Hushshshsh…

The title word of this post is Marathi for “phew!”—not for “hush hush.” (But, to me, the Marthi word is more expressive. [BTW, the “hu” is to be pronounced as “hoo”.])

The reason for this somewhat accentuated and prolonged exhalation is this: I am done with the version “0.1-beta” of my note on flux (see my last post). I need a break.

As of now, this note is about 27 pages, and with figures and some further (< 5%) additions, the final number of pages for the version 0.1 should easily go into the early 30s. … To be readable, it will have to brought down to about 15 pages or fewer, including diagrams. Preferably, < 10 pages. Some other day. For now, I find that I have grown plain sick and tired of working on that topic. I need to get away from it all. I am sure that I will return to it later on—may be after a month or so. But for the time being, I simply need a break—from it. I’ve had enough of this flux and vectors and tensors thing. … Which brings me to the next topic of this post.

There are also other announcements.


I think that I have also had enough of QM.

QM was interesting, very interesting, to me. It remained that way for some four decades. But now that I have cracked it (to my satisfaction), my interest in the topic has begun dwindling down very rapidly.

Sure I will conduct a few simulations, deliver the proposed seminar(s) I had mentioned in the past, and also write a paper or two about it. But I anticipate that I won’t go much farther than what I have already understood. The topic, now, simply has ceased to remain all that interesting.

But, yes, I have addressed all the essential QM riddles. That’s for certain.


And then, I was taking a stock of my current situation, and here are a few things that stood out:

  • I am not getting an academic job in Pune (because of the stupid / evil SPPU rules), and frankly, the time when a (full) Professor’s job could have meant something to me is already over. If I were to get such a job well in time—which means years ago—then I could have done some engineering research (especially in CFD), guided a few students (in general in computational science and engineering), taught courses, developed notes, etc. But after having lost a decade or so due to that stupid and/or evil Metallurgy-vs-Mechanical Branch Jumping issue, I don’t have the time to pursue all that sort of a thing, any more.
  • You would know this: All my savings are over; I am already in debts.
  • I do not wish to get into a typical IT job. It could be well paying, but it involves absolutely no creativity and originality—I mean creativity involving theoretical aspects. Deep down in my heart, I remain a “theoretician”—and a programmer. But not a manager. There is some scope for creativity in the Indian IT industry, but at my “seniority,” it is mostly limited, in one way or the other, only to “herd-management” (to use an expression I have often heard from my friends in the industry). And, I am least bothered about that. So, to say that by entering the typical Indian IT job, my best skills (even “gifts”) would go under-utilized, would be an understatement.
  • For someone like me, there is no more scope, in Pune, in the CFD field either. Consultants and others are already well established. I could keep my eyes and ears open. But it looks dicey to rely on this option. The best period for launching industrial careers in CFD here was, say, up to the early naughties. … I still could continue with some research in CFD. But guess it no longer is a viable career option for me. Not in Pune.
  • Etc.

However, all is not gloomy. Not at all. Au contraire.

I am excited that I am now entering a new field.

I will not ask you to take a guess. This career route for people with my background and skills is so well-established by now, that there aren’t any more surprises left in it. Even an ANN would be able to guess it right.

Yes, that’s right. From now on, I am going to pursue Data Science.


This field—Data Science—has a lot of attractive features, as far as I am concerned. The way I see it, the following two stand out:

  1. There is a very wide variety of application contexts; and
  2. There is a fairly wide range of mathematical skills that you have to bring to bear on these problems.

Notice, the emphasis is on the width, not on the depth.

The above-mentioned two features, in turn, lead to or help explain many other features, like:

  1. A certain open ended-ness of solutions—pretty much like what you have in engineering research and design. In particular, one size doesn’t fit all.
  2. A relatively higher premium on the individual thinking skills—unlike what your run-of-the-mill BE in CS does,┬áthese days [^].

Yes, Data Science, as a field, will come to mature, too. The first sign that it is reaching the first stage of maturity would be an appearance of a book like “Design Patterns.”

However, even this first stage is, I anticipate, distant in future. All in all, I anticipate that the field will not come to mature before some 7–10 years pass by. And that’s long enough a time for me to find some steady career option in the meanwhile.


There are also some other plus points that this field holds from my point of view.

I have coded extensively—more than 1 lakh (100,000) lines of C++ code in all, before I came to stop using C++, which happened especially after I entered academia. I am already well familiar with Python and its eco-system, though am not an expert when it comes to writing the fastest possible numerical code in Python.

I have handled a great variety of maths. The list of equations mentioned in my recent post [^] is not even nearly exhaustive. (For instance, it does not even mention whole topics like probability and statistics, stereology, and many such matters.) When it comes to Data Science, a prior experience with a wide variety of maths is a plus point.

I have not directly worked with topics like artificial neural networks, deep learning, the more advanced regression analysis, etc.

However, realize that for someone like me, i.e., someone who taught FEM, and had thought of accelerating solvers via stochastic means, the topic of constrained optimization would not be an entirely unknown animal. Some acquaintance has already been made with the conjugate gradient (though I can’t claim mastery of it). Martingales theory—the basic idea—is not a complete unknown. (I had mentioned a basic comparison of my approach vis-a-vis the simplest or the most basic martingales theory, in my PhD thesis.)

