Causality. And a bit miscellaneous.

0. I’ve been too busy in my day-job to write anything at any one of my blogs, but recently, a couple of things happened.


1. I wrote what I think is a “to read” (if not a “must read”) comment, concerning the important issue of causality, at Roger Schlafly’s blog; see here [^]. Here’s the copy-paste of the same:

1. There is a very widespread view among laymen, and unfortunately among philosophers too, that causality requires a passage of time. As just one example: In the domino effect, the fall of one domino leads to the fall of another domino only after an elapse of time.

In fact, all their examples wherever causality is operative, are of the following kind:

“If something happens then something else happens (necessarily).”

Now, they interpret the word `then’ to involve a passage of time. (Then, they also go on to worry about physics equations, time symmetry, etc., but in my view all these are too advanced considerations; they are not fundamental or even very germane at the deepest philosophical level.)

2. However, it is possible to show other examples involving causality, too. These are of the following kind:

“When something happens, something else (necessarily) happens.”

Here is an example of this latter kind, one from classical mechanics. When a bat strikes a ball, two things happen at the same time: the ball deforms (undergoes a change of shape and size) and it “experiences” (i.e. undergoes) an impulse. The deformation of the ball and the impulse it experiences are causally related.

Sure, the causality here is blatantly operative in a symmetric way: you can think of the deformation as causing the impulse, or of the impulse as causing the deformation. Yet, just because the causality is symmetric here does not mean that there is no causality in such cases. And, here, the causality operates entirely without the dimension of time in any way entering into the basic analysis.

Here is another example, now from QM: When a quantum particle is measured at a point of space, its wavefunction collapses. Here, you can say that the measurement operation causes the wavefunction collapse, and you can also say that the wavefunction collapse causes (a definite) measurement. Treatments on QM are full of causal statements of both kinds.

3. There is another view, concerning causality, which is very common among laymen and philosophers, viz. that causality necessarily requires at least two separate objects. It is an erroneous view, and I have dealt with it recently in a miniseries of posts on my blog; see https://ajitjadhav.wordpress.com/2017/05/12/relating-the-one-with-the-many/.

4. Notice, the statement “when(ever) something happens, something else (always and/or necessarily) happens” is a very broad statement. It requires no special knowledge of physics. Statements of this kind fall in the province of philosophy.

If a layman is unable to think of a statement like this by way of an example of causality, it’s OK. But when professional philosophers share this ignorance too, it’s a shame.

5. Just in passing, noteworthy is Ayn Rand’s view of causality: http://aynrandlexicon.com/lexicon/causality.html. This view was basic to my development of the points in the miniseries of posts mentioned above. … May be I should convert the miniseries into a paper and send it to a foundations/philosophy journal. … What do you think? (My question is serious.)

Thanks for highlighting the issue though; it’s very deeply interesting.

Best,

–Ajit


3. The other thing is that the other day (the late evening of the day before yesterday, to be precise), while entering a shop, I tripped over its ill-conceived steps, and suffered a fall. Got a hairline crack in one of my toes, and also a somewhat injured knee. So, had to take off from “everything” not only on Sunday but also today. Spent today mostly sleeping relaxing, trying to recover from those couple of injuries.

This late evening, I naturally found myself recalling this song—and that’s where this post ends.


4. OK. I must add a bit. I’ve been lagging on the paper-writing front, but, don’t worry; I’ve already begun re-writing (in my pocket notebook, as usual, while awaiting my turn in the hospital’s waiting lounge) my forth-coming paper on stress and strain, right today.

OK, see you folks, bye for now, and take care of yourselves…


A Song I Like:

(Hindi) “zameen se hamen aasmaan par…”
Singer: Asha Bhosale and Mohammad Rafi
Music: Madan Mohan
Lyrics: Rajinder Krishan

 

See, how hard I am trying to become an Approved (Full) Professor of Mechanical Engineering in SPPU?—2

Remember the age-old decade-old question, viz.:

“Stress or strain: which one is more fundamental?”

I myself had posed it at iMechanica about a decade ago [^]. Specifically, on 8th March 2007 (US time, may be EST or something).

