“The spiritual heritage of India”

I wrote a few comments at Prof. Scott Aaronson’s blog, in response to his post of the title: “30 of my favorite books”, here [^].

Let me give you the links to my comments: [^], [^], [^] and [^].

Let me reproduce the last one of my four comments, with just so slight bit of editing. [You know I couldn’t have resisted the opportunity, right?]:

Since I mentioned the “upnishad”s above (i.e. here [ ^]), and as far as this topic is concerned, since the ‘net is so full of the reading material on this topic which isn’t so suitable for this audience, let me leave you with a right kind of a reco.

If it has to be just one short book, then the one which I would pick up is this:

Swami Prabhavananda (with assistance of Frederick Manchester), “The Spiritual Heritage of India,” Doubleday, New York, 1963.

A few notes:

1. The usual qualifications apply. For instance, I of course don’t agree with everything that has been said in the book. And, more. I may not even agree that a summary of something provided here is, in fact, a good summary thereof.

2. I read it very late in life, when I was already past my 50. Wish I had laid my hands on it, say, in my late 20s, early 30s, or so. I simply didn’t happen to know about it, or run into a copy, back then.

3. Just one more thing: a tip on how to read the above book:

First, read the Preface. Go through it real fast. (Reading it faster than you read the newspapers would be perfectly OK—by me).

Then, if you are an American who has at least a smattering of a knowledge about Buddhism, then jump directly on to the chapter on Jainism. (Don’t worry, they both advocate not eating meat!) And, vice-versa!!

If you are not an American, or,  if you have never come across any deeper treatment on any Indian tradition before, