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
Singer: Mohammad Rafi [Some beautiful singing here…]

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Work Is Punishment

Work is not worship—they said.

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

One that is to be smilingly borne.

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…

.

/

An update on my research

28th February is the National Science Day in India.

The story goes that it was on this day (in 1928) that C. V. Raman discovered the effect known by his name.

I don’t believe that great discoveries like that are made in just one single day. There is a whole sequence of many crucially important days involved in them.

Yes, on this day, Raman might have achieved a certain milestone or made a key finding regarding his discovery. However, even if true in this case (which I very much doubt), it’s not true in general. Great discoveries are not made in a single day; they are usually spread over much longer span of time. A particular instant or a day has more of just a symbolic value—no matter how sudden the discovery might have looked to someone, including to the discoverer.

There of course was a distinguished moment when Kekule, in his famous dream, saw a snake swallowing its own tail. However, therefore to say that he made the discovery concerning the ring structure of the benzene molecule, just in a single moment, or in a single flash of imagination, is quite a bit of a stretch.

Try it out yourself. Think of a one-line statement that encapsulates the findings of a discovery made by a single man. Compare it with another statement which encapsulates any of the previous views regarding the same matter (i.e., before this discovery came along). This way, you can isolate the contributions of a single individual. Then analyze those contributions. You would invariably find that there are several different bits of progress that the discovery connected together, and these bits themselves (i.e., the contributions made individually by the discoverer himself) were not all discovered on the same day. Even if a day or an hour is truly distinctive in terms of the extent of progress made, it invariably has the character of taking an already ongoing process to a state of completion—but not of conducting that entire process. Mystical revelation is never a good metaphor to employ in any context—not even in the spiritual matters, let alone in the scientific ones.

Anyway, it’s nice that they didn’t choose Raman’s birth-day for this Day, but instead chose a day that was related to his most famous work in science. Good sense! And easy to remember too: 28-02-’28.

Let me celebrate this year’s Science Day in my own, small, personal way. Let me note down a bit of an update on my research.

1. I have had a bit of a correspondence, regarding my new approach, with a couple of physicists. Several objections were made by them, but to cut a long story short, neither seemed to know how to get into that mode kind of thinking which most naturally leads to my main thesis, and hence helps understand it.

The typical thought process both these physicists displayed was the one which is required in finding analytical solutions of problems of a certain kind, using an analysis of a specific kind. But it is not the kind of thought process which is typically required in the computational modeling of complex phenomena. Let me remind you that my theory is nonlinear in nature. Nonlinearity, in particular, is best approached only computationally—you would be hopelessly out of your wits if you try to find analytical solutions to a nonlinear system. What you should instead pursue is: thinking in terms of the following ingredients: certain objects, an algorithm to manipulate their states, and tracing the run-time evolution of the system. You try this algorithmic way of thinking, and the whole thing (I mean understanding the nature of a nonlinear system) becomes easy. Otherwise, it looks hopelessly complicated, incomprehensible, and therefore, deeply suspicious, if not outright wrong. Both the physicists with who I interacted seemed to be thinking in terms of the linear theory of QM, thereby restricting their thought modes to only the traditional formalism based on the abstract Hilbert-spaces and linear Hermitian operators. Uh oh! Not good. QM is fundamentally nonlinear; the linear formulations of QM are merely approximations to its true nature. No matter how analytically rigorous you can get in the traditional QM, it’s not going to help you understand the true nature of quantum phenomena, simply because a linear system is incapable of throwing much light on the nonlinear system of which it is an approximation.

I believe it was out of this reason—their continuing to think in terms of linear systems defined over hyperspaces and the operator algebra—that one of them raised the objection that if $\Psi$ in MSQM (mainstream QM) is defined on a $3ND$ configuration space, how come my $\Psi(x,t)$ could be defined over the physical $3D$ space. He didn’t realize, even after I supplied the example of the classical $N$-particle molecular dynamics (MD) simulations, that using an abstract higher-dimensional space isn’t the only viable manner in which you can capture the physics of a situation. (And I had indicated right in the Outline document too, that you first try to understand how a Newtonian evolution would work for multiple, charged, point-particles as in classical physics, and only then modify this evolution by introducing the system wavefunction.)

I came to gather that apparently, some people (who follow the Bohmian mechanics doctrine) have tried to find a $3ND \leftrightarrow 3D$ correspondence for a decade, if not more. Apparently, they didn’t succeed. I wonder why, because doing so should be so damn straight-forward (even if it would not be easy). You only have to realize that a configuration space refers to all possible configurations, whereas what an evolution over a $3D$ physical space directly deals with is only one initial configuration at a time. That is what specifying the ICs and the BCs does for you.

