# Expanding on the procedure of expanding: Where is the procedure to do that?

Update on 18th June 2017:

See the update to the last post; I have added three more diagrams depicting the mathematical abstraction of the problem, and also added a sub-question by way of clarifying the problem a bit. Hopefully, the problem is clearer and also its connection to QM a bit more apparent, now.

Here I partly expand on the problem mentioned in my last post [^]. … Believe me, it will take more than one more post to properly expand on it.

The expansion of an expanding function refers to and therefore requires simultaneous expansions of the expansions in both the space and frequency domains.

The said expansions may be infinite [in procedure].

In the application of the calculus of variations to such a problem [i.e. like the one mentioned in the last post], the most important consideration is the very first part:

Among all the kinematically admissible configurations…

[You fill in the rest, please!]

A Song I Like:

[I shall expand on this bit a bit later on. Done, right today, within an hour.]

(Hindi) “goonji see hai, saari feezaa, jaise bajatee ho…”
Music: Shankar Ahasaan Loy
Lyrics: Javed Akhtar

# An interesting problem from the classical mechanics of vibrations

Update on 18 June 2017:
Added three diagrams depicting the mathematical abstraction of the problem; see near the end of the post. Also added one more consideration by way of an additional question.

TL;DR: A very brief version of this post is now posted at iMechanica; see here [^].

How I happened to come to formulate this problem:

As mentioned in my last post, I had started writing down my answers to the conceptual questions from Eisberg and Resnick’s QM text. However, as soon as I began doing that (typing out my answer to the first question from the first chapter), almost predictably, something else happened.

Since it anyway was QM that I was engaged with, somehow, another issue from QM—one which I had thought about a bit some time ago—happened to now just surface up in my mind. And it was an interesting issue. Back then, I had not thought of reaching an answer, and even now, I realized, I had not very satisfactory answer to it, not even in just conceptual terms. Naturally, my mind remained engaged in thinking about this second QM problem for a while.

In trying to come to terms with this QM problem (of my own making, not E&R’s), I now tried to think of some simple model problem from classical mechanics that might capture at least some aspects of this QM issue. Thinking a bit about it, I realized that I had not read anything about this classical mechanics problem during my [very] limited studies of the classical mechanics.

But since it appeared simple enough—heck, it was just classical mechanics—I now tried to reason through it. I thought I “got” it. But then, right the next day, I began doubting my own answer—with very good reasons.

… By now, I had no option but to keep aside the more scholarly task of writing down answers to the E&R questions. The classical problem of my own making had begun becoming all interesting by itself. Naturally, even though I was not procrastinating, I still got away from E&R—I got diverted.

I made some false starts even in the classical version of the problem, but finally, today, I could find some way through it—one which I think is satisfactory. In this post, I am going to share this classical problem. See if it interests you.

Background:

Consider an idealized string tautly held between two fixed end supports that are a distance $L$ apart; see the figure below. The string can be put into a state of vibrations by plucking it. There is a third support exactly at the middle; it can be removed at will.

Assume all the ideal conditions. For instance, assume perfectly rigid and unyielding supports, and a string that is massive (i.e., one which has a lineal mass density; for simplicity, assume this density to be constant over the entire string length) but having zero thickness. The string also is perfectly elastic and having zero internal friction of any sort. Assume that the string is surrounded by the vacuum (so that the vibrational energy of the string does not leak outside the system). Assume the absence of any other forces such as gravitational, electrical, etc. Also assume that the middle support, when it remains touching the string, does not allow any leakage of the vibrational energy from one part of the string to the other. Feel free to make further suitable assumptions as necessary.

The overall system here consists of the string (sans the supports, whose only role is to provide the necessary boundary conditions).

Initially, the string is stationary. Then, with the middle support touching the string, the left-half of the string is made to undergo oscillations by plucking it somewhere in the left-half only, and immediately releasing it. Denote the instant of the release as, say $t_R$. After the lapse of a sufficiently long time period, assume that the left-half of the system settles down into a steady-state standing wave pattern. Given our assumptions, the right-half of the system continues to remain perfectly stationary.

The internal energy of the system at $t_0$ is $0$. Energy is put into the system only once, at $t_R$, and never again. Thus, for all times $t > t_R$, the system behaves as a thermodynamically isolated system.

