Why is the physical space 3-dimensional?

Why I write on this topic?

Well, it so happened that recently (about a month ago) I realized that I didn’t quite understand matrices. I mean, at least not as well as I should. … I was getting interested in the Data Science, browsing through a few books and Web sites on the topic, and soon enough realized that before going further, first, it would be better if I could systematically write down a short summary of the relevant mathematics, starting with the topic of matrices (and probability theory and regression analysis and the lot).

So, immediately, I fired TeXMaker, and started writing an “article” on matrices. But as is my habit, once I began actually typing, slowly, I also began to go meandering—pursuing just this one aside, and then just that one aside, and then just this one footnote, and then just that one end-note… The end product quickly became… unusable. Which means, it was useless. To any one. Including me.

So, after typing in a goodly amount, may be some 4–5 pages, I deleted that document, and began afresh.

This time round, I wrote only the abstract for a “future” document, and that too only in a point-by-point manner—you know, the way they specify those course syllabi? This strategy did help. In doing that, I realized that I still had quite a few issues to get straightened out well. For instance, the concept of the dual space [^][^].

After pursuing this activity very enthusiastically for something like a couple of days or so, my attention, naturally, once again got diverted to something else. And then, to something else. And then, to something else again… And soon enough, I came to even completely forget the original topic—I mean matrices. … Until in my random walk, I hit it once again, which was this week.

Once the orientation of my inspiration thus got once again aligned to “matrices” last week (I came back via eigen-values of differential operators), I now decided to first check out Prof. Zhigang Suo’s notes on Linear Algebra [^].

Yes! Zhigang’s notes are excellent! Very highly recommended! I like the way he builds topics: very carefully, and yet, very informally, with tons of common-sense examples to illustrate conceptual points. And in a very neat order. A lot of the initially stuff is accessible to even high-school students.

Now, what I wanted here was a single and concise document. So, I decided to take notes from his notes, and thereby make a shorter document that emphasized my own personal needs. Immediately thereafter, I found myself being engaged into that activity. I have already finished the first two chapters of his notes.

Then, the inevitable happened. Yes, you guessed it right: my attention (once again) got diverted.

What happened was that I ran into Prof. Scott Aaronson’s latest blog post [^], which is actually a transcript of an informal talk he gave recently. The topic of this post doesn’t really interest me, but there is an offhand (in fact a parenthetical) remark Scott makes which caught my eye and got me thinking. Let me quote here the culprit passage:

“The more general idea that I was groping toward or reinventing here is called a hidden-variable theory, of which the most famous example is Bohmian mechanics. Again, though, Bohmian mechanics has the defect that it’s only formulated for some exotic state space that the physicists care about for some reason—a space involving pointlike objects called “particles” that move around in 3 Euclidean dimensions (why 3? why not 17?).”

Hmmm, indeed… Why 3? Why not 17?

Knowing Scott, it was clear (to me) that he meant this remark not quite in the sense of a simple and straight-forward question (to be taken up for answering in detail), but more or less fully in the sense of challenging the common-sense assumption that the physical space is 3-dimensional.

One major reason why modern physicists don’t like Bohm’s theory is precisely because its physics occurs in the common-sense 3 dimensions, even though, I think, they don’t know that they hate him also because of this reason. (See my 2013 post here [^].)

But should you challenge an assumption just for the sake of challenging one? …

It’s true that modern physicists routinely do that—challenging assumptions just for the sake of challenging them.

Well, that way, this attitude is not bad by itself; it can potentially open doorways to new modes of thinking, even discoveries. But where they—the physicists and mathematicians—go wrong is: in not understanding the nature of their challenges themselves, well enough. In other words, questioning is good, but modern physicists fail to get what the question itself is, or even means (even if they themselves have posed the question out of a desire to challenge every thing and even everything). And yet—even if they don’t get even their own questions right—they do begin to blabber, all the same. Not just on arXiv but also in journal papers. The result is the epistemological jungle that is in the plain sight. The layman gets (or more accurately, is deliberately kept) confused.

Last year, I had written a post about what physicists mean by “higher-dimensional reality.” In fact, in 2013, I had also written a series of posts on the topic of space—which was more from a philosophical view, but unfortunately not yet completed. Check out my writings on space by hitting the tag “space” on my blog [^].