In case of MD simulations, you don’t define a function over the entire $3ND$ configuration space in the first place. You don’t try to produce an evolution equation which relies on only those kinds of operators which modify all parts of the entire hyperspace-function in one shot, simultaneously. Since you don’t think in such hyperspace terms in the first place, you also don’t have to think in terms of the projection operators bringing the system dynamics down to $3D$ in particular cases either. You don’t do that in the context of MD simulations, and you don’t do it in the context of my approach either.

This physicist also didn’t want me to say something using analogies and metaphors, and so I didn’t mention it to him, but I guess I can use an analogy here. It will allow even a layman to get a sense of the issue right.

This physicist was insisting on having a map of an entire territory, and was more or less completely dismissing my approach on the grounds that I only supply the surveying instruments like the theodolite and the triangulation algorithm. He expected to see the map—even when a theory is at a fledgling stage. He nevertheless was confident that I was wrong because I was insisting that each physical object in the actual territory is only at one place at any given instant, that it is not spread all over the map. This analogy is not exact, but it is helpful: it does bring out the difference of focusing on only the actually followed trajectory in the configuration space, vs. an insistence on using the entirety of the configuration space for any description of an evolution. But that guy didn’t get this point either. And he wanted equations, not analogies or metaphors.

Little wonder they have not been successful in finding out what logical connection there is between the abstract $3ND$ hyperspace on the one hand, and the $3D$ physical space on the other hand. Little wonder they don’t progress despite having worked on the problem for a decade or so (as this guy himself said).

Yeah, physicists, work harder, I say! [LOL!]

2. Apart from it all—I mean all those “discussions”—I have also realized that there are several errors or confusing explanations in the Outline document which I uploaded at iMechanica on 11th February 2019. Of course, these errors are more minor in nature. There are many, many really important ideas in that document which are not in error.

The crucially important and new ideas which are valid include, just to cite a few aspects: (i) my insistence on using only those potentials that are singularly anchored into the point-particle charges, (ii) the particular nonlinearity I have proposed for the system evolution, (iii) the idea that during a measurement it is the Instrument whose state undergoes a cascade of bifurcations or catastrophic changes, whereas the System state essentially remains the same (that there is no wavefunction collapse). And, many, many other ideas too. These ideas are not only crucial to my approach but they also are absolutely new and original. (Yes, you can be confident about this part, too—else, Americans would have pointed out the existing precedence by now. (They are just looking to find errors in what(ever) I say.)) All these ideas do remain intact. The confusing part or the one having erroneous statements indeed is more minor. It concerns more with how I tried to explain things. And I am working on removing these errors too.

I have also come to realize that I need to explicitly give a set of governing equations, as well as describe the algorithm that could be used in building the simulations. Yes, the physicist had asked me for an evolution equation. I thought that any one, given the Schrodinger equation and my further verbal additions / modifications to it, could easily “get” it. But apparently, he could not. So, yes, I will explicitly write down the evolution equation for my approach, as an equation that is separate from Schrodinger’s. In the next revision of the document (or addition to it) I will not rely on the only implicitly understood constraints or modifications to the TDSE.

3. There also are some other issues which I noticed entirely on my own, and I am working on them.

One such issue concerns the way the kinetic energy is captured in the MSQM vs. how my approach ought to handle and capture it.

In MSQM, the kinetic energy consists of a sum of 1-particle Laplacian operators that refer to particle coordinates. Given the fact that my approach has the wavefunction defined over the $3D$ space, how should this aspect be handled? … By the time I wrote my Outline document (version 11 February 2019), I had not thought a lot about the kinetic energy part. Now, I found out, I have to think really deep about it. May be, I will have to abandon the form of Schrodinger’s equation itself to a further extent. Of course, the energy analysis will progress on the same lines (total energy = kinetic + potential), and the de Broglie relations will have to be honored. But the form of the equation may turn out to be a bit different.

You see, what MSQM does is to represent the particles using only the $\Psi(x,t)$ field. The potential energy sure can be constructed in reference to a set of discrete particle positions even in MSQM, but what the $\hat{V}$ operator then yields is just a single number. (In case of time-dependent potentials, the value of this variable varies in time.) The multiplication by the hyperspace-function $\Psi(x,t)$ then serves to distribute this much amount of energy (that single number) over the entire hyperspace. Now realize that $|\Psi(x,t)|^2$ gives the probability. So, in a way, indirectly, even if you can calculate / compute the potential energy of the system starting from a certain set of particle positions, in the MSQM, you then have to immediately abandon them—the idea of the discrete particles. The MSQM formalism doesn’t need it—the particle positions. You deal only with the hyperspace-occupying $\Psi(x,t)$. The formulation of kinetic energy also refers to only the $\Psi(x,t)$ field. Thus, in MSQM, particles are ultimately represented only via the $\Psi(x,t)$ field. The $\Psi(x,t)$ is the particles.

