# Absolutely Random Notings on QM—Part 3: Links to some (really) interesting material, with my comments

The “pride of place” for this post goes to a link to this book:

Norsen, Travis (2017) “Foundations of Quantum Mechanics: An Exploration of the Physical Meaning of Quantum Theory,” Springer

This book is (i) the best supplementary book for a self-study of QM, and simultaneously, also (ii) the best text-book on a supplementary course on QM, both at the better-prepared UG / beginning PG level.

A bit expensive though, but extensive preview is available on Google books, here [^]. (I plan to buy it once I land a job.)

I was interested in the material from the first three chapters only, more or less. It was a delight even just browsing through these chapters. I intend to read it more carefully soon enough. But even on the first, rapid browsing, I noticed that several pieces of understanding that I had so painstakingly come to develop (over a period of years) are given quite straight-forwardly here, as if they were a matter of well known facts—even if other QM text-books only cursorily mention them, if at all.

For instance, see the explanation of entanglement here. Norsen begins by identifying that there is a single wavefunction, always—even for a multi-particle system. Then after some explanation, he states: “But, as usual in quantum mechanics, these states do not exhaust the possibilities—instead, they merely form a basis for the space of all possible wave functions. …”… Note the emphasis on the word “basis” which Norsen helpfully puts.

Putting this point (which Norsen discusses with a concrete example), but in my words: There is always a single wavefunction, and for a multi-particle system, its basis is bigger; it consists of the components of the tensor product (formed from the components of the basis of the constituent systems). Sometimes, the single wavefunction for the multi-particle system can be expressed as a result of a single tensor-product (in which case it’s a separable state), and at all other times, only as an algebraic sum of the results of many such tensor-products (in which case they all are entangled states).

Notice how there is no false start of going from two separate systems, and then attempting to forge a single system out of them. Notice how, therefore, there is no hand-waving at one electron being in one galaxy, and another electron in another galaxy, and so on, as if to apologize for the very idea of the separable states. Norsen achieves the correct effect by beginning on the right note: the emphasis on the single wavefunction for the system as a whole to begin with, and then clarifying, at the right place, that what the tensor product gives you is only the basis set for the composite wavefunction.

There are many neat passages like this in the text.

I was about to say that Norsen’s book is the Resnick and Halliday of QM, but then came to hesitate saying so, because I noticed something odd even if my browsing of the book was rapid and brief.

Then I ran into

Ian Durham’s review of Norsen’s book, at the FQXi blog,

which is our link # 2 for this post [^].

Durham helpfully brings out the following two points (which I then verified during a second visit to Norsen’s book): (i) Norsen’s book is not exactly at the UG level, and (ii) the book is a bit partial to Bell’s characterization of the quantum riddles as well as to the Bohmian approach for their resolution.

The second point—viz., Norsen’s fascination for / inclination towards Bell and Bohm (B&B for short)—becomes important only because the book is, otherwise, so good: it carries so many points that are not even passingly mentioned in other QM books, is well written (in a conversational style, as if a speech-to-text translator were skillfully employed), easy to understand, thorough, and overall (though I haven’t read even 25% of it, from whatever I have browsed), it otherwise seems fairly well balanced.

It is precisely because of these virtues that you might come out giving more weightage to the B&B company than is actually due to them.

Keep that warning somewhere at the back of your mind, but do go through the book anyway. It’s excellent.

At Amazon, it has got 5 reader reviews, all with 5 stars. If I were to bother doing a review there, I too perhaps would give it 5 stars—despite its shortcomings/weaknesses. OK. At least 4 stars. But mostly 5 though. … I am in an indeterminate state of their superposition.

… But mark my words. This book will have come to shape (or at least to influence) every good exposition of (i.e. introduction to) the area of the Foundations of QM, in the years to come. [I say that, because I honestly don’t expect a better book on this topic to arrive on the scene all that soon.]

