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?

The answer is “simple” enough.

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.


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.


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.]


(A)theism, God, and Soul

TL;DR: The theism vs. atheism debate isn’t very important; the concept of soul is. To better understand soul, one has to turn to the issues pertaining to the divine. The divine is an adjective, not a noun; it is a modality of perception (of reality, by a soul); it is a special but natural modality that in principle is accessible to anyone. The faithful destroy the objectivity of the divine by seizing the concept and embedding it into the fold of religious mysticism; the materialists and skpetics help them in this enterprise by asserting, using another form of mysticism, that the divine does not even exist in the first place (because, to them, soul itself doesn’t).  Not all points are explicated fully, and further, the writing also is very much blogsome (more or less just on-the-fly).

Also see an important announcement at the end of this post.

This post has its origins in a comment which I tried to make at Anoop Verma’s blog, here: [^]. Since his blog accepts only comments that are smaller than 4KB, and since my writing had grown too long (almost 12 KB), I then tried sending that comment by email to him. Then, rather than putting him through the bother of splitting it up into chunks of 4KB each, I decided to run this comment at my own blog, as a post here.

After a rapid reading of Varma’s above-mentioned post [^], I was immediately filled with so many smallish seeds of thoughts, rushing in to me in such a random order, that I immediately found myself trapped in a state of an n-lemma (which word is defined as a quantitative generalization of “dilemma”). After idly nursing this n-lemma together with a cup of coffee for a while, both with a bit of fondness, I eventually found me saying to myself:

“Ah! And I don’t even know where to begin writing my comment!”.

Soon enough thereafter, I realized that the n-lemma persists precisely because I don’t know where to begin. … Begin. … Begin. … It’s Begin. … It’s the beginning! … Which realization then immediately got me recognizing that what is involved here belongs to the level of the basic of the basics—i.e., at the level of philosophic axioms.

Let me deal with the issue at that level, at the level of axiomatics, even though this way, my comment will not be as relevant to Varma’s specific post as it could possibly have been. But, yes, if I could spell out where to begin, then the entire problem would have been at least half-conquered. That’s because, this way, at least an indication of (i) the nature of the problem, and (ii) of its context, would have been given. As they say, a problem well defined is a problem half solved.

My main rhetorical point here is: It isn’t really necessary for one to try to get to know what precisely the term “god” means. By itself, it even looks like a non-issue. Mankind has wasted too much time on the issue of god. (Here, by “god,” I also include the God of Christianity, and of any other monotheistic/other religion.)

I mean to say: you could have a logically complete philosophy, and therefore could live a logically complete (i.e. “fullest” etc.) life, even if you never do come across the specific word: “god.”

(BTW, you could have completeness of life in this way only if you weren’t to carry even an iota of faith anywhere in your actual working epistemology. … Realize, faith is primarily an issue from epistemology, not metaphysics; the consequences of faith-vs-reason in morality, religion, society, organized religion, and politics are just that—only consequences.)

So, it isn’t really necessary to know what god means or therefore even to search for one—or to spend time proving its presence or absence. That’s what I think. Including “wasting” time debating about theism vs. atheism.

But it is absolutely necessary, for the aforementioned logical completeness to be had, to know what the term “soul” means—and what all it presupposes, entails, and implies.

Soul is important.

When it comes to soul, you metaphysically have one anyway, and further, theoretical questions pertaining to its existence and identity (or a research pertaining to them) logically just does not arise. The concept is a fundamental self-evident primary—i.e. a philosophic axiom. (Of course, there have been people like David Hume, but I am focusing here mainly on establishing a positive, not on polemics.)

As I said in the past [^][^], soul, to me, is an axiomatic concept.

Now, like in any other field of knowledge and endeavor, the greater the extent and refinement of your knowledge (of something), the better is your efficacy (in that regard). In other words, the better off you are.

Ditto, with regard to this concept too.

A case in point: Suppose you yourself were capable of originally and independently reaching that philosophical identification which is contained in Ayn Rand’s axiom “existence exists,” and suppose that you held it in a truly in-depth manner, i.e. qua axiom. Just assume that. Just assume, for the sake of argument, that you were the one who reached that universal truth which is encapsulated by this axiom, for the first time in the world! But an axiom by itself is nothing if it isn’t tied-in non-contradictorily with all its prior cognitive preparation and logical implications. Suppose that you did that too—to match whatever extent of knowledge you did have. Now consider the extent and richness of the (philosophic) knowledge which you would have thus reached, and compare it to that which Ayn Rand did. (For instance, see Dr. Harry Binswanger’s latest post here [^] with a PDF of his 1982 writings here [^], which is a sort of like an obit-piece devoted to Ayn Rand.) … What do you get as a result of that comparison?