In contrast, in my approach, the particles are represented directly as point-phenomena, and their positions remain significant throughout. The $\Psi(x,t)$ field of my approach connects, and causally interacts with, the particles. But it does not represent the particles. Ontologically, $\Psi(x,t)$ is basically different from particles, even if the background object does interacts with the particles. Naturally, why should I represent their kinetic energies via the Laplacian terms? … Got the idea? The single number that is the kinetic energy of the particles, need not be regarded as being distributed over the $3D$ space at all, in my approach. But in 11th February version of the Outline document, I did say that the governing equation is only Schrodinger’s. The modifications required to be made to the TDSE on account of the kinetic energy term, is something I had not even thought of, because in writing that version, I was trying focusing on getting as many details regarding the potential energy out as possible. After all, the nonlinear nature of QM occurs due to the potential term, doesn’t it?

So, I need to get issues like these straightened out too.

… All in all, I guess I can say that I am more or less (but not completely) done with the development concerning the spin-less 1-particle systems, esp. the time-independent states. So far, it seems that my approach does work fine with them. Of course, new issues continue to strike me all the time, and I continue finding answers to them as well—as happens in any approach that is completely new. New, right from the stage of the very basic ideation  concerning what kind of objects there should be, in the theory.

I have just about begun looking into the (spin-less) multi-particle states. That is the natural order in which the theory should progress, and my work is tracing just this same path. But as I said, I might also be revising some parts of the earlier presented theory, as and when necessary.

4. I also realized on my own, but only after the interaction with the physicists was already over, that actually, I need not wait for the entire multi-particle theory to get developed before beginning with simulations. In fact, it should be possible to handle some simple 1-particle $1D$ cases like the particle in a box or the QHO (quantum-mechanical oscillator) right away.

I plan to pursue these simulations right in the near future. However, I will not be able to complete pursuing all their aspects in the near future—not even in the simple cases involving just $1D$ simulations. I plan to do a preliminary simulation or two, and then suspend this activity until the time that I land a well-paying job in data science in Pune.

No songs section this time because I happened to post several entries almost back to back here, and in the process, I seem to have used up all the songs that were both new (not run here before) and also on the top of my mind. … May be I will return later and add a song if one strikes me easily.

Bye for now, and have a happy Science Day!

Minor editing may be done later today. Done by 20:15 hrs the same day.

/

What would a Platonic Word be like?

What would a Platonic Word be like?

Here, “Word” refers to the Microsoft Word—the software. The adjective “Platonic” applies to the software itself (i.e., to the software proper, as apart from the people developing, marketing, or even using it).

The occasion that raised this question in my mind, was an article by Edward Mendelson in The New York Review of Books. Though connecting philosophy with technology, this article thankfully was not about quantum mechanics/computing, but about the mundane “software instruments for writing.” Prof. Abinandanan of the “nanopolitan” blog highlighted this article yesterday, and I immediately found it interesting. I also wrote a rapid comment at that blog. What I will do here is to post an expanded and edited version of my comment. In fact, I seem to have already begun doing that. If you are interested, see Abi’s post (just an excerpt) and my comment, here [^]. And, do make sure to go through the original article. [^]

About the NYRB article: You can make it out, way before finishing this article, that it’s been written by someone who seemingly is quite used to writing very well, in a cultured and refined manner, even in a persuasive sort of a way. When I wrote my comment, I hadn’t checked who the author was. Turns out that he is Professor in the Humanities, at Columbia [USA]. Hmmm…

….Anyway, getting back to the issue, here is what Abi highlighted from that article:

The original design of Microsoft Word, in the early 1980s, was a work of clarifying genius, but it had nothing to do with the way writing gets done. The programmers did not think about writing as a sequence of words set down on a page, but instead dreamed up a new idea about what they called a “document.” This was effectively a Platonic idea: the “form” of a document existed as an intangible ideal, and each tangible book, essay, love letter, or laundry list was a partial, imperfect representation of that intangible idea.

A document, as Word’s creators imagined it, is a container for other ideal forms. Each document contains one or more “sections,” what everyone else calls chapters or other subdivisions. Each section contains one or more paragraphs. Each paragraph contains one or more characters. Documents, sections, paragraphs, and characters all have sets of attributes, most of which Word calls “styles.” […]

This was more than enough to get me curious. But while going through the article, I obviously couldn’t even directly connect Platonism with MS Word, let alone attribute the former to the latter. So, I tried to find the actual cause—the software idiosyncrasy that might have supplied the motivation to connect the two. And, sure enough, I found this one:

Word, it seems, obeys the following rule: when a “style” is applied to text that is more than 50 percent “direct-formatted” (like the italics I applied to the magazine titles), then the “style” removes the direct formatting.