Which brings us to someone who wouldn’t assign the $|4\rangle + |5\rangle$ stars to this book. Namely, Lubos Motl.

If Norsen has moved in the Objectivist circles, and is partial to the B&B company, Motl has worked in the string theory, and is not just partial to it but even today defends it very vigorously—and oddly enough, also looks at that “supersymmetric world from a conservative viewpoint.” More relevant to us: Motl is not partial to the Copenhagen interpretation; he is all the way into it. … Anyway, being merely partial is something you wouldn’t expect from Motl, would you?

But, of course, Motl also has a very strong grasp of QM, and he displays it well (even powerfully) when he writes a post of the title:

“Postulates of quantum mechanics almost directly follow from experiments.” [^]

Err… Why “almost,” Lubos? 🙂

… Anyway, go through Motl’s post, even if you don’t like the author’s style or some of his expressions. It has a lot of educational material packed in it. Chances are, going through Motl’s posts (like the present one) will come to improve your understanding—even if you don’t share his position.

As to me: No, speaking from the new understanding which I have come to develop regarding the foundations of QM [^] and [^], I don’t think that all of Motl’s objections would carry. Even then, just for the sake of witnessing the tight weaving-in of the arguments, do go through Motl’s post.

Finally, a post at the SciAm blog:

“Coming to grips with the implications of quantum mechanics,” by Bernardo Kastrup, Henry P. Stapp, and Menas C. Kafatos, [^].

The authors say:

“… Taken together, these experiments [which validate the maths of QM] indicate that the everyday world we perceive does not exist until observed, which in turn suggests—as we shall argue in this essay—a primary role for mind in nature.”

No, it didn’t give me shivers or something. Hey, this is QM and its foundations, right? I am quite used to reading such declarations.

Except that, as I noted a few years ago on Scott Aaronson’s blog [I need to dig up and insert the link here], and then, recently, also at

Roger Schlafly’s blog [^],

you don’t need QM in order to commit the error of inserting consciousness into a physical theory. You can accomplish exactly the same thing also by using just the Newtonian particle mechanics in your philosophical arguments. Really.

Yes, I need to take that reply (at Schlafly’s blog), edit it a bit and post it as a separate entry at this blog. … Some other time.

For now, I have to run. I have to continue working on my approach so that I am able to answer the questions raised and discussed by people such as those mentioned in the links. But before that, let me jot down a general update.

A general update:

Oh, BTW, I have taken my previous QM-related post off the top spot.

That doesn’t mean anything. In particular, it doesn’t mean that after reading into materials such as that mentioned here, I have found some error in my approach or something like that. No. Not at all.

All it means is that I made it once again an ordinary post, not a sticky post. I am thinking of altering the layout of this blog, by creating a page that highlights that post, as well as some other posts.

But coming back to my approach: As a matter of fact, I have also written emails to a couple of physicists, one from IIT Bombay, and another from IISER Pune. However, things have not worked out yet—things like arranging for an informal seminar to be delivered by me to their students, or collaborating on some QM-related simulations together. (I could do the simulations on my own, but for the seminar, I would need an audience! One of them did reply, but we still have to shake our hands in the second round.)

In the meanwhile, I go jobless, but I keep myself busy. I am preparing a shortish set of write-ups / notes which could be used as a background material when (at some vague time in future) I go and talk to some students, say at IIT Bombay/IISER Pune. It won’t be comprehensive. It will be a little more than just a white-paper, but you couldn’t possibly call it even just the preliminary notes for my new approach. Such preliminary notes would come out only after I deliver a seminar or two, to physics professors + students.

At the time of delivering my proposed seminar, links like those I have given above, esp. Travis Norsen’s book, also should prove a lot useful.

