Python scripts for simulating QM, part 0: A general update

My proposed paper on my new approach to QM was not accepted at the international conference where I had sent my abstract. (For context, see the post before the last, here [^] ).

“Thank God,” that’s what I actually felt when I received this piece of news, “I can now immediately proceed to procrastinate on writing the full-length paper, and also, simultaneously, un-procrastinate on writing some programs in Python.”

So far, I have written several small and simple code-snippets. All of these were for the usual (text-book) cases; all in only 1D. Here in this post, I will mention specifically which ones…


Time-independent Schrodinger equation (TISE):

Here, I’ve implemented a couple of scripts, one for finding the eigen-vectors and -values for a particle in a box (with both zero and arbitrarily specified potentials) and another one for the quantum simple harmonic oscillator.

These were written not with the shooting method (which is the method used in the article by Rhett Allain for the Wired magazine [^]) but with the matrix method. … Yes, I have gone past the stage of writing all the numerical analysis algorithm in original, all by myself. These days, I directly use Python libraries wherever available, e.g., NumPy’s LinAlg methods. That’s why, I preferred the matrix method. … My code was not written from scratch; it was based on Cooper’s code “qp_se_matrix”, here [PDF ^]).


Time-dependent Schrodinger equation (TDSE):

Here, I tried out a couple of scripts.

The first one was more or less a straightforward porting of Ian Cooper’s program “se_fdtd” [PDF ^] from the original MatLab to Python. The second one was James Nagel’s Python program (written in 2007 (!) and hosted as a SciPy CookBook tutorial, here [^]). Both follow essentially the same scheme.

Initially, I found this scheme to be a bit odd to follow. Here is what it does.

It starts out by replacing the complex-valued Schrodinger equation with a pair of real-valued (time-dependent) equations. That was perfectly OK by me. It was their discretization which I found to be a bit peculiar. The discretization scheme here is second-order in both space and time, and yet it involves explicit time-stepping. That’s peculiar, so let me write a detailed note below (in part, for my own reference later on).

Also note: Though both Cooper and Nagel implement essentially the same method, Nagel’s program is written in Python, and so, it is easier to discuss (because the array-indexing is 0-based). For this reason, I might make a direct reference only to Nagel’s program even though it is to be understood that the same scheme is found implemented also by Cooper.


A note on the method implemented by Nagel (and also by Cooper):

What happens here is that like the usual Crank-Nicolson (CN) algorithm for the diffusion equation, this scheme too puts the half-integer time-steps to use (so as to have a second-order approximation for the first-order derivative, that of time). However, in the present scheme, the half-integer time-steps turn out to be not entirely fictitious (the way they are, in the usual CN method for the single real-valued diffusion equation). Instead, all of the half-integer instants are fully real here in the sense that they do enter the final discretized equations for the time-stepping.

The way that comes to happen is this: There are two real-valued equations to solve here, coupled to each other—one each for the real and imaginary parts. Since both the equations have to be solved at each time-step, what this method does is to take advantage of that already existing splitting of the time-step, and implements a scheme that is staggered in time. (Note, this scheme is not staggered in space, as in the usual CFD codes; it is staggered only in time.) Thus, since it is staggered and explicit, even the finite-difference quantities that are defined only at the half-integer time-steps, also get directly involved in the calculations. How precisely does that happen?

The scheme defines, allocates memory storage for, and computationally evaluates the equation for the real part, but this computation occurs only at the full-integer instants (n = 0, 1, 2, \dots). Similarly, this scheme also defines, allocates memory for, and computationally evaluates the equation for the imaginary part; however, this computation occurs only at the half-integer instants (n = 1/2, 1+1/2, 2+1/2, \dots). The particulars are as follows:

The initial condition (IC) being specified is, in general, complex-valued. The real part of this IC is set into a space-wide array defined for the instant n; here, n = 0. Then, the imaginary part of the same IC is set into a separate array which is defined nominally for a different instant: n+1/2. Thus, even if both parts of the IC are specified at t = 0, the numerical procedure treats the imaginary part as if it was set into the system only at the instant n = 1/2.

Given this initial set-up, the actual time-evolution proceeds as follows:

  • The real-part already available at n is used in evaluating the “future” imaginary part—the one at n+1/2
  • The imaginary part thus found at n+1/2 is used, in turn, for evaluating the “future” real part—the one at n+1.

At this point that you are allowed to say: lather, wash, repeat… Figure out exactly how. In particular, notice how the simulation must proceed in integer number of pairs of computational steps; how the imaginary part is only nominally (i.e. only computationally) distant in time from its corresponding real part.

Thus, overall, the discretization of the space part is pretty straight-forward here: the second-order derivative (the Laplacian) is replaced by the usual second-order finite difference approximation. However, for the time-part, what this scheme does is both similar to, and different from, the usual Crank-Nicolson scheme.

Like the CN scheme, the present scheme also uses the half-integer time-levels, and thus manages to become a second-order scheme for the time-axis too (not just space), even if the actual time interval for each time-step remains, exactly as in the CN, only \Delta t, not 2\Delta t.

However, unlike the CN scheme, this scheme still remains explicit. That’s right. No matrix equation is being solved at any time-step. You just zip through the update equations.