My last year’s post on the multi-dimensional reality [^] did address the issue of the $n > 3$ dimensions, but the writing in a way was geared more towards understanding what the term “dimension” itself means (to physicists).

In contrast, the aspect which now caught my attention was slightly different; it was this question:

Just how would you know if the physical space that you see around you is indeed was 3-, 4-, or 17-dimensional? What method would you use to positively assert the exact dimensionality of space? using what kind of an experiment? (Here, the experiment is to be taken in the sense of a thought experiment.)

I found an answer this question, too. Let me give you here some indication of it.

First, why, in our day-to-day life (and in most of engineering), do we take the physical space to be 3-dimensional?

The question is understood better if it is put more accurately:

What precisely do we mean when we say that the physical space is 3-dimensional? How do we validate that statement?

Mark a fixed point on the ground. Then, starting from that fixed point, walk down some distance $x$ in the East direction, then move some distance $y$ in the North direction, and then climb some distance $z$ vertically straight up. Now, from that point, travel further by respectively the same distances along the three axes, but in the exactly opposite directions. (You can change the order in which you travel along the three axes, but the distance along a given axis for both the to- and the fro-travels must remain the same—it’s just that the directions have to be opposite.)

What happens if you actually do something like this in the physical reality?

You don’t have to leave your favorite arm-chair; just trace your finger along the edges of your laptop—making sure that the laptop’s screen remains at exactly 90 degrees to the plane of the keyboard.

If you actually undertake this strenuous an activity in the physical reality, you will find that, in physical reality, a “magic” happens: You come back exactly to the same point from where you had begun your journey.

That’s an important point. A very obvious point, but also, in a way, an important one. There are other crucially important points too. For instance, this observation. (Note, it is a physical observation, and not an arbitrary mathematical assumption):

No matter where you stop during the process of going in, say the East direction, you will find that you have not traveled even an inch in the North direction. Ditto, for the vertical axis. (It is to ensure this part that we keep the laptop screen at exactly 90 degrees to the keyboard.)

Thus, your $x$, $y$ and $z$ readings are completely independent of each other. No matter how hard you slog along, say the $x$-direction, it yields no fruit at all along the $y$– or $z$– directions.

It’s something like this: Suppose there is a girl that you really, really like. After a lot of hard-work, suppose you somehow manage to impress her. But then, at the end of it, you come to realize that all that hard work has done you no good as far as impressing her father is concerned. And then, even if you somehow manage to win her father on your side, there still remains her mother!

To say that the physical space is 3-dimensional is a positive statement, a statement of an experimentally measured fact (and not an arbitrary “geometrical” assertion which you accept only because Euclid said so). It consists of two parts:

The first part is this:

Using the travels along only 3 mutually independent directions (the position and the orientation of the coordinate frame being arbitrary), you can in principle reach any other point in the space.

If some region of space were to remain unreachable this way, if there were to be any “gaps” left in the space which you could not reach using this procedure, then it would imply either (i) that the procedure itself isn’t appropriate to establish the dimensionality of the space, or (ii) that it is, but the space itself may have more than 3 dimensions.

Assuming that the procedure itself is good enough, for a space to have more than 3 dimensions, the “unreachable region” doesn’t have to be a volume. The “gaps” in question may be limited to just isolated points here and there. In fact, logically speaking, there needs to be just one single (isolated) point which remains in principle unreachable by the procedure. Find just one such a point—and the dimensionality of the space would come in question. (Think: The Aunt! (The assumption here is that aunts aren’t gentlemen [^].))

Now what we do find in practice is that any point in the actual physical space indeed is in principle reachable via the above-mentioned procedure (of altering $x$, $y$ and $z$ values). It is in part for this reason that we say that the actual physical space is 3-D.

The second part is this:

We have to also prove, via observations, that fewer than 3 dimensions do fall short. (I told you: there was the mother!) Staircases and lifts (Americans call them elevators) are necessary in real life.

Putting it all together:

If $n =3$ does cover all the points in space, and if $n > 3$ isn’t necessary to reach every point in space, and if $n < 3$ falls short, then the inevitable conclusion is: $n = 3$ indeed is the exact dimensionality of the physical space.

QED?

Well, both yes and no.

Yes, because that’s what we have always observed.

No, because all physics knowledge has a certain definite scope and a definite context—it is “bounded” by the inductive context of the physical observations.