But no, I haven’t seen something like my approach being covered anywhere, so far, not even Norsen’s book. There was a vague mention of just a preliminary part of it somewhere on Roger Schlafly’s blog several years ago, only once or so, but I can definitely say that I had already had grasped even that point on my own before Schlafly’s post came. And, as far as I know, Schlafly hasn’t come to pursue that thread at all, any time later…

But speaking overall, at least as of today, I think I am the only one who has pursued this (my) line of thought to the extent I have [^].

So, there. Bye for now.

I Song I Like:
(Hindi) “suno gajar kya gaaye…”
Singer: Geeta Dutt
Music: S. D. Burman
Lyrics: Sahir Ludhianvi
[There are two Geeta’s here, and both are very fascinating: Geeta Dutt in the audio, and Geeta Bali in the video. Go watch it; even the video is recommended.]

As usual, some editing after even posting, would be inevitable.

Some updates made and some streamlining done on 30 July 2018, 09:10 hrs IST.

# And to think…

Many of you must have watched the news headlines on TV this week; many might have gathered it from the ‘net.

Mumbai—and much of Maharashtra—has gone down under. Under water.

And to think that all this water is now going to go purely to waste, completely unused.

… And that, starting some time right from say February next year, we are once again going to yell desperately about water shortage, about how water-tankers have already begun plying on the “roads” near the drought-hit villages. … May be we will get generous and send not just 4-wheeler tankers but also an entire train to a drought-hit city or two…

Depressing!

OK. Here’s something less depressing. [H/t Jennifer Ouellette (@JenLucPiquant) ]:

“More than 2,000 years ago, people were able to create ice in the desert even with temperatures above freezing!” [^]

The write-up mentions a TED video by Prof. Aaswath Raman. Watched it out of idle interest, checked out his Web site, and found another TED video by him, here [^]. Raman cites statistics that blew me!

They spend “only” $24 billion on supermarket refrigeration (and other food-related cooling), but they already spend$42 billion on data-center cooling!!

But, any way, I did some further “research” and landed at a few links, like the Wiki on Yakhchal [^], on wind-catcher [^], etc.  Prof. Raman’s explanation in terms of the radiative cooling was straight-forwards, but I am not sure I understand the mechanism behind the use of a qanat [^] in Yakhchal/windcatcher cooling. It would be cool to do some CFD simulations though.

Finally, since I am once again out of a job (and out of all my saved money and in fact also into credit-card loans due to some health issue cropping up once again), I was just idly wondering about all this renewable energy business, when something struck me.

The one big downside of windmills is that the electricity they generate fluctuates too much. You can’t rely on it; the availability is neither 24X7 nor uniform. Studies in fact also show that in accommodating the more or less “random” output of windmills into the conventional grid, the price of electricity actually goes up—even if the cost of generation alone at the windmill tower may be lower. Further, battery technology has not improved to such a point that you could store the randomly generated electricity economically.

So, I thought, why not use that randomly fluctuating windmill electricity in just producing the hydrogen gas?

No, I didn’t let out a Eureka. Instead, I let out a Google search. After all, the hydrogen gas could be used in fuel-cells, right? Would the cost of packaging and transportation of hydrogen gas be too much? … A little searching later, I landed at this link: [^]. Ummm… No, no, no…. Why shoot it into the natural gas grid? Why not compress it into cylinders and transport by trains? How does the cost economics work out in that case? Any idea?

Addendum on the same day, but after about a couple of hours:

Yes, I did run into this link: “Hydrogen: Hope or Hype?” [^] (with all the links therein, and then, also this: [^]).

But before running into those links, even as my googling on “hydrogen fuel energy density” still was in progress, I thought of this idea…

Why at all transport the hydrogen fuel from the windmill farm site to elsewhere? Why not simply install a fuel cell electricity generator right at the windmill farm? That is to say, why not use the hydrogen fuel generated via electrolysis as a flywheel of sorts? Get the idea? You introduce a couple of steps in between the windmill’s electricity and the conventional grid. But you also take out the fluctuations, the bad score on the 24X7 availability. And, you don’t have to worry about the transportation costs either.

