On whether A is not non-A

This post has its origin in a neat comment I received on my last post [^]; see the exchange starting here: [^].

The question is whether I accept that A is not non-A.

My answer is: No, I do not accept that, logically speaking, A is not non-A—not unless the context to accept this statement is understood clearly and unambiguously (and the best way to do that is to spell it out explicitly).

Another way to say the same thing is that I can accept that “A is not non-A,” but only after applying proper qualifications; I won’t accept it in an unqualified way.

Let me explain by considering various cases arising, using a simple example.

The Venn diagram:

Let’s begin by drawing a Venn diagram.

Draw a rectangle and call it the set R. Draw a circle completely contained in it, and call it the set A. You can’t put a round peg to fill a rectangular hole, so, the remaining area of the rectangle is not zero. Call the remaining area B. See the diagram below.

The Venn Diagram

Case 1: All sets are non-empty:

Assume that neither A nor B is empty. Using symbolic terms, we can say that:
A \neq \emptyset,
B \neq \emptyset, and
R \equiv A \cup B
where the symbol \emptyset denotes an empty set, and \equiv means “is defined as.”

We take R as the universal set—of this context. For example, R may represent, say the set of all the computers you own, with A denoting your laptops and B denoting your desktops.

I take the term “proper set” to mean a set that has at least one element or member in it, i.e., a set which is not empty.

Now, focus on A. Since the set A is a proper set, then it is meaningful to apply the negation- or complement-operator to it. [May be, I have given away my complete answer right here…] Denote the resulting set, the non-A, as A^{\complement }. Then, in symbolic terms:
A^{\complement } \equiv R \setminus A.
where the symbol \setminus denotes taking the complement of the second operand, in the context of the first operand (i.e., “subtracting” A from R). In our example,
A^{\complement } = B,
and so:
A^{\complement } \neq \emptyset.
Thus, here, A^{\complement } also is a proper (i.e. non-empty) set.

To conclude this part, the words “non-A”, when translated into symbolic terms, means A^{\complement }, and this set here is exactly the same as B.

To find the meaning of the phrase “not non-A,” I presume that it means applying the negation i.e. the complement operator to the set A^{\complement }.

It is possible to apply the complement operator because A ^{\complement } \neq \emptyset. Let us define the result of this operation as A^{\complement \complement}; note the two ^{\complement}s appearing in its name. The operation, in symbols becomes:
A^{\complement \complement} \equiv R \setminus A^{\complement} = R \setminus B = A.
Note that we could apply the complement operator to A and later on to A^{\complement} only because each was non-empty.

As the simple algebra of the above simple-minded example shows,
A = A^{\complement\complement},
which means, we have to accept, in this example, that A is not non-A.

Remarks on the Case 1:

However, note that we can accept the proposition only under the given assumptions.

In  particular, in arriving at it, we have applied the complement-operator twice. (i) First, we applied it to the “innermost” operand i.e. A, which gave us A^{\complement}. (ii) Then, we took this result, and applied the complement-operator to it once again, yielding A^{\complement\complement}. Thus, the operand for the second complement-operator was A^{\complement}.

Now, here is the rule:

Rule 1: We cannot meaningfully apply the complement-operator unless the operand set is proper (i.e. non-empty).

People probably make mistakes in deciding whether A is not non-A, because, probably, they informally (and properly) do take the “innermost” operand, viz. A, to be non-empty. But then, further down the line, they do not check whether the second operand, viz. A^{\complement} turns out to be empty or not.

Case 2: When the set A^{\complement} is empty:

The set A^{\complement} will be empty if B = \emptyset, which will happen if and only if A = R. Recall, R is defined to be the union of A and B.

So, every time there are two mutually exclusive and collectively exhaustive sets, if any one of them is made empty, you cannot doubly apply the negation or the complement operator to the other (nonempty) set.

Such a situation always occurs whenever the remaining set coincides with the universal set of a given context.

In attempting a double negation, if your first (or innermost) operand itself is a universal set, then you cannot apply the negation operator for the second time, because by Rule 1, the result of the first operator comes out as an empty set.

The nature of an empty set:

But why this rule that you can’t negate (or take the complement of) an empty set?

An empty set contains no element (or member). Since it is the elements which together impart identity to a set, an empty set has no identity of its own.

As an aside, some people think that all the usages of the phrase “empty set” refers to the one and the only set (in the entire universe, for all possible logical propositions involving sets). For instance, the empty set obtained by taking an intersection of dogs and cats, they say, is exactly the same empty set as the one obtained by taking an intersection of cars and bikes.

I reject this position. It seems to me to be Platonic in nature, and there is no reason to give Plato even an inch of the wedge-space in this Aristotlean universe of logic and reality.

