Loitering around…

Update:

OK. I am getting back to working on the remaining topics, in particular, taking down detailed notes on the QM spin. I plan to begin this activity starting this evening. Also, I can now receive queries, from “any” one, regarding my work on QM, including the bit mentioned in the post below. [The meaning of ` “any” one ‘ is explained below.]

[2021.03.24 13:17 IST]


Am just about completing one full day of plain loitering around, doing nothing.

No, of course, it couldn’t possibly have been literally nothing—whether of the शून्य (“shoonya”) variety, or the शुन्य (“shunya”) one. (Go consult a good Sanskrit dictionary for the subtle differences in the meaning of these two terms.)

So, what I mean to say by “doing nothing” is this:

The last entry in my research journal has the time-stamp of 2021.03.18 21:40:34 IST. So, by now, it’s almost like a full day of doing “nothing” for me.

It’s actually worse than that…

In fact, I started loitering around, including on the ‘net, even earlier, i.e., a few days ago. May be from 16th March, may be earlier. However, my journal pages (still loose, still not filed into the plastic folder) do show some entries, which get shorter and shorter, well until the above time-stamp. …The entry before the afore-mentioned has the time-stamp: 2021.03.18 19:12:52 IST.

But not a single entry over the past whole day.


So, what did I do over the last one day? and also, over a few days before it?

Well, the list is long.

I browsed. (Yes, including Twitter, Instagram, and FaceBook—others’ accounts, of course!)

I also downloaded a couple of research papers, and one short history-like book. I generally tried to read through them. Unsurprisingly, I found that I could not. The reason is: I just don’t have any mental energy left to do anything meaningful.

Apparently, I have exhausted all my energy in thinking about the linear momentum operator.

I think that by now I have thought about this one topic in most every way any human being possibly could. At least in parts (i.e., one part taken at a time). I have analyzed and re-analyzed, and re-re-analyzed. I kept on jotting down my “thoughts” (also in a way that would be mostly undecipherable to any one).

I kept getting exhausted, and still, I kept pushing myself. I kept on analyzing. Going back to my earlier thoughts, refining them and/or current thoughts. Et cetera.

In the end, finally, I reached the point where I couldn’t even push myself any longer—in spite of all my stamina to keep pursuing threads in “thinking”. I’ve some stories to share here, but some other time. …To cut all of them long stories short:

Some 12 hours after I thus fully crashed out of all my mental energies, at some moment, I somehow realized that:

I had already built a way to visualize a path in between my approach and the mainstream QM, regarding the linear momentum operator.

I made a briefest possible entry (consisting of exactly one small sketch over some 2″ by 5″ space). Which was at 2021.03.18 21:40:34 IST.

Then, I stopped pursuing it too.

Why bother? Especially when I can now visualize “it” any time I want?


But how good is it?

I think, it should work. But it also appears to be too shaky and too tenuous a connection to me—between the mainstream QM and my new approach.

Of course I’ve noted down a bit of maths to go with it too, and also the physical units for the quantities involved. Yet, two points remain:

As a relatively minor point: I haven’t had the energy to work out (let alone to do even the quick and dirty simulations for) all possible permutations and combinations of the kind of elements I am dealing with. So, there is a slim possibility that terms may cancel each other and so the formulation may not turn out to be general enough. (I’ve been fighting with such a thing for a long time by now.)

But as a relatively much more important point: As I said, this whole way of thinking about it seems too tenuous to me. Even if it works out OK (i.e., after considering all the permutations and combinations involved), this very way of looking at the things would still look at best tenuous to any one.

The only consolation I have is this idea (which had already become absolutely banal even decades ago):

Every thing about QM is different from the pre-quantum theories.

That’s the only thin thread of logic by which I my ideas hang. … Not as good as I wanted it. But not as bad as hanging all loose either…

And, yes, I’ve thought through the ontological aspects as well. … The QM ontology is radically different from the ontologies of all the pre-quantum theories. Especially, that of NM (Newtonian mechanics of particles and rigid bodies). But it is not so radically different from the ontology already required for EM (the Maxwell-Lorentz electrodynamics)—though there is a lot of difference between the EM and the QM ontologies.

And that’s what the current status looks like.


“So, when do you plan to publish it?”

Ummm… Not a good question. A better question, for me, is this:

What do I propose to do with my time, now?

The answer is simple. I will go in for what I know is going to be the most productive route.

Which is: I am going to continue loitering around.