What do you think?

Addendum on 12th July 2018, 13:27 hrs IST

Further, I also browsed a few links that explore another,  solution: using compressed air: a press report [^], and a technical paper [^]. (PDF of the paper is available, but the paper would be accessible only to mechanical engineers though. Later Update: As to the press report, well, the company it talks about has already merged with another company, and has abandoned the above-ground storage of compressed air [^])

I think that such a design reduces the number of steps of energy conversions. However, that does not necessarily mean that the solution involving hydrogen fuel generation and utilization (both right at the wind-farm) isn’t going to be economical.

Economics determines (or at least must determine) the choice. Enough on this topic for now. Wish I had a student working with me; I could have then written a paper after studying the solution I have proposed above. (The idea is worth a patent too. Too bad I don’t have the money to file one. Depressing, once again!!)

OK. Enough for the time being. I may later on add the songs section if I feel like it. And, iterative modifications will always be done, but will be mostly limited to small editorial changes. Bye for now.

# QM: A couple of defensible statements. Also, a bit on their implications for the QC.

A Special Note (added on 17th June 2018): This post is now a sticky post; it will remain, for some time, at the top of this blog.

I am likely to keep this particular post at the top of this blog, as a sticky post, for some time in the future (may be for a few months or so). So, even if posts at this blog normally appear in the reverse chronological order, any newer entries that I may post after this one would be found below this one.

[In particular, right now, I am going through a biography: “Schrodinger: Life and Thought” by Walter Moore [^]. I had bought this book way back in 2011, but had to keep it aside back then, and then, somehow, I came to forget all about it. The book surfaced during a recent move we made, and thus, I began reading it just this week. I may write a post or two about it in the near future (say within a couple of weeks or so) if something strikes me while I am at it.]

A Yawningly Long Preamble:

[Feel free to skip to the sections starting with the “Statement 1” below.]

As you know, I’ve been thinking about foundations of QM for a long, long time, a time running into decades by now.

I thought a lot about it, and then published a couple of papers during my PhD, using a new approach which I had developed. This approach was used for resolving the wave-particle duality, but only in the context of photons. However, I then got stuck when it came to extending and applying this same approach to electrons. So, I kept on browsing a lot of QM-related literature in general. Then, I ran, notably, into the Nobel laureate W. E. Lamb’s “anti-photon” paper [^], and also the related literature (use Google Scholar). I thought a lot about this paper—and also about QM. I began thinking about QM once again from the scratch, so to speak.

Eventually, I came to abandon my own PhD-time approach. At the same time, with some vague but new ideas already somewhere at the back of my mind, I once again started studying QM, once again with a fresh mind, but this time around much more systematically. …

… In the process, I came to develop a completely new understanding of QM!… It’s been at least months since I began talking about it [^]. … My confidence in this new understanding has only increased, since then.

Today’s post will be based on this new understanding. (I could call it a new theory, perhaps.)

My findings suggest a few conclusions which I think I should not hold back any longer. Hence this post.

I have been trying to locate the right words for formulating my conclusions—but without much satisfaction. Finally, I’ve decided to go ahead and post an entry here anyway, regardless of whether the output comes out as being well formulated or not.

In other words, don’t try to pin me down with the specific words I use here in this post! Instead, try to understand what I am trying to get at. In still other words: the particular words I use may change, but the intended meaning will, from now on, “always” remain the same—ummm…. more or less the same!

OK, so here are the statements I am making today. I think they are well defensible:

Notation:
QM: Quantum Mechanics, quantum mechanically, etc.
CM: Classical Mechanics
QC: Quantum Computer
QS: Quantum Supremacy ([^] and [^])

Statement 1: It is possible to explain all quantum mechanical phenomena on the basis of those principles which are already known (or have already been developed) in the context of classical mechanics.

