Some Aspects of Continua, Continued…
This post carries forward the subject that began in one of my recent posts, here.
In the last post, we highlighted the necessity to distinguish between the infinitesimal and the finite, and the relevance of this matter in continuum theory, esp. in reference to CFD simulations of vortex shedding. Now, rather than directly answering the issues then raised, let me continue the application of the Socratic method a bit further, by taking some more examples…
Consider a (mathematically) simpler case of flow, that of the ideal fluid. As you would know, such the ideal fluid has no viscosity and the ideal flow is irrotational.
Contrary to a misconception widely held by the beginning student, even the ideal fluid can have a finite angular velocity—despite the flow being irrotational. Sure enough, the term irrotational flow means that a certain measure of fluid flow, called vorticity, is zero. However, this still doesn’t mean that the fluid cannot at all have vortices in it; e.g., see here. … What the assumption of irrotationality really implies is this: if a given ideal fluid flow did not have a vortex in it to begin with, then it is impossible for it to develop one, on its own, later on. Anyway, this was a bit of a digression.
Returning to our main thread, for the simplicity of the discussion here, let us assume that there are no vortices to begin with in our ideal flow. Further, for simplicity, consider a flow in a 2D space, not 3D. Thus, consider the ideal fluid flow in a plane cavity, past a planar obstacle. For example, refer to Prof. Davenport’s Ideal Flow Machine Web site here [^], in particular, this diagram.
There is a symmetry of flow in that diagram. Consider the two horizontal lines at the center of the diagram. There are a couple of stagnation points on them. Stagnation points, as you know, are the points where the fluid velocity is zero. The local parcel of the fluid won’t go anywhere else, no matter how great is the velocity or the pressure.
Now, here is the funny part concerning my last post. Consider two fluid particles in the neighborhood of a stagnation point lying on opposite sides of that central horizontal line.
Now, here is a question: Would these two points move apart? If yes, do they have to be a finite distance apart? Or is it the case that even two fluid particles that initially are just infinitesimal distance apart can also grow a finite distance away? What does this example tell you vis-a-vis our discussion in my last post? in particular, that experiment with ink in a thick fluid? 🙂 … How do we square off the two sets of observations? More generally: does the notion of singularity have any role to play in settling such questions?
… Think about it and let me know… We will return to this topic once again, in some future post.
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The Terror Attack at Pune on Feb 13, 2010
My prayers for the unfortunate dead victims—all of them being innocent ones—to yesterday’s bloody terror attack in Pune. Also, my condolences to their families.
Yes, the Osho Ashram may be “just 200 m” away. But what about the Southern Command? It too isn’t more than 2 km away from the place of the incidence! Will our government and media realize this in their reporting of the event?
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On the Need to Contain the Indira Congress
There was much media hullabaloo [is this word derived from the Hindi phrase: “halla bol”?] over, variously, MNIK, Shah Rukh Khan, Shiv Sena, Rahul Gandhi, the Constitution of India, and whatnot, the last week and for some time preceding it.
Since everything that could conceivably have been said or written against Shiv Sena has already been, I find no need to reiterate it all here. (And, by that, I mean the valid objections against some aspects of Shiv Sena’s stand(s).)
Having said that, let me emphasize here that there is still another important part that no blogger, commentator, debater, analyst, pundit or politician has mentioned. Namely, the inescapably highly organized character of the entire media coverage of this “debate.” And the specifically intellectual bankruptcy of New Delhi (and to a minor extent, of the UP politicians including Rahul Gandhi) that the coverage and its nature helped bring forth.
There is a lot that can be written on this topic, and I do hope that someone picks it up at least in the coming weeks. … In any case, my own thoughts on this topic aren’t very well organized. (Most of the times, for most of the current political happenstances, esp. those in India, it anyway is impossible to be well organized. But I mean much more than that here. … And, further, I am not a politics junkie anyway.) … So, rather write something immature and thereby invite ridicule of the Delhi “intellectual” establishment, here, I would rather jump ahead and make a few direct points here and there and raise a few questions that need to be raised ASAP—these cannot be postponed.
(1) Will The Great Stammerer and/or The Great Dimpler acquire enough intellectuality (it’s too late for either to systematically develop one, but they could at least hire some) to be able to name at least two great contradictions in the Preamble to our Constitution? Both of these—and all of their “intellectual” cronies—were busy invoking the Constitution over and over again, with such a frequency that one just had to think of this one.
(2) Apparently, The Great Stammerer had in the past gone on record identifying himself as a devout Muslim. I believe this was sometime during the BJP regime. (I vaguely recall his insistence that he was an Indian first and only then a Muslim—and I do believe that he would have been completely honest in saying so. No doubt/no question on that count.) …. That way, religious beliefs are, first and foremost, a personal matter.
