret the RGB (or HSL/HSV) values now as the $xx$-, $xy$-, and $yy$-components of a symmetrical 2D tensor, and go on to write the code to produce the corresponding vector and scalar fields.

Yes, as my resume shows, I was going to write a paper on a simple, interactive, pedagogical, software tool called “ToyDNS” (from Toy + Displacements, Strains, Stresses). I had written an extended abstract, and it had even got accepted in a renowned international conference. However, at that time, I was in an industrial job, and didn’t get the time to write the software or the paper. Even later on, the matter kept slipping.

I now plan to surely take this up on priority, as soon as I am done with (i) the notes currently in progress, and immediately thereafter, (ii) my upcoming stress-definition paper (see my last couple of posts here and the related discussion at iMechanica).

Anyway, the ideas in the points 1. and 2. above were, originally, a part of my planned “ToyDNS” paper.

3.

You can induce a “zen-like” state in you, or if not that, then at least a “TV-watching” state (actually, something better than that), simply by pursuing this URL [^], and pouring in all your valuable hours into it. … Or who knows, you might also turn into a closet meteorologist, just like me. [And don’t tell anyone, but what they show here is actually a vector field.]

4.

You can listen to this song in the next section…. It’s one of those flowy things which have come to us from that great old Grand-Master, viz., SD Burman himself! … Other songs falling in this same sub-sub-genre include, “yeh kisine geet chheDaa,” and “ThanDi hawaaein,” both of which I have run before. So, now, you go enjoy yet another one of the same kind—and quality. …

A Song I Like:

[It’s impossible to figure out whose contribution is greater here: SD’s, Sahir’s, or Lata’s. So, this is one of those happy circumstances in which the order of the listing of the credits is purely incidental … Also recommended is the video of this song. Mona Singh (aka Kalpana Kartik (i.e. Dev Anand’s wife, for the new generation)) is sooooo magical here, simply because she is so… natural here…]

(Hindi) “phailee huyi hai sapanon ki baahen”
Music: S. D. Burman
Lyrics: Sahir
Singer: Lata Mangeshkar

But don’t forget to write those Python scripts….

Take care, and bye for now…

# My answers to the Edge questions

I was supposed to come back and write a better version of the QM-related comment which I had made at Scott Aaronson’s blog (see my last post). However, I am not going to do that right away because of two reasons: (i) I think that leaving aside a typo or two, the comment isn’t in all that bad a condition, and (ii) I have begun thinking about some of the issues involved, and so would like to come back only after getting them straightened out (with a better order of presentation).

In the meanwhile, I decided to check out my blog-ideas folder (yes, I do “maintain” one), and found that I already had some material for a post.

It had so happened that while going through Scott’s post on the Edge question, especially the beginning of that post, an idea had struck me:

why not write my own one-line answers to all the Edge questions thus far?

So, I had gone to the Edge home page, and jotted down my answers in a .txt file. That was on 4th January 2016, between 4:17 PM–5:43 PM, IST (which means, one day before I wrote my comment on Scott’s blog). The answers were jotted down very, very rapidly—average time between reading a question and starting typing answer could be barely 10–15 seconds. That’s because we were very busy with the accreditation related work, remember? Though I don’t remember that particular day, I must have finished the day’s work and only then done this thing. Here I am going to mostly copy-paste its contents.

A couple of notes before we go over to my answers:

1. I just copy-pasted the Edge questions in the order I saw them on their home page. The order of answers was, thus, determined more or less by their Web page layout. So, the answers are not in the chronological sequence of the years over which they were raised.
2. I am reproducing the contents of a very whimsically written file (which was written, as I said, near the end of a long work-day), and without effecting any editing at all. Today, right within a week of writing the answers, I find that I want to change the answers to some of the questions. In any case, I would certainly want to make the answers more streamlined. But, today’s editing is minimal; whatever whimsicality that had crept in, I have decided to keep its original flavor as is.

So, here we go, with a copy-paste from that file:

The front velocity in the linear diffusion is a finite quantity (and in the first-order analysis, it is a constant).

2003 : WHAT ARE THE PRESSING SCIENTIFIC ISSUES FOR THE NATION AND THE WORLD, AND WHAT IS YOUR ADVICE ON HOW I CAN BEGIN TO DEAL WITH THEM? – GWB

The nation (i.e. USA): I don’t care a hoot about. The position was reciprocally derived.
The world: More or less the same. More or less the same.
My advise (to any President of the USA): Embrace 100% pure capitalism.