Aha! So that did it!!

So here is how the argument essentially goes: Word does something crazy (many would say “as usual”); the user can’t see how to get around the programmer’s quirky mind; and since the software wouldn’t yield to the user and since its intended usage-metaphor clearly involves a hierarchical organization, therefore, its designer must be Platonic.

The root of a technical problem like this one, lies in the fact that a software for writing must carry two classes of mark-ups: (i) those for a logical division of the write-up (e.g. that it would be a document to be hierarchically divided into parts, chapters, sections, etc.), and (ii) those for controlling the graphical look and feel of the output, or, the “style” of formatting.

The real trouble occurs because both these elements can simultaneously operate on the same textual matter. In the event that they do, then, the issue becomes: how the software resolves the conflict.

The TeX and its derivatives (e.g. LaTeX) take one extreme end of the possible positions. In their case, the logical division reigns supreme. It completely controls the graphical (or stylistic) attributes. (At least in the original design, it does. But then, Knuth also introduced a Turing-complete scripting language in it, which means you can play havoc within or with LaTeX! [(PDF)^])

Certain other packages in the past took the other extreme position: there was almost no provision for any logical mark-up at all. For instance, the early WordStar had only stylistic mark-ups: Ctrl-K+B for bold, and Ctrl-K+S for underlining, etc., but none for marking a section or a sub-section. The up-side is that you are not tied into a rigid hierarchy of document–sections–sub-sections, etc. The logical format is yours to design as you go about doing your writing, and as you wish—if you wish, that is. The downside is that the user has to make sure to separately apply the same formatting again and again to each section-heading or paragraph-heading. Mistakes are likely in performing this kind of a repetitive task.

HTML vs XML provide a later and clearer example of this logical vs stylistic mark-ups. HTML 1.0 had only stylistic markups, and XML has always had only the logical division mark-ups.

You might think that the issue is simple enough. Just begin only with the logical mark-up (say an XML document), ask the user to supply the logical-to-graphical mapping (say via style sheets), and be done with it. That is the one-way logical-to-stylistical model. Let’s call it the LaTeX model. But it doesn’t always work that way. Not in the real world.

The LaTeX model obviously fails in the humanities:  what if a poet wants to have one empty line separating the stanzas in general, but at only one special place, he would deliberately like to leave, say, two empty lines before the next line of  verse appears, just for some dramatic impact? What if he wants to have separate formatting for only some of his foot-notes, not all?

And, have you seen the kind of resumes that LaTeX produces when a common template is enforced on every one?  Have a look [^].

The LaTeX model often fails also in the S&T fields themselves, though people don’t as often talk about it. About the only place where it works well is in mathematics. But students from science and engineering always run into the rigidity of the LaTeX model while writing thesis. Suppose you want to open a chapter with a brief remark or just one prerequisite equation, before getting into the main sections of the chapter. Should you then give those opening lines a separate section number all by itself? If so, then its importance gets unduly promoted in the table of contents: here is this one-line section, and then there are those 8, 10 or even 30 page sections, and all of them get placed on an equal footing. It looks odd. On the other hand, if you don’t give that one line or brief remark a section number, then it finds no place in a quick glance, and so, you invite a suspicion about its omission. Ideally, you would like to have a minor kind of special formatting for this introductory remark. What should you do? If you apply the sub-sub-section style, it generates empty section and sub-section numbers, too, which again looks bad. Students then get away either by dropping any formatting for it, or, in LaTeX, they use the starred styles (which eliminate numbering), but going away from the standard LaTeX usage does leave them with a bit of an uncomfortable feeling. And, there is more. The part/chapter/section/etc. numbers imply a strictly linear reading order, whereas the actual connections among these elements may be more like a graph. Or, an expanding spiral. Etc.

So, the issue is not as simple as it seems. The one-way street from the logical to the stylistic mapping, as in the LaTeX model, does not meet all the usage scenarios even in the S&T fields. The software design therefore must allow additional stylistic mark-ups, and then, the introduction of this additional facility creates conflicts like the one the author highlighted.

The commercially most successful packages (e.g. Adobe and Mac products, and MS Word) therefore have chosen to explore the entirety of the space in between these two extremes, but sometimes their particular heuristics are not at all obvious to any one. The author points out one particularly bad example with certain version(s) of Word. No other package would do something like what he points out. (Not even Microsoft Bob!)

But, frankly, even though the author displays a seemingly good command of the philosophy of Platonism, I don’t quite see how it applies as an explanatory basis for this aspect of software packages.

Does the existence of a hierarchical organization in a document by itself imply Platonism? If the LaTeX model fails, then should the software designer completely do away with any logical formatting? And, if so, would an absence of any logical hierarchy thereby make it a Subjectivist software? Why is WordStar or WordPerfect not a  Hedonistic software?