Naturally, the zipping through comes with a “cost”: The very scheme itself comes equipped with a stability criterion; it is not unconditionally stable (the way CN is). In fact, the stability criterion now refers to half of the time-interval, not full, and thus, it is a bit even more restrictive as to how big the time-step (\Delta t) can be given a certain granularity of the space-discretization (\Delta x). … I don’t know, but guess that this is how they handle the first-order time derivatives in the FDTD method (finite difference time domain). May be the physics of their problems itself is such that they can get away with coarser grids without being physically too inaccurate, who knows…


Other aspects of the codes by Nagel and Cooper:

For the initial condition, both Cooper and Nagel begin with a “pulse” of a cosine function that is modulated to have the envelop of the Gaussian. In both their codes, the pulse is placed in the middle, and they both terminate the simulation when it reaches an end of the finite domain. I didn’t like this aspect of an arbitrary termination of the simulation.

However, I am still learning the ropes for numerically handling the complex-valued Schrodinger equation. In any case, I am not sure if I’ve got good enough a handle on the FDTD-like aspects of it. In particular, as of now, I am left wondering:

What if I have a second-order scheme for the first-order derivative of time, but if it comes with only fictitious half-integer time-steps (the way it does, in the usual Crank-Nicolson method for the real-valued diffusion equation)? In other words: What if I continue to have a second-order scheme for time, and yet, my scheme does not use leap-frogging? In still other words: What if I define both the real and imaginary parts at the same integer time-steps n = 0, 1, 2, 3, \dots so that, in both cases, their values at the instant n are directly fed into both their values at n+1?

In a way, this scheme seems simpler, in that no leap-frogging is involved. However, notice that it would also be an implicit scheme. I would have to solve two matrix-equations at each time-step. But then, I could perhaps get away with a larger time-step than what Nagel or Cooper use. What do you think? Is checker-board patterning (the main reason why we at all use staggered grids in CFD) an issue here—in time evolution? But isn’t the unconditional stability too good to leave aside without even trying? And isn’t the time-axis just one-way (unlike the space-axis that has BCs at both ends)? … I don’t know…


PBCs and ABCs:

Even as I was (and am) still grappling with the above-mentioned issue, I also wanted to make some immediate progress on the front of not having to terminate the simulation (once the pulse reached one of the ends of the domain).

So, instead of working right from the beginning with a (literally) complex Schrodinger equation, I decided to first model the simple (real-valued) diffusion equation, and to implement the PBCs (periodic boundary conditions) for it. I did.

My code seems to work, because the integral of the dependent variable (i.e., the total quantity of the diffusing quantity present in the entire domain—one with the topology of a ring) does seem to stay constant—as is promised by the Crank-Nicolson scheme. The integral stays “numerically the same” (within a small tolerance) even if obviously, there are now fluxes at both the ends. (An initial condition of a symmetrical saw-tooth profile defined between y = 0.0 and y = 1.0, does come to asymptotically approach the horizontal straight-line at y = 0.5. That is what happens at run-time, so obviously, the scheme seems to handle the fluxes right.)

Anyway, I don’t always write everything from the scratch; I am a great believer in lifting codes already written by others (with attribution, of course :)). Thus, while thus searching on the ‘net for some already existing resources on numerically modeling the Schrodinger equation (preferably with code!), I also ran into some papers on the simulation of SE using ABCs (i.e., the absorbing boundary conditions). I was not sure, however, if I should implement the ABCs immediately…

As of today, I think that I am going to try and graduate from the transient diffusion equation (with the CN scheme and PBCs), to a trial of the implicit TDSE without leap-frogging, as outlined above. The only question is whether I should throw in the PBCs to go with that or the ABCs. Or, may be, neither, and just keep pinning the  \Psi values for the end- and ghost-nodes down to 0, thereby effectively putting the entire simulation inside an infinite box?

At this point of time, I am tempted to try out the last. Thus, I think that I would rather first explore the staggering vs. non-staggering issue for a pulse in an infinite box, and understand it better, before proceeding to implement either the PBCs or the ABCs. Of course, I still have to think more about it… But hey, as I said, I am now in a mood of implementing, not of contemplating.


Why not upload the programs right away?

BTW, all these programs (TISE with matrix method, TDSE on the lines of Nagel/Cooper’s codes, transient DE with PBCs, etc.) are still in a fluid state, and so, I am not going to post them immediately here (though over a period of time, I sure would).

The reason for not posting the code runs something like this: Sometimes, I use the Python range objects for indexing. (I saw this goodie in Nagel’s code.) At other times, I don’t. But even when I don’t use the range objects, I anyway am tempted to revise the code so as to have them (for a better run-time efficiency).

Similarly, for the CN method, when it comes to solving the matrix equation at each time-step, I am still not using the TDMA (the Thomas algorithm) or even just sparse matrices. Instead, right now, I am allocating the entire N \times N sized matrices, and am directly using NumPy’s LinAlg’s solve() function on these biggies. No, the computational load doesn’t show up; after all, I anyway have to use a 0.1 second pause in between the rendering passes, and the biggest matrices I tried were only 1001 \times 1001 in size. (Remember, this is just a 1D simulation.) Even then, I am tempted a bit to improve the efficiency. For these and similar reasons, some or the other tweaking is still going on in all the programs. That’s why, I won’t be uploading them right away.