The question had generated quite a bit of discussion at that time. Even as of today, this thread remains within the top 5 most-hit posts at iMechanica.

In fact, as of today, with about 1.62 lakh reads (i.e. 162 k hits), I think, it is the second most hit post at iMechanica. The only post with more hits, I think, is Nanshu Lu’s, providing a tutorial for the Abaqus software [^]; it beats mine like hell, with about 5 lakh (500 k) hits! The third most hit post, I think, again is about sharing scripts for the Abaqus software [^]; as of today, it lags mine very closely, but could overtake mine anytime, with about 1.48 lakh (148 k) hits already. There used to be a general thread on Open Source FEM software that used to be very close to my post. As of today, it has fallen behind a bit, with about 1.42 lakh (142 k) hits [^]. (I don’t know, but there could be other widely read posts, too.)

Of course, the attribute “most hit” is in no fundamental way related to “most valuable,” “most relevant,” or even “most interesting.”

Yet, the fact of the matter also is that mine is the only one among the top 5 posts which probes on a fundamental theoretical aspect. All others seem to be on software. Not very surprising, in a way.

Typically, hits get registered for topics providing some kind of a practical service. For instance, tips and tutorials on software—how to install a software, how to deal with a bug, how to write a sub-routine, how to produce visualizations, etc. Topics like these tend to get more hits. These are all practical matters, important right in the day-to-day job or studies, and people search the ‘net more for such practically useful services. Precisely for this reason—and especially given the fact that iMechanica is a forum for engineers and applied scientists—it is unexpected (at least it was unexpected to me) that a “basically useless” and “theoretical” discussion could still end up being so popular. There certainly was a surprise about it, to me. … But that’s just one part.

The second, more interesting part (i.e., more interesting to me) has been that, despite all these reads, and despite the simplicity of the concepts involved (stress and strain), the issue went unresolved for such a long time—almost a decade!

Students begin to get taught these two concepts right when they are in their XI/XII standard. In my XI/XII standard, I remember, we even had a practical about it: there was a steel wire suspended from a cantilever near the ceiling, and there was hook with a supporting plate at the bottom of this wire. The experiment consisted of adding weights, and measuring extensions. … Thus, the learning of these concepts begins right around the same time that students are learning calculus and Newton’s  3 laws… Students then complete the acquisition of these two concepts in their “full” generality, right by the time they are just in the second- or third-year of undergraduate engineering. The topic is taught in a great many branches of engineering: mechanical, civil, aerospace, metallurgical, chemical, naval architecture, and often-times (and certainly in our days and in COEP) also electrical. (This level of generality would be enough to discuss the question as posed at iMechanica.)

In short, even if the concepts are so “simple” that UG students are routinely taught them, a simple conceptual question involving them could go unresolved for such a long time.

It is this fact which was (honestly) completely unexpected to me, at least at the time when I had posed the question.

I had actually thought that there would surely be some reference text/paper somewhere that must have considered this aspect already, and answered it. But I was afraid that the answer (or the reference in which it appears) could perhaps be outside of my reach, my understanding of continuum mechanics. (In particular, I knew only a little bit of tensor calculus—only that as given in Malvern, and in Schaum’s series, basically. (I still don’t know much more about tensor calculus; my highest reach for tensor calculus remains limited to the book by Prof. Allan Bower of Brown [^].)) Thus, the reason I wrote the question in such a great detail (and in my replies, insisted on discussing the issues in conceptual details) was only to emphasize the fact that I had no hi-fi tensor calculus in mind; only the simplest physics-based and conceptual explanation was what I was looking for.

And that’s why, the fact that the question went unresolved for so long has also been (actually) fascinating to me. I (actually) had never expected it.


And yes, “dear” Officially Approved Mechanical Engineering Professors at the Savitribai Phule Pune University (SPPU), and authorities at SPPU, as (even) you might have noticed, it is a problem concerning the very core of the Mechanical Engineering proper.


I had thought once, may be last year or so, that I had finally succeeded in nailing down the issue right. (I might have written about it on this blog or somewhere else.) But, still, I was not so sure. So, I decided to wait.

I now have come to realize that my answer should be correct.


I, however, will not share my answer right away. There are two reasons for it.