“What’s the point,” you ask?

The point is this: The better the integrations, the better the knowledge. The non-contradictorily woven-in relations, explanations, implications, qualifications, applications, etc. is what truly makes an axiom “move” a body of knowledge—or a man. And on this count, you would find Rand beating you by “miles and miles”—or at least I presume Varma would agree to that.

Realize, by the grace of the nature of man (including the nature of knowledge), something similar holds also for the concept of soul.

And here, in enriching the meaning, applications, etc. of this concept, you would find that most (or all) of the best material available to you has come to you from houses of spirituality, or for that matter, even of religion (by which, I emphatically mean, first and foremost (though not exclusively), the Indian religions)—not from Ayn Rand.

The extant materials pertaining to soul come from houses of spirituality and religion (or rarely, e.g. in the Upanishads, of ancient Indian philosophy). Given the nature of their sources—ancient, scattered, disparate, often mere notings without context, and most importantly, only in the religious or mystical context—it is very easy to see that they must have been written via an exercise of faith. This is an act of faith on the writer’s part—and sometimes, he has been nothing more than a mere scribe to what appears to be some inestimably better Guru, who probably wouldn’t have himself espoused faith or mysticism. But, yes, the extant materials on the philosophy of mind are like that. (Make sure to distinguish between epistemology and philosophy of mind. Ayn Rand had the former, but virtually nothing on the latter.) Further, the live sources about this topic also most often do involve encouragement to faith on the listener’s/reader’s part. They often are very great practitioners but absolutely third-class intellectualizers. Given such a preponderance of faith surrounding these matters, there easily arises a tendency to (wrongly) label the good with the poison that is faith—and as the seemingly “logical” next step, to dismiss the whole thing as a poison.

Which is an error. An error that occurs at a deep philosophic level—and if you ask me, at the axiomatic level.

In other words, there exists a “maayaa” (or a veil) of faith, which you have to penetrate before you can get to the rich, very rich, insights on the phenomenon of soul, on the philosophy of the mind.

Of those who declare themselves to be religious or faithful, some are better than others; they sometimes (implicitly) grasp the good part concerning the nature of the issue, at least partly. Some of these people therefore can be found even trying to defend religion and its notions—such as faith—via a mostly misguided exercise of reason! (If you want to meet some of them: People like Varma, being in India, would be fortunate in this regard. Just spend a week-end in a “waari,” or in an “aashram” in the Himalya, or at a random “ghaaTa” on a random river, or in a random smallish assembly under some random banyan or peepul tree…. You get the idea.)

Thus to make out (i.e. distinguish) the better ones from the rotten ones (i.e. the actually faithful among those who declare themselves to believe in faith), you yourself have to know (or at least continue keeping an unwavering focus on) the idea of  the“soul” (not to mention rational philosophic ideas such as reason). You have to keep your focus not on organized religion primarily, not even on religion … and not even, for that matter, even on spirituality. Your underlying and unwavering focus has to be on the idea of “soul,” and the phenomena pertaining to it.

You do that, and you soon enough find that issues such as atheism vs. theism more or less evaporate away. At least, they no longer remain all that interesting. At least, not as interesting as they used to be when you were a school-boy or a teenager.

The word “atheism” is derived from the word “theism,” via a negation (or at least logical complimentation) thereof. “Atheism” is not a word that can exist independently of “theism.”

Etymologically, “theism” is a corrupt form (both in spelling and meaning) of the original (historical) Western term “dei-ism,” which came from something like “dieu”, which came from a certain ancient Sanskrit root involving “d”.  The Sanskrit root “d” is involved in the stems that mean: to give, and by implication and in appropriate context, also to receive. It is a root involved in a range of words: (i) “daan,” meaning giving; (ii) “datta,” meaning, the directly presented (in the perceptual field)—also the given—and then, also the giver (man), in particular, the (bliss)-giving son of the sage “atri” and his wife “anasuya” (an_ + a + su + y + aa, i.e., one without ill-will (or jealousy or envy)), and (iii) “divya”, meaning, divine (the same “div” root!).