Can we ascribe a general philosophy to a piece of software, simply because there seems to be some resemblance between certain features of a philosophic system and the  abstract design or mode of usage of the software?

Can we ascribe a philosophy to a product of technology?

The answer tends to become obvious when you try to place the issue in a broader context and raise questions like I just raised: Why is WordPerfect not a Hedonistic software? And, more questions:

What would an Intrinsicist Word be like? … Or to make it easier for those who haven’t studied philosophy: What would a Subjectivist Word be like?

… And, to make it easier for those who have studied philosophy: What would a Kantian Word be like? An Aristotlean Word? An Objectivist Word?

And then, what would a Mystic computer be like? An Altruistic train engine? A Collectivist vacuum cleaner?

Is it possible to ascribe a particular philosophy to a product of technology? to a technology? to a branch of engineering? to a science? to physics?

As far as my position goes, the common to answer all such questions is: “no.” … There can’t be an Objectivist Physics, for example.

Which then suggests another set of questions:

Does philosophy have any connection at all with any of the STEM fields? Can it have one? If not, then then isn’t it really speaking just an extraneous nuisance, of no practical significance?

In short, if there can’t be a Feminist iPhone charger then why would any one in California need philosophy?

* * * * *   * * * * *   * * * * *

A Song I Like:

(Marathi) “man pisaaT maajhe aDale re…”
Lyrics: N. G. Deshpande
Singer: Krishna Kalle
Music: Yashwant Deo

[E&OE]

An idea for the final year student projects in CS departments

In this post, let me jot down an idea that is suitable for a final year project by the CS/IT undergraduates (or, in a suitably expanded form, also by the CS/IT post-graduates) in engineering schools. Or, students from other similar courses like the MCA, MSc (CS) etc. The idea is (to me) neat and useful, and not at all difficult to implement. Do consider it in place of those usual topics like railway reservation/airline booking system, payroll system, etc.

The idea is to create an online searchable database of the history of science topics, that gives out customized timelines as query outputs or reports over the ‘net.

The idea occurred to me while doing literature search for my book. (BTW, idiots in those humanities departments degrade the word “research,” by using it for such things as plain literature search. The management and marketing folks do worse: they call activities like the Gallup polls, “research.”)

So long as a time-line involves only tens of items, it is easy to manage its contents manually. As an example of a small time-line, see my previous blog post. (In fact, I got the items in that time-line in an almost fully ready-made form from Manjit Kumar’s book: “Quantum.”)

However, while preparing for the pre-requisites part of my planned QM book, I found that no suitable time-line existed in a ready-made form for those classical physics topics.

One reason is that the pre-requisites of QM are so very many and so very diverse. For a neat visualization of physics as it existed some 70 years ago, see the “1939 map of physics”[^].

Another reason is that the sources of the detailed historical accounts are, again, so very numerous, and not all of them are equally accurate, authentic, or detailed.

While accuracy and authenticity are important, as far as the design work for this particular project goes, I think that the issue of the non-uniformity of the available details is of much greater importance.  The original sources of information themselves are not equally detailed.  For instance, see the Wiki timeline on the luminiferous aether [^], and ask yourself: would any one of the Encyclopedia Britannica’s timelines concerning the aether ever be as detailed as this one?

Of course, the administrators of the database may not rely only on the existing timelines. They may consult books to feed the data to create more detailed timelines. Once again, issues like the unevenness of details and the matter of ascribing proper dates at a detailed level, come up.

For instance, consider the Fourier analysis. Most books mention 1822 as the date of its beginning. It’s wrong.

We don’t have any specific record to answer the question of the precise time when Fourier first thought of this idea of spectral decomposition. However, we do have some evidence which indicates that he began working on the problem of heat propagation in solid bodies as early as 1804, and that he had presented a paper on this topic to the Paris Institute as early as on 21st December 1807. Though Fourier wanted to publish the paper in print, he didn’t (or perhaps couldn’t) do so, because it ran into some criticism. (Off hand, I would suppose, from Poisson.) Fourier had only the sines, not also the cosines, in that first 1807 paper of his. Though important, relatively speaking, it’s a minor omission. What is more important is the fact that he had already had the big idea right, viz. that any arbitrary function could be expanded as (possibly an infinite) series. Now the funny thing is this. While Fourier didn’t know the necessity to include the cosines, neither did his critics. They were rather against the completeness aspect of his idea, viz., that any arbitrary function could be expanded in this way, even the discontinuous functions. On that count, he was on the right track. However, it was hard to convince the established critics. One way or the other, the paper didn’t get published that same year. He sent a revised draft to a competition of the French Academy in 1811, and won it.  The critics, however, still were not satisfied. Fourier ultimately wrote and published the further revised account some 15 years later, in 1822.