Informal Explanation 1.1: Statement 1 holds true. It’s just that when it comes to explaining the QM phenomena (i.e., when it comes to supplying a physical mechanism for QM), even if the principles do remain the same, the way they are to be combined and applied is different. These differences basically arise because of a reason mentioned in the next Informal Explanation.

Informal Explanation 1.2: Yes, the tradition of 80+ years, involving an illustrious string of Nobel laureates and others, is, in a way, “wrong.” The QM principles are not, fundamentally speaking, very different from those encountered in the CM. It’s just that some of the objects that QM assumes and talks about are different (only partly different) from those assumed in the CM.

Corollary 1 of Statement 1: A quantum computer could “in principle” be built as an “application layer” on top of the “OS platform” supplied by the classical mechanics.

Informal Explanation 1.C1.1: Hierarchically speaking, QM remains the most fundamental or the “ground” layer. The aspects of the physical reality that CM refers to, therefore, indeed are at a layer lying on top of QM. This part does continue to remain the same.

However, what the Corollary 1 now says is that you can also completely explain the workings of QM in terms of a virtual QM machine that is built on top of the well-known principles of CM.

If someone builds a QC on such a basis (which would be a virtual QC on top of CM), then it would be just a classical mechanically functioning simulator—an analog simulator, I should add—that simulates the QM phenomena.

Informal Explanation 1.C1.2: The phrase “in principle” does not always translate into “easily.” In this case, it in factt is very easily possible that building a big enough a QC of this kind (i.e. the simulating QC) may very well turn out to be an enterprise that is too difficult to be practically feasible.

Corollary 2 of Statement 1: A classical system can be designed in such a way that it shows all the features of the phenomenon of quantum entanglement (when the classical system is seen from an appropriately high-level viewpoint).

Informal Explanation 1.C2.1: There is nothing “inherently quantum-mechanical” about entanglement. The well-known principles of CM are enough to explain the phenomena of entanglement.

Informal Explanation 1.C2.2: We use our own terms. In particular, when we say “classical mechanics,” we do not mean these words in the same sense in which a casual reader of the QM literature, e.g. of Bell’s writings, may read them.

What we mean by “classical mechanics” is the same as what an engineer who has never studied QM proper means, when he says “classical mechanics” (i.e., the Newtonian mechanics + the Lagrangian and Hamiltonian reformulations including variational principles, as well as the more modern developments such as studies of nonlinear systems and the catastrophe theory).

Statement 2: It can be shown that even if the Corollary 1 above does hold true, the kind of quantum computer it refers to would be such that it will not be able to break a sufficiently high-end RSA encryption (such as what is used in practice today, at the high-end).

Aside 2.1: I wouldn’t have announced Statement 1 unless I was sure—absolutely goddamn sure, in fact—about the Statement 2. In fact, I must have waited for at least half a year just to make sure about this aspect, looking at these things from this PoV, then from that PoV, etc.

Statement 3: Inasmuch as the RSA-beating QC requires a controlled entanglement over thousands of qubits, it can be said, on the basis of the new understanding (the one which lies behind the Statement 1 above), that the goal of achieving even “just” the quantum supremacy seems highly improbable, at least in any foreseeable future, let alone achieving the goal of breaking the high-end RSA encryption currently in use. However, proving these points, esp. that the currently employed higher-end RSA cannot be broken, will require further development of the new theory, particularly a quantitative theory for the mechanism(s) involved in the quantum mechanical measurements.

Informal Explanation 3.1: A lot of funding has already gone into attempts to build a QC. Now, it seems that the US government, too, is considering throwing some funds at it.

The two obvious goal-posts for a proper QC are: (i) first gaining enough computational power to run past the capabilities of the classical digital computers, i.e., achieving the so-called “quantum supremacy,” and then, (ii) breaking the RSA encryption as is currently used in the real-world at the high-end.

The question of whether the QC-related researches will be able to achieve these two goals or not depends on the question of whether there are natural reasons/causes which might make it highly improbable (if not outright impossible) to achieve these two goals.