For simplicity, assume that the standing waves in the left-half form the fundamental mode for that portion (i.e. for the length $L/2$). Denote the frequency of this fundamental mode as $\nu_H$, and its max. amplitude (measured from the central line) as $A_H$.

Next, at some instant of time $t = t_1$, suppose that the support in the middle is suddenly removed, taking care not to disturb the string in any way in the process. That is to say, we  neither put in any more energy in the system nor take out of it, in the process of removing the middle support.

Once the support is thus removed, the waves from the left-half can now travel to the right-half, get reflected from the right end-support, travel all the way to the left end-support, get reflected there, etc. Thus, they will travel back and forth, in both the directions.

Modeled as a two-point BV/IC problem, assume that the system settles down into a steadily repeating pattern of some kind of standing waves.

The question now is:

What would be the pattern of the standing waves formed in the system at a time $t_F \gg t_1$?

The theory suggests that there is no unique answer!:

Since the support in the middle was exactly at the midpoint, removing it has the effect of suddenly doubling the length for the string.

Now, simple maths of the normal modes tells you that the string can vibrate in the fundamental mode for the entire length, which means: the system should show standing waves of the frequency $\nu_F = \nu_H/2$.

However, there also are other, theoretically conceivable, answers.

For instance, it is also possible that the system gets settled into the first higher-harmonic mode. In the very first higher-harmonic mode, it will maintain the same frequency as earlier, i.e., $\nu_F = \nu_H$, but being an isolated system, it has to conserve its energy, and so, in this higher harmonic mode, it must vibrate with a lower max. amplitude $A_F < A_H$. Thermodynamically speaking, since the energy is conserved also in such a mode, it also should certainly be possible.

In fact, you can take the argument further, and say that any one or all of the higher harmonics (potentially an infinity of them) would be possible. After all, the system does not have to maintain a constant frequency or a constant max. amplitude; it only has to maintain the same energy.

OK. That was the idealized model and its maths. Now let’s turn to reality.

Relevant empirical observations show that only a certain answer gets selected:

What do you actually observe in reality for systems that come close enough to the above mentioned idealized description? Let’s take a range of examples to get an idea of what kind of a show the real world puts up….

Consider, say, a violinist’s performance. He can continuously alter the length of the vibrations with his finger, and thereby produce a continuous spectrum of frequencies. However, at any instant, for any given length for the vibrating part, the most dominant of all such frequencies is, actually, only the fundamental mode for that length.

A real violin does not come very close to our idealized example above. A flute is better, because its spectrum happens to be the purest among all musical instruments. What do we mean by a “pure” tone here? It means this: When a flutist plays a certain tone, say the middle “saa” (i.e. the middle “C”), the sound actually produced by the instrument does not significantly carry any higher harmonics. That is to say, when a flutist plays the middle  “saa,” unlike the other musical instruments, the flute does not inadvertently go on to produce also the “saa”s from any of the higher octaves. Its energy remains very strongly concentrated in only a single tone, here, the middle “saa”. Thus, it is said to be a “pure” tone; it is not “contaminated” by any of the higher harmonics. (As to the lower harmonics for a given length, well, they are ruled out because of the basic physics and maths.)

Now, if you take a flute of a variable length (something like a trumpet) and try very suddenly doubling the length of the vibrating air column, you will find that instead of producing a fainter sound of the same middle “saa”, the flute instead produces the next lower “saa”. (If you want, you can try it out more systematically in the laboratory by taking a telescopic assembly of cylinders and a tuning fork.)

Of course, really speaking, despite its pure tones, even the flute does not come close enough to our idealized description above. For instance, notice that in our idealized description, energy is put into the system only once, at $t_R$, and never again. On the other hand, in playing a violin or a flute we are continuously pumping in some energy; the system is also continuously dissipating its energy to its environment via the sound waves produced in the air. A flute, thus, is an open system; it is not an isolated system. Yet, despite the additional complexity introduced because of an open system, and therefore, perhaps, a greater chance of being drawn into higher harmonic(s), in reality, a variable length flute is always observed to “select” only the fundamental harmonic for a given length.

How about an actual guitar? Same thing. In fact, the guitar comes closest to our idealized description. And if you try out plucking the string once and then, after a while, suddenly removing the finger from a fret, you will find that the guitar too “prefers” to immediately settle down rather in the fundamental harmonic for the new length. (Take an electric guitar so that even as the sound turns fainter and still fainter due to damping, you could still easily make out the change in the dominant tone.)