Anything else about my new approach, like delivering a seminar or so? Any news from the Indian physicists?

I had already contacted a couple of physics professors from India, both from Pune: one, about 1.5 years ago, and another, within the last 6 months. Both these times, I offered to become a co-guide for some computational physics projects to be done by their PG/UG students or so. Both times (what else?) there was absolutely no reply to my emails. … If they were to respond, we could have together progressed further on simulating my approach. … I have always been “open” about it.

The above-mentioned experience is precisely similar to how there have been no replies when I wrote to some other professors of physics, i.e., when I offered to conduct a seminar (covering my new approach) in their departments. Particularly, from the young IISER Pune professor whom I had written. … Oh yes, BTW, there has been one more physicist who I contacted recently for a seminar (within the last month). Once again, there has been no reply. (This professor is known to enjoy hospitality abroad as an Indian, and also use my taxpayer’s money for research while in India.)

No, the issue is not whether the emails I write using my Yahoo! account go into their span folder—or something like that. That would be too innocuous a cause, and too easy to deal with—every one has a mobile-phone these days. But I know these (Indian) physicists. Their behaviour remains exactly the same even if I write my emails using a respectable academic email ID (my employers’, complete with a .edu domain). This was my experience in 2016, and it repeated again in 2017.

The bottom-line is this: If you are an engineer and if you write to these Indian physicists, there is almost a guarantee that your emails will go into a black-hole. They will not reply to you even if you yourself have a PhD, and are a Full Professor of engineering (even if only on an ad-hoc basis), and have studied and worked abroad, and even if your blog is followed internationally. So long as you are engineer, and mention QM, the Indian physicists simply shut themselves off.

However, there is a trick to get them to reply you. Their behavior does temporarily change when you put some impressive guy in your cc-field (e.g., some professor friend of yours from some IIT). In this case, they sometimes do reply your first email. However, soon after that initial shaking of hands, they somehow go back to their true core; they shut themselves off.

And this is what invariably happens with all of them—no matter what other Indian bloggers might have led you to believe.

There must be some systemic reasons for such behavior, you say? Here, I will offer a couple of relevant observations.

Systemically speaking, Indian physicists, taken as a group (and leaving any possible rarest of the rare exceptions aside), all fall into one band: (i) The first commonality is that they all are government employees. (ii) The second commonality they all tend to be leftists (or, heavily leftists). (iii) The third commonality is they (by and large) share is that they had lower (or far lower) competitive scores in the entrance examinations at the gateway points like XII, GATE/JAM, etc.

The first factor typically means that they know that no one is going to ask them why they didn’t reply (even to people like with my background). The second factor typically means that they don’t want to give you any mileage, not even just a plain academic respect, if you are not already one of “them”. The third factor typically means that they simply don’t have the very intellectual means to understand or judge anything you say if it is original—i.e., if it is not based on some work of someone from abroad. In plain words: they are incompetent. (That in part is the reason whenever I run into a competent Indian physicist, it is both a surprise and a pleasure. To drop a couple of names: Prof. Kanhere (now retired) from UoP (now SPPU), and Prof. Waghmare of JNCASR. … But leaving aside this minuscule minority, and coming to the rest of the herd: the less said, the better.)

In short, Indian physicists all fall into a band. And they all are very classical—no tunneling is possible. Not with these Indian physicists. (The trends, I guess, are similar all over the world. Yet, I definitely can say that Indians are worse, far worse, than people from the advanced, Western, countries.)

Anyway, as far as the path through the simulations goes, since no help is going to come from these government servants (regarded as physicists by foreigners), I now realized that I have to get going about it—simulations for my new approach—entirely on my own. If necessary, from the basic of the basics. … And that’s how I got going with these programs.


Are these programs going to provide a peek into my new approach?

No, none of these programs I talked about in this post is going to be very directly helpful for simulations related to my new approach. The programs I wrote thus far are all very, very standard (simplest UG text-book level) stuff. If resolving QM riddles were that easy, any number of people would have done it already.

… So, the programs I wrote over the last couple of weeks are nothing but just a beginning. I have to cover a lot of distance. It may take months, perhaps even a year or so. But I intend to keep working at it. At least in an off and on manner. I have no choice.

And, at least currently, I am going about it at a fairly good speed.

For the same reason, expect no further blogging for another 2–3 weeks or so.


But one thing is for certain. As soon as my paper on my new approach (to be written after running the simulations) gets written, I am going to quit QM. The field does not hold any further interest to me.

Coming to you: If you still wish to know more about my new approach before the paper gets written, then you convince these Indian professors of physics to arrange for my seminar. Or, else…

… What else? Simple! You. Just. Wait.

[Or see me in person if you would be visiting India. As I said, I have always been “open” from my side, and I continue to remain so.]