As a clarification, notice, we are talking of the basic and universal logic here, not the implementation details of a programming language. A programming language may choose to point all the occurrences of the NULL string to the same memory location. This is merely an implementation choice to save on the limited computer memory. But it still makes no sense to say that all empty C-strings exist at the same memory location—but that’s what you end up having if you call an empty set the empty set. Which brings us to the next issue.

If an empty set has no identity of its own, if it has no elements, and hence no referents, then how come it can at all be defined? After all, a definition requires identity.

The answer is: Structurally speaking, an empty set acquires its meaning—its identity—“externally;” it has no “internally” generated identity.

The only identity applicable to an empty set is an abstract one which gets imparted to it externally; the purpose of this identity is to bring a logical closure (or logical completeness) to the primitive operations defined on sets.

For instance, intersection is an operator. To formally bring closure to the intersection operation, we have to acknowledge that it may operate over any combination of any operand sets, regardless of their natures. This range includes having to define the intersection operator for two sets that have no element in common. We abstractly define the result of such a case as an empty set. In this case, the meaning of the empty set refers not to a result set of a specific internal identity, but only to the operation and the disjoint nature the operands which together generated it, i.e., via a logical relation whose meaning is external to the contents of the empty set.

Inasmuch as an empty set necessarily includes a reference to an operation, it is a concept of method. Inasmuch as many combinations of various operations and operands can together give rise to numerous particular instances of an empty set, there cannot be a unique instance of it which is applicable in all contexts. In other words, an empty set is not a singleton; it is wrong to call it the empty set.

Since an empty set has no identity of its own, the notion cannot be applied in an existence-related (or ontic or metaphysical) sense. The only sense it has is in the methodological (or epistemic) sense.

Extending the meaning of operations on an empty set:

In a derivative sense, we may redefine (i.e. extend) our terms.

First, we observe that since an empty set lacks an identity of its own, the result of any operator applied to it cannot have any (internal) identity of its own. Then, equating these two lacks of existence-related identities (which is where the extension of the meaning occurs), we may say, even if only in a derivative or secondary sense, that

Rule 2: The result of an operator applied to an empty set again is another empty set.

Thus, if we now allow the complement-operator to operate also on an empty set (which, earlier, we did not allow), then the result would have to be another empty set.

Again, the meaning of this second empty set depends on the entirety of its generating context.

Case 3: When the non-empty set is the universal set:

For our particular example, assuming B = \emptyset and hence A = R, if we allow complement operator to be applied (in the extended sense) to A^{\complement}, then

A^{\complement\complement} \equiv R \setminus A^{\complement} = R \setminus (R \setminus A) = R \setminus B = R \setminus (\emptyset) = R = A.

Carefully note, in the above sequence, the place where the extended theory kicks in is at the expression: R \setminus (\emptyset).

We can apply the \setminus operator here only in an extended sense, not primary.

We could here perform this operation only because the left hand-side operand for the complement operator, viz., the set R here was a universal set. Any time you have a universal set on the left hand-side of a complement operator, there is no more any scope left for ambiguity. This state is irrespective of whether the operand on the right hand-side is a proper set or an empty set.

So, in this extended sense, feel free to say that A is not non-A, provided A is the universal set for a given context.

To recap:

The idea of an empty set acquires meaning only externally, i.e., only in reference to some other non-empty set(s). An empty set is thus only an abstract place-holder for the result of an operation applied to proper set(s), the operation being such that it yields no elements. It is a place-holder because it refers to the result of an operation; it is abstract, because this result has no element, hence no internally generated identity, hence no concrete meaning except in an abstract relation to that specific operation (including those specific operands). There is no “the” empty set; each empty set, despite being abstract, refers to a combination of an instance of proper set(s) and an instance of an operation giving rise to it.


E1: Draw a rectangle and put three non-overlapping circles completely contained in it. The circles respectively represent the three sets A, B, C, and the remaining portion of the rectangle represents the fourth set D. Assuming this Venn diagram, determine the meaning of the following expressions:

(i) R \setminus (B \cup C) (ii) R \setminus (B \cap C) (iii) R \setminus (A \cup B \cup C) (iv) R \setminus (A \cap B \cap C).

(v)–(viii) Repeat (i)–(iv) by substituting D in place of R.

(ix)–(xvi) Repeat (i)–(viii) if A and B partly overlap.

E2: Identify the nature of set theoretical relations implied by that simple rule of algebra which states that two negatives make a positive.

A bit philosophical, and a form better than “A is not non-A”:

When Aristotle said that “A is A,” and when Ayn Rand taught its proper meaning: “Existence is identity,” they referred to the concepts of “existence” and “identity.” Thus, they referred to the universals. Here, the word “universals” is to be taken in the sense of a conceptual abstraction.