2002 : WHAT IS YOUR QUESTION? … WHY?

In his evolution, exactly for how long has the modern man been in the junglee-like state? (Rough estimates go like: lakhs of years of the jungle state vs. 5700 years of civilization, if you want to believe in the Western/modern science.)

Why it’s important? From many viewpoints: What led to the dominance of reason implicit in civilization? To what extent are the biological structural features really important in the mind-body connection? In what subtle ways must we still be junglee-like?

2001 : WHAT NOW?

Revising my viewpoint concerning non-relativistic quantum mechanics.
Reaching a conclusion concerning the issue of “stress or strain—which one is more fundamental?”
Writing some toy CFD code

2001 : WHAT QUESTIONS HAVE DISAPPEARED?

Whether the following phenomena are real or not: (i) rebirth, (ii) tele-many things such as telepathy, mind-reading, etc. (iii) psychic attacks, (iv) the actual American depravity in practice. Also the question of where Osama was hiding. Answer: In a cantonment town in a mostly army-ruled country that is a friend of USA.

2000 : WHAT IS TODAY’S MOST IMPORTANT UNREPORTED STORY?

How telecommunications actually changed the attitudes of rural people in India

1999 : WHAT IS THE MOST IMPORTANT INVENTION IN THE PAST TWO THOUSAND YEARS?

I don’t answer such silly questions. Idea? I would have attempted; generalization is possible with ideas. But not with inventions.

1998 : WHAT QUESTIONS ARE YOU ASKING YOURSELF?

Are the reported incidents in which some people could predict the future events true? If yes, what could be the mechanism in the pycho-somatic i.e. yogic terms? What implication does it hold for free will (properly defined, most fundamentally, only as the choice to focus or to evade), and the nature of soul and of consciousness.

2015: WHAT DO YOU THINK ABOUT MACHINES THAT THINK?

It’s a stupid idea. Thinking requires a conceptual (i.e. volitional) consciousness, which in turn requires life.

2014: WHAT SCIENTIFIC IDEA IS READY FOR RETIREMENT?

None. Proper ideas belonging to proper science never retire, they get subsumed away.

There are any number of ideas that should be retired because they were neither proper ideas nor scientific. For instance, the idea of an infinite physical universe. Or, the idea that ascribing anything quantitative to the universe (as a whole) is epistemologically valid. Etc. Also, string theory.

2013 : WHAT *SHOULD* WE BE WORRIED ABOUT?

The String Theory.

More seriously, government control of science and education.

2012: WHAT IS YOUR FAVORITE DEEP, ELEGANT, OR BEAUTIFUL EXPLANATION?

The mathematical aspects of the non-relativistic quantum mechanics. (A proper theory for its physical aspects is not yet available—despite my own attempts to build one.)

2011: WHAT SCIENTIFIC CONCEPT WOULD IMPROVE EVERYBODY’S COGNITIVE TOOLKIT?

The idea that all physical theories should be local.

I wrote that down, and then realized that the question asks for a toolkit.

I think computational modeling as easily realizable using Python and its ecosystem. It should be a part of every scientist’s grooming up. (Python is already being used to introduce programming to the CBSE XI-XII students in India.)

2010: HOW IS THE INTERNET CHANGING THE WAY YOU THINK?

It hasn’t changed *my* way of thinking, much. I always was more conceptual, and always had relatively lower working memory (and therefore also lessser maths skills) as compared to the class-mates who I ended up competing or at least [being] compared with. Internet has made more people forgetful and overall more like me, simply because they can just google up a lot of the concrete information.

2009: WHAT WILL CHANGE EVERYTHING?

I have no idea. Also, I don’t think it really is important or even desirable to change everything.

My view of quantum mechanics. I used to think that physicists were conceptually dumb. I now know that the original discoverers were not dumb—not even conceptually—but that their major flaw was either too much of careless[ness] about basic philosophical ideas, or too much of a diffidence towards bad philosophers.

Also, my view of Objectivists, Americans, and in fact, Western people in general. I no longer think that any of them could be fully relied on, practically speaking. They are not bad. [Here I meant morally bad.] In fact, they are pretty OK. They are just OK in the sense, they can be nice if you already are a practical success yourself. But if you are not a success, [they won’t bother to find that] hidden talent or spark in you. They are too crude and/or dumb and/or isolated, to be able to do that. Especially to an Indian-born. (They are rather like Brahmins in the Indian cities [and in the SF Bay Area]. The Brahmin-borns are not bad [by birth]. It’s just that a Maratha-born growing up rural areas cannot rely on them. He may receive acknowledgement of his talents from them, but not so reliably frequently to be a social norm. [Note today: It’s the elite vs non-elite phenomenon, really speaking, but the point is: I had never imagined as a young man that it would be as bad as it is, esp. in America.]