OK. Enough of empirical observations. Back to the connection of these observations with the theory of physics (and maths).

The question:

Thermodynamically, an infinity of tones are perfectly possible. Maths tells you that these infinity of tones are nothing but the set of the higher harmonics (and nothing else). Yet, in reality, only one tone gets selected. What gives?

What is the missing physics which makes the system get settled into one and only one option—indeed an extreme option—out of an infinity of them of which are, energetically speaking, equally possible?

Update on 18 June 2017:

Here is a statement of the problem in certain essential mathematical terms. See the three figures below:

The initial state of the string is what the following figure (Case 1) depicts. The max. amplitude is 1.0. Though the quiescent part looks longer than half the length, it’s just an illusion of perception.:

Case 1: Fundamental tone for the half length, extended over a half-length

The following figure (Case 2) is the mathematical idealization of the state in which an actual guitar string tends to settle in. Note that the max. amplitude is greater (it’s $\sqrt{2}$) so  as to have the energy of this state the same as that of Case 1.

Case 2: Fundamental tone for the full length, extended over the full length

The following figure (Case 3) depicts what mathematically is also possible for the final system state. However, it’s not observed with actual guitars. Note, here, the frequency is half of that in the Case 1, and the wavelength is doubled. The max. amplitude for this state is less than 1.0 (it’s $\dfrac{1}{\sqrt{2}}$) so as to have this state too carry exactly the same energy as in Case 1.

Case 3: The first overtone for the full length, extended over the full length

Thus, the problem, in short is:

The transition observed in reality is: $T1:$ Case 1 $\rightarrow$ Case 2.

However, the transition $T2:$ Case 1 $\rightarrow$ Case 3 also is possible by the mathematics of standing waves and thermodynamics (or more basically, by that bedrock on which all modern physics rests, viz., the calculus of variations). Yet, it is not observed.

Why does only $T1$ occur? why not $T2$? or even a linear combination of both? That’s the problem, in essence.

While attempting to answer it, also consider this : Can an isolated system like the one depicted in the Case 1 at all undergo a transition of modes?

Enjoy!

Update on 18th June 2017 is over.

That was the classical mechanics problem I said I happened to think of, recently. (And it was the one which took me away from the program of answering the E&R questions.)

Find it interesting? Want to give it a try?

If you do give it a try and if you reach an answer that seems satisfactory to you, then please do drop me a line. We can then cross-check our notes.

And of course, if you find this problem (or something similar) already solved somewhere, then my request to you would be stronger: do let me know about the reference!

In the meanwhile, I will try to go back to (or at least towards) completing the task of answering the E&R questions. [I do, however, also plan to post a slightly edited version of this post at iMechanica.]

Update History:

07 June 2017: Published on this blog

8 June 2017, 12:25 PM, IST: Added the figure and the section headings.

8 June 2017, 15:30 hrs, IST: Added the link to the brief version posted at iMechanica.

18 June 2017, 12:10 hrs, IST: Added the diagrams depicting the mathematical abstraction of the problem.

A Song I Like:

(Marathi) “olyaa saanj veli…”
Music: Avinash-Vishwajeet
Singers: Swapnil Bandodkar, Bela Shende
Lyrics: Ashwini Shende

# Miscellaneous: my job situation, the Tatas, and taking a break…

This year’s Diwali isn’t going great for me. I am still jobless—without reason or rhyme. It is difficult to enjoy Diwali against that backdrop.

As you know, engineering colleges affiliated to the Savitribai Phule Pune University (SPPU for short) have been telling me that my Metallurgy+Mechanical background isn’t acceptable, even though the rules have changed to the contrary, and say that I now qualify (in my interpretation).

Recently I attended an interview, and it seems like I may be able to obtain a clear-cut answer on my eligibility (i.e. the equivalence of Metallurgy and Mechanical) from SPPU.

The thing is, SPPU has been having no Dean for its Engineering faculty for about a year or more by now, because the Maharashtra state government hasn’t so far undertaken the procedure to elect (or select) the next Dean.

This recent interview which I mentioned above, was for a Principal’s post, and I was short-listed. As is the common practice here, the short-listed candidates were all invited at the same time, and thus, I had an opportunity to interact with these other, senior-level professors.

These senior professors (some of them already active as Principals at other colleges) told me that it isn’t just SPPU, but all the universities in Maharashtra. They all are currently having only an in-charge or acting Dean for their engineering faculties, because the procedure to appoint the next set of Deans, which was due to occur this month (October) has once again been postponed by yet another year.