A song I like:
(Hindi) “bheegee bheegee fizaa…”
Music: Hemant Kumar
Singer: Asha Bhosale
Lyrics: Kaifi Aazmi


History:
Originally published: 2018.11.26 18:12 IST
Extension and revision: 2018.11.27 19.29 IST

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Suspension of blogging

Earlier, within a day of my posting the last blog entry here, i.e. right by 26th September morning, my laptop developed a problem, which led to a series of problems, which meant that, for a while, I could not at all blog or even surf on the ‘net effectively.

The smartphone screen is too small for me to do any serious browsing very effectively, let alone doing any blogging / writing / coding.


Never did buy into that idiotic Steve Jobs’ ridiculous claims anyway; bought my smartphone only because it’s good for things like storing phone numbers and listening to songs—and, yes, also for browsing a bit on google maps, and for taking snaps once in a while. But that’s about it. Nothing more than that. In particular, no social media, no banking, no e-payments, no emails, no real browsing. And, as to that prized (actually wretched) thin-ness and/or the delicate-ness of this goddamn thing. It is annoying. Just hold the damn thing in your palm, and it seems as if it itself auto-punches a few buttons and proceeds to close all the windows you had kept active. Or, worse: it launches a new window all by itself, forcing you to take a hike into an ad-link or sundry news item.

A good 1 inch thick and sturdy instrument with goodly big buttons would have been a better design choice, far better—not those bloody thin slivers on the sides which pass for buttons.


Anyway, the troubles with the laptop were these:

(i) In 2014, the screen panel of the laptop had cracked near a corner a bit, and then, subsequently, over a period of years or so, the front and the back covering parts of the screen panel had come to split apart, though only just slightly, only partially. I had shown the problem to the authorized dealer. He had advised me to do nothing about it. (If the problem were to be worse, he would have advised me to replace the screen, he had said. This was about 2 years ago.)

(ii) Then, slowly, friction began developing in only one of the hinges of the screen panel, the hinge near the same (cracked) corner. Finally, came this day when this partial splitting suddenly led to the panel-studs breaking apart (with a clean, brittle fracture). How did it happen? Because—I figured out only after the fact—the friction in the hinges together with the partial split up meant that an interior part of the screen panel was getting excessively bent, near the broken panel corner. This excessive bending was putting enormous bending moment on the studs holding the two parts of the partially split up panel near the hinges. (The overall frame of the screen panel was effectively acting as a large lever arm serving to bend the small plastic studs.)

(iii) In getting the above-mentioned problem fixed (by 29th September), some short-circuiting also occurred, with the result that now the graphics chip conked up. (No, the authorized dealer didn’t accept the machine. He advised replacement of both the mother-board and the screen. So, I did a google search and went through two private repairs-men, one of them being much better than the other. He fixed it right.)

Fixing the graphics problem took time because a replacement chip was not readily available in the local market, and there was a national holiday in between (on 2nd October) which kept the concerned courier services closed on that day.

(iv) Then, after replacing the graphics chip, once the screen finally started working, now it was the turn of the USB ports to begin malfunctioning. I got the delivery of my laptop last evening, and noticed it only after coming home.

This is a problem which has not yet been fixed. Getting it fixed is important because only 1 out of the 3 USB ports is currently functioning, and if it too is gone, backups will become impossible. I am not willing to lose my data once again.


The problem with the machine meant that my studies (and programming) of ANNs too got interrupted.

They still remain interrupted.

I guess the remaining problem (regarding the malfunctioning USB ports) is relatively a minor issue.

What I mean to say is that I could have resumed my regular sort of blogging.

However, last night, at around 00:40 hrs IST on 05 October 2018 there was a psychic attack on me which woke me up from sleep. (Also note the update in my last post). In view of this attack, I have finally decided to say it clear and loud, (perhaps once again):

“To hell with you, LA!”


If you wonder why I was so confident about “LA,” check out the visits pattern for the earlier part of the day yesterday, and juxtapose them with the usual patterns of visits here, overall.

In case you don’t know, all local newspapers of all California towns have been full of advertisements for psychic “consultants” providing their “services” for a fee—which would be almost nothing when measured in US dollars.


I have had enough of these bitches and bastards. That’s why, I am temporarily suspending my blog. When the psychic attacks come to a definitive stop, I will resume my own blogging, as also my commenting on other blogs, and posting any research notes etc.


And, yes, one more point: No, don’t believe what Ayn Rand Institute tells you. Psychic attacks are for real (though they are much, much rarer, and they indeed are effected in far more controlled ways, than what folklore or your average street-side vendor of the “services” says.)


No songs section this time round, for obvious reasons.


PS: BTW, no, I still haven’t seen my approach to QM mentioned in any of the papers / books, or in any discussions of any papers anywhere (including some widely followed blogs / twitter feeds), as yet. Apparently, my judgment that my approach is indeed new, continues to hold.

 

 

Flames not so old…

The same picture, but two American interpretations, both partly misleading (to varying degrees):

NASA releases a photo [^] on the FaceBook, on 24 August at 14:24, with this note:

The visualization above highlights NASA Earth satellite data showing aerosols on August 23, 2018. On that day, huge plumes of smoke drifted over North America and Africa, three different tropical cyclones churned in the Pacific Ocean, and large clouds of dust blew over deserts in Africa and Asia. The storms are visible within giant swirls of sea salt aerosol (blue), which winds loft into the air as part of sea spray. Black carbon particles (red) are among the particles emitted by fires; vehicle and factory emissions are another common source. Particles the model classified as dust are shown in purple. The visualization includes a layer of night light data collected by the day-night band of the Visible Infrared Imaging Radiometer Suite (VIIRS) on Suomi NPP that shows the locations of towns and cities.