The absence in the Western etymologies of the derivation of the English word “divine” from the ancient “d,” “diue,” “div-,” etc. is not only interesting psychologically but also amply illuminating morally.

The oft-quoted meaning of “divya” as “shining, or glimmering” appears to be secondary; it seems to be rather by association. The primary meaning is: the directly given in the perception—but here the perception is to be taken to be of a very special kind. The reason why “shimmering” gets associated with the word is because of the very nature of the “divya-druShTi” (divine vision). Gleening from the sources, divine vision (i) seems to be so aetherial and evanescent, flickering in the way it appears and disappears, and (ii) seems to include the perceived objects as if they were superimposed on the ordinary perceptual field of the usual material objects “out there,” say in a semi-transparent sort of a manner, and only for a fleeting moment or two. The “shimmering” involved, it would seem, is analogous to the mirage in the desert, i.e. the “mrigajaLa” illusion. Since a similar phenomenon also occurs due to patterns of cold-and-dense and hot-and-rarefied air near and above an oil lamp, and since the lamp is bright, the “di”-whatever root also gets associated with “shining.” However, this meaning is rather by association; it’s a secondary meaning. The primary meaning of “divya” is as in the “specially perceived,” with the emphasis being on specially, and with the meaning of course referring to the process of perception, not to this perceived object vs. that.

Thus, “divya” is an adjective, not a noun; it applies to a quality of a perception, not to that which has thus been perceived. It refers to a form or modality of perception (of (some definite aspect of) reality). This adjective completely modifies whatever that comes after it. For instance, what is perceptible to a “divya”-“druShTi” (divine vision) cannot be captured on camera—the camera has no soul. The object which is perceived by the ordinary faculty of vision can be captured on camera, but not the object which is perceptible via “divya-druShTi.” The camera would register merely the background field, not the content of the divine vision.

(Since all mental phenomena and events have bio-electro-chemo-etc-physical correlates, it is conceivable that advancement in science could possibly be able to capture the content of the “divya-druShTi” on a material medium. Realize that its primary referent still would belong to the mental referents. A soul-less apparatus such as a camera would still not be able to capture it in the absence of a soul experiencing it.)

Notice how the adjective ”divya”, once applied to “druShTi”, completely changs the referent from a perception of something which is directly given to the ordinary vision in the inanimate material reality (or the inanimate material aspects of a living being), to the content of consciousness of an animate, soulful, human being.

This does not mean that this content does not refer to reality. If the “divya-druShTi” is without illusions or delusions, what is perceived in this modality of perception necessarily refers to reality. Illusions and delusions are possible with the ordinary perception too. It is a fallacy to brand all occurrences of “divya-druShTi” as just “voices” and “hallucinations/delusions/illusions” just because: (i) that mode of perception too is fallible, and (ii) you don’t have it anyway. (Here, the “it” needs some elaboration. What you don’t have (or haven’t yet had) is: a well-isolated instance of a “divya” perception, as a part of your past experience. That doesn’t mean that other people don’t or cannot have it. Remember, the only direct awareness you (a soul) have is of your own consciousness—not someone else’s.)

“deva” or “god” (with a small `g’) is that which becomes accessible (i.e. perceivable) to you when your perception has (temporarily) acquired the quality of the “divya.”

Contrary to a very widespread popular misconception, the word “divya” does not come from a more primary“dev”; it does not mean that which is given by “dev” (i.e. a god). In other words, in principle, you are not at the mercy of a god to attain the “divya” modality.

The primacy, if there is any at all, is the other way around: the idea of “dev” basically arises with that kind of a spiritual (i.e. soul-related) phenomenon which can be grasped in your direct perception when the modality of that direct perception carries the quality of the “divya.” (The “d” is the primary root, and as far as my guess-work goes, a likely possibility is that both the “di” (from which comes“divya”) and the “de” (from which comes the“dev”) are off-shoots.) T

This special modality of perception is apparently not at all constant in time—not to most people who begin to have it anyway. It comes and goes. People usually don’t seem to be reaching a level of mastery of this modality to the extent that they can bring it completely under their control. That is what you can glean from the extant materials as well as from (the better ones among) the living people who claim such abilities.

Yet, in any case, you don’t have to have any notion of god, not even thereby just meaning “dev,” in order to reach the “divya.” That is my basic point.