If concepts—any concepts, not necessarily only the philosophical axioms—are to be represented in terms of the set theory, how can we proceed doing that?

(BTW, I reject the position that the set theory, even the so-called axiomatic set theory, is more fundamental than the philosophic abstractions.)

Before we address this issue of representation, understand that there are two ways in which we can specify a set: (i) by enumeration, i.e. by listing out all its (relatively concrete) members, and (ii) by rule, i.e. by specifying a definition (which may denote an infinity of concretes of a certain kind, within a certain range of measurements).

The virtue of the set theory is that it can be applied equally well to both finite sets and infinite sets.

The finite sets can always be completely specified via enumeration, at least in principle. On the other hand, infinite sets can never be completely specified via enumeration. (An infinite set is one that has an infinity of members or elements.)

A concept (any concept, whether of maths, or art, or engineering, or philosophy…) by definition stands for an infinity of concretes. Now, in the set theory, an infinity of concretes can be specified only using a rule.

Therefore, the only set-theoretic means capable of representing concepts in that theory is to specify their meaning via “rule” i.e. definition of the concept.

Now, consider for a moment a philosophical axiom such as the concept of “existence.” Since the only possible set-theoretic representation of a concept is as an infinite set, and since philosophical axiomatic concepts have no antecedents, no priors, the set-theoretic representation of the axiom of “existence” would necessarily be as a universal set.

We saw that the complement of a universal set is an empty set. This is a set-theoretic conclusion. Its broader-based, philosophic analog is: there are no contraries to axiomatic concepts.

For the reasons explained above, you may thus conclude, in the derivative sense, that:

“existence is not void”,

where “void” is taken as exactly synonymous to “non-existence”.

The proposition quoted in the last sentence is true.

However, as the set theory makes it clear and easy to understand, it does not mean that you can take this formulation for a definition of the concept of existence. The term “void” here has no independent existence; it can be defined only by a negation of existence itself.

You cannot locate the meaning of existence in reference to void, even if it is true that “existence is not void”.

Even if you use the terms in an extended sense and thereby do apply the “not” qualfier (in the set-theoretic representation, it would be an operator) to the void (to the empty set), for the above-mentioned reasons, you still cannot then read the term “is” to mean “is defined as,” or “is completely synonymous with.” Not just our philosophical knowledge but even its narrower set-theoretical representation is powerful enough that it doesn’t allow us doing so.

That’s why a better way to connect “existence” with “void” is to instead say:

“Existence is not just the absence of the void.”

The same principle applies to any concept, not just to the most fundamental philosophic axioms, so long as you are careful to delineate and delimit the context—and as we saw, the most crucial element here is the universal set. You can take a complement of an empty set only when the left hand-side operator is a universal set.

Let us consider a few concepts, and compare putting them in the two forms:

  • from “A is not non-A”
  • to “A is not the [just] absence [or negation] of non-A,” or, “A is much more than just a negation of the non-A”.

Consider the concept: focus. Following the first form, a statement we can formulate is:

“focus is not evasion.”

However, it does make much more sense to say that

“focus is not just an absence of evasion,” or that “focus is not limited to an anti-evasion process.”

Both these statements follow the second form. The first form, even if it is logically true, is not as illuminating as is the second.


Here are a few sentences formulated in the first form—i.e. in the form “A is not non-A” or something similar. Reformulate them into the second form—i.e. in the form such as: “A is not just an absence or negation of non-A” or “A is much better than or much more than just a complement or negation of non-A”. (Note: SPPU means the Savitribai Phule Pune University):

  • Engineers are not mathematicians
  • C++ programmers are not kids
  • IISc Bangalore is not SPPU
  • IIT Madras is not SPPU
  • IIT Kanpur is not SPPU
  • IIT Bombay is not SPPU
  • The University of Mumbai is not SPPU
  • The Shivaji University is not SPPU

[Lest someone from SPPU choose for his examples the statements “Mechanical Engg. is not Metallurgy” and “Metallurgy is not Mechanical Engg.,” we would suggest him another exercise, one which would be better suited to the universal set of all his intellectual means. The exercise involves operations mostly on the finite sets alone. We would ask him to verify (and not to find out in the first place) whether the finite set (specified with an indicative enumeration) consisting of {CFD, Fluid Mechanics, Heat Transfer, Thermodynamics, Strength of Materials, FEM, Stress Analysis, NDT, Failure Analysis,…} represents an intersection of Mechanical Engg and Metallurgy or not.]


A Song I Like:

[I had run this song way back in 2011, but now want to run it again.]