[Emphasis in bold added by me.]

For your convenience, I reproduce the picture here:

Aerosol data by NASA

Aerosol data by NASA. Red means: Carbon emissions. Blue means: Sea Salt. Purple means: Dust particles.

Nicole Sharp blogs [^] about it at her blog FYFD, on Aug 29, 2018 10:00 am, with this description:

Aerosols, micron-sized particles suspended in the atmosphere, impact our weather and air quality. This visualization shows several varieties of aerosol as measured August 23rd, 2018 by satellite. The blue streaks are sea salt suspended in the air; the brightest highlights show three tropical cyclones in the Pacific. Purple marks dust. Strong winds across the Sahara Desert send large plumes of dust wafting eastward. Finally, the red areas show black carbon emissions. Raging wildfires across western North America are releasing large amounts of carbon, but vehicle and factory emissions are also significant sources. (Image credit: NASA; via Katherine G.)

[Again, emphasis in bold is mine.]

As of today, Sharp’s post has collected some 281 notes, and almost all of them have “liked” it.

I liked it too—except for the last half of the last sentence, viz., the idea that vehicle and factory emissions are significant sources (cf. NASA’s characterization):


My comment:

NASA commits an error of omission. Dr. Sharp compounds it with an error of commission. Let’s see how.

NASA does find it important to mention that the man-made sources of carbon are “common.” However, the statement is ambiguous, perhaps deliberately so. It curiously omits to mention that the quantity of such “common” sources is so small that there is no choice but to regard it as “not critical.” We may not be in a position to call the “common” part an error of commission. But not explaining that the man-made sources play negligible (even vanishingly small) role in Global Warming, is sure an error of omission on NASA’s part.

Dr. Sharp compounds it with an error of commission. She calls man-made sources “significant.”

If I were to have an SE/TE student, I would assign a simple Python script to do a histogram and/or compute the densities of red pixels and have them juxtaposed with areas of high urban population/factory density.


This post may change in future:

BTW, I am only too well aware of the ugly political wars being waged by a lot of people in this area (of Global Warming). Since I do appreciate Dr. Sharp’s blog, I would be willing to delete all references to her writing from this post.

However, I am going to keep NASA’s description and the photo intact. It serves as a good example of how a good visualization can help in properly apprehending big data.

In case I delete references to Sharp’s blog, I will simply add another passage on my own, bringing out how man-made emissions are not the real cause for concern.

But in any case, I would refuse to be drawn into those ugly political wars surrounding the issue of Global Warming. I have neither the interest nor the bandwidth to get into it, and further, I find (though can’t off-hand quote) that several good modelers/scientists have come to offer very good, detailed, and comprehensive perspectives that justify my position (mentioned in the preceding paragraph). [Off-hand, I very vaguely remember an academic, a lady, perhaps from the state of Georgia in the US?]


The value of pictures:

One final point.

But, regardless of it all (related to Global Warming and its politics), this picture does serve to highlight a very important point: the undeniable strength of a good visualization.

Yes I do find that, in a proper context, a picture is worth a thousand words. The obvious validity of this conclusion is not affected by Aristotle’s erroneous epistemology, in particular, his wrong assertion that man thinks in terms of “images.” No, he does not.

So, sure, a picture is not an argument, as Peikoff argued in the late 90s (without using pictures, I believe). If Peikoff’s statement is taken in its context, you would agree with it, too.

But for a great variety of useful contexts, as the one above, I do think that a picture is worth a thousand words. Without such being the case, a post like this wouldn’t have been possible.


A Song I Like:
(Hindi) “dil sajan jalataa hai…”
Singer: Asha Bhosale
Music: R. D. Burman [actually, Bertha Egnos [^]]
Lyrics: Anand Bakshi


Copying it right:

“itwofs” very helpfully informs us [^] that this song was:

Inspired in the true sense, by the track, ‘Korbosha (Down by the river) from the South African stage musical, Ipi Ntombi (1974).”

However, unfortunately, he does not give the name of the original composer. It is: Bertha Egnos (apparently, a white woman from South Africa [^]).

“itwofs” further opines that:

Its the mere few initial bars that seem to have sparked Pancham create the totally awesome track [snip]. The actual tunes are completely different and as original as Pancham can get.

I disagree.

Listen to Korbosha and to this song, once again. You will sure find that it is far more than “mere few initial bars.” On the contrary, except for a minor twist here or there (and that too only in some parts of the “antaraa”/stanza), Burman’s song is almost completely lifted from Egnos’s, as far as the tune goes. And the tune is one of the most basic—and crucial—elements of a song, perhaps the most crucial one.

However, what Burman does here is to “customize” this song to “suit the Indian road conditions tastes.” This task also can be demanding; doing it right takes a very skillful and sensitive composer, and R. D. certainly shows his talents in this regard, too, here. Further, Asha not only makes it “totally, like, totally” Indian, she also adds a personal chutzpah. The combination of Egnos, RD and Asha is awesome.