For fundamental physics theories, we often don’t exactly know the bounds. That’s OK. The most typical way in which the bounds get discovered is by “lying” to ourselves that no such bounds exist, and then experimentally discovering a new phenomena or a new range in which the current theory fails, and a new theory—which merely extends and subsumes the current theory—is validated.

Applied to our current problem, we can say that we know that the physical space is exactly three-dimensional—within the context of our present knowledge. However, it also is true that we don’t know what exactly the conceptual or “logical” boundaries of this physical conclusion are. One way to find them is to lie to ourselves that there are no such bounds, and continue investigating nature, and hope to find a phenomenon or something that helps find these bounds.

If tomorrow we discover a principle which implies that a certain region of space (or even just one single isolated point in it) remains in principle unreachable using just three dimensions, then we would have to abandon the idea that $n = 3$, that the physical space is 3-dimensional.

Thus far, not a single soul has been able to do that—Einstein, Minkowski or Poincare included.

No one has spelt out a single physically established principle using which a spatial gap (a region unreachable by the linear combination procedure) may become possible, even if only in principle.

So, it is 3, not 17.

QED.

All the same, it is not ridiculous to think whether there can be 4 or more number of dimensions—I mean for the physical space alone, not counting time. I could explain how. However, I have got too tired typing this post, and so, I am going to just jot down some indicative essentials.

Essentially, the argument rests on the idea that a physical “travel” (rigorously: a physical displacement of a physical object) isn’t the only physical process that may be used in establishing the dimensionality of the physical space.

Any other physical process, if it is sufficiently fundamental and sufficiently “capable,” could in principle be used. The requirements, I think, would be: (i) that the process must be able to generate certain physical effects which involve some changes in their spatial measurements, (ii) that it must be capable of producing any amount of a spatial change, and (iii) that it must allow fixing of an origin.

There would be the other usual requirements such as reproducibility etc., though the homogeneity wouldn’t be a requirement. Also observe Ayn Rand’s “some-but-any” principle [^] at work here.

So long as such requirements are met (I thought of it on the fly, but I think I got it fairly well), the physically occurring process (and not some mathematically dreamt up procedure) is a valid candidate to establish the physically existing dimensionality of the space “out there.”

Here is a hypothetical example.

Suppose that there are three knobs, each with a pointer and a scale. Keeping the three knobs at three positions results in a certain point (and only that point) getting mysteriously lit up. Changing the knob positions then means changing which exact point is lit-up—this one or that one. In a way, it means: “moving” the lit-up point from here to there. Then, if to each point in space there exists a unique “permutation” of the three knob readings (and here, by “permutation,” we mean that the order of the readings at the three knobs is important), then the process of turning the knobs qualifies for establishing the dimensionality of the space.

Notice, this hypothetical process does produce a physical effect that involves changes in the spatial measurements, but it does not involve a physical displacement of a physical object. (It’s something like sending two laser beams in the night sky, and being able to focus the point of intersection of the two “rays” at any point in the physical space.)

No one has been able to find any such process which even if only in principle (or in just thought experiments) could go towards establishing a $4$-, $2$-, or any other number for the dimensionality of the physical space.

I don’t know if my above answer was already known to physicists or not. I think the situation is going to be like this:

If I say that this answer is new, then I am sure that at some “opportune” moment in future, some American is simply going to pop up from nowhere at a forum or so, and write something which implies (or more likely, merely hints) that “everybody knew” it.

But if I say that the answer is old and well-known, and then if some layman comes to me and asks me how come the physicists keep talking as if it can’t be proved whether the space we inhabit is 3-dimensional or not, I would be at a loss to explain it to him—I don’t know a good explanation or a reference that spells out the “well known” solution that “everybody knew already.”

In my (very) limited reading, I haven’t found the point made above; so it could be a new insight. Assuming it is new, what could be the reason that despite its simplicity, physicists didn’t get it so far?

Answer to that question, in essential terms (I’ve really got too tired today) is this:

They define the very idea of space itself via spanning; they don’t first define the concept of space independently of any operation such as spanning, and only then see whether the space is closed under a given spanning operation or not.

In other words, effectively, what they do is to assign the concept of dimensionality to the spanning operation, and not to the space itself.

It is for this reason that discussions on the dimensionality of space remain confused and confusing.