We have already mentioned that it can be shown that it will not be possible for a classical (analog) quantum simulator (of the kind we have in mind) to break the RSA encryption.

• Combination 1: CM-based QC Simulator that is able to break the RSA encryption.

We have said that it can be shown (i.e. proved) that the above combination would be impossible to have. (The combination is that extreme.)

However, it still leaves open 3 more combinations of a QC and a goal-post:

• Combination 2: CM-based QC Simulator that exceeds the classical digital computer
• Combination 3: Proper QC (working directly off the QM platform) that exceeds the classical digital computer
• Combination 4: Proper QC (working directly off the QM platform) that is able to break the RSA encryption.

As of today, a conclusive statement cannot be made regarding the last three combinations, not even on the basis of my newest approach to the quantum phenomena, because the mathematical aspects which will help settle questions of this kind, have not yet been developed (by me).

Chances are good that such a theory could be developed, at least in somewhat partly-qualitative-and-partly-quantitative terms, or in terms of some quantitative models that are based on some good analogies, sometime in the future (say within a decade or so). It is only when such developments do occur that we will be able to conclusively state something one way or the other in respect of the last three combinations.

However, relying on my own judgment, I think that I can safely state this much right away: The remaining three combinations would be tough, very tough, to achieve. The last combination, in particular, is best left aside, because the combination is far too complex that it can pose any real threat, at least as of today. I can say this much confidently—based on my new approach. (If you have some other basis to feel confident one way or the other, kindly supply the physical mechanism for the same, please, not just “math.”)

So, as of today, the completely defensible statements are the Statement No. 1 and 2 (with all their corollaries), but not the Statement 3. However, a probabilistic judgment for the Statement 3 has also been given.

A short (say, abstract-like) version:

A physical mechanism to explain QM phenomena has been developed, at least in the bare essential terms. It may perhaps become possible to use such a knowledge to build an analog simulator of a quantum computer. Such a simulator would be a machine based only on the well-known principles of classical mechanics, and using the kind of physical objects that the classical mechanics studies.

However, it can also be easily shown that such a simulator will not be able to break the RSA encryption using algorithm such as Shor’s. The proof rests on an idealized abstraction of classical objects (just the way the ideal fluid is an abstraction of real fluids).

On the basis of the new understanding, it becomes clear that trying to break RSA encryption using a QC proper (i.e. a computer that’s not just a simulator, but is a QC proper that directly operates at the level of the QM platform itself) would be a goal that is next to impossible to achieve. In fact, even achieving just the “quantum supremacy” (i.e., beating the best classical digital computer) itself can be anticipated, on the basis of the new understanding, as a goal that would be very tough to achieve, if at all.

Researches that attempt to build a proper QC may be able to bring about some developments in various related areas such as condensed matter physics, cryogenics, electronics, etc. But it is very highly unlikely that they would succeed in achieving the goal of quantum supremacy itself, let alone the goal of breaking the RSA encryption as it is deployed at the high-end today.

A Song I Like:

(Hindi) “dilbar jaani, chali hawaa mastaanee…”
Music: Laxmikant Pyarelal
Singers: Kishore Kumar, Lata Mangeshkar
Lyrics: Anand Bakshi

PS: Note that, as is usual at this blog, an iterative improvement of the draft is always a possibility. Done.

Revision History:

1. First posted on 2018.06.15, about 12:35 hrs IST.
2. Considerably revised the contents on 2018.06.15, 18:41 hrs IST.
3. Edited to make the contents better on 2018.06.16, 15:30 hrs IST. Now, am mostly done with this post except, may be, for a minor typo or so, here or there.
4. Edited (notably, changed the order of the Combinations) on 2018.06.17, 23:50 hrs IST. Also corrected some typos and streamlined the content. Now, I am going to leave this post in the shape it is. If you find some inconsistency or so, simple! Just write a comment or shoot me an email.
5. 2018.06.27 02:07 hrs IST. Changed the song section.