Of course, I realize that those whose actual working epistemology is faith and mysticism, have long, long ago seized the idea of “dev” (i.e. god), and endowed it with all sorts of mystical and irrational attributes. One consequence of such a mystification is the idea that the “divya” is not in the metaphysical nature of man but a mystical gift from god(s). … An erroneous idea, that one is.

A “divya” mode of perception is accessible to anyone, but only after developing it with proper discipline and practice. Not only that, it can also be taught and learnt, though, gleening from literature, it would be something like a life-time of a dedication to only that one pursuit. (In other words, forget computational modeling, engineering, quantum physics, blogging… why, even maths and biology!)

In the ancient Indian wisdom, the “divya,” “dev,” and the related matters also involve a code of morality pertaining to how this art (i.e. skill) is to be isolated and grasped, learnt, mastered, used, and taught.

Misuse is possible, and ultimately, is perilous to the abuser’s own soul—that’s what the ancient Indian wisdom explicitly teaches, time and again. That is a very, very important lesson which is lost on the psychic attackers. … BTW, “veda”s mention also of this form of evil. (Take a moment to realize how it can only be irrationality—mysticism and faith in particular—which would allow the wrongful practitioner to attempt to get away with it—the evil.)

The “divya” mode is complementary to the conceptual mode of perception. (Here, I use the term “perception” in the broadest possible sense, as meaning an individual’s consciousness of reality via any modality, whether purely sensory-perceptual, perceptual, or conceptual—or, now, “divya”-involving).

Talking of the ordinary perceptual and the “divya” modalities, neither is a substitute for the other. Mankind isn’t asked to make a choice between seeing and listening (or listening and tasting, etc.). Why is then a choice brought in only for the “divya”, by setting up an artificial choice between the “divya” and the ordinary perceptual?

Answer: In principle, only because of faith.

To an educated man living in our times, denying the existence of the divine (remember, it’s an adjective, not a noun) most often is a consequence of blindly accepting for its nature whatever assertion is put forth by the (actually) faithful, the (actually) mystic, to him. It’s an error. It may be an innocent error, yet, by the law of identity, it’s an error. Indeed, it can be a grave error.

The attempt to introduce a choice between the ordinary perceptual and the “divya”-related perceptual is not at all modern; from time immemorial, people (including the cultured people of the ancient India) have again and again introduced this bad choice, with the learned ones (Brahmins, priests) typically elevating the “divya” over the ordinary perceptual. Often times, they would go a step even further and accord primacy to the “divya.” For instance, in India, ask yourself: How often have you not heard the assertion that“divya-dnyaana” (the divine knowledge, i.e., the conceptual knowledge obtained via the divine modality of perception) is superior to the “material” knowledge (i.e. the one obtained via the ordinary modalities of perception)? This is a grave error, an active bad.

The supposed “gyaanee”s (i.e. a corrupt form of “dnyaani”, the latter meaning: the knowledgeable or the wise) of ancient India have not failed committing this error either. They, too, did not always practice the good. They, too, would often both (i) mystify the process of operating in the “divya” mode, and (ii) elevate it above the ordinary perceptual mode.

Eventually, Plato would grab this bit from some place influenced by the ancient Indian culture, go back to Greece, and expound this thing as an entire system of a very influential philosophy in the West. And, of course, Western scholars have been retards enough in according originality of the invention to Plato. But the Western scholars are not alone. There are those modern Indian retards (esp. the NRIs (esp. Californians), Brahminism-espousers, etc.) too, who clamor for the credit for this invention to be restored back to the Indian tradition, but who themselves are such thorough retards that they cannot even notice in the passing how enormously bad that philosophy is—including, e.g., how bad this kind of a view of the term “divya” itself represents. (Or, may be, they get attracted to the Platonic view precisely because they grasp that it resonates with their kinds of inner motives of subjugating the rest of us under their “intellectual” control.)

Finally, though I won’t explicate on it, let me revisit the fact that the “divya” mode also is every bit as natural as is the ordinary mode. Nothing supernatural here—except when the faithful enter the picture.

In particular, speaking of the “divya” (or the original meaning of the term “divine”) in terms of the never-approachable and mystical something—something described as “transcendental,” belonging to the “higher dimensions,” something literally supposed to be “the one and the only, beyond all of us,” etc.—is ridiculous.