Most books will tell you that the Fourier analysis began in 1822. However, unless you take into account the 1804–1807 genesis of this branch of analysis, the overall historical progression does not appear as smooth as it should be.

The question then becomes, in a time line, what date would you include for reporting? 1804? 1807? 1811? 1822? All the four?

Some cases are even more intriguing, and possibly of more than trivial interest to a researcher. For instance, consider Schrodinger’s formulation of quntum mechanics. His very first paper (written in January 1926) is concerned about the famous non-relativistic wave equation, now bearing his name. Yet, even before that very first paper was written, in fact barely just a month before, in December 1925, Schrodinger had initially worked on a relativistic wave equation. It doesn’t work fully satisfactorily, and so Schrodinger worked out the non-relativistic version before sending it out for publication. But wouldn’t the fact that Schrodinger had those relativistic ideas right in the last month of 1925, be important while tracing the development of the relativistic QM? After all, physicists in that era were unusually open in their communications and collaborations. For example, Pauli had begun working on his paper merely on the basis of a draft of Heisenberg’s paper. (I mean the manual draft as well as detailed physics notes Heisenberg exchanged with him—not even the printer’s proofs let alone what today we would call the preprint.) Similarly, Pauli’s (1924?) idea regarding a two-valued quantum number was known to Goudsmit and Uhlenbeck when they proposed the electronic spin (October, 1925).

Should such details be entered into the database? Should there be an attribute specifying the granularity of information that is being carried by a database entry? Should the queries allow various levels of granularities to be included in the search results?

And, going back to Fourier’s case, suppose that your database initially includes an entry for only one of the three dates (1804—1807, 1811 and 1822). Someone points out the other dates to you (i.e. to the system administrators populating the database) only later on. How would you allow for the conciliations of data items like these, in a mechanical sort of a way? What software mechanism would you provide?

Would you handle it via some attributes of the individual entries  in the database? Would these attributes be finalized beforehand, say a pre-determined set like: “Initial Idea/Presentation/Publication/Revision” etc? Or would it be possible and desirable to keep the set of such attributes extensible—say, on lines similar to how you apply attributes or tags to your blog posts, complete with an intellisense feature that shows the already applied attributes? Can the overall structure thus be kept a bit fluid? Is a relational database the optimal data structure, given such objectives? How about the queries on it? Should they be sensitive only to the attributes, or to the “full text”?

I think these are just some of the questions that the students will themselves have to handle. Here, all that I am now going to do is to give some idea of how the usage scenarios would look like. In my description here, I will use the terms like database etc., but only in a broad sense—it doesn’t necessarily mean a traditional data structure like the relational database.

First, there will be a set of users who will populate the database using appropriate sources. They will have the authority to edit the database, and may be called system administrators. The database may sit on a remote secure Web server. The sys admins should be able to use, say, secure http-based (i.e. https-based) forms to edit the database, i.e. to add/modify/delete the entries.

Then there will be the end-users. The end-users should be able to access the database using plain http. Typically, they will use a user-friendly form to send their queries to the server over plain http, and get answers as reports consisting of Web pages. [More on this, in my next post.]

The database will, at the minimum, have information on the following attributes. (If this were an RDBMS, it will have the following as fields or columns): date, scientist, work, remarks, source reference (for the database entry—not the citation record itself), subject areas to which the entry belongs. Many of these attributes are tricky.

There are multiple meanings of “date” in a context like this. Some historical sources give dates only in years, others also in months, still other right up to the day and the time. For some advances, the dates are known only vaguely. For example: “He began working on it during the late 1820s, and continued up to 1826-end” or “fl. 1810s”, or “circa 3rd quarter of 1925”. The calender systems may have changed. Then, there are those BC dates. (Not all database software handle all the dates very smoothly anyway.) Sometimes, the date a scientist sent his manuscript may be more important than when it was published, but not always. Sometimes, the published accounts may be somewhat misleading: Newton did get the basic ideas of calculus right during that plague-related vacation, around 1666. Yet, it also is a fact that he still was working on many of the important calculus ideas in the few years before the publication in 1687 of the Principia. Newton didn’t have everything ready right in 1666, contrary to many stories you might have heard. (There has been a tendency to ascribe too much of a genius to the years of the early youth; wit a dim-wit like Hammings—dim-wit, when it comes to the age at which scientists created their best original ideas.)

The database must store the precise way the date was stated in the original sources. Yet, when a user sends in a query, regardless of the specific original recording, it should still be possible to sort out all the entries, with a certain smartness built into the system. The student will have to resolve the issue of how to put all the entries in (some sort of an) order—vague entries like “in the decade prior to the I WW” together with the more precise entries like “in the afternoon, after lunch, on October 7, 1900.” (Anyone knows what’s special with that time? I would be delighted to know from you!)