Policy decisions such as the Metallurgy and Mechanical equivalence at SPPU have been pending, they told me, because the acting Dean can easily say that he has no powers to do that. Though the other universities are clear that I would qualify, if a genius running an engineering college under SPPU thinks that I don’t, then the matter normally goes to the Dean. If the Dean is not official, if he is only acting, he doesn’t want to take “risk,” so he takes no decision at all. Not just the equivalence issues, there are certain other policy decisions too, which have been pending, they told me. The in-charge Deans have been processing only the routine work, and not taking any policy decisions. The next set of Deans were expected to get appointed by June 2016, and then, after postponement, by October 2016. (“achhchhe din!”)

Now that the appointments have been officially postponed by one whole year (“achhchhe din,” again!), the colleges themselves have begun going to the universities for obtaining the professor’s approvals, arguing that faculty approvals is a routine matter, and that they cannot properly function without having approved faculty.

Thus, the university (SPPU) has begun appointing panels for faculty interviews. There has been a spate of faculty recruitment ads after the current semester got going (“achhchhe din!”).

The particular interview which I attended, these other candidates informed me, was with a University-appointed panel—i.e., of the kind which allows approvals. (Otherwise, the appointments are made by the affiliating colleges on their own, but only on a temporary, ad-hoc basis, and therefore, for a limited time.)

Please note, all the above is what I gathered from their talk. I do not know what the situation is exactly like. (Comments concerning “achhchhe din!,” however, are strictly mine.)

But yes, it did turn out that the interview panel here was from the university. Being a senior post (Principal), the panel included both the immediately past Dean (Prof. G. K. Kharate) and the new, in-charge Dean (Prof. Dr. Nerkar, of PVG College, Pune).

During my interview, if the manner in which Prof. Kharate (the past Dean) now said things is any indication, it means that I should now qualify even in the SPPU. This would be according to the new GR about which I had written a few months ago, here [^]. Essentially, Prof. Kharate wondered aloud as to why there was any more confusion because the government had already clarified the situation with the new rules.

I took that to mean that I qualify.

Of course, these SPPU geniuses are what they are, and therefore, they—these same two SPPU Deans—could very well say, in future, that I don’t qualify. After all, I didn’t ask them the unambiguous question “With my Metallurgy background, do I qualify for a Mechanical Engineering (full) Professor’s job or not? Yes, or no?;”  and they didn’t then answer in yes or no terms.

Of course, right in the middle of an on-going job interview couldn’t possibly have been the best time and place to get them to positively confirm that I do qualify. (Their informal indications, however, were clearly along the lines that I do qualify.)

Now that the Diwali break has arrived, the colleges are closed, and so, I would be able to approach Prof. Dr. Nerkar (the currently acting/in-charge Dean) only after a week or so. I intend to do that and have him pin down the issue in clear-cut terms.

At the conclusion of my interview, I told the interview committee exactly the same thing which I told you at the beginning of this post, viz., that this Diwali means darkness to me.

But yes, we can hope that Prof. Dr. Nerkar would issue the clarification at least after the Diwali. If not, I intend to approach Prof. Dr. Gade, the Vice-Chancellor of SPPU. … I could easily do that. I am very social, that way.

And, the other reason is, at the university next door—the Shivaji University—they did answer my email asking them to clarify these branch-equivalence issues. The SPPU is the worst university among the three in the Western Maharashtra region (the other two being, the University of Mumbai and the Shivaji University Kolhapur). [I want to teach in Pune only because it’s my home-town, and thus convenient to me and my family, not because SPPU’s standards are high.]

Anyway, I now do have something in hand to show Prof. Dr. Gade when I see him—the letter from the Shivaji University staff. … At the Shivaji University, I didn’t have to go and see anyone in person there—not even the administrative staff let alone the acting Dean or the Vice-Chancellor. The matter got clarified just via a routine email. There is a simple lesson that SPPU may learn from the Shivaji and Mumbai universities, and under Prof. Dr. Gade, I hope they do.

… Of course, I do also hope that I don’t have to see Prof. Dr. Gade (the Vice-Chancellor). I do hope that meeting just Prof. Dr. Nerkar (the in-charge Dean) should be sufficient.