If the Indian reader’s “pride” got hurt: For a reverse situation of “phoreenn” people customizing our songs, go see how well Paul Mauriat does it.

One final word: The video here is not recommended. It looks (and is!) too gaudy. So, even if you download a YouTube video, I recommend that you search for good Open Source tools and use it to extract just the audio track from this video. … If you are not well conversant with the music software, then Audacity would confuse you. However, as far as just converting MP4 to MP3 is concerned, VLC works just as great; use the menu: Media \ Convert/Save. This menu command works independently of the song playing in the “main” VLC window.


Bye for now… Some editing could be done later on.

Caste Brahmins, classification, and ANN

1. Caste Brahmins:

First, a clarification: No, I was not born in any one of the Brahmin castes, particularly, not at all in the Konkanastha Brahmins’ caste.

Second, a suggestion: Check out how many caste-Brahmins have made it to the top in the Indian and American IT industry, and what sort of money they have made—already.

No, really.

If you at all bother visiting this blog, then I do want you to take a very serious note of both these matters.

No. You don’t have to visit this blog. But, yes, if you are going to visit this blog, to repeat, I do want you to take  matters like these seriously.

Some time ago, perhaps a year ago or so, a certain caste-Brahmin in Pune from some place (but he didn’t reveal his shakha, sub-caste, gotra, pravar, etc.) had insulted me, while maintaining a perfectly cool demeanor for himself, saying how he had made so much more money than me. Point taken.

But my other caste-Brahmin “friends” kept quiet at that time; not a single soul from them interjected.

In my off-the-cuff replies, I didn’t raise this point (viz., why these other caste-Brahmins were keeping quiet), but I am sure that if I were to do that, then, their typical refrain would have been (Marathi) “tu kaa chiDatos evhaDa, to tar majene bolat hotaa.” … English translation: Why do you get so angry? He was just joking.

Note the usual caste-Brahmin trick: they skillfully insert an unjustified premise; here, that you are angry!

To be blind to the actual emotional states or reactions of the next person, if he comes from some other caste, is a caste-habit with the caste-Brahmins. The whole IT industry is full of them—whether here in India, or there in USA/UK/elsewhere.

And then, today, another Brahmin—a Konkanastha—insulted me. Knowing that I am single, he asked me if I for today had taken the charge of the kitchen, and then, proceeded to invite my father to a Ganesh Pooja—with all the outward signs of respect being duly shown to my father.


Well, coming back to the point which was really taken:

Why have caste-Brahmins made so much money—to the point that they in one generation have begun very casually insulting the “other” people, including people of my achievements?

Or has it been the case that the people of the Brahmin castes always were this third-class, in terms of their culturally induced convictions, but that we did not come to know of it from our childhood, because the elderly people around us kept such matters, such motivations, hidden from us? May be in the naive hope that we would thereby not get influenced in a bad manner? Possible.

And, of course, how come these caste-Brahmins have managed to attract as much money as they did (salaries in excess of Rs. 50 lakhs being averagely normal in Pune) even as I was consigned only to receive “attract” psychic attacks (mainly from abroad) and insults (mainly from those from this land) during the same time period?

Despite all my achievements?

Do take matters like these seriously, but, of course, as you must have gathered by now, that is not the only thing I would have, to talk about. And, the title of this post anyway makes this part amply clear.


2. The classification problem and the ANNs:

I have begun my studies of the artificial neural networks (ANNs for short). I have rapidly browsed through a lot of introductory articles (as also the beginning chapters of books) on the topic. (Yes, including those written by Indians who were born in the Brahmin castes.) I might have gone through 10+ such introductions. Many of these, I had browsed through a few years ago (I mean only the introductory parts). But this time round, of course, I picked them up for a more careful consideration.

And soon enough (i.e. over just the last 2–3 days), I realized that no one in the field (AI/ML) was talking about a good explanation of this question:

Why is it that the ANN really succeeds as well as it does, when it comes to the classification tasks, but not others?

If you are not familiar with Data Science, then let me note that it is known that ANN does not do well on all the AI tasks. It does well only on one kind of them, viz., the classification tasks. … Any time you mention the more general term Artificial Intelligence, the layman is likely to think of the ANN diagram. However, ANNs are just one type of a tool that the Data Scientist may use.

But the question here is this: why does the ANN do so well on these tasks?

I formulated this question, and then found an answer too, and I would sure like to share it with you (whether the answer I found is correct or not). However, before sharing my answer, I want you to give it a try.

It would be OK by me if you answer this question in reference to just one or two concrete classification tasks—whichever you find convenient. For instance, if you pick up OCR (optical character recognition, e.g., as explained in Michael Nielson’s free online book [^]), then you have to explain why an ANN-based OCR algorithm works in classifying those MNIST digits / alphabets.


Hint: Studies of Vedic literature won’t help. [I should know!] OTOH, studies of good books on epistemology, or even just good accounts covering methods of science, should certainly come in handy.

I will give you all some time before I come back on that question.