(Hindi) “are nahin nahin nahin nahin, nahin nahin, koee tumasaa hanseen…”
Singers: Kishore Kumar, Asha Bhosale
Music: Rajesh Roshan
Lyrics: Anand Bakshi

[But I won’t disappoint you. Here is another song I like and one I haven’t run so far.]

(Hindi) “baaghon mein bahaar hain…”
Music: S. D. Burman [but it sounds so much like R.D., too!]
Singers: Mohamad Rafi, Lata Mangeshkar
Lyrics: Anand Bakshi

[Exercise, again!: For each song, whenever a no’s-containing line comes up, count the number of no’s in it. Then figure out whether the rule that double negatives cancel out applies or not. Why or why not?]


[Mostly done. Done editing now (right on 2016.10.22). Drop me a line if something isn’t clear—logic is a difficult topic to write on.]


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.]


Analyzing the Eco-Cooler, part 1

OK, that was ample time for you to have hit your fluid mech/heat transfer/thermo books, and to have it verified whether the 5 deg. C drop was believable or not… You must have made your notes, too, no?…  So, in this post, let’s cross-check our notes.

On my part, I will first present the simplest (and the most approximate) model, and also give you a simple Python script to play with, to see what kind of predictions this model makes. Then, we will go on considering more and more complicated but still approximate “engineering” models that hopefully become more and more realistic. We will cross-check their predictions too. We may eventually find that a full-fledged CFD analysis is called for. However, I will save that—I mean doing a full-fledged CFD analysis—for another day. (I in fact plan to write a paper on this problem, using CFD. (…Some day…).)

The reason we follow this method—from the simplest and crudest models to the more complicated and better ones—is because for problems related to fluid mechanics, it is this method which works best!

I mean to say, the full-fledged Navier-Stokes equations are too complicated to solve for, even when they are applied to the simplest of practically encountered geometries—e.g., the flow of air through the Eco-Cooler bottle. Since the NS equations cannot be solved exactly, the traditional engineering models (which are based on analytical or semi-analytical solutions) fall short, and then, a CFD analysis is called for.

But the fact of the matter also is, even CFD itself is only an approximate technique. CFD solutions sometimes even happen to carry more numerical artifacts than real physics. We therefore cannot approach CFD blindly. We ourselves have to have some good idea in the first place of what the desired solution should look like. We should have this idea right before we even think of setting up a CFD model/simulation. The traditional engineering models provide precisely these insights.

Yes, that’s right.

The traditional engineering models actually are more approximate than CFD. Yet, since they are also simpler than CFD, and since they explicitly carry conceptual connections with the major fluid mechanical phenomena in a more direct manner, they also make it easier to gain insights about both the nature of the problem, and the nature of the expected solution. No similar insights can be had by directly using CFD, for several reasons. The CFD theory itself is too complicated, and the CFD practice involves too many different analysis options. In the jungle of all those parameters, iterations, and convergence requirements, CFD happens to loose the directness of the conceptual connections with the basic analytical theory—with the fluid dynamical phenomena.

That’s why we first deal with the simplest engineering models, even though they are known to be approximate—and therefore, they are easily capable of giving us wrong results. But this way, we can build insights. Building insights is an art, and the process progresses slowly.

As I said, we will follow an iterative scheme of model building. In each phase or iteration of the model building activity, we will actually be applying the same set of principles: the conservation of mass, momentum, and energy. However, in going from a model-building phase to the next, we will aim to incorporate an increasing level of complexity or sophistication—and accuracy, hopefully.

Actually, in the fluid dynamics theory, all the three conservation equations come coupled to each other. You cannot solve for conservation of only the mass, or the momentum, or the energy, by neglecting any of the other two. However, for this particular problem (of the Eco-Cooler), for various reasons (which you will come to appreciate slowly), it so turns out that we can get away considering the mass, momentum and energy equations in a decoupled manner, and in the order stated: first mass, then momentum, and then energy. (It’s no accident that text-books spell out these three principles in this order. Many fluids-related phenomena with which we are well familiar through our direct experience of the world are such that for solving problems involving these phenomena, this order happens to be the best one to follow.)

So, with that big introduction, let’s now get going calculating—even though we will not shut up even while performing those calculations.

Model-Building Phase I: The Simplest Possible Model:


Consider the plastic-bottles used in the Eco-Cooler; they all lie horizontally. Consider one of these bottles. A tube has been obtained by cutting off the base of the bottle. Let the base-plane be identified by the subscript 1 and the neck-plane by 2. See the figure below:






Air flows from the base-plane (1) to the neck-plane (2).