Then, I will begin with taking detailed notes on the QM spin—the next topic from the mainstream QM—as soon as my mental energy returns.

That’s right. I won’t be even considering writing down my thoughts about that goddamn linear momentum operator. Not for any time in the near future. That’s the only way to optimize productivity. My productivity, that is.

So, sorry, I won’t be writing anything on the linear momentum any time soon, even if it precisely was the topic that kept me pre-occupied for such a long time—and also formed the topic of blogging for quite some over the recent past. So, sorry, this entire blog-post (the present one) is going to remain quite vague to you, for quite some time. You even might feel cheated at this point.

Well, but I do have a strong defence from my side: I’ve always said, time and once again, that I was always ready to share all my thoughts to “any” one. I mean, any one who (i) knows the theory of the mainstream QM (including its foundational issues), and (ii) also has looked into the experimental aspects of it (at least in the schematic form.)

So, any such a person can always drop a line to me.

Oh wait!

Don’t write anything to me right away. Hold on for a few days. I just want to kill my time around for now. That’s why.

I’ll let you know (may be via an update here), once I begin actually taking down my notes on the QM spin. That’s the time you—“you” the “any” one—may get in touch with me. That is, if “you” want to know what I’ve thought about that goddamn linear momentum operator. [OK. As the update at the top of the post indicates, now I’m ready.]

OK, bye for now, take care in the meanwhile, and don’t be surprised if I also visit your blog and all…


A Many songs I like:

[I also listened to a lot of songs over the past few days. I couldn’t find a single song that went very well with any one of my overall moods over the past few days… So, don’t try to read too much into this choice. And, I’ve got bored, so I won’t offer any further comment on this song either. (And, one way or the other, I actually don’t know why I like this song or the extent to which I actually like it. Not as of now, any way!)

(Hindi) जनम जनम का साथ है निभाने को (“janam janam kaa saath hai nibhaane ko”)
Singer: Mohammad Rafi
Music: Shankar-Jaikishan
Lyrics: Hasrat Jaipuri

I could not find a good quality original audio track. The “revival” version is here: [^]. It was this version which I first listened to, and used to listen to, while taking leisurely evening drives (for up to, say, 50 miles almost every day) in the area around Santa Rosa. Which was in California. But it didn’t feel that way. (It also was the home town of the “Peanuts” comics creator.) …

…OK, I will throw in one more:

(Marathi) तूं तेव्हा तशी (“too, tevhaa tashee”)
Music and Singer: Pt. Hridayanath Mangeshkar
Lyrics: Aaratee Prabhu

Which is yet another poem by Aaratee Prabhu, converted into a song by Hridayanath. But I won’t be able to talk about it. Not as of today anyway. Listening is good. A good quality audio is here [^].

…And, since I have been listening to songs a lot over the past few days, one more, just for this time around…

(Western, Pop) “How deep is your love”
Band: Bee Gees

I don’t know what the “Official Video” means, but it is here: [^]. I also don’t know what the “Deluxe Edition” of the audio means, but it’s here [^]. … I always happened to listen to the audio, which was, you know, at many places in Pune like in the `H’ club (of the student-run mess at COEP hostels); at the movie theatres running English movies in Pune (like Rahul, the old West-End, and Alka); most all restaurants from the Pune Camp area (and also a few from the Deccan area); also in the IIT Madras hostels; etc. All of this was during the ’80s, only. I don’t know why, but seems like I never came across this song, even at any of these places, once it was ’90s. … As usual, I didn’t even know the words, and so, couldn’t have searched for it. A few days ago, I was just going through a compilation of songs of ’70s when I spotted this one, and then searched on its lyrics and credits and all. I had remembered—and actually known—only the music… But yes, now that I know them, the words too seem pretty good…

Anyway, enough is enough. I already wrote a lot!  High time to go back to doing nothing…
]


History:
2021.03.19 22:27 IST: Originally published.
2021.03.24 13:25 IST: Update noted at the top of the post and also inline. Some minor corrections/editing.

 

 

Still if-ish…

1. Progress has slowed down:

Yep. … Rather, progress has been coming in the sputters.

I had never anticipated that translating my FDM code (for my new approach to QM) into a coherent set of theoretical statements is going to be so demanding or the progress so uneven. But that’s what has actually occurred.

To be able to focus better on the task at hand, I took this blog and my Twitter account off the ‘net from 26th February through 09th March.[* See the footnote below]

Yes, going off the ‘net did help.