2007: WHAT ARE YOU OPTIMISTIC ABOUT?

That my new theory of QM will work out.

Actually, on most things, and speaking in terms of how I am habitually like, I am neither optimistic nor pessimistic. Habitually, if there is any one option towards which I do almost habitually get inclined, it is that: I like to know.

2006: WHAT IS YOUR DANGEROUS IDEA?

Dangerous in general? I have none. But if you mean those tiny cultural points of conversation that society people and people of culture (esp. writers of novels like Ayn Rand) use, you know, BS like: “he is too dangerous because he is too independent,” etc., then guess *my* most dangerous idea has been my sharing of the dimmed view of many people (Americans, Objectivists, Brahmins, army people, Indian University people, Westerners). Dangerous to me, that is.

2005: WHAT DO YOU BELIEVE IS TRUE EVEN THOUGH YOU CANNOT PROVE IT?

But I don’t always look for proofs, that’s the point. Validation is one thing, proofs is another. I do make sure to know the meaning and the roots of the concepts that I use. (And, sometimes, I have spent decades understanding their meaning and/or roots.)

But knowing the roots isn’t the same as proving, esp. to someone else, esp. to his satisfaction. You know how increasingly pointless and dangerous this enterprise gets.

Anyway, as the “cultural” kind of a fraud kind of an answer: My new theory of QM.

2016: WHAT DO YOU CONSIDER THE MOST INTERESTING RECENT [SCIENTIFIC] NEWS? WHAT MAKES IT IMPORTANT?

I can’t think of any. It has to be at least interesting, right? And, it has to be recent. Sorry. Can’t think of something that has both. At least not off the hand.

It would also be fun writing my own answers afresh some time later on.

A Song I Like:

(Hindi) “dil lagaa kar hum yeh samajhe”

Singers (separate versions each): Mahendra Kapoor and Asha Bhosale
Music: C. Ramchandra

[Another whimsicality of mine: Unlike most people whose opinions I usually find sensible, here I find that it is tough to decide which singer’s version is better. I mean to say, I don’t automatically find Asha’s version better. In fact, I like Mahendra Kapoor’s version [just] a shade better.]

[E&OE]

# The Mechanical-vs-Metallurgy “Branch-Jumping” Issue—Part II: Not Attending Inter-/Multi-/Trans-Disciplinary Conferences

0. To know the context and the primary intended readership of this post, please see my earlier post in this series, here: [^]. Of course, as mentioned earlier, everyone else is welcome to read this series, too.

1. The 57th (annual) Congress of the Indian Society of Theoretical and Applied Mechanics (An International Meet) was held at Pune this week, from 17th through 20th December, 2012 [^]. The venue was the Defence Institute of Advanced Technology (now a deemed university) [^]. (Caveat: Their Web site is often down, and with the PDF documents almost always missing. For example, try to download their faculty recruitment form.) I attended it, but this time round, without presenting any paper.

2. The conference was inaugurated by Dr. V. K. Saraswat [^], himself a PhD in combustion engineering. [Yes, the stupid primary intended readership [see part I to know exactly who all], this too is a topic common to both metallurgy and mechanical engineering.] The inaugural and valedictory functions were presided over by Dr. Prahlada [^], the vice-chancellor of the host institute (DIAT).

3. Some 180 papers were presented in the parallel sessions, many of them of multi-/trans-/inter-disciplinary nature, and with their authors coming from almost all departments of science and engineering. Even including electronics engineering, and mining engineering, apart from, of course, the usual ones: applied mechanics, mechanical engg., aerospace engg., civil engg., metallurgical/materials engg., mathematics, physics and astrophysics.

4. Even going just by my personal informal observations, people came to this conference from a lot of places: Guwahati, Kharagpur, Coimbatore, Kanpur, Chennai, Bangalore, Visakhapattanam, Hyderabad, Gulbarga, Surat, Mumbai, etc.