Conservation of mass:

The simplest possible expression for mass conservation, applied to the bottle geometry, would be the continuity equation, given below:
A_1 U_1 = A_2 U_2
where A_1 and A_2 are cross-sectional areas of the bottle, and U_1 and U_2 are wind velocities, at the base and the neck, respectively. Rearranging for U_2, we get:
U_2 = \dfrac{A_1}{A_2} U_1             …(1)

We can use this simple an equation for mass conservation only if the flow is incompressible. To determine if our flow is incompressible or not, we have to calculate the Mach number for the flow. To do that, we have to first know the expected wind velocities.

Referring to the Wiki article on the Beaufort scale [^], we may make an assumption that the inlet speed can go up to about 60 kmph. Actually, the wind-speeds covered by the Beaufort scale go much higher (in excess of 118 kmph). However, practically speaking, the only times such high wind-speeds (gales etc.) occur in India is when rains also accompany them. The rains bring down the ambient temperature anyway, thereby obviating the need for any form of a cooler. Thus, we have to consider only the lower range of speeds.

Assuming the speed of sound in air to be about 340 m/s, we find that the Mach number (for the range of the winds we consider) goes up to about 0.65. Now, for \text{Ma} < 0.33, the flow is sub-sonic, and can be regarded as incompressible. For 0.33 < \text{Ma} < 1.0, the flow is trans-sonic, meaning, the changes in pressures do not adjust “instantaneously” everywhere in the flow, and so, it is increasingly not possible to even idealize the flow as incompressible.

Therefore, in the interest of simplicity, for our first solution cut, we choose to consider only the wind-speeds up to 100 m/s, i.e. 28 kmph, so that the incompressibility assumption can be justified. Making this assumption about the highest possible wind-speed, we are then free to use the simplest form of mass conservation equation given above as Eq. (1).

For a typical one liter bottle, the base diameter is 7.5 cm, and the neck diameter is 2 cm (both referring to IDs i.e. inner diameters). (I measured them myself!) So, the area ratio \frac{A_1}{A_2} turns out to be about 14.

Thus, the wind accelerates inside the bottle; the outlet velocity is about 14 times the inlet velocity!

This looks like a remarkable bit of acceleration to happen over just some 20 cm of length. (The bottle is cut somewhere in the middle.) More on it, later.

Conservation of momentum:

The simplest possible equation to use for momentum conservation is the steady-state Bernoulli’s equation:
\dfrac{P_1}{\rho} + \dfrac{U_1^2}{2} = \dfrac{P_2}{\rho} + \dfrac{U_2^2}{2}        …(2)
where we have ignored the potential head term (gz) because the tube is horizontal as well as symmetrical about its central horizontal axis (and because the air is so thin that its weight can be easily neglected here).

Carefully note the assumptions behind Eq (2). It holds only for a steady-state and laminar flow, and only after neglecting viscosity.

Since we are in a hurry, we will assume them all, and proceed!

Rearranging Eq (2) for P_2, we obtain:
P_2 = P_1 + \dfrac{\rho}{2} \left( U_1^2 - U_2^2 \right)

Conservation of energy:

We basically need the equation of energy conservation only in order to calculate the temperature at the neck (T_2), from a knowledge of: (i) the temperature at the base, T_1, and (ii) the pressures P_1 and P_2.

In the last line, I said “from.” This usage implies that there already is an assumption I made, viz., that the energy equation can be decoupled from the momentum equation. How reasonable is this assumption? It seems pretty OK. Think: can air flowing through a 7.5 cm or a 2.0 cm diameter tube at under 100 m/s get heated up to a significant fraction of 5 deg. C, over a length of just a foot or less? Not likely. Can heating up the neck region cause the air flow to come a halt, say because it helps build up a sufficient amount of pressure? Not even remotely likely. So, we may get away by decoupling the two.

The simplest equation to compute T_2 from the other three quantities would be: the ideal gas law, given as:
\dfrac{P_1 V_1}{T_1} = \dfrac{P_2 V_2}{T_2}.

We have already found that the flow can be considered incompressible (at least up to 28 kmph of wind-speeds). Hence, the volume of each fluid part remains constant, i.e., V_1 = V_2. (Note, in this equation, we have to consider the volume of a fluid element or a part, not the volume for a unit axial length at a given cross-section of the bottle.) For constant volume, the ideal gas law reduces to:
\dfrac{P_1}{T_1} = \dfrac{P_2}{T_2},
from which we can conclude:
T_2 = P_2 \dfrac{T_1}{P_1}.