Still, gone is that more of less smooth (or “linear”) flow of progress which I experienced in, say, mid-December 2020 through mid-January 2021 times or so, especially in January. Indeed, looking back at the past couple of weeks or so, I can say that a new pattern seems to have emerged. This pattern goes like this:

  • On day 1, I get some good idea about how to capture / encapsulate / present something, or put it in a precise mathematical form. So, I get excited. (I even feel like coming back on the ‘net and saying something.)
  • But right on day 2, I begin realizing that it doesn’t capture the truth in sufficient generality, i.e., that the insight is only partial. Or, may be, the idea even has loopholes in it, which come to the light only when I do a quick and dirty simulation about it.
  • By the time it’s day 2-end, day 3 or at most day 4, I have become discouraged, and even begin thinking of postponing everything to a June-July 2021-based schedule.
  • However, soon enough, I get some idea, hurriedly write it down…
  • …But only for the whole cycle to repeat once again!

This kind of a cycle has repeated some 3–4 times within the past 15–20 days alone.

“Tiring” isn’t the right word. “Fatigue” is.

But there is no way out. I don’t have any one to even discuss anything (though I am ready, as always, from my side.)

And, it still isn’t mid-March yet. So, I keep going back to the “drawing board.” Somehow.

[* Footnote: Curiously though, both WordPress and RevolverMaps have reported hits to this blog right in this period—even when it was not available for public viewing! … What’s going on?]


2. Current status:

In a way, persistence does seem to have yielded something on the positive side, though it has not been good enough (and, any progress that did come, has been coming haltingly).

In particular, with persistence, I kept on finding certain loop-holes in my thinking (though not in the special cases which I have implemented in code). These are not major conceptual errors. But errors, they still are. Some of these can be traced back to the June-July times last year. Funny enough, as I flip through my thoughts (and at times through my journal pages), some bits of some ideas regarding how I could possibly get out of these loop-holes, seem to have occurred, in some seed form (or half-baked form), right back to those times. …

Anyway, the current status is that I think that I am nearing completing a correct description, for the new approach, for the linear momentum operator.

This is the most important operator, because in QM, you use this operator, together with the position operators, in order to derive the operators for so many other dynamical quantities, e.g. the total energy, the angular momentum, etc. (See Shankar’s treatment, which was reproduced in the postulates document here [^].)

The biggest source of trouble for the linear momentum operator has been in establishing a mathematically precise pathway (and not just a conceptual one) between my approach and the mainstream QM. What I mean to say is this:

I could have simply postulated an equation (which I used in my code), and presented it as simply coming out of the blue, and be done with it. It would work; many people in QM have followed precisely this path. But I didn’t want to do that.

I also wanted to see if I can make the connections between my new approach and the MSQM as easy to grasp as possible (i.e., for an expert of MSQM). Making people understand wasn’t the only motive, however. I also wanted to anticipate as many objections as I could—apart from spotting errors, that is. Another thing: Given my convictions, I also have to make sure that whatever I propose, there has to be a consistent ontological “picture” which goes with it. I don’t theorize with ontology as an after-thought.

But troubles kept coming up right in the first consideration—in clearly spelling out the precise differences of the basic ideas between my approach and the MSQM.

And yes, MSQM does have a way of suddenly throwing up issues that are quite tricky to handle.

Just for this topic of linear momentum, check out, for instance, this thread at the Physics StackExchange [^] (especially, Dr. Luboš Motl’s answer), and this thread [^] (especially, Dr. Arnold Neumaier’s answer). The more advanced parts of both these threads are, frankly, beyond my capacity. Currently, I only aim for that level of rigour which is at, say, exactly and precisely the first three sentences from Motl’s answer!…

…We the engineers can happily ignore any unpleasant effects that might occur at the singular and boundary points. We simply try and see if we can get away ejecting such isolated domain points from any theoretical consideration! If something workable can still be obtained even after removing such points out of consideration, we go for it. So, that’s the first thing we check. Usually, it turns out we can isolate them out, and so we proceed to do precisely that! And that is precisely the level at which I am operating…

Even then, issues are tricky. And, at least IMO, a good part of the blame must lie with the confusions wrought by the Instrumentalist’s dogma.

… What the hell, if \Psi(x,t) isn’t an observable itself, then why does it find a place in their theory (even if only indirectly, as in Heisenberg’s formulation)? … Why can’t I just talk of a property that exists at each infinitesimal CV (control volume) \text{d}x? why must I instead take something of interest, then throw in the middle an operator (say a suitable Dirac’s delta), and then bury it all behind an integral sign? why can’t those guys (I mean the mathematical terms) break the cage of the integral sign, and come out in the open, just to feel some neat fresh air?