# Some suggested time-pass (including ideas for Python scripts involving vectors and tensors)

Actually, I am busy writing down some notes on scalars, vectors and tensors, which I will share once they are complete. No, nothing great or very systematic; these are just a few notings here and there taken down mainly for myself. More like a formulae cheat-sheet, but the topic is complicated enough that it was necessary that I have them in one place. Once ready, I will share them. (They may get distributed as extra material on my upcoming FDP (faculty development program) on CFD, too.)

While I remain busy in this activity, and thus stay away from blogging, you can do a few things:

1.

Think about it: You can always build a unique tensor field from any given vector field, say by taking its gradient. (Or, you can build yet another unique tensor field, by taking the Kronecker product of the vector field variable with itself. Or, yet another one by taking the Kronecker product with some other vector field, even just the position field!). And, of course, as you know, you can always build a unique vector field from any scalar field, say by taking its gradient.

So, you can write a Python script to load a B&W image file (or load a color .PNG/.BMP/even .JPEG, and convert it into a gray-scale image). You can then interpret the gray-scale intensities of the individual pixels as the local scalar field values existing at the centers of cells of a structured (squares) mesh, and numerically compute the corresponding gradient vector and tensor fields.

Alternatively, you can also interpret the RGB (or HSL/HSV) values of a color image as the x-, y-, and z-components of a vector field, and then proceed to calculate the corresponding gradient tensor field.

Write the output in XML format.

2.

Think about it: You can always build a unique vector field from a given tensor field, say by taking its divergence. Similarly, you can always build a unique scalar field from a vector field, say by taking its divergence.

So, you can write a Python script to load a color image, and interpret the RGB (or HSL/HSV) values now as the $xx$-, $xy$-, and $yy$-components of a symmetrical 2D tensor, and go on to write the code to produce the corresponding vector and scalar fields.

Yes, as my resume shows, I was going to write a paper on a simple, interactive, pedagogical, software tool called “ToyDNS” (from Toy + Displacements, Strains, Stresses). I had written an extended abstract, and it had even got accepted in a renowned international conference. However, at that time, I was in an industrial job, and didn’t get the time to write the software or the paper. Even later on, the matter kept slipping.

I now plan to surely take this up on priority, as soon as I am done with (i) the notes currently in progress, and immediately thereafter, (ii) my upcoming stress-definition paper (see my last couple of posts here and the related discussion at iMechanica).

Anyway, the ideas in the points 1. and 2. above were, originally, a part of my planned “ToyDNS” paper.

3.

You can induce a “zen-like” state in you, or if not that, then at least a “TV-watching” state (actually, something better than that), simply by pursuing this URL [^], and pouring in all your valuable hours into it. … Or who knows, you might also turn into a closet meteorologist, just like me. [And don’t tell anyone, but what they show here is actually a vector field.]

4.

You can listen to this song in the next section…. It’s one of those flowy things which have come to us from that great old Grand-Master, viz., SD Burman himself! … Other songs falling in this same sub-sub-genre include, “yeh kisine geet chheDaa,” and “ThanDi hawaaein,” both of which I have run before. So, now, you go enjoy yet another one of the same kind—and quality. …

A Song I Like:

[It’s impossible to figure out whose contribution is greater here: SD’s, Sahir’s, or Lata’s. So, this is one of those happy circumstances in which the order of the listing of the credits is purely incidental … Also recommended is the video of this song. Mona Singh (aka Kalpana Kartik (i.e. Dev Anand’s wife, for the new generation)) is sooooo magical here, simply because she is so… natural here…]

(Hindi) “phailee huyi hai sapanon ki baahen”
Music: S. D. Burman
Lyrics: Sahir
Singer: Lata Mangeshkar

But don’t forget to write those Python scripts….

Take care, and bye for now…

/