In the meanwhile, have fun—if you wish to, and of course, if you are able to. With questions of this kind. (Translating the emphasis in the italics into chaste Marathi: “laayaki asali tar.” Got it?)


A song I like:
(Marathi) “ooncha nicha kaahi neNe bhagawant”
Lyrics: Sant Tukaram
Music and Singer: Snehal Bhatkar

 

Links…

Here are a few interesting links I browsed recently, listed in no particular order:


“Mathematicians Tame Turbulence in Flattened Fluids” [^].

The operative word here, of course, is: “flattened.” But even then, it’s an interesting read. Another thing: though the essay is pop-sci, the author gives the Navier-Stokes equations, complete with fairly OK explanatory remarks about each term in the equation.

(But I don’t understand why every pop-sci write-up gives the NS equations only in the Lagrangian form, never Eulerian.)


“A Twisted Path to Equation-Free Prediction” [^]. …

“Empirical dynamic modeling.” Hmmm….


“Machine Learning’s `Amazing’ Ability to Predict Chaos” [^].

Click-bait: They use data science ideas to predict chaos!

8 Lyapunov times is impressive. But ignore the other, usual kind of hype: “…the computer tunes its own formulas in response to data until the formulas replicate the system’s dynamics. ” [italics added.]


“Your Simple (Yes, Simple) Guide to Quantum Entanglement” [^].

Click-bait: “Entanglement is often regarded as a uniquely quantum-mechanical phenomenon, but it is not. In fact, it is enlightening, though somewhat unconventional, to consider a simple non-quantum (or “classical”) version of entanglement first. This enables us to pry the subtlety of entanglement itself apart from the general oddity of quantum theory.”

Don’t dismiss the description in the essay as being too simplistic; the author is Frank Wilczek.


“A theoretical physics FAQ” [^].

Click-bait: Check your answers with those given by an expert! … Do spend some time here…


Tensor product versus Cartesian product.

If you are engineer and if you get interested in quantum entanglement, beware of the easily confusing terms: The tensor product and the Cartesian product.

The tensor product, you might think, is like the Cartesian product. But it is not. See mathematicians’ explanations. Essentially, the basis sets (and the operations) are different. [^] [^].

But what the mathematicians don’t do is to take some simple but non-trivial examples, and actually work everything out in detail. Instead, they just jump from this definition to that definition. For example, see: “How to conquer tensorphobia” [^] and “Tensorphobia and the outer product”[^]. Read any of these last two articles. Any one is sufficient to give you tensorphobia even if you never had it!

You will never run into a mathematician who explains the difference between the two concepts by first directly giving you a vague feel: by directly giving you a good worked out example in the context of finite sets (including enumeration of all the set elements) that illustrates the key difference, i.e. the addition vs. the multiplication of the unit vectors (aka members of basis sets).

A third-class epistemology when it comes to explaining, mathematicians typically have.


A Song I Like:

(Marathi) “he gard niLe megha…”
Singers: Shailendra Singh, Anuradha Paudwal
Music: Rushiraj
Lyrics: Muralidhar Gode

[As usual, a little streamlining may occur later on.]

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.

 

Absolutely Random Notings on QM—Part 2: LOL!

I intend to aperiodically update this post whenever I run into the more “interesting” write-ups about QM and/or quantum physicists. Accordingly, I will mention the dates on which I update this post.

I will return back to Heisenberg and Schrodinger in the next part of this series. But in the meanwhile, enjoy the “inaugaral” link below.


1. Post first published on 08 July 2018, 13:28 hrs IST with the following “interesting” write-up:

Wiki on “Fundamental Fysiks [sic] Group”: [^]


A Song I Like:

(English, “Western”): “old turkey buzzard…” from the movie “MacKenna’s Gold”
[I here mostly copy-paste, dear gentlemen, for, while I had enjoyed the song especially during the usual turbulent teens, I have not had the pleasure to locate the source of the same–back then, or ever. Hence relying on the ‘net.[Oh, BTW, it requires another post on the movie itself, though! [Just remind me, that’s all!]]]
Music: Quincy Jones
Lyrics: Freddy Douglass
Singer: Jose Feliciano

 

 

May the person from Oakland, CA, USA, please stand up and be counted?

May the person from Oakland, CA, USA, please stand up and be counted?

I mean the one who has been hitting my blog, in the rather more recent times, a bit too far often to be otherwise statistically justifiable?

Hmmm….?

[The predecessor to him, during the Obama years, was someone similar from “Mississauga, Canada.”

But nearly not as noticeable, robotic, and therefore, not so readily noticeable. At least to me, back then.]


And once again: If you are/want to be fake, leave this blog alone. I don’t need your support.

For one simple reason: I know you can’t give me that.

Another reason, viz. the fact that I have been a programmer, and so know: Robots are controlled by people.


No songs section for this post.

 

To the “subscribers” of this blog

This post is being written entirely on-the-fly.


I have over some period of time observed that far too many of the subscribers of this blog (may be more than half of them) actually are/should be fake accounts.

But, as you perhaps might know, I have been, say, “follow-up”ed for a somewhat longer length of a time—and, with those “followers” never having to have had created any email account any-where, to be able to “follow-up” on me—in real life, too.