However, inasmuch as the “divya” modality is hard to execute, as with any skill that requires hard-work to master,  the attainment of the “divya” too calls for appropriate forms of respect, admiration, and even exaltation and worship for some (provided the notion is not corrupted via mysticism or faith). … This looks gobbledygook, so let me concretize it a bit. Just because I regard such things natural, I do not consider them pedestrian. One does not normally think of greeting a saintly man with a casual “hey dude, whatssup, buddy?” That is the common sense most everyone has, and I guess, it is sufficient.

Already too long a comment… More, may be later (but don’t press me for it).

An Important Announcement:

I had decided not to blog any more until the time that I land a job—a Mechanical Engineering Professor’s job in Pune. That’s why, even as continuing to make quite a few comments at other people’s blogs, I did not post anything new here. I wanted the readers’ eyes to register the SPPU Mechanical Engineering Professors’ genius once again. And then, again. And again.

And again.

Now that I have updated this blog (even if I have not landed a job this academic hiring season), does it mean that I have given in to the plan of their genius?

Answer: No. I have not. I have just decided to change my blogging strategy. (I can’t control their motives and their plans. But I can control my blogging.)

With this post, I am resuming my blogging, which will be, as usual, on various topics. However, a big change is this: Whenever I feel like the topic of my last post isn’t getting the due attention which it deserves, I will simply copy-paste my last post, and re-post it as a brand new post once again, so that the topic not only gets re-publicised in the process but also reclaims back the honor of being the first post visible here on this blog.

Genius needs to be recognized. Including the SPPU Mechanical Engineering Professors’ (and SPPU authorities’) genius.

I will give them that.

A Song I Like:

(Old Rajasthani Hindi) “nand-nandan diThu paDiyaa, maaee, saavaro…”
Singer: Lata Mangeshkar
Lyrics: (Traditionally asserted as being an original composition by) Saint Meera
Music: Hridaynath Mangeshkar


[I have streamlined this post a bit since its publication right today. I may come back and streamline it further a bit, may be after a day or two. Finished streamlining on 2016.09.09 morning; I will let the remaining typos and even errors remain intact as they are, for these would be beyond mere editing and streamlining—these would take a separate unit of thinking for explanation or even to get them straightened out better.]


Is the physical universe infinite?

Is the physical universe infinite? What is the physics-related reason behind the fact that physicists use this term in their theories?

Let’s deal with these two questions one at a time.

Is the physical universe infinite?

This is one question that strikes most people some time in childhood, certainly at least by the time they are into high-school. (By high-school, I mean: standards V through X, both included.) They may not yet know a concept like infinity. But they do wonder about where it all ends.

A naive expectation kept in those years is that as one grows up and learns more, one sure would gain enough knowledge to know a definite answer to that question.

Then, people certainly grow up, and possibly continue learning more, and sometimes even get a PhD in one of the STEM fields. Yet, somewhat oddly, people are found still continuing to think that one day they (or someone else) would be able to at least deal with this question right. If the nature of opinions expressed in the history of science is any indication, for most of them, such a day never comes. So, the quest goes on to continue even further, well after their PhD and all. At least for some of them.

At least, to me, it did. And, I found that there also were at least a few others who had continued attempting an answer. A couple of notable names here would be (in the chronological order in which I ran into their writings): Eric Dennis, and Ron Pisaturo. But of course, their writings was not the first time any clarification had at all arrived; it was Ayn Rand’s ITOE, second edition, in the winter of 1990. In fact, both the former writings were done only in reference to Ayn Rand’s clarifications. (Comparatively very recently, Roger Schlafly’s casual aside threw the matter up once again for me. More on his remark, later.)

Ayn Rand said that the infinity is a concept of method, that it is a concept of mathematics, and that infinity cannot metaphysically exist. Check out at least the Lexicon entry on infinity, here [^].

A wonderful answer, and a wonderful food for some further thought!

The question to deal with, then, immediately becomes this one: If everything that metaphysically exists is finite, including the physical universe, then it is obvious that the physical universe would have to be finite. For physical entities, and therefore for the physical universe, definiteness includes: the definiteness of extension.

If so, what happens when you reach the (or an) end of it? What do you see from that vantage point of view, and looking outward? In fact, Dennis (in a blogsome essay on a Web page he used to maintain as a PhD student—the page is I guess long gone) and Pisaturo (in an essay) have attempted precisely this question.