As far as this problem of sorting of entries of varying degrees of precision of time-specification is concerned, I do have an idea how it could be done. However, I would rather let the students try to work on it. [OK, I promise to give some hint in my next post on the topic.]

The “scientist” field may undergo changes. A plain guy like Thomson is the same as (the first Baron/Lord) Kelvin (after whom the temperature scale is named). “Snellius” is the same guy as Snell (of the laws of optics). A real gauntlet to us in the 21st century was thrown by a single Swiss family: There is a Daniel who, being one of a family, carries the same last name as Jacob, who is the same as Jakob is the same as Jacques is the same as James.  It doesn’t end there. Johann, is the same as John is the same as Jean, but different from James. And then, there are Johann-II and also Johann-III. Worse: Sometimes they had a feud in the open. The famous brachistochrone problem was posed because one brother tried to show the other brother down. (The other brother succeeded, together with Lebniz and his credits-wise adversary, the “lion’s paws”-bearing Newton.) There has been a son in that family who thought his father had taken credit really due to him. The point? Your user should not get confused, and should be given all the relevant information as to which Bernoulli it was.

Some users may be interested in getting a time-line of all the works of just “Newton.” Others may wish to access a similar information for “Isaac Newton, Jr.” … Yes, the falling apple guy was named after his father, though few people know it, and even fewer (if ever) add the “Jr.” suffix to his name. A more likely search string, especially if originating from a tiny island lying above France and to the west of, say, Finland, might be: “Sir Isaac Newton.”

The “work” field needs to have both succinct information (so that the idea of a time-line or an Excel spreadsheet like report makes sense), but also a place for additional informative details. For instance, less known or less advertised factoids like the fact that Leibniz didn’t originate the idea of the “vis viva,” but was inspired by its descriptions in Huygens’ writings. The additional details should perhaps be supplied only in a more verbose report, but the point is that the database itself should be well-designed that there is a systematic and unambiguous way to tell such things if the need be.

The subjects attributes is important. It identifies all the subject areas in which a given advance of science falls. It will enable the end-user to run subject-specific queries. For example, a query like: “Give me a time-line of the kinetic theory,” which is slightly different from “Give me a time-line of the statistical mechancis,” which is slightly different from “Give me a time-line of the thermodynamics.” Contrary to the current pedagogy followed in the engineering schools, development in statistical mechanics was almost concurrent to thermodynamics. … Incidentally, thermodynamics didn’t exactly begin with Joule. It had sprung into action right after Watt’s engine, with Lazare Carnot, the father of Sadi Carnot, having a lot of thoughts related to the energetics program in physics. In case you have ever wondered how come the Second Law of Thermo came on the scene before the First one did, such a bit might be of interest to you.

Thus, the subject attributes may be both coarse-grained or fine-grained, and they may have multiple abstract hierarchies among them. The system administrators may invite subject experts (e.g. professors) to apply these attributes. This task, though complex and time-consuming, should not too difficult in a way: the attributes to use may come from certain standardized classification schemes such as the PACS classification [^], the AMS classifications [^], etc. What is more important for this project on the CS side is this requirement: the application mechanisms of subject attributes should be sufficiently neat that the application people—the subject experts—should find it very easy to find all the relevant attributes suggested to them in a handy way, when they apply these attributes to the individual entries.

As indicated above, one real tricky point is this: Some discoveries/inventions span across fine-grained descriptions. Another tricky point is the following: Some discoveries span across many fine-grained description only in the context of a later discovery—not otherwise. Therefore, they should not get applied for reports-generation unless the later discovery also is included in the search results. For instance, consider the topic of Fermat’s principle. This is a from classical, geometric, optics. It would not have been a potentially very important candidate for inclusion in mechanics-related searches until Schrodinger made it impossible to avoid it. … Actually, the idea of looking at Fermat’s principle as a mechanical principle goes centuries back; off-hand, I suppose it was Huygens (again), right in the 17th century, who first linked the mechanics of transfer of momentum (he would call it “the motion”) and Fermat’s principle. Then, in the 19th century, there was Hamilton who got inspired by the same conceptual link. But the point here is, before Schrodinger, not identifying the topic as a mechanical one, could, perhaps, have been an excusable omission. After Schrodinger, it is entirely inexcusable.

Each entry should clearly and explicitly identify the source(s) of the information on which it is based. For instance, McTutor’s, Encl. Brit., a certain book, a certain paper, etc. There could be multiple original sources objectively required for the same entry. For instance, when a subject expert rightly ascribes to Euler the impetus provided for development of the calculus of variation (CoV), he would need to take it away from Maupertuis, and for the same reason, he would need original sources authored by both.