… Little wonder these MSQM folks live with an in-principle oscillatory universe. It’s a weird universe they have.

In their universe, Schrodinger’s cat is initially in a superposition of being alive and dead. But that’s not actually the most surprising part. Schrodinger’s cat then momentarily (or for a long but finite time) becomes full dead; but then, immediately, it “returns” from that state (of being actually dead) to once again be in a superposition of dead + alive; it spends some time in that superposition; it then momentarily (or for a long but finite time) becomes fully alive too; but only to return back into that surreal superposition…

And it is this whole cycle which goes on repeating ad infinitum.

… No one tells you. But that’s precisely what the framework of MS QM actually predicts.

MSQM doesn’t predict that once a cat does somehow become dead, it remains dead forever. And that’s because, in the MSQM, the only available mathematical machinery (which has any explanation for the quantum phenomena), in principle, predicts only infinite cycles of superposition–life–superposition–death–superposition–….

The postulates of the MS QM necessarily lead to a forever oscillatory universe! Little wonder they can’t solve the measurement problem!

One consequence of such a state of the MS QM theory is that thinking through any aspect becomes that much harder. It isn’t impossible. But hard, yes, it certainly is, where hard means: “tricky”.

Anyway, since the day before yesterday, it has begun looking like this topic (of linear momentum operator), and to the depth I mentioned above, might get over in a few days’ time. At least, that day 1–day 2–etc. pattern seems to have broken—at least for now!

If things go right at least this time round, then I might be able to finish the linear momentum operator by, say, 15th of March. Or 18th. Or 20th.

Addendum especially for Indians reading this post: No, the oscillatory universe of the MSQM people is not your usual birth-life-death-rebirth cycle as mentioned in the ancient Indian literature. The MSQM kind of “oscillations” aren’t about reincarnations of the same soul but in different bodies. In MSQM, the cat “return”s from being dead with exactly the same physical body. So, it’s not a soul temporarily acquiring one body for a brief while, and then discarding it upon its degeneration, only to get another body eventually (due to “karma” or whatever).

So, the main point is: In MSQM, Schrodinger’s cat not just manages to keep the same body, the physical laws mandate that it be exactly the same body (the same material) too! … And, the MS QM doesn’t talk of a soul anyway; it concerns itself purely with the physical aspects—which is a good thing if you ask me. (Just check the postulates document, and pick up a text book to see their typical implications.)


3. Other major tasks to be done (after the linear momentum operator):

  • Write down a brief but sufficiently accurate description of the measurement process following my new approach. This is the easiest task among all the remaining ones, because much of such a description can only be qualitative.
  • Translate my ideas for the orbital angular momentum into precise mathematical terms—something to be done, but here I guess that with almost all possible troubles having already shown up right in the linear momentum stage, the angular momentum should proceed relatively smoothly (though it too is going take quite some time).
  • And then, the biggest remaining task. Actually, many sub-tasks:
    • Study and take notes on the QM spin.
    • Think through and integrate my new approach to it.
    • Write down as much using quantitative terms as possible.

At this stage, I don’t know how long it’s going to take. However, for now, I’ve decided on the following plan for now…


4. Plan for now:

If there remain some issues with the linear momentum operator (actually, in respect of its multi-faceted usages in the MSQM, and in explaining these from the PoV of my approach including ontology), and if these still remain not satisfactorily resolved even by 15th or 18th of March (roughly, one week from now), then I will take a temporary (but long) break from QM, and instead turn my attention to Data Science.

However, if my description for \hat{p}() (i.e. the linear momentum operator) does go through smoothly during the next week, then I will immediately proceed with the remaining QM-related tasks too (i.e., only those which are listed above).


5. Bottom-line:

Expect a blog post in a week’s time or so, concerning an update with respect to the linear momentum operator and all. (I will try to keep this blog open for the upcoming week, but I guess my Twitter account is best kept closed for now—I just don’t have the time to keep posting updates there.)

In the meanwhile, take care and bye for now.


A song I like:

(Marathi) ती येते आणिक जाते (“tee yete aaNik jaate…”)
Lyrics: Aaratee Prabhu
Music: Pt. Hridaynath Mangeshkar
Singer: Mahendra Kapoor

[ Mahendra Kapoor has sung this song very well (even if he wasn’t a native Marathi speaker). Hridaynath Mangeshkar’s music, as usual, pays real good attention to words, even as also managing to impart an ingenious melodic quality to the tune—something that’s very rare for pop music in any language.