If they refuse me an appointment, I will get even more social than my usual self—I will approach certain eminent retired people from Pune such as Dr. Bhatkar (the founder of C-DAC) or Dr. Mashelkar (the former Director General of CSIR, India).

Here is a hoping that I don’t have to turn into a social butterfly, and that soon after Diwali, the matters would get moving smoothly. Let’s hope so.

And with that hope in my heart, let me wish you all a very happy and prosperous Diwali. … As to me, I will try to make as much good of a bad situation that I can.

Still, I don’t find myself to be too enthusiastic. I don’t feel like doing much anything. [In a way, I feel tired.] Therefore, I am going to take a break from blogging.

I have managed to write something more on the concept of space. I found that I should be able to finish this series now. I had begun it in 2013; see here [^].

Concepts like space and time are very deep matters, and I still have to get enough clarity on a few issues, though all such remaining issues are relatively quite minor. I should be able to get through them in almost no time.

From the new material which I have written recently, I guess it would be enough to write just one or two posts, and then the series would get over. What then will remain would be mostly polemics, and that part can be taken on the fly whenever the need to do so arises.

I may also think of giving some indications on the concept of time, but, as I said, I find myself too lacking in enthusiasm these days. Being jobless—despite having the kind of resume I have—does have a way of generating a certain amount of boredom in you, a certain degree of disintegration at least to your energy and enthusiasm, even if not to your soul.

So, let’s see. Let the Diwali vacations get over, and I should come back and resume my blogging, telling you what all transpired in my meeting/interaction with the in-charge Dean, and the related matters.

Since I am not going to be blogging for some time, let me note a couple of notable things.

One, the US Presidential elections. I am not at all interested in that. So let me leave it aside.

Two, the Tata Sons issue. It does interest me a bit, so let me write down a bit on it.

I was not as surprised as some of the newspaper editorials and columns say they were. The days of JRD are long gone. The Tatas already were a changed company when Cyrus Mistry took over from Ratan Tata.

Once I returned from the USA in 2001, despite my resume, I never got a chance with the new Tatas (either at TRDDC or at TCS). Such a thing would have been unthinkable during JRD’s times. … Even keeping it aside, what all I observed about the Tatas over the past 1.5 decades was enough for me not to be at all surprised by something like the current fiasco.

No, Prof. Pratap Bhanu Mehta, reading things from where I sit, the Tata fiasco doesn’t do any significant harm to the social legitimacy of Capitalism in India. People—common people—have long ago observed and concluded what had to be. If what the common people think were to be caricatured, it would look like the position you ascribe to the “cynics”. But no, IMO, this position isn’t cynical. To carry realistic impressions about hallowed icons is not quite the same as being a cynic.

Yes, as Harsh Goenka astutely pointed out in his comment in today’s ToI, Ratan Tata’s tenure coincided with the semi-liberalization era: 1991–2012. Whenever you come to compare Ratan Tata with Cyrus Mistry, you cannot overlook that broad context.

I have always thought that JRD left too big shoes for any one to fill in. But, with due respect to Ratan Tata, I still would have to say that no one could possibly entertain thinking in similar terms, when it comes to Ratan Tata’s retirement.

Looking at the facts and figures reported this week, I don’t think Mistry was doing a lousy job. Reading through his letter, I in fact marvel at how well he understood his job—and for this reason, I speculate that he must have been doing his job pretty well. …

Realize, the letter was written within a day or two after an unceremonious removal from the top post of a 100+ years old Indian icon, a \$100 billion behemoth. Seen against this backdrop, the letter is extraordinarily restrained; it shows an unusual level of maturity. To expect any more “restraint” is to actually confess ignorance of such basic things as human nature and character. (Sadhus, let me remind you, are known to kill each other in their fights at the Kumbh Mela, just for the priority in taking the Shahi Snaan. Keep that in mind the next time you utter something on nobility of character and culture.)

And yes, I also had come to think that the Nano project was doomed—I just didn’t have the sales and profitability figures, which got reported only today. My reasons were simple; they were purely from an ordinary consumer’s point of view. If you are selling the Nano at around Rs. 2.5 lakhs, just think of the alternatives that the consumer has today: you could get a used car in a “good enough” condition, not just Maruti Alto but even a somewhat more used Toyota Innova, at roughly the same price.

Anyway, I don’t understand these corporate matters much, so let me shut up.

But, yes, knowing the house of Tatas and their brand managers, I can predict right away that in the near future, you are going to see the Tatas announce a product like “Tata Quantum Dot,” or “Tata Silicon Dot,” or something like that. … Why do I think so?