But precisely because The Great Stammerer has been made into a Great Issue by the Delhi “intellectual” establishment, would any of them please come forward and ask The Great Stammerer to identify what his stand precisely is with respect to all those “fatwa”s that are routinely raised by the priests/clerics of his religion? Does, as a Muslim, he believe in those, too? Why?
…. And I do think it is important to raise this issue, because (a) it does not only concern the private practise of a religion by an individual but does belong to the public sphere too, (b) a lot has recently been repeated concerning extra-constitutional authority—how any such center cannot be allowed to be created or left functioning.
… To be fair, it might be expected that a similar thing might be raised concerning the Hindu religion as well. (Yes, it’s a religion, too! No, it has not been very highly organized—though that part is now changing.) It would be indeed be possible to raise such a thing, except that the comparable aspects of the Hindu institutions (e.g. Shankaraachaaryas) have not exactly been caught issuing the equivalent of such “fatwa”s. And, when the other parties or spokesmen speaking for Hinduism did say similar thing, they ought to have been shown their place. In fact, they have been. That’s how the BJP regime came to an end. (And, I did support the secular side of those debates.) Anyway, so mucky is our current politics that a lot of mental space simply has to go waste in just dealing with context and side issues of any given issue.
To return to the main issue here: Why does none of the Delhi “intellectual” establishment (geographically spread from Kashmir to Kanyakumari etc.) ever dare raise this question to The Great Stammerer (or any others like him)? When can we expect these Delhi-“wallahs” to begin doing so?
(3) When will our fearless media—[in no particular order] from The Times of India to DNA to Indian Express to…, and from NDTV to IBN to Times Now to Aaj Tak to…—begin identifying a couple of crucially important details about The Great Stammerer, namely, that (a) his in-laws come from the influential Delhi military circles; (b) he and his family are personal friends of Mrs. Priyanka Gandhi (the wife of Mr. Robert Vadra—the same gentleman businessman who, shoulder to shoulder with the President of India, the Prime Minister of India, the Chief Justice of India, and other persons occupying institutional posts of high standing, has been exempted from frisking at the airports). If The Great Stammerer can be discussed only to be praised in the editorial pages/TV shows, then, surely such a detail is not out of place considering the decisively mixed character of our nation state? (Also see my point (1) above.)
And, while we are on it, will our fearless media also begin identifying that Shiv Sena happens to be a political party whose member was the Loksabha Speaker as in the recent past as in the last decade… No matter what your judgment concerning Shiv Sena might be, this is a fact. It cannot be ordered by fiat to be dissolved as a political party… Dr. Mani Shankar Aiyer, is your memory that poor that someone like me has to remind you of this fact? I don’t think so … If it the reader haven’t got the actual importance of this statement, look up the order of succession for India. (The order of succession means such things as: who runs the country if, say, the PM gets assassinated—and what if the person second in line also dies/gets killed, etc. Or, who is eligible to administer oaths to whom, etc.)
(4) I think I will stop here. But one more statement does need to be made before I stop.
Mixed economies and the only semi-consistently constituted nations like India, are always susceptible to degeneration through various avenues such as populism. This is to be understood as a matter of principle. [As Ayn Rand had pointed out, if you mix food with poison, it is the poison that wins.] In the political context, what this translates to is that in any such nation (today’s USA unfortunately included), the better people, esp. the intellectuals among them, just have to continually ensuring that the balance doesn’t get lost beyond a point.
I think that the Indira Congress has come to this point today after being in power for the past five+ consecutive years at the center. It has come to that point both in the Maharashtra state and at the Center—and, I cannot tell where it is doing worse.
As such, it is time to ask to begin a containment of the Indira Congress.
Mind you, I am not saying, scrap this government and hold the elections and vote some other party into the power. Nope. (I don’t know if it would be worse—all that I do know right now, and what really matters right now, is that any other alternative such as the BJP also would be bad—that it would still not fall in the good category.)
But for the time being, looking at the entire spectrum of events in the preceding weeks or so, I am appealing, with as much strength as I possess, to every thinker in/concerned with India: Contain the Indira Congress. Immediately. Full stop.
(Yesterday’s terror attack has nothing to do with this; I would have written exactly the same thing even if this attack were not to take place.)
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A Couple of Songs I Like [For once, not at all at random]
1. (Hindi) “man_maani se hargiz naa Daro…”
Lyrics: Amit Khanna (?)
Singer: Kishore Kumar
Music: Rajesh Roshan
2. (Marathi) “khar_ mhaNje aapaN ekTe sukhaat jagat…”
Lyrics: Sudhir Moghe (?)
Singers: Nandu Bhende (?) and (who is the lady singer?)
Music: Nandu Bhende (?)
PS: I might revise this post just a bit, adding/streamlining the content in a day or two or so.