Guess you have noticed the difficult spot: Seeing is a form of perception, and before you can perceive anything, it must first exist. If the entirety of the universe itself has been exhausted by getting to its edge, and since there is literally nothing left to see on the other side of it, you couldn’t possibly see anything. The imagery of the cliff (complete with that Hollywood/Bollywood sort of a smoke gently flowing out into the abyss at that edge) cannot apply. In principle.



“But why not?” The child in you cries out. “I want to see what is there,” it tugs at your heart with a wistful intensity. (In comparison, even the Calvin would be more reasonable—not just with the Hobbes but also with the Susie. (Yes, I think, the use of the the is right, here.))

The answers devised by Pisaturo and Dennis (and I now recollect that the matter was also discussed at the HBL), are worth going through.

I myself had written something similar, and at length (though it must have gone in my recent HDD crash). In fact, many of my positions were quite similar to Pisaturo’s. I, however, never completed writing it;  something else caught my attention and the issue somehow fizzled out. See my incomplete series on the nature of space, for an indication of my positions, starting here [^], and going over the next four posts.

The question grabbed my attention once again, in the recent past.

This time round, I decided to attack it from a different angle: with even more of an emphasis on the physics side of the mathematical vs. physical distinction.

In particular, I thought: If the concept is valid only mathematically and not valid metaphysically (in the sense: infinity does not metaphysically exist), and thus, if it was invalid also physically, then why do physicists use it, in their theories?

Note, my question is not how the physicists use the term “infinity;” it is: why.

It is perfectly fine to pursue the how, but only inasmuch as this pursuit helps clarify anything regarding the why.

I intend to address this question, in the next post. I sure will. It’s just that I want to give your independent thinking a chance. I just want to see if in thinking about it independently, some neat/novel points come up or not.

A little bit of suspense is good, you know… Not too much of it, but just a little bit of it…

A Song I Like:

(Hindi) “saare sapane kahin kho gaye…”
Lyrics: Javed Akhtar
Singer: Alka Yagnik
Music: Raju Singh


What mental imagery for “QM” do I carry?—part 1

I haven’t written on QM for some time, and today I found myself wondering a bit about the title question.

When it comes to concepts, especially those of the physical sciences, we always carry some visual images concerning them.

No, the meaning of a concept isn’t the image—that would be an erroneous view of concept. Concepts are necessarily abstract. However, since sense-percepts indeed are both the beginning material as well as the ultimate foundation of concepts, it seems obvious to me that we should also have some kind of a sensory-perceptual data associated with concepts in an “informal” sort of a way. The data serve a certain psycho-epistemological function, viz., that of helping you recall the meaning of a concept, say, with great “vividness.”

Definitions are there. They do give identity to concepts. But most of the concepts that we use—in our daily life, but even more so in the physical sciences—are at a rather high (or even very high) level. They are far removed away from the direct sensory-perceptual data lying underneath them. Due to this distance from the perceptual data, definitions for most concepts themselves are abstract, too.

Definitions tell you that which is denoted by a concept. However, there also are other means that the mind uses in recalling and correctly using concepts. An important means here is the mental imagery: say a prominent picture, a sound, a schematic diagram, or even an instance of a kinesthetic sense—or a cluster of all these. They get associated with a concept, and their use gives you not only of a sense of the various underlying layers of meaning of that concept, but also the connections that a given concept has with the other concepts. I don’t know whether I am using a rigorously correct word or not, but at least for my personal usage, I call such things the connotations of a concept.

With many thinkers, esp. Objectivists, there is this tendency to look down upon connotations. I think this is wrong. If you are going to substitute connotations for denotations, then, of course, it’s a significant error; it is bad. But what if you don’t?

Realize, connotations (in the sense I use the term) themselves do not equate to mere “feelings.” It’s not as if denotations equal to Reason and connotations to Feelings. No. [In fact such a position would be Rationalistic.]

What I call connotations are not some generalized, difficult-to-verbalize, and background sort of vague feelings that occupy your feelings-sphere when you consider a concept. They instead are very specific items of imagery, of some perceptual data. The subconscious seems to work more efficiently when you involve these items. Especially if the concepts are abstract, if they are at a high level.

Let me give you some examples.

Since maths always is fully abstract, it’s inevitable that our minds would use the connotative imagery to even greater extent than in the other sciences.

