Stay tuned to the NSF on the next evening…

Update on 2019.04.10 18:50 IST: 

Dimitrios Psaltis, University of Arizona in Tucson, EHT project scientist [^]:

The size and shape of the shadow matches the precise predictions of Einstein’s general theory of relativity, increasing our confidence in this century-old theory. Imaging a black hole is just the beginning of our effort to develop new tools that will enable us to interpret the massively complex data that nature gives us.”

Update over.

Stay tuned to the NSF on the next evening (on 10th April 2019 at 06:30 PM IST) for an announcement of astronomical proportions. Or so it is, I gather. See: “For Media” from NSF [^]. Another media advisory made by NSF roughly 9 days ago, i.e. on the Fool’s Day, here [^]. Their news “report”s [^].

No, I don’t understand the relativity theory. Not even the “special” one (when it’s taken outside of its context of the so-called “classical” electrodynamics)—let alone the “general” one. It’s not one of my fields of knowledge.

But if I had to bet my money then, based purely on my grasp of the sociological factors these days operative in science as practised in the Western world, then I would bet a good amount (even Indian Rs. 1,000/-) that the announcement would be just a further confirmation of Einstein’s theory of general relativity.

That’s how such things go, in the Western world, today.

In other words, I would be very, very, very surprised—I mean to say, about my grasp of the sociology of science in the Western world—if they found something (anything) going even apparently contrary to any one of the implications of any one of Einstein’s theories. Here, emphatically, his theory of the General Relativity.

That’s all for now, folks! Bye for now. Will update this post in a minor way when the facts are on the table.

TBD: The songs section. Will do that too, within the next 24 hours. That’s a promise. For sure. (Or, may be, right tonight, if a song nice enough to listen to, strikes me within the next half an hour or so… Bye, really, for now.)

A song I like:

(Hindi) “ek haseen shaam ko, dil meraa kho_ gayaa…”
Lyrics: Raajaa Mehdi Ali Khaan
Music: Madan Mohan
Singer: Mohammad Rafi [Some beautiful singing here…]




Work Is Punishment

Work is not worship—they said.

It’s a punishment, full stop!—they said.

One that is to be smilingly borne.

Else you lose your job.

And so lose everything else too. …

Hmmm… I said. … I was confused.

Work is enjoyment, actually. … I then discovered.

I told them.

They didn’t believe.

Not when I said it.

Not because they ceased believing in me.

It’s just that. They. Simply. Didn’t. Believe. In. It.

And they professed to believe in

a lot of things that never did make

any sense to themselves.

They said so.

And it was so.

A long many years have passed by, since then.

Now, whether they believe in it or not,

I have come to believe in this gem:

Work is punishment—full stop.

That’s the principle on the basis of which I am henceforth going to operate.

And yes! This still is a poem alright?

[What do you think most poems written these days are like?]

It remains a poem.

And I am going to make money. A handsome amount of money.

For once in my life-time.

After all, one can make money and still also write poems.

That’s what they say.

Or do science. Real science. Physics. Even physics for that matter.

Or, work. Real work, too.

It’s better than having no money and…





Where are those other equations?

Multiple header images, and the problem with them:

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

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

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

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

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

Ummm… OK.

A quick question:

Here is the problem statement:

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

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

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

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

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

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


…No, really!


Ummm… Still with me?

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

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

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

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

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

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

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

General update:

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

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

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

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

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


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

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