I started writing on quantum mechanics, and roughly around the same time, the cable-less Internet, based on the electromagnetic waves (mobile, Wi-Fi) was getting going in India. So, the Tatas came out with the Tata Photon. Yes, “Photon”. The Tata Photon. … It meant nothing more than the usual Internet dongle (2G, and then 3G) that everybody else was already supplying anyway. (And the Tata Photon never worked too well in areas other than in the Mumbai city.)

Then, the USA was abuzz with the catch-words like nano-technology, and the Tata brand managers decided to do something with that name, and thus came the Tata “Nano.” By now, every one knows what it means.

Today, the USA and other countries are abuzz with words like “Quantum Supremacy” and things like that. You can only expect some Tata brand managers to latch on to this buzzword, and launch a product like, say, Tata Quantum Dot or Tata Silicon Dot—or both!

Tata Silicon Dot, I predict, would signal the arrival of the house of Tatas into the business of supplying the sand required for civil engineering construction.

Tata Quantum Dot, on the other hand, would mean that the house of Tatas had taken an entry into the business of plastic dart toys. Or, the business of the “bindi”s that ladies wear. That is what the house of Tatas would mean by the name Tata Quantum Dot.

And here our policy analysts think that something happening to the house of Tatas is going to affect the credibility or social legitimacy of Capitalism itself in India! Oh wow!!

Ummm…. Does any policy research center in India have any data on the proportion of the private business in the overall Indian economy (including both the organized and the unorganized sectors) over the years, say starting from 1930s? Also, the quantum of the government expenditure in the Indian economy, and its proportion in the national GDP over the same period? Would they care to share it, please? Or is it that they don’t have to look at such data for their policy research purposes? … As to me, I have been on the lookout for data like that for quite some time now, but never could see it compiled anywhere. That’s why the request. Please drop me a line if you spot a reliable source.

OK, bye for now.

A Song I Like:

Since I won’t be blogging for a while, let me give away the “other” song right away, I mean the song which had somehow happened to strike me as being similar to the song “too laali hai savere waali”; see the Song I Like section here [^]. This other song is:

(Hindi) “bhigee bhigee raaton mein…”
Music: R. D. Burman
Singers: Kishore Kumar, Lata Mangeshkar
Lyrics: Anand Bakshi

I take the “raaga” of the earlier song (“too laali hai”) as “pahaaDee”—or at least that’s what I got from an Internet search. The “raaga” of the current song (“bhigee…”) isn’t listed at any Web site. Assuming it’s not “pahaaDee” (or a variant on that), the question becomes, why the two songs might have struck at least somewhat similar to me—why, humming one song, I very naturally and casually happened to remember the other song.

It would be interesting to see if Data Science can be used to spot (and quantify) similarities in songs. The traditional music theory puts too much emphasis, IMO, on “raaga” alone. But there can be other bases for similarities, too. The sound patterns of musical pieces, I think, don’t get exhaustively (and at times not even essentially) characterized by the idea of the “raaga” alone. Talking of these two songs in particular, the similarity I caught might have been connected with certain ups and downs in notes with a somehow similarly sounding tempo. The style of the tunes sounds similar. Guess Data Science might be able to shed some light on things like that…. It would be interesting, to look into that, no? That’s what I had thought…

I mean, I had thought. … But then, these days, as I said, I am unable to work on this topic, too…  I just don’t have any enthusiasm left. Honest. I somehow finished this post, only because I won’t be posting for a while…

So, there. Bye for now, take care, and best!

[E&OE]

# Yo—9: The lost song

[Update on 2015.01.29 appears at the end.]

This will really, really be a Yo post—short and sweet.

As I had mentioned in the “A Song I Like” section of my past blog post of 2009.09.06 [^], there was a certain song whose words I simply could not remember well, and so, I had also failed to locate the song anywhere on the ‘net. (I had asked `n’ number of “songs-knowing” friends, family members, and also acquaintances in general, before doing those extensive Google searches I mentioned in that post.)

Now some five+ years later, I am happy to let you know that I have found the song! … Via a search on the ‘net, of course. [On 2015.01.24, if you must know.]

Locating the song now became possible only thanks to this popular (and impressively extensive) blog maintained by one Atul (and a few pals); the blog is named “Atul’s Bollywood Song A Day” [^]. [Back in 2009, the song had not yet been listed on Atul’s site/blog.]