So, being “follow-up”ed, but without causing immediate trouble in my immediate life/surroundings, was a bit of a curiosity for me, and so, I tolerated them—these recent email IDs, so to speak.

No, not with a sense of amusement, but with that of keeping them, as they say, “under observation.”


Anyway, as to the non-authentic ones:

I invite these “subscribers” to get themselves off, silently if they prefer, but very certainly—and, very immediately.

[Yes, they may “post” their “protests” in the forms that are able to more silently hit me in ways more than just a few postings here and there on the ‘net. I don’t care, any longer.

Neither about these account “creators”, nor even about those who are (and were) skeptical about what such forms could possibly be—even if I wrote about such forms honestly.]

But for those among my “subscribers” who are willingly to unsubscribe from this blog, I shall give them a time-period, of until:

2 \text{April\ } 2018  - \epsilon \text{\ IST\ }

where (\epsilon \rightarrow 0) is: what even an idiot who has never studied beyond XI/XII science would be able to tell them—or, should be.

In other words, the Fool’s Day is their last day, as far as this blog of mine is concerned.


In other words, I “promise” to grant them a personal pardon that if they do wind themselves up, off my blog, in the due time-limit.

… No, I don’t expect them to do that. …

But if not, I shall do the latter for them.


[… No, never ‘been afraid of an extra bit of a work, ever in my life. …]


A Song I Like:

(Hindi) “kitnaa pyaaraa waadaa hai in matwaali aankhon kaa…”
Music: R. D. Burman
Singers: Mohamad Rafi, Lata Mangeshkar
Lyrics: Majrooh Sultanpuri

 

HNY (Marathi). Also, a bit about modern maths.

Happy New (Marathi) Year!

OK.

I will speak in “aaeechee bhaashaa”  (lit.: mother’s language).

“gudhi-paaDawyaachyaa haardik shubhechchhaa.” (lit.: hearty compliments [on the occasion] of “gudhi-paaDawaa” [i.e. the first day of the Marathi new year  [^]].)


I am still writing up my notes on scalars, vectors, tensors, and CFD (cf. my last post). The speed is good. I am making sure that I remain below the RSI [^] detection levels.


BTW, do you know how difficult it can get to explain even the simplest of concepts once mathematicians have had a field day about it? (And especially after Americans have praised them for their efforts?) For instance, even a simple idea like, say, the “dual space”?

Did any one ever give you a hint (or even a hint of a hint) that the idea of “dual space” is nothing but a bloody stupid formalization based on nothing but the idea of taking the transpose of a vector and using it in the dot product? Or the fact that the idea of the transpose of a vector essentially means nothing than more than taking the same old three (or n number of) scalar components, but interpreting them to mean a (directed) planar area instead of an arrow (i.e. a directed line segment)? Or the fact that this entire late 19th–early 20th century intellectual enterprise springs from no grounds more complex than the fact that the equation to the line is linear, and so is the equation to the plane?

[Yes, dear American, it’s the equation not an equation, and the equation is not of a line, but to the line. Ditto, for the case of the plane.]

Oh, but no. You go ask any mathematician worth his salt to explain the idea (say of the dual space), and this modern intellectual idiot would immediately launch himself into blabbering endlessly about “fields” (by which he means something other than what either a farmer or an engineer means; he also knows that he means something else; further, he also knows that not knowing this fact, you are getting confused; but, he doesn’t care to even mention this fact to you let alone explain it (and if you catch him, he ignores you and turns his face towards that other modern intellectual idiot aka the theoretical physicist (who is all ears to the mathematician, BTW))), “space” (ditto), “functionals” (by which term he means two different things even while strictly within the context of his own art: one thing in linear algebra and quite another thing in the calculus of variations), “modules,” (neither a software module nor the lunar one of Apollo 11—and generally speaking, most any modern mathematical idiot would have become far too generally incompetent to be able to design either), “ring” (no, he means neither an engagement nor a bell), “linear forms,” (no, neither Picasso nor sticks), “homomorphism” (no, not not a gay in the course of adding on or shedding body-weight), etc. etc. etc.

What is more, the idiot would even express surprise at the fact that the way he speaks about his work, it makes you feel as if you are far too incompetent to understand his art and will always be. And that’s what he wants, so that his means of livelihood is protected.

(No jokes. Just search for any of the quoted terms on the Wiki/Google. Or, actually talk to an actual mathematician about it. Just ask him this one question: Essentially speaking, is there something more to the idea of a dual space than transposing—going from an arrow to a plane?)

So, it’s not just that no one has written about these ideas before. The trouble is that they have, including the extent to which they have and the way they did.

And therefore, writing about the same ideas but in plain(er) language (but sufficiently accurately) gets tough, extraordinarily tough.

But I am trying. … Don’t keep too high a set of hopes… but well, at least, I am trying…


BTW, talking of fields and all, here are a few interesting stories (starting from today’s ToI, and after a bit of a Google search)[^][^] [^][^].


A Song I Like:

(Marathi) “maajhyaa re preeti phulaa”
Music: Sudhir Phadake
Lyrics: Ga. Di. Madgulkar
Singers: Asha Bhosale, Sudhir Phadke