Consider the concept: “derivative.” The first thing that comes to my mind when I begin to think of this concept is that std. XI graph of a curve, a point on that curve, and a series of chords approaching the tangent to the curve at that point. Everything that I have ever thought of “derivative” or “differential” is tied to this diagram, an image. [Indeed, since the chord approaches the tangent only from one side, every time I sit down to consider the concept of derivative, I still get an uncomfortable feeling about that asymmetry—the tangent isn’t approached from both the sides. I feel a bit comfortable even today, after all these 35+ years.]

Now, take a moment to consider what that imagery for “derivative” is like. The first thing to realize here is that this image is not a instance of a direct sense-perception. In nature, you never see a tangent or a series of chords. For that matter, you don’t even see a 1D curve. All you ever see are the 3D objects and their perceived limits (or extensions), which themselves are idealized as surfaces are curves. Thus, the connotative imagery itself consists of an abstract diagram. Yet, it helps you concretize the concept.

Recently, I was talking to a couple of mathematicians. [Yes, I am talkative. I can talk with any one—even mathematicians!] The issue was pretty abstract, even though we were talking mostly at the “physical intuitive” level. We were arguing at the blackboard [in actuality it was a whiteboard] from many different points of view, and we were doing the argumentative exchange fairly rapidly. So, inevitably, we were picking up only the highlights of an idea of a concept—just those bare tidbits that would be enough for the other person get the gist of how the argument from your side was progressing. For instance, here is what I once said during the discussion: “…Now, as far as the variational calculus goes, that’s not a problem with me [i.e. for the problem I was considering]… You see…” I rapidly drew XY axes, a step function, a flat line at the mid-height, rapidly hatched the area only under the step function. Then without pointing out to anything specific, I just said, “Both these areas are equal, and so, I am home free!” They understood. Even if I had never in fact pointed out the second area!

Clearly, not just me, but they, too, were using these connotative images. Else, communications would have been impossible.

That reminds of something… A girl had once [more than two decades ago] articulately told me, complete with her suave Mumbai accent, that she was not good in communications—with an emphasis on “communications.” That way, many, many people, have told me the same thing—in fact far too many people for my liking. But for some odd reason, this particular instance with this girl has stayed in my mind. My instinctive reaction back then was—the one which I didn’t share with her—that probably her problem was in understanding [anything straight], not in communicating whatever it was that she did understand. If she were only to “get it right,” it was very obvious to me, that she would have absolutely no problem in articulating it. An articulate dumb is an easy possibility; it’s not a contradiction in terms—even though I was (relatively more) new to the phenomenon back then.

But getting back to this recent discussion, if I myself were to make use of these “physical intuitive” imageries, then it would have been perfectly OK—I am an engineer. But the point is, at one point in discussion, in thinking aloud, one of these mathematicians themselves said something like: “So, when you integrate, you are going get this quantity [i.e. an expression he had written on the board] under the integral sign.” Then, in the same flow, he added without any distinct pause, still continuing to think aloud, still not addressing the line to anyone in particular: “You know integration—sum of areas under the curve. And so, …”

Clearly, even in his professional mathematical work, when it came to exploring a new path, [even if that path was only in a known territory], he wasn’t using either the formal epsilon-delta definition or the idea of the anti-derivative or the fundamental theorem of calculus. He was using a finite sum of finite number of finite areas under a curve. He would sure formalize his argument later on, and that’s when these beasts of formalization would come in. But in actually working out that new path, he was using only the simple connotative imagery.

We all always do.

So, as the thought of QM came up to me during my “purpose-less” kind of an idle arm-chair wondering on this fine monsoon evening, while comfortably sipping a cup of coffee at home, I happened to ask myself: what imagery do I really use when I say “QM”?

By “QM,” I meant, first and foremost, the concept itself. Not the implications of the findings of this field of science, but “quantum mechanics” as the idea.

I answered the question to myself immediately, of course. [How else could such imagery be of any use, in the first place?] I wanted to write about that question today. Instead, in explaining the meaning of imagery and connotations, I have ended up writing so much [about 1500 words] that I must now split this intended post into two parts. Accordingly, this writeup now becomes the part 1 of a (hopefully only) 2-part series of posts.

I will come to QM in the second part, hopefully soon enough. In the meanwhile, think about what your answer to that same question is like. [Yes, critical takes are perfectly welcome, too. Especially if they are sarcastic.]

* * * * *   * * * * *   * * * * *

A Song I Like:
(Western popular) “The day before you came”
Band: ABBA