BTW, this entry (on the impetus to CoV) would be different from another entry that is concerned with the first correct formalization of the CoV, which would involve a 19-year old Lagrange. And, both these entries would be different form the first-ever problem of CoV correctly posed and applied with correct a correct solution approach, which would be a credit due in (off-hand speaking, a 50+ year-old) Newton’s account (more than a century before Lagrange’s work).

Thus, the individual database entries should carry links to other, related, entries. Such things may come in the Remarks section, or there could be a special “See Also” section.

On the second thoughts, there could an extra attribute (to be carried by a database entry) for specifying the set of pre-requisite entries for it.

Further on the second thoughts, there could also be another, separate attribute that specifies a linkage to the other entries immediately preceding it and constituting the “prior development” for a given entry. (The prior development is not necessarily the same as a pre-requisite. For instance, the caloric fluid theory of heat is a prior development to the kinetic theory, but it’s not a pre-requisite.)

All the report fields may carry hyperlinks to the resources on the ‘net.

It might be desirable to include other information like the biographical details for scientists: dates (!) of birth and death, places thereof, nationalities (e.g. Prussia, West Germany, United Germany, etc!), educational institutions attended and degrees, if any, received, the career-wise affiliating institutes for each database entry.  (Consider: would the work as a patent clerk qualify as an affiliating institute for a discovery in physics?) Details like these are not so important, and may be taken up during the version 2.0 of the project.

Finally, I would like to jot down a couple of resources. Informations from multiple sources like these needs to come together in a single, easily accessible database:

The McTutor Chronology [^]
The Wiki List of Timelines [^] (We need only the S&T related timelines. For version 1.0, focus only on physics and mathematics. For version 2.0, add: inventions/patents, engineering and technology. For version 3.0, add: biological sciences. For history of the humanities kind—who killed who to grab which power when and had how many wives—my advice to you would be: don’t bother.)

Now, a few things of business, if you are interested in picking this up as a project.

Don’t get in touch with me simply to ask if you can use this idea. Of course you can, so long as you acknowledge the intellectual credit due to me, and so long as you don’t release this idea into the Open Source/CopyLeft sort of a domain, and so long as you are not going to make any money out of it—I reserve all the rights to this idea in the first place.

However, do drop me a line before you begin any work on this idea. To repeat, I do reserve all the rights to this idea in the first place.

Also, if you are a student, don’t get in touch with me to ask if I could be become a guide to you. I won’t. What I have done here is to give you the basic idea in general (but in enough details). The particular fleshing out and the particular implementation is basically between you and your official college guide. This much should have been obvious, but the politics junkies and/or IB and/or CIA etc. have used a trick in the past, simply to harass me. For instance, when I was applying for a job as a professor to a college in Pune, someone from Gadchiroli or Ichalkaranji, claiming to be an undergraduate student, would call me, ask me if I can go to their place to be a guide—but could not name the name of his college principal.

However, once your official guide himself approaches me—which he must, if you are going to work on this project idea (see the above point again)—at that point, if he himself requests me to be an official co-guide, I wouldn’t necessarily mind—I will think about it, and let him know regarding my decision in this respect.

Finally, if you are a student, don’t get in touch with me to ask me if I could implement this project for some money from you. I won’t. It is true that as of today I am jobless, and that, even otherwise, I am always looking for ways to make money. But, I have not, don’t, would not ever sell finished (or even “half”-finished) projects to students for a charge.

I would rather write blogs and go further and harass the Maharashtra CM (any one occupying that post), possibly to (his or her) death, (correctly) blaming him (or her or they) for my joblessness, than start selling student projects for a charge. The first should come easier to me. That’s why.

Now, see if you wish to pick it up as a project. It will be useful. To a great degree. (And, perhaps, for this same reason, it won’t be suitable as a JPBTI project. Though, I couldn’t care less if IIT students pick it up as their project topic.)

As I said, there are a few more things about this project that I could say. I will write another blog post about it.

* * * * *   * * * * *   * * * * *

No “A Song I Like” section, once again. I still go jobless. Keep that in mind—if your mind is not so small as not to have the capacity to carry this factoid.

Prithviraj (the BITS Pilani- and Berkeley-trained CM)? Jairam (the IIT Bombay- and MIT-trained JPBTI)? Others like you? Ashamed of the fact that I still don’t have a job? Or not so? Or, perhaps, not at all so? What say? Not even on a Gandhi Jayanti day? Have borrowed that convenient “maun vrat” from a certain someone from Ralegan Siddhi? Really?

[This is revision 1, published on October 2, 2012, 12:35 PM IST. Initial draft posted on October 1, 2012, 4:10 PM, IST. I think I am done with the additions/clarifications for this post, and probably won’t come back to further update this post (unless a grammatical error is too glaring). The promised related post should appear in a few days’ time.]
[E&OE]