The foreign participation was somewhat limited this time round, with just a couple of Americans (both of Indian origin, both well-honored HoDs of mechanical or mechanics departments), and, off-hand, I suppose, one or two leading researchers or professors each from Canada, Germany, Israel, Japan, Taiwan, etc.

But, come, they did.

In contrast, the IIT Bombay QIP PhD D. W. Pande (of mechanical engineering branch from Aurangabad, now lording over at COEP); the meteorology (?) PhD degree holder G. B. Pant (sitting on the board of governors of COEP [a new addition to the stupid intended readership that should have been effected right the last time, and I will explain the reason for his inclusion the next time]); the Dean of the Faculty of Engineering of the University of Pune, PhD degree holder Gajanan Kharate (from Amaravati, now lording over at Pune, and per government, perhaps an OBC); his PhD guide the IIT Bombay QIP PhD Ashok A. Ghatol (formerly, Director, COEP, per government, certainly an OBC) did not come. Neither any of the others of their ilk.

Not even if they all are employed, and even if the places of their employment are all in or around Pune, and the conference was held right in Pune. [And that being academics, they would get discounts for the conference registration fees, and being government/university employed etc., they would get the conference fee refunded back anyway. Unlike me, who borrowed Rs. 3,500/- to attend it. Despite all that discount and its refunds, these characters still did not attend.]

And, of course, they didn’t send a single student of theirs to attend this conference either. Forget for paper presentation, not even for plain attendance.

The acceptance rate this time round was a bit higher, at about 60%. In the earlier ISTAMs which I attended, it has been 50% and lower; in fact, perhaps as low as 33% (if not 25%, but I don’t remember it too well, so let’s say, 33%). Pretty decent. Better than many reputed international journals. Even then, they still didn’t send a single student. [And, I am sure, this evil + stupid primary intended readership, while evaluating my employment application, would immediately pounce on the fact that I have no journal paper to my credit, only conference papers—if they could get past this metallurgy-to-mechanical “branch-jump” issue.]

These stupid idiots (and possibly evil characters—remember, free will as the basis of morality) with government-assured jobs and pensions and prestige, perhaps realized that if they attended the ISTAM conference, they might run into inter-/multi-/trans-disciplinary researches in mechanics and mechanical engineering. They perhaps also further realized that such a fact might then run counter to the one specific belief they fondly cuddle, cherish, openly advocate, defend and profess, and unhesitatingly act on: namely, that metallurgical graduates with PhD in mechanical cannot teach in or be hired by mechanical departments.

5. As to the research presented in the conference, much of it was not related to my current interests. But still, getting to know about the topics that other people are working on, the ideas they are pursuing, is always intellectually invigorating. I would like to write about the research part separately. Research, in fact any productive work, is such a noble thing. In contrast, for this post, I would not like to dilute the intensity of the focus on my joblessness due to the downright stupidity/evil of these above-mentioned professors/directors/government’s son in laws, etc.

However, I guess I could still mention just a couple of things in the passing.

5.1 One was the mention of the infinite speed of propagation of heat flux in conduction, during the invited lecture by Prof. I. Chung Liu of the National Chi Nan University, Taiwan. (I involuntarily sat up straight from my habitual slump while sitting in that cozy main auditorium at DIAT.) The approach Prof. Liu began with, was already known to me from my arXiv browsing. [No, the stupid intended readership of Mechanical Engineering Professors, Deans and Directors etc., arXiv usually does not have mechanical engineering related articles. So, you need not bother with this research any further, going by your government-funded and -enforced “logic.”] This approach consists of having a hyperbolic equation (the telegrapher’s equation) in place of the usual parabolic one. These days, a fairly neat Wiki page also exists to explain this approach; see here [^]. After his talk, I walked up to him and tried to explain how a particles-based approach makes it possible to remove the instantaneous action at a distance (IAD). However, Prof. Liu was not very well conversant with the Brownian movement/Weiner processes, and so, I could not pursue the conversation further. I just passingly mentioned my own research on diffusion equation to him. [The stupid primary intended readership of government-funded Mechanical Engineering Professors, University Deans and Directors etc., wouldn’t be able to make out why the IAD at all is an issue in the first place. They wouldn’t be able to make out even after being explicitly told twice.] Anyway, even if very brief, this discussion with Prof. Liu did help bring up some of my own thoughts. There is a certain paper on diffusion equation by a Berkeley professor which I had discovered after publishing my paper, and I would like to discuss it. Guess I will write a post at iMechanica (and, naturally, also here) about it, before sending a revised paper on this topic to a journal.