But still, frankly, this song is almost as nothing if you don’t get the lyrics of it.

And, to get the lyrics here, it’s not enough to know Marathi (the language) alone. You also have to “get” what precisely the poet must have meant when he used some word; for instance, the word “ती” (“she”). [Hint: Well, the hint has already been given. …Notice, I said “what”, and not “who”, in the preceding sentence!]

But yes, once you begin to get the subtle shades of the poetry here, then you can also begin to appreciate Hridaynath’s composition even better—you begin to see the more subtle musical phrases, the twists and turns and twirls in the tune which you had missed earlier. So, there’s a kind of a virtuous feedback circle going on here, between poetry and music… And yes, you also appreciate Mahendra Kapoor’s singing better as you go through the circle.

This song originally appeared as a part of a compilation of Aaratee Prabhu’s poems. If I mistake not (speaking purely from memory, and from a distance of several decades), the book in question was जोगवा (“jogawaa”). I had bought a copy of it during my UG days at COEP, out of my pocket-money.

We in fact had used another poem from this book as a part of our dramatics for the Firodiya Karandak. It was included on my insistence; I was a co-author of the script. As to the competition, we did win the first prize, but not so much because of the script. We won mainly because our singing and music team had such a fantastic, outstanding, class to them. Several of them later on went on to make full-time career in music…. The main judge was the late music composer Anand Modak, who later on went to win National awards too, but back then, he was at a fledgling stage of his career. But yes, talking of the script itself, in the informal chat after the prize announcement ceremony, he did mention, unprompted and on his own, that our script was good too! (Yaaaay!!) …Back then, there was no separate prize for the best script, but if there were to be one, then we would’ve probably won it. During that informal chat, the judges hadn’t bothered to even passingly mention any script by any other team!)

…Coming back to the book of poetry (Aaratee Prabhu’s), I think I still have my copy lying somewhere deep in one of the boxes, though by now, due to too many moves and all (I had also taken it to USA the first time I went there), its cover already had got dislodged from the book itself. Then, a couple of weeks ago, I saw only the title page peeping out of some bunch of unrelated and loose papers, and so, looks like, the book by now has reached a more advanced stage of disrepair! … Doesn’t matter; no one else is going to read it anyway!

A good quality audio is here [^].

]


History:
2021.03.10 20:57 IST: Originally published.
2021.03.10 22.45 IST: Added links to the Physics StackExchange threads and the subsequent comments up to the mention of the measurement problem. Other minor editing. Done with this post now!
2021.03.12 18.43 IST: Some further additions, especially in section 2, including the Addendum written for Indian readers. Also, some further additions in the songs section. Some more editing. Now, am really done with this post!

The problem is presentation

Development of a new theory is a completely weird business.

I posted the last entry here on this blog on 21 February 2021. In that post, I talked about yet another error that I had found in my approach, and said (I quote)

This “development” implies having to draw up a new schedule. Indeed, I will have to work through everything completely afresh, find some suitable solutions to the issue that came to the notice, and satisfy myself that the solutions I now think of indeed are satisfactory. Then (or simultaneously), I will also have to write code and undertake calculations via completely fresh sets of trials. Only then will I be able to get back to writing the planned document on my new approach.

But Lady Luck had something else in Her Mind.

Right the next day, i.e., on 22 February 21, I realized that:

  • The solutions I now think of indeed ought to be satisfactory.
  • Working through everything completely afresh is going to be super-fast.
  • I can use more or less the same code, with changes to just a few lines.
  • Conducting fresh trials should not take too long; indeed the issue is similar to the error I had made on around 11th January 2021, and had corrected by 13th January 2021 [^].

So, right the same day, I went to the Twitter and posted an update. The as-posted update said:

Let me note down the text here, just in case the link between WordPress and Twitter doesn’t work at times or whatever:

1/n
Re. My blog post of yesterdays’.

The situation is actually not at all as bad as the post might indicate. I now realize that the new approach *has* to work out! (Even for the spin.)

If a PhD physicist with a good understanding of
* the QM postulates, &
* measurement expts

2/2
wishes to have a rapid (but logically complete) *preview* of my upcoming document, then, given that I can lean on *his* understanding, I could easily write a 2-page document (an extended abstract) and send it to him, say within a couple of days at the most.

Just let me know!