First, I would like it if someone else gives it a try, too. It would be nice to see someone else crack it, too. A little bit of a wait is nothing to trade in for that. (As far as I am concerned, I’ve got enough “popularity” etc. just out of posing it.)

Second, I also wish to see if the Officially Approved Mechanical Engineering Professors at the Savitribai Phule Pune University (SPPU)) would be willing and able to give it a try.

(Let me continue to be honest. I do not expect them to crack it. But I do wish to know whether they are able to give it a try.)

In fact, come to think of it, let me do one thing. Let me share my answer only after one of the following happens:

  • either I get the Official Approval (and also a proper, paying job) as a Full Professor of Mechanical Engineering at SPPU,
  • or, an already Officially Approved Full Professor of Mechanical Engineering at SPPU (especially one of those at COEP, especially D. W. Pande, and/or one of those sitting on the Official COEP/UGC Interview Panels for faculty interviews at SPPU) gives it at least a try that is good enough. [Please note, the number of hits on the international forum of iMechanica, and the nature of the topic, once again.]

I will share my answer as soon as either of the above two happens—i.e., in the Indian government lingo: “whichever is earlier” happens.


But, yes, I am happy that I have come up with a very good argument to finally settle the issue. (I am fairly confident that my eventual answer should also be more or less satisfactory to those who had participated on this iMechanica thread. When I share my answer, I will of course make sure to note it also at iMechanica.)


This time round, there is not just one song but quite a few of them competing for inclusion on the “A Song I Like” section. Perhaps, some of these, I have run already. Though I wouldn’t mind repeating a song, I anyway want to think a bit about it before finalizing one. So, let me add the section when I return to do some minor editing later today or so. (I certainly want to get done with this post ASAP, because there are other theoretical things that beckon my attention. And yes, with this announcement about the stress-and-strain issue, I am now going to resume my blogging on topics related to QM, too.)

Update at 13:40 hrs (right on 19 Dec. 2016): Added the section on a song I like; see below.


A Song I Like:

(Marathi) “soor maagoo tulaa mee kasaa? jeevanaa too tasaa, mee asaa!”
Lyrics: Suresh Bhat
Music: Hridaynath Mangeshkar
Singer: Arun Date

It’s a very beautiful and a very brief poem.

As a song, it has got fairly OK music and singing. (The music composer could have done better, and if he were to do that, so would the singer. The song is not in a bad shape in its current form; it is just that given the enormously exceptional talents of this composer, Hridaynath Mangeshkar, one does get a feel here that he could have done better, somehow—don’t ask me how!) …

I will try to post an English translation of the lyrics if I find time. The poem is in a very, very simple Marathi, and for that reason, it would also be very, very easy to give a rough sense of it—i.e., if the translation is to be rather loose.

The trouble is, if you want to keep the exact shade of the words, it then suddenly becomes very difficult to translate. That’s why, I make no promises about translating it. Further, as far as I am concerned, there is no point unless you can convey the exact shades of the original words. …

Unless you are a gifted translator, a translation of a poem almost always ends up losing the sense of rhythm. But even if you keep a more modest aim, viz., only of offering an exact translation without bothering about the rhythm part, the task still remains difficult. And it is more difficult if the original words happen to be of the simple, day-to-day usage kind. A poem using complex words (say composite, Sanskrit-based words) would be easier to translate precisely because of its formality, precisely because of the distance it keeps from the mundane life… An ordinary poet’s poem also would be easy to translate regardless of what kind of words he uses. But when the poet in question is great, and uses simple words, it becomes a challenge, because it is difficult, if not impossible, to convey the particular sense of life he pours into that seemingly effortless composition. That’s why translation becomes difficult. And that’s why I make no promises, though a try, I would love to give it—provided I find time, that is.


Second Update on 19th Dec. 2016, 15:00 hrs (IST):

A Translation of the Lyrics:

I offer below a rough translation of the lyrics of the song noted above. However, before we get to the translation, a few notes giving the context of the words are absolutely necessary.

Notes on the Context:

Note 1:

Unlike in the Western classical music, Indian classical music is not written down. Its performance, therefore, does not have to conform to a pre-written (or a pre-established) scale of tones. Particularly in the Indian vocal performance, the singer is completely free to choose any note as the starting note of his middle octave.