5.2 The second thing was this idea that had struck me while teaching a course on FEM to the COEP undergraduates in Spring 2009. [Yes, stupid/evil intended readership, I did teach the students of the mechanical branch as well, but only as a visiting faculty, and only for one semester. I was not repeated, despite very good student feedback [which Prof. Anil Sahasrabudhe, Director, COEP, didn’t quite share with me, unlike with his practice with other professors, but I do surmise with some pretty good basis—the direct feedback of students to me–that even my official student evaluation/feedback must have been pretty good.]] The idea is concerning finding a physical interpretation for the method of weighted residuals (MWR)—or, at the least, connecting some more mathematical context to MWR, anyway. My idea being too premature, I had not shared it with these undergraduate students back then. However, since the MTech-level students are a bit more mature, I did briefly hint at it while teaching the course on FEM at Symbiosis this year.

SPOILER ALERT: I may write a paper on this idea.

The idea is this: It first struck me that there was some kind of an analog between fitting a straight line to a scatter plot (say, the least-squares fit), and the method of weighted residuals. Sure, the first is an algebraic system and the second one involves differential equations. (Even if the ansatz is algebraic (a polynomial), before getting to the residuals, you still have to differentiate it, thereby changing the nature of the game.) The algebraic vs the infinitesimal is a big difference, and it is there. Yet, the idea of a residual (and setting it to zero) is common.

Then, I recalled that it was basically the same guy who had thought of both of these ideas, at least in their seed form: C. F. Gauss. (Ok, off-hand, I think that the least squares had already been used by someone else, before Gauss, but Gauss reinvented it independently, anyway. (Turns out, that earlier guy was Legendre [^])). The fact that the same mind had invented both the techniques helped gain more confidence in this idea of treating something like the least squares as an analog of the MWR.

In this conference, I got a chance to sound out this idea to two senior professors of mathematics: Prof. Kaloni of University of Windsor, and Prof. Rathish Kumar of IIT Kanpur. Specifically, I asked them if someone had already worked out something following, say, a function spaces-based approach.

Here, I was trying very hard to recall my earlier general reading decades ago concerning topological interpretation of the differentiation operation and all, and its recent mention by Prof. Tim Poston in a brief communication that I had with him. (It was a point which I had not at all understood at all.) Now at this conference, while talking in the hallways and all, I was trying to recollect those words. But somehow, in the hustle and bustle of the conference and the very short time available for those lounge/hall discussions, I could not recall any of such words. So, I tossed the first word I could catch hold of: function spaces.

Prof. Kaloni thought that someone must have worked on it already. In contrast, Prof. Rathish Kumar raised an entirely different point: where is convergence on the algebraic side of it, he asked. According to him, MWR was not limited to just getting to the residual and setting its domain integral to zero. The essence of MWR also had to include the idea of convergence—of a (possibly infinite) sequence of steps, of a systematic process of reducing the discretization error. In contrast, on the algebraic side of it, he observed, it’s just a one-time affair: you just take the fit, and that’s it. There is nothing more to be done; there is no second step; there is no sequence; the idea of convergence doesn’t apply.

In the busy-ness of such sideways discussions, there was no time to explain that I could get (i.e. I already was thinking of) an algebraic system that can still involve the ideas of convergence. In fact, I thought about it and got at an example right on the fly. But I was sure I couldn’t have explained it in the right words—the idea just flashed right during the conversation. So, not to waste his time, I asked him what would he think of it if I could get such a system (a multi-step, converging but algebraic system), and try to establish an analog with the differential equations-involving MWR. He then said that perhaps such a thing has not been done before, and that it would be nice to have a connection like that formally worked out. [I will repeat this part in a separate post, also at iMechanica, but in the meanwhile, if you know that someone has already worked out something along these lines, please drop me a line; thanks in advance.]

So there. The stupid/evil primary intended readership, these discussions, per your government-funded and government-enforced “logic,” had nothing to do with mechanical engineering. After all, both the professors were from the department of mathematics. So, you the stupid/evil primary intended readership (consisting of folks like G. K. Kharate, A. A. Ghatol, D. W. Pande, G. B. Pant, their friends, etc.), you all sit cozy and quiet and keep on drawing your respective 6th-pay commission-enhanced salaries, allowances, refunds, etc. Keep faithfully doing that, you stupids/idiots/evils.

[I remain jobless; the “A Song I Like” section is once again being dropped.]

[E&OE]