2:46 PM · Feb 22, 2021

My original update was a little different. I had written it in a text file, and so, it’s available. Let me quote it too!:

Monday 2021 February 22 13:58:34 IST

The situation is not at all as bleak as my yesterday’s post might indicate.

If a PhD physicist with a very good understanding of the QM postulates wishes to have a preview of my upcoming document stating the essentials of my new approach to understanding and using QM, then, given that I can lean on his understanding, I could easily write a two page document (an extended abstract of sorts) and send it to him within a couple of days at the most.

Monday 2021 February 22 14:03:19 IST


The situation has steadily progressed for the better even after then, and as of today, the situation is this.

  • I do think that I’ve got it right.
  • Even if the theory that I now have is erroneous, it’s worth writing a document and publishing it informally (say at iMechanica for externally verifiable time-stamp, and simultaneously here).

As to the nature of my theory:

  • My theory makes introduces a few completely new postulates, and views the existing postulates of the mainstream QM in a completely new conceptual light.
    • Therefore, the best way would be to present my theory as a completely new system of postulates, and not as extensions and restrictions on the postulates of the mainstream QM.
    • However, I am quite clear that my set of postulates, when taken and applied correctly, do uniquely lead to the postulates of the mainstream QM.
      • In this sense, there is no contradiction between my theory and the mainstream QM.
      • In particular, in my theory, I introduce a distinction between the dynamical state as it actually is vs. the dynamical state as it is abstractly represented in the mainstream QM.
        • I connect the two via a description of the measurement processes as they actually occur in actual experiments.
        • I also show how the implications of the measurement processes are encapsulated / represented in my theory, as in contrast to their encapsulation / representation in the mainstream QM.
    • There also are a lot of ontological issues to be clarified.
      • I am quite clear on them.
      • But the issues are quite complicated.
      • I am still working on what is more primary and what is secondary.

But there is a problem. (Isn’t there one, always?):

  • Because my new postulates “sound” very similar to those of the mainstream QM, chances are significant that people, on casual reading, might mistake them for what they don’t actually say.

All in all,

  • I am clear as to what all needs to be said, eventually
    • But this is a material that is too huge, too scattered, and requires too new a way of looking at things.
  • So, I am not at all clear in what order I need to say it, and in what way I should put it (to provide a path of least resistance to the reader).
  • And yes, I am also too close to my theory to spot any errors if they are still left
  • Another thing. I am also too ignorant of the special relativity to tell if my kind of theorization provides a nice and neat path for building a new (my kind of) theory for the special relativistic QM
    • I’ve begun suspecting that something like this should be possible
  • One final point. I haven’t studied the spin yet. However,
    • I have the right theory for the Schrodinger wavefunction operators.
    • In the non-relativistic theory, I know that the spin has to be introduced only on an ad-hoc basis, as an additional postulate.

Considering all the aforementioned points (and other, similar, issues), the bottom-line I guess is:

  • I know I have got something.
  • But I don’t know how to present it.
    • I have written 15 pages, and still not gotten through half (or 1/3rd) of my points.
      • And, what I’ve written is not very good; I don’t like it
      • I can’t go on like that—writing 10+ pages of just trial material. I need to finish this fast.

What should I do now?

I am thinking about that one too.

Yes, theory-building is a weird business. Had I known that it’s going to get this weird, I wouldn’t have ventured into it in the first place. But then, by now, it’s too late…


A song I like:

(Marathi) नवल वर्तले गे माये, उजळला प्रकाशु (“naval vartale ge maaye, ujaLalaa prakaashu”)
Lyrics: G. D. Madgulkar
Music: C. Ramachandra
Singer: Asha Bhosale

[ Not a song that’s from my top favourites; certainly not in the usual sense of the word.

But yesterday around noon time, I was lazily lying on the bed, thinking of the momentum operator and my ideas surrounding it, and I thought of a neat way to view, capture, and condense what I was looking for. So, I got up from the bed and generally began walking towards the sunlit balcony, all in delight. At that very moment, somehow, I found myself humming this song. Just like that, automatically, without any traceable reason. (Didn’t hear it on radio or so either; haven’t listened to it for years on.) Yes, even though my natural neural network classifier doesn’t put this song in the top favourites category as such, it is a good song IMO. The lyrics, in particular, are absolutely outstanding and wonderful (and note, the lyrics come from Madgulkar, not Sant Dnyaneshwar). And yes, I do like it too. …So, that’s how I decided to run it.

I good quality audio is here [^]. ]