Food for thought:

What does a $2.5$-dimensional space mean? Hint: Lookup any book on fractals.

Why didn’t we consider such a procedure here? (We in fact don’t admit it as a proper procedure) Hint: We required that it must be possible to conduct the process in the physical reality—which means: the process must come to a completion—which means: it can’t be an infinite (indefinitely long or interminable) process—which means, it can’t be merely mathematical.

[Now you know why I hate mathematicians. They are the “gap” in our ability to convince someone else. You can convince laymen, engineers and programmers. (You can even convince the girl, the father and the mother.) But mathematicians? Oh God!…]

A Song I Like:

(English) “When she was just seventeen, you know what I mean…”
Band: Beatles

[May be an editing pass tomorrow? Too tired today.]

[E&OE]

Shaken, because of a stir

We have demonstrably been shaken here on earth, because of a stir in the cosmos.

The measured peak strain was $10^{-21}$ [^].

For comparison: In our college lab, we typically measure strains of magnitude like $10^{-3}$ or at the most $10^{-4}$. (Google search on “yield strain of mild steel” does not throw up any directly relevant page, but it does tell you that the yield strength of mild steel is 450 MPa, and all mechanical (civil/metallurgical/aero/etc.) engineers know that Young’s modulus for mild steel is 210 GPa. … You get the idea. …)

Einstein got it wrong twice, but at least eventually, he did correct himself.

But other physicists (and popular science writers, and blog-writers), even after getting a full century to think over the issue, still continue to commit blunders. They continue using terms like “distortions of spacetime.” As if, space and time themselves repeatedly “bent” (or, to use a euphemism, got “distorted”) together, to convey the force through “vacuum.”

It’s not a waving of the “spacetime” through a vaccum, stupid! It’s just the splashing of the aether!!

The Indian credit is, at the most, 1.3%.

If it could be taken as 3.7%, then the number of India’s science Nobels would also have to increase dramatically. Har Gobind Singh Khorana, for instance, would have to be included. The IAS-/MPSC-/scientist-bureaucrats “serving” during my childhood-days had made sure to include Khorana’s name in our school-time science text-books, even though Khorana had been born only in (the latter-day) Pakistan, and even if he himself had publicly given up on both Pakistan and India—which, even as children, we knew! Further, from whatever I recall of me and all my classmates (from two different schools), we the (then) children (and, later, teen-agers) were neither inspired nor discouraged even just a tiny bit by either Khorana’s mention or his only too willing renunciation of the Indian citizenship. The whole thing seemed too remote to us. …

Overall, Khorana’s back-ground would be a matter of pride etc. only to those bureaucrats and possibly Delhi intellectuals (and also to politicians, of course, but to a far lesser extent than is routinely supposed). Not to others.

Something similar seems to be happening now. (Something very similar did happen with the moon orbiter; check out the page 1 headlines in the government gazettes like Times of India and Indian Express.)

Conclusion: Some nut-heads continue to run the show from Delhi even today—even under the BJP.

Anyway, the reason I said “at most” 1.3 % is because, even though I lack a knowledge of the field, I do know that there’s a difference between 1976, and, say, 1987. This fact by itself sets a natural upper bound on the strength of the Indian contribution.

BTW, I don’t want to take anything away from Prof. Dhurandhar (and from what I have informally gathered here in Pune, he is a respectable professor doing some good work), but reading through the media reports (about how he was discouraged 30 years ago, and how he has now been vindicated today etc.) made me wonder: Did Dhurandhar go without a job for years because of his intellectual convictions—the way I have been made to go, before, during and after my PhD?

As far as I am concerned, the matter ends there.

At least it should—I mean, this post should end right here. But, OK, let me make an exception, and note a bit about one more point.

The experimental result has thrown the Nobel bookies out of business for this year—at least to a great part.

It is certain that Kip Thorne will get the 2016 Physics Nobel. There is no uncertainty on that count.

It is also nearly as certain that he will only co-win the prize—there will be others to share the credit (and obviously deservingly so). The only question remaining is, will it be just one more person or will it be two more (Nobel rules allow only max 3, I suppose), what will be their prize proportions, and who those other person(s) will be (apart from Thorne). So, as far as the bettors and the bookies are concerned, they are not entirely out of the pleasure and the business, yet.