Typically, before the actual singing begins, the lead singer (or the main instrument player) thinks of some tone that he thinks might best fit how he is feeling that day, how his throat has been doing lately, the particular settings at that particular time, the emotional interpretation he wishes to emphasize on that particular day, etc. He, therefore, tentatively picks up a note that might serve as the starting tone for the middle octave, for that particular performance. He makes this selection not in advance of the show and in private, but right on the stage, right in front of the audience, right after the curtain has already gone up. (He might select different octaves for two successive songs, too!)

Then, to make sure that his rendition is going to come out right if he were to actually use that key, that octave, what he does is to ask a musician companion (himself on the stage besides the singer) to play and hold that note on some previously well-tuned instrument, for a while. The singer then uses this key as the reference, and tries out a small movement or so. If everything is OK, he will select that key.

All this initial preparation is called (Hindi) “soor lagaanaa.” The part where the singer turns to the trusted companion and asks for the reference note to be played is called (Hindi) “soor maanganaa.” The literal translation of the latter is: “asking for the tone” or “seeking the pitch.”

After thus asking for the tone and trying it out, if the singer thinks that singing in that specific key is going to lead to a good concert performance, he selects it.

At this point, both—the singer and that companion musician—exchange glances at each other, and with that indicate that the tone/pitch selection is OK, that this part is done. No words are exchanged; only the glances. Indian performances depend a great deal on impromptu variations, on improvizations, and therefore, the mutual understanding between the companion and the singer is of crucial importance. In fact, so great is their understanding that they hardly ever exchange any words—just glances are enough. Asking for the reference key is just a simple ritual that assures both that the mutual understanding does exist.

And after that brief glance, begins the actual singing.

Note 2:

Whereas the Sanskrit and Marathi word “aayuShya” means life-span (the number of years, or the finite period that is life), the Sanskrit and Marathi word “jeevan” means Life—with a capital L. The meaning of “jeevan” thus is something like a slightly abstract outlook on the concrete facts of life. It is like the schema of life. The word is not so abstract as to mean the very Idea of Life or something like that. It is life in the usual, day-to-day sense, but with a certain added emphasis on the thematic part of it.

Note 3:

Here, the poet is addressing this poem to “jeevan” i.e., to the Life with a capital L (or the life taken in its more abstract, thematic sense). The poet is addressing Life as if the latter is a companion in an Indian singing concert. The Life is going to help him in selecting the note—the note which would define the whole scale in which to sing during the imminent live performance. The Life is also his companion during the improvisations. The poem is addressed using this metaphor.

Now, my (rough) translation:

The Refrain:
[Just] How do I ask you for the tone,
Life, you are that way [or you follow some other way], and I [follow] this way [or, I follow mine]

Stanza 1:
You glanced at me, I glanced at you,
[We] looked full well at each other,
Pain is my mirror [or the reference instrument], and [so it is] yours [too]

Stanza 2:
Even once, to [my] mind’s satisfaction,
You [oh, Life] did not ever become my [true]  mate
[And so,] I played [on this actual show of life, just whatever] the way the play happened [or unfolded]

And, finally, Note 4 (Yes, one is due):

There is one place where I failed in my translation, and most any one not knowing both the Marathi language and the poetry of Suresh Bhat would.

In Marathi, “tu tasaa, [tar] mee asaa,” is an expression of a firm, almost final, acknowledgement of (irritating kind of) differences. “If you must insist on being so unreasonable, then so be it—I am not going to stop following my mind either.” That is the kind of sense this brief Marathi expression carries.