But we have to know whether the assumption of the ideal gas itself can be used in our problem—for the real air—or not. For doing that, we have to know the critical pressure and temperature of air. Cengel (“Thermodynamics: An Engineering Approach,” 8th SI units edition) lists them (Appendix A1) as 132.5 K, and 3.77 MPa. Using these values, the reduced temperature and the reduced pressure of air turn out to be T_{1_R} = (30 + 273.15)/132.5 \approx 2.29, and P_{1_R} = (101.32\times10^3)/(3.77\times 10^6) \approx 0.027. Further, the expected drops in the pressure and temperature would be just small fractions of the inlet values. Hence, the reduced quantities for the outlet also would not differ significantly from those for the inlet. Referring to the chart and the remarks on p. 139 in Cengel, it seems like we can get away using the ideal gas law.

Note, we are using the ideal gas law not as an approximation to the energy equation, but in place of it, simply because looking at the variables, we noticed that T_2 had to be determined from the other three variables, and this set of variables reminded us of the ideal gas law! Then, referring to the reduced pressure and temperature, the ideal gas approximation seemed to be OK. In short, we have not directly considered the energy conservation principle at all. We may subsequently have an occasion to revisit this issue.

Assumed data:

Now, let us make assumptions about the data to be used for our calculations.

Suppose that the ambient temperature is 30 deg C, and the Eco-Cooler is kept at the mean sea level (MSL), say by the sea-side (rather than somewhere on a slope going down into the Death Valley [^]). Now, seated at a sea-side, the evaporative cooler isn’t going to be feasible because of humidity, and that’s the reason why we are at all considering using the Eco-Cooler. Alright. So to wrap up this point, we have to use data values at the MSL.

Suppose that we can use the ambient MSL atmospheric pressure for the inlet of the bottle; it would then mean that P_1 = 101330 Pa. (Note, this is an assumption; like with many other assumptions, we may have occasion to revisit it later on.) The air density at MSL and at 30 deg. C may be taken to be \rho = 1.169 kg/m^3. (Minor changes to this value turn out to have minimal impact on the predictions, so it’s OK to use, even if we might have made a mistake in looking it up hurriedly.)

For wind-speeds, let’s assume that the speed at the inlet (i.e., at the base of the bottle, which is exposed to the outside) is the same as the ambient wind-speed. (Again, this is an assumption; we may have the occasion to revisit it later on.)

Since the wind-speeds vary, and since the pressure drop (and hence the temperature drop) obviously depends on the inlet wind-speed, we will have to repeat our calculations for each wind-speed, again and again.

Referring again to the Wiki article for the Beaufort scale [^], to have representative wind-speed values, we choose to take the averages of the lower and upper wind speeds which together define the range for each wind-grade on the Beaufort scale. Thus, our U_1 could be one of: 0.5, 3.0, 8.5, 15.5, 24.0, 33.5, 44.0, all in kmph.

We are now ready to do our calculations. To recap: First, we calculate U_2 from U_1 using the continuity (mass conservation) equation and the known area ratio (which is about 14). Then we substitute the data in the re-arranged Bernoulli’s equation (which brings in its own assumptions) and obtain P_2, the pressure at the outlet (i.e. the neck of the bottle). From the ideal gas law (being used in place of the energy equation proper), we then calculate T_2.

Python script:

We use a Python script only because the calculations for T_2 have to be repeated again and again for different wind-speeds. Anyway, here is the Python script:

This Python script calculates the expected
outlet temperature for a bottle in the Eco-Cooler.
See the relevant blog posts by Ajit R. Jadhav.
All units are in SI.

d1 = 7.5 # ID at the inlet (i.e. at the base), in cm
d2 = 2.0 # ID at the outlet (i.e. at the neck), in cm
AR = (d1*d1)/(d2*d2) # Area ratio for the bottle

T1 = 30.0 # Ambient temp., in deg. C
T1 = T1 + 273.15 # Conversion from deg. C to K
rho = 1.169 # Density of air, in kg/m^3
P1 = 101330 # Ambient pressure, in Pa

# The Beaufort Scale wind speeds in kmph, and their text descriptions
bsa = [0.5, 3.0, 8.5, 15.5, 24.0, 33.5, 44.0]
bsta = ["Calm","Light air", "Light breeze", "Gentle breeze", "Moderate breeze", "Fresh breeze", "Strong breeze"]

# Calculate the expected temperatures for various wind-speeds
for i in range(7):
    s1 = bsa[i] # wind-speed, in kmph
    sText = bsta[i] # wind-speed description

    U1 = s1 / 3.6 # conversion from kmph to m/s
    U2 = U1*AR

    # Calculate P2 using Bernoulli's equation
    P2 = P1 + rho*(U1*U1 - U2*U2)/2.0

    # Calculate T2 using the ideal gas law
    T2 = T1*P2/P1
    TC = T2 - 273.15 # conversion from K to deg. C
    print( "%20s %6.1f %6.2lf %10.0f %6.1f" % (sText, s1, U1, P2, TC) )

The program written using Python is so simple, that you can very easily modify it, say to report any additional calculations that were made along the way.