Anyway, my point here was twofold: (i) The 2016 Physics Nobel will not be given for any other discovery, and (ii) Kip Thorne will be one of the (richly deserving) recipients.

[E&OE]

/

What do physicists mean by “multidimensional” physical reality?

Update on 2015.09.07, 07 AM: I have effected a few corrections. In particular, I have made it explicit that the third quantity isn’t the strength of an independently existing third property, but merely a quantity that is registered when the two independent quantities are both being varied. Sorry about that. If the need be, I will simplify this discussion further and write another blog post clarifying such points, some time later.

The last time, I said that I am falling short on time these days. This shortfall, generally speaking, continues. However, it just so happens that I’ve essentially finished a unit each for both the UG courses by today. Therefore, I do have a bit of a breather for this week-end (only); I don’t have to dig into texts for lecture preparations this evening. (Also, it turns out that despite the accreditation-related overtime work, we aren’t working on Sundays, though that’s what I had mentioned the last time round). All in all, I can slip in a small note, and the title question seems right.

We often hear that the physical reality, according to physicists, is not the $3$-dimensional reality that we perceive. Instead, it is supposed to be some $n$-dimensional entity. For instance, we are told that space and time are not independent; that they form a $4$-dimensional continuum. (One idea which then gets suggested is that space and time are physically inter-convertible—like iron and gold, for instance. (You mean to say you had never thought of it, before?)) But that’s only for the starters. There are string theorists who say that physical universe is $10$-, $n$-, or $\infty$-dimensional.

What do physicists mean when they say that reality is $n$-dimensional where $n >3$? Let’s try to understand their viewpoint with a simple example. … This being a brief post, we will not pursue all the relevant threads, even if important. … All that I want to touch upon here is just one simple—but often missed—point, via just one, simple, illustration.

Take a straight line, say of infinite length. Take a point on this line. Suppose that you can associate a physical object with this point. The object itself may have a finite extent. For example, the object may be extended over a small segment of this line. In such a case, we will associate, say the mid-point of the segment with this object.

Suppose this straight line, together with the $1$-dimensionally spread-out object, defines a universe. That is a supposition; just accept that.

The $1$-dimensional object, being physical, carries some physical properties (or attributes), denoted as $p_1, p_2, p_3, \cdots$. For example, for the usual $3$-dimensional universe, each object may have some extent (which we have already seen above), as well as some mass (and therefore density), color, transmissivity, velocity, spinning rate, etc. Also, position from a chosen origin.

Since we live in a $3$-dimensional universe, we have to apply some appropriate limiting processes to make sense of this $1$-dimensional universe. This task is actually demanding, but for the sake of the mathematical simplicity of the resulting model, we will continue with a $1$-dimensional universe.

So, coming back to the object and its properties, each property it possesses exists in a certain finite amount.

Suppose that the strength of each property depends on the position of the object in the universe. Thus, when the object is at the origin (any arbitrary point on the line chosen as the reference point), the property $p_1$ exists with the strength $s_1(0)$, the property $p_2$ exists with the strength $s_2(0)$, etc. In short the $i$th property $p_i$ exists with a strength $s_i(x)$ where $x$ is the position of the object in the universe (as measured from the arbitrarily selected origin.) Suppose the physicist knows (or chooses to consider) $n$ number of such properties.

For each of these $n$ number of properties, you could plot a graph of its strength at various positions in the universe.

To the physicist, what is important and interesting is not the fact that the object itself is only $1$-dimensionally spread; it is: how the quantitative measures $s_i(x)$s of these properties $p_i$s vary with the position $x$. In other words, whether or not there is any co-variation that a given $i$th property has with another $k$th property, or not, and if yes, what is the nature of this co-variation.

If the variation in the $i$th property has no relation (or functional dependence) to the $k$th property, then the physicist declares these two properties to be independent of each other. (If they are dependent on each other, the physicist simply retains only one of these two properties in his basic or fundamental model of the universe; he declares the other as the derived quantity.)

Assuming that a set of some $n$ chosen properties such that they are independent of each other, his next quest is to find the nature of their functional dependence on position $x$.

To this end, he considers two arbitrarily selected points, $x_1$ and $x_2$. Suppose that his initial model has only three properties: $p_1$, $p_2$ and $p_3$. Suppose he experimentally measures their strengths at various positions $x_1, x_2, x_3, x_4, \cdots$.