There are some reasons why I could not get to this song any time earlier (despite very extensive Google searches on several occasions).

First, there is this feature of many old Hindi film songs whereby the song does not begin immediately. Instead, there is this yawningly long spoken “preamble” of sorts at the beginning, which then is followed by a sleep-inducing piece of a “subdued” kind of a music. People with extreme cases of amnesia insomnia[see update at the end] report that this piece is always very efficient in generating pathos of sorts. Here, the music directors of those olden golden days could accomplish their goal by using just a single violin or a flute, they then add. Even then, the song itself still does not show any sign of beginning.  The aforementioned delivery is further followed by a veeeery loooooooong silence. (In some songs, the combination repeats a couple of times or so.)

And then, if any one around is still left awake, he then becomes qualified to listen to the actual song. Which is a very different tune, of course.

The trouble is, it is this latter part which can be quite hummable and likeable.

More to the present point, as a rule, even the words used in that “preamble” have nothing [or almost nothing] to do with the subsequent (Hindi) “mukhaDaa” itself. [For my Western readers: A (Hindi) “mukhaDaa” or a  (Marathi, Sanskrit) “dhrupad” is more or less the same as the refrain in the Western pop songs.]

Now, what Google did was to index this song by its “preamble,” but not by the “mukhaDaa”. … Not their fault, actually. Even back in 2009, there existed a few sites that would tell you which Hindi song is based on what (Hindi, Sanskrit) “raag.” [Such sites are supposedly very useful for instantaneous acquisition of IQ + MQ + EQ.] A couple of these sites had chosen to be very faithful to their tradition, and so, they had done their listing using only the “preamble.” [OK. Drop that IQ part.]

In contrast, Atul, being a layman, did the right thing: in 2012, he listed the song by the “mukhaDaa,” thereby making it possible for me to locate it in my recent search.

Another reason, as I had indicated in my above-mentioned post, was that I had only a vague recollection of the words.

Anyway, let me not stretch your patience any more. On Atul’s blog, the entry for this song can be found here: [^].

[Feel free to check out my earlier post, and then write an ink-blot sort of a psychoanalysis of mine, based on what I had remembered right, what I had forgotten, and what I had distorted. Just one request: do share your psycho-analysis with me. […No, you don’t have to hesitate at all!… I also read newspaper astrology columns.]]

And, if it is not a (Hindi, Sanskrit) “bhairavi,” then please do drop me a line. (And, BTW, should the spelling be “bhairavee,” and not “bhairavi”? In Hindi? in Marathi? in Sanskrit?)

Anyway, hope you like this song.

[Though once again this post has grown a bit too long, at least I managed to keep it restricted to just one section, and at less than 1000 words. Yo!]

[Update on 2015.01.29: Edited the post to substitute “insomnia” in place of “amnesia.”Also, changed the order of the two paragraphs near where I write something about psycho-analysis. Also, cut out some erroneous portion in entirety.

Now, a few words about amnesia and insomnia:

When I first wrote that line, I knew what I wanted was “insomnia” (i.e. sleep deprivation or difficulty to go to sleep) . But I still wrote “amnesia” (forgetfulness). And, while writing the wrong word, I did actually pause and think twice, and even confirmed to myself, what I was writing was the correct word (“amnesia, of course, is sleep deprivation”), even though on the second reading (but only after the final publishing) I myself figure out that what I wrote was wrong…

Why does it always happen with me? I have no idea.

… In my entire primary and secondary school, I never got cent-percent marks in maths. And that wasn’t because I found maths difficult to follow or because I failed to “get” it, but simply because I made so many silly mistakes—before, during and after examinations. I mean, I could easily analyse some difficult sum, find the correct approach to solve it, and then, when it came to an intermediate simplifying step like, say: $x + 4 = 6$, I would explicitly write it down. But still, right in the next step, I could then easily write: $x = -2$! I would go on to use this wrong value in all my further steps, in a problem that others wouldn’t even choose to tackle.  Why would I do that—randomly picking up problems to solve, in the process picking up even a more difficult sum, and then introducing silly mistakes in it? I have no idea.

… Neither do I any longer care.

So, as the last word, let me say, I could at least do enough sums write to get through my engineering education, and now, I can at least ex post “publisho” catch my posting errors. … Hey, I must be doing some thing right, right?]

[E&OE]