Output data:

Here is the output data I get. The columns are: wind description in words, wind speed in kmph, wind speed in m/s, outlet pressure, and outlet temperature:

    Wind Description        U_1        P2, Pa   T2, deg. C                     
                        kmph  m/s      
                Calm    0.5   0.14     101328   30.0
           Light air    3.0   0.83     101250   29.8
        Light breeze    8.5   2.36     100689   28.1
       Gentle breeze   15.5   4.31      99198   23.6
     Moderate breeze   24.0   6.67      96219   14.7
        Fresh breeze   33.5   9.31      91372    0.2
       Strong breeze   44.0  12.22      84151  -21.4

Interpretation of results:

Our model predicts that when the breeze is strong (but less strong than when the tube is held near the window of a car that is traveling on an expressway), we should get ice formation at the neck of the bottle—in fact, it should be a super-cooled ice!

From your knowledge of what happens on the Indian sea-side, do you expect a mere half-foot tube of variable diameter, to begin to have ice-formation at its neck?

Obviously, the model we dreamt up has gone wrong somewhere. …

… But precisely where? … We have made so many assumptions…. Which of these assumptions are likely to have impacted our analysis the most? In what all places should we bring in the corrections to our model?

I have already given a lot of explicit notes—not just hints—while writing down the analysis above. So, go through the entire post once again, now pausing especially at the assumptions, and think how we may go on to improve our model.

I will return to the business of improving our model, in my next post.

And as always, sure drop me a line if you think I am going wrong somewhere.

… For instance, also give it a thought as to whether my analysis scheme, based on fluid mechanics, itself is wrong or what. … Here, you may want to refer to the comments on the blog post I had linked to last time [^], esp. the comments made there by Arnaut Jaspers and others. (Jaspers’ and others’ comments appear somewhere in the middle of all the comments, so you have to ask the Web page to load more comments some 3–4 times; the exact URL where the comments in question begin is this: [^]).

Alright, enjoy!

Ummm… Since I have given you Python scripts to play with, guess the usual section on a song I like has become redundant. So, let me mention the “other” song (re. my last post) when I finish this series of posts—which will take one, or at the most two more posts).

[I may come back and cross-check the latex entries in this post, grammar, etc., later on today itself, when I may perhaps edit this post just a bit, but not much. Done on 2016.10.02 itself.]



A few remarks on the Eco-Cooler

While generally browsing ISHRAE[^]’s Web site after a long while today, I ran into this coverage of the so-called Eco-Cooler [^] in their News Section.

… My earlier coverage of another creative usage of the used plastic bottles was here: [^] (see the “farm ponds” section in that post).

Anyway, coming back to the Eco-Cooler, a simple Google search on the inventor’s name (“Ashis Paul”) will give you quite a few links, e.g. here [^] and here [^]. A sketchy story as to how Paul ended up inventing the cooler is mentioned here [^].

The idea is so simple that you just have to wonder why no one else thought of it before!

Apart from the cultural reasons (people in this part of the world arguably don’t always try to tackle their life’s problems creatively; they arguably just sit idle and whine and complain) the other reason, I think, is that to a learned engineer (and I will call myself that), it would be difficult to think that the cooling effect obtained this way could be significant—the claim is a drop of up to 5 degrees Celcius (i.e. 9 degrees Fahrenheit) in the room temperature!

… I don’t know why, but somehow, at least on the face of it, a claim of this big a temperature drop does seem unbelievable, at least initially.

Anyway, here are a few things you could pursue, especially if you are a student of mechanical engineering:

  • First, name (or hit your text books and find out) the principle that explains the cooling effect.
  • Then, assume suitable values for the air flow, and using the appropriate thermodynamic/psychrometric charts and property tables, determine whether the inventor’s claim is acceptable. (I have not done this cross-check myself before writing this post; I just assumed that someone at ISHRAE must have done it!)
  • Now check out the DIY YouTube videos on this invention. If interested, think of building an Eco-Cooler and measuring its performance yourself. (And if you do that, and if you are from Pune or a nearby place, then do drop me a line. I would love to come over and check it out myself.) Alternatively, think of doing a “simple” CFD analysis and compute the estimated temperature drop. [… And to think how people keep asking me where I get all my student-project ideas from!]

Next are a few notings (assuming that the cooling effect is indeed big enough) to help you put it all in the right context, and then also some pointers as to how you could try and modify (and even optimize) the existing design.