While doing this experimentation, suppose he has the freedom to vary only one property at a time, keeping all others constant. Or, vary two properties simultaneously, while keeping all others constant. Etc. In short, he can vary combinations of properties.

By way of an analogy, you can think of a small box carrying a few on-off buttons and some readout boxes on it. Suppose that this box is mounted on a horizontal beam. You can freely move it in between two fixed points $x = x_1$ and $x = x_2$. The on-off’ buttons can be switched on or off independent of each other.

Suppose you put the first button $b_1$ in the on’ position and keep the the rest of the buttons in the off’ position. Then, suppose you move the box from the point $x_1$ to the point $x_2$. The box is designed such that, if you do this particular trial, you will get a readout of how the property $p_1$ varied between the two points; its strength at various positions $s_1(x)$ will be shown in a readout box $b_1$. (During this particular trial, the other buttons are kept switched off, and so, the other readout boxes register zero).

Similarly, you can put another button $b_2$ into the on’ position and the rest in the off’ position, and you get another readout in the readout box $b_2$.

Suppose you systematize your observations with the following notation: (i) when only the button $b_1$ is switched on (and all the other buttons are switched off), the property $p_1$ is seen to exist with $s_1(x_1)$ units at the position $x = x_1$ and $s_1(x_2)$ units at $x = x_2$; this readout is available in the box $b_1$. (ii) When only the button $b_2$ is switched on (and all the other buttons are switched off), the property $p_2$ exists with $s_2(x_1)$ units at $x = x_1$ and $s_2(x_2)$ units at $x = x_2$; this readout is available in the box $b_2$. So on and so forth.

Next, consider what happens when more than one switch is put in the on’ position.

Suppose that the box carries only two switches, and both are put in the on’ position. The reading for this combination is given in a third box: $b_{(1+2)}$; it refers to the variation that the box registers while moving on the horizontal beam. Let’s call the strengths registered in the third box, at $x_1$ and $x_2$ positions, as $s_{(1+2)}(x_1)$ and $s_{(1+2)}(x_2)$, respectively; these refer to the $(1+2)$ combination (i.e. both the switches $1$ and $2$ put in the on’ position simultaneously).

Next, suppose that after his experimentation, the physicist discovers that the following relation holds:

$[s_{(1+2)}(x_2) - s_{(1+2)}(x_1)]^2 = [s_1(x_2) - s_1(x_1)]^2 + [s_2(x_2) - s_2(x_1)]^2$

(Remember the Pythogorean theorem? It’s useful here!) Suppose he finds the above equation holds no matter what the specific values of $x_1$ and $x_2$ may be (i.e. whatever be the distances of the two arbitrarily selected points from the same origin).

In this case, the physicist declares that this universe is a $2$-dimensional vector space, with respect to these $p_1$ and $p_2$ properties taken as the bases.

Why? Why does he call it a $2$-dimensional universe? Why doesn’t he continue calling it a $1$-dimensional universe?

Because, he can take a $2$-dimensional graph paper by way of an abstract representation of how the quantities of the properties (or attributes) vary, plot these quantities $s_1$ and $s_2$ along the two Cartesian axes, and then use them to determine the third quantity $s_{(1+2)}$ from them. (In fact, he can use any two of these strengths to find out the third one.)

In particular, he happily and blithely ignores the fact that the object of which $p_i$ are mere properties (or attributes), actually is spread (or extended) over only a single dimension, viz., the $x$-axis.

He still insists on calling this universe a $2$-dimensional universe.

That’s all there is to this $n$-dimensional nonsense. Really.

But what about the $n$-dimensional space, you ask?

Well, the physicist just regards the extension and the position themselves to form the set of the physical properties $p_i$ under discussion! The physicist regards distance as a property, even if he is going to measure the strengths or magnitudes of the properties (i.e. distances, really speaking) only in reference to $x$ (i.e. positions)!!

But doesn’t that involve at least one kind of a circularity, you ask?

The answer is embedded right in the question.

Understand this part, and the entire mystification of physics based on the “multi-dimensional” whatever vaporizes away.

But don’t rely on the popular science paperbacks to tell you this simple truth, though!