And, the poet, Suresh Bhat, is peculiar: despite being a poet, despite showing exquisite sensitivity, he just never stops being manly, at the same time. Pain and sorrow and suffering might enter his poetry; he might acknowledge their presence through some very sensitively selected words. And yet, the underlying sense of life which he somehow manages to convey also is as if he is going to dismiss pain, sorrow, suffering, etc., as simply an affront—a summarily minor affront—to his royal dignity. (This kind of a “royal” sense of life often is very well conveyed by ghazals. This poem is a Marathi ghazal.) Thus, in this poem, when Suresh Bhat agrees to using pain as a reference point, the words still appear in such a sequence that it is clear that the agreement is being conceded merely in order to close a minor and irritating part of an argument, that pain etc. is not meant to be important even in this poem let alone in life. Since the refrain follows immediately after this line, it is clear that the stress gets shifted to the courteous question which is raised following the affronts made by one fickle, unfaithful, even idiotic Life—the question of “Just how do I treat you as a friend? Just how do I ask you for the tone?” (The form of “jeevan” or Life used by Bhat in this poem is masculine in nature, not neutral the way it is in normal Marathi.)

I do not know how to arrange the words in the translation so that this same sense of life still comes through. I simply don’t have that kind of a command over languages—any of the languages, whether Marathi or English. Hence this (4th) note. [OK. Now I am (really) done with this post.]


Anyway, take care, and bye for now…


Update on 21st Dec. 2016, 02:41 AM (IST):

Realized a mistake in Stanza 1, and corrected it—the exchange between yours and mine (or vice versa).


[E&OE]

Conservation of angular momentum isn’t [very] fundamental!

What are the conservation principles (in physics)?

In the first course on engineering mechanics (i.e. the mechanics of rigid bodies) we are taught that there are these three conservation principles: Conservation of: (i) energy, (ii) momentum, and (iii) angular momentum. [I am talking about engineering programs. That means, we live entirely in a Euclidean, non-relativistic, world.]

Then we learn mechanics of fluids, and the conservation of (iv) mass too gets added. That makes it four.

Then we come to computational fluid dynamics (CFD), and we begin to deal with only three equations: conservation of (i) mass, (ii) momentum, and (iii) energy. What happens to the conservation of the angular momentum? Why does the course on CFD drop it? For simplicity of analysis?

Ask that question to postgraduate engineers, even those who have done a specialization in CFD, and chances are, a significant number of them won’t be able to answer that question in a very clear manner.

Some of them may attempt this line of reasoning: That’s because in deriving the fluids equations (whether for a Newtonian fluid or a non-Newtonian one), the stress tensor is already assumed to be symmetrical: the shear stresses acting on the adjacent faces are taken to be equal and opposite (e.g. \sigma_{xy} = \sigma_{yx}). The assumed equality can come about only after assuming conservation of the angular momentum, and thus, the principle is already embedded in the momentum equations, as they are stated in CFD.

If so, ask them: How about a finite rotating body—say a gyroscope? (Assume rigidity for convenience, if you wish.) Chances are, a great majority of them will immediately agree that in this case, however, we have to apply the angular momentum principle separately.

Why is there this difference between the fluids and the finite rotating bodies? After all, both are continua, as in contrast to point-particles.

Most of them would fall silent at this point. [If not, know that you are talking with someone who knows his mechanics well!]


Actually, it so turns out that in continua, the angular momentum is an emergent/derivative property—not the most fundamental one. In continua, it’s OK to assume conservation of just the linear momentum alone. If it is satisfied, the conservation of angular momentum will get satisfied automatically. Yes, even in case of a spinning wheel.

Don’t believe me?

Let me direct you to Chad Orzel; check out here [^]. Orzel writes:

[The spinning wheel] “is a classical system, so all of its dynamics need to be contained within Newton’s Laws. Which means it ought to be possible to look at how angular momentum comes out of the ordinary linear momentum and forces of the components making up the wheel. Of course, it’s kind of hard to see how this works, but that’s what we have computers for.” [Emphasis in italics is mine.]

He proceeds to put together a simple demo in Python. Then, he also expands on it further, here [^].


Cool. If you think you have understood Orzel’s argument well, answer this [admittedly deceptive] question: How about point particles? Do we need a separate conservation principle for the angular momentum, in addition to that for the linear momentum at least in their case? How about the earth and the moon system, granted that both can be idealized as point particles (the way Newton did)?

Think about it.


A Song I Like:

(Hindi) “baandhee re kaahe preet, piyaa ke sang”
Singer: Sulakshana Pandit
Music: Kalyanji-Anandji
Lyrics: M. G. Hashmat

 

[E&OE]