  • Bamboo Curtains: First, try to put it in some context: People in India often use bamboo “chaTai”s or mats [^] as window covers/curtains. (Also the khus curtains.) Some of these “chaTai”s do carry regularly spaced holes. Do such mats (or even Venetian blinds) give rise to any cooling effect? Can they? Why or why not?
  • Flow Pattern: Using ink blobs or other tracers in a flow of water, visualize the geometry of the flow going into a hole, and ask yourself: Is a bottle surface at all necessary? Why? When?
  • Shape and Size: Would you get a better effect if you modify the dimensions of the bottles used in the Eco-Cooler? Is the size of the water bottle optimal? How about the shape?
  • Mounting: What if you mount the bottles on the board not at the neck but at the base? Would it be more stable? Would it be more convenient because nothing goes protruding outside the room? Many questions below assume mouting on the base, such that the bottles come protruding inside the room. Let me call it the Internally Protrduding Design (IPD for short), as compared to the Externally Protruding Design (EPD, which is shown in the original photographs and videos).
  • Materials: How about changing the material? What if you use clay for the tube?
  • Evaporative Cooling: Assume IPD. Would keeping the clay tubes wet help enhance the cooling? You could keep them wet via a simple system of water from an overhead tank running over or percolating through the thickness of the clay tubes. For this purpose, arrange the base circles in a hexagonal lattice arrangement (rather than the simple square lattice they show in the original sketches and videos). In any case, compare the cooling obtained using the dry Eco-Cooler vs. that using the desert cooler. Then, compare it with the wet Eco-Cooler. To do that, first find out the natural cooling limitations of the desert cooler. (Something like this was a unit test question I had asked my ME (Heat Power) students last year.) Where would the wet Eco-Cooler be more effective—in the humid coastal areas (e.g. in Mumbai), or in the dry-and-hot areas (like in the plains or Delhi)?
  • Cooling Achieved: Estimate the size of the biggest room that may be effectively cooled using EPD. Repeat for IPD. Also find out (by CFD analysis or by experiment) the locations where the cooling would be effective enough to bring (at least a bit of) comfort to a human being.
  • Forced Circulation: What if you use forced air circulation with IPD? Would it lead to any better cooling? Don’t guess! Bring out your charts, tables and calculators once again, assume suitable values for fans, and provide a quantitative estimate. Then, also figure out if a forced air circulation could be economical enough.
  • Enhanced Natural Circulation: (Assume both designs in turn.) Think if you could possibly enhance the natural air circulation by using some simple cardboard flaps erected on the outside of the room. (Do a quick-and-simple CFD analysis if you wish.)
  • Radiation: How much of the temperature drop can be attributed to the obvious reduction in the radiative heating alone?
  • Internal Reflection: Is the total internal reflection an important factor here? Would using clay tubes (of varying cross section) reduce the glare due to total internal reflection?
  • Noise Generation: Does the arrangement emit sound (as in a patch of bamboo trees)?
  • Aesthetics: Assume IPD: Think of how the cooler design may be used creatively for aesthetic enhancements of the room interiors in a middle-class apartment or bungalow. (The cooler doesn’t have to be used only in the slums!) Could ready-made panels of standard sizes be made in clay or alternative materials (e.g. cheap ceramics) just as cost-effectively? Would painting the bottles help?
  • Reverberations: Assume IPD: Refer to technical acoustics. Can you reduce the sound reverberations if you use such shapes near walls? Could plastic bottles be at all effective in this respect? How about the clay tubes? Would the existence of the holes modify the sound-dampening effect due to the protruding tubes? Would they introduce unwanted modulations? Estimate the range of sound-frequencies (or of musical tones) that stand to get impacted (for the better or for the worse) due to the presence of the Eco-Cooler.


A Song I Like:

(Hindi) “too laalee hai savere waalee, gagan rang de tu mere man kaa…”
Music: Sapan-Jagmohan
Singers: Kishore Kumar, Asha Bhosale
Lyrics: Indivar Naqsh Lyallpuri [^]

[BTW, this song reminds me of another song which has a similar tune. (I don’t know music well enough to make out “raaga”s. In fact, I often cannot even make out tones! I can only compare the tones in a hand-waving sort of a manner, that’s all! … It’s just that sometimes I happen to notice some similarities.) See if you can guess it—the other song. I will tell you the answer in my next post.]

[I have a habit of coming back and modifying my post a bit even after publication. But guess, at least for this post, there really isn’t anything left to add or modify.  Actually, I did modify! [sigh!] I clarified the two designs and even added the names for them. I even changed the title a bit!!…  Anyway, bye for now, and take care…]


(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.]