Other minor points are these. This field also (i) involves visualization abilities, (ii) encourages good model building at the right level of abstraction, and (iii) places premium on presentation. I am not sure if I am good on the third count, but I sure am confident that I do pretty well on the first two. The roots of all my new research ideas, in fact, can be traced back to having to understand physical principles in 3+1 D settings.


Conclusion 1: I should be very much comfortable with Data Science. (Not sure if Data Science itself (i.e., Data Scientists themselves) would be comfortable with me or not. But that’s something I could deal later on.)

Conclusion 2: Expect blogging here going towards Data Science in the future.


A Song I Like:

(Marathi) “uff, teri adaa…”
Music: Shankar-Ahsaan-Loy
Singer: Shankar Mahadevan
Lyrics: Javed Akhtar

[By any chance, was this tune at least inspired (if not plagiarized) from some Western song? Or is it through and through original? …In any case, I like it a lot. I find it wonderful. It’s upbeat, but not at all banging on the ears. (For contrast, attend any Ganapati procession, whether on the first day, the last day, or any other day in between. You will have ample opportunities to know what having your ears banged out to deafness means. Nay, these opportunities will be thrust upon you, whether you like it or not. It’s our “culture.”)]

 

 

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Where are those other equations?

Multiple header images, and the problem with them:

As noted in my last post, I have made quite a few changes to the layout of this blog, including adding a “Less transient” page [^].

Another important change was that now, there were header images too, at the top.

Actually, initially, there was only one image. For the record, it was this: [^] However, there weren’t enough equations in it. So, I made another image. It was this [^]. But as I had already noted in the last post, this image was already crowded, and even then, it left out some other equations that I wanted to include.

Then, knowing that WordPress allows multiple images that can be shown at random, I created three images, and uploaded them. These are what is being displayed currently.

However, randomizing means that even after re-loading a page a couple of times, there still is a good chance that you will miss some or the other image, out of those three.

Ummm… OK.


A quick question:

Here is the problem statement:

There are three different header images for this blog. The server shows you only one of them during a single visit. Refreshing the page in the browser also counts as a separate visit. In each visit, the server will once again select an image completely at random.

Assume also that the PDF for the random sequence is uniform. That is to say, there is no greater probability for any of the three images during any visit. Cookies, e.g., play no role.

Now, suppose you make only three visits to this blog. For instance, suppose you visit some page on this blog, and then refresh the same page twice in the browser. The problem is to estimate the chances that you will get to see:

  • all of the three different images, but in only three visits
  • one and the same image, each time, during exactly three visits
  • exactly two different images, during exactly three visits

Don’t read further until you solve this problem, right now: right on-the-fly and right in your head (i.e. without using paper and pencil).

(Hint [LOL!]: There are three balls of different colors (say Red, Green, and Blue) in a box, and \dots.)


 

…No, really!

 


Ummm… Still with me?

OK. That tells me that you are now qualified to read further.

Just in case you were wondering what was there in the “other” header images, here is a little document I am uploading for you. Go, see it (.PDF [^]), but also note the caveat below.

Caveats: It is a work in progress. If you spot a mistake or even just a typo, then please do let me know. Also, don’t rely on this work.

For example, the definition of stress given in the document is what I have not so far read in any book. So, take it with a pinch of the salt—even if I feel confident that it is correct. Similarly, there might be some other changes, especially those related to the definition of the flux and its usage in the generic equation. Also, I am not sure if the product ansatz for the separation of variables technique began with d’Alembert or not. I vaguely remember its invention being attributed to him, but it was a long time ago, and I am no longer sure. May be it was before him. May be it was much later, at the hands of Fourier, or, even still later, by Lame. … Anyway let it be…

…BTW, the equations in the images currently being shown are slightly different—the PDF document is the latest thing there is.

Also, let me have your suggestions for any further inclusions, too, if any. (As to me: Yes, I would like to add a bit on the finite volume method, too.)

As usual, I may change the PDF document at any time in future. However, the document will always carry the date of compilation as the “version number”.


General update:

These days, I am also busy converting my already posted CFD snippets [^] into an FVM-based code.

The earlier posted code was done using FDM, not FVM, but it was not my choice—SPPU (Pune University) had thrust it upon me.

Writing an illustrative code for teaching purposes is fairly simple and straight-forward, esp. in Python—and especially if you treat the numpy arrays exactly as if they were Python arrays!! (That is, very inefficiently.) But I also thought of writing some notes on at least some initial parts of FVM (in a PDF document) to go with the code. That’s why, it is going to take a bit of time.

Once all this work is over, I will also try to model the Schrodinger equation using FVM. … Let’s see how it all goes…

…Alright, time to sign off, already! So, OK, take care and bye for now. …

 


A Song I Like:
(Hindi) “baharon, mera jeevan bhee savaron…”
Music: Khayyam
Singer: Lata Mangeshkar
Lyrics: Kaifi Aazmi


[The obligatory PS: In all probability, I won’t make any changes to the text of this post. However, the linked PDF document is bound to undergo changes, including addition of new material, reorganization, etc. When I do revise that document, I will note the updates in the post, too.]