Hopefully, the description above is not too dumbed down, and further, hopefully, it doesn’t have too significant an error. (It would be easy for me (or for that matter any one else) to commit an error—even a conceptual error—on this topic. So, if you spot something, please do point it out to me, and I will correct the description accordingly. On my part, I will come back sometime next week, and read this post afresh, and then decide whether what I wrote makes sense or not.)

A Song I Like:

For this time round, I am going to list a song even if I don’t actually evaluate it to be a very great song.

In fact, in violation of the time-honored traditions of this blog, what I am going to do is to list the video of a song. It’s the video of a 25+ years old song that I found I liked, when I checked it out recently. As to the song, well, it has only a nostalgia value to me. In fact, even the video, for the most part, has only a nostalgia value to me. The song is this:

(Hindi) “may se naa minaa se na saaki se…”
Music: Rajesh Roshan
Lyrics: Farooq Qaisar

Well, those were the technical details (regarding this song). To really quickly locate the song (and the video), forget the lyrics mentioned above. Instead, just google “aap ke aa jaane se,” and hit the first video link that the search throws up. (Yes, it’s the same song.)

As I said, I like this video mainly for its nostalgic value (to me). It instantaneously takes me back to the 1987–88 times. The other reasons are: the utter natural ease with which both the actors perform the dance here (esp. Neelam!). They both in fact look like they are authentically enjoying their dancing. Watch Neelam’s steps, in particular. She was reputed to be a good dancer, and you might think that this song must have been a cake-walk for her. Well, check out her thin (canvas-like) shoes, and the kind of rough ground in the mountains and in the fields over which she seems so effortlessly to take those steps. Govinda, in comparison, must have had it a bit easier (with his thicker, leather shoes), but in any case, in actuality, it must have been some pretty good hard work for both of them—it’s just that the hard work doesn’t show in the song. … Further, I also like the relative simplicity of the picturization. And, the catchy rhythm. Also, the absence, here, of those gaudy gestures which by now are so routine in Hindi film songs (and in fact were there even in the times of this song, and in fact also for about a decade or more earlier). I mean: those pelvic thrusts, that passing off of a thousand of people doing their PT exercises on a new, sprawling suburban street in Mumbai/Gurgaon/Lutyens’ Delhi as an instance of dance, etc.

… I don’t know if you end up liking this song or not. To me, however, it unmistakably takes me to the times when I was a freshly minted MTech from IIT Madras, was doing some good (also satisfying) work in NDT, had just recently bought a bike (the Yamaha RX 100), and was looking forward to life in general with far more enthusiasm (and in retrospect, even naivete) than I can manage to even fake these days. So, there.

[As I said, drop a line if there are mistakes in the main post. Main mistake (or omission) corrected. As I said, drop a line if there are further mistakes in the main post. And, excuse me for some time, esp. the next week-end, esp. the next Saturday late night (IST). I may not find any time the next Sunday, because I would once again be in the middle of teaching a couple of new units over the next 2–3 weeks.]

[E&OE]

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Concerning our series of posts on the concept of space, I have jotted down my thoughts on paper, but not yet made any progress on creating the diagrams to go with them. (Plain laziness.) Hence, the delay in posting it.

In the meanwhile, here are a few links to some reading that I found interesting over the past few days (in no particular order).

1. R. J. Lipton of GeorgiaTech on how “Teaching helps research” [^]

2. Ricardo Heras, “Individualism: The legacy of great physicists,” arXiv:1310.7326 [physics.pop-ph] [^]. Heras is a first year graduate student at University College, London. Check out the Fermi quote at the end of this paper. (And, also, the quote by Max Planck at the opening.)

3. Roger Schlafly puts in one place all the links to his blog posts updating his book “How Einstein Ruined Physics,” [^].

4. Tony Rothman, “Lost in Einstein’s shadows” [^]

5. Physics World, 25th Anniversary Issue, available for free downloads [^] (HT to QuantumFrontiers [^]). This special issue has the magazine’s lists of 5 images, 5 discoveries, 5 questions, 5 spin-offs, and 5 people, that mattered over the last 25 years.

6. Paul G. Kwiat, on what he calls it “interaction-free measurement” [^]. You think it’s mysterious? (LOL!)

And, in place of the usual “A Song I Like” section, yet another link!:

7. Tom Swanson, a physicist himself, offers physicists a horoscope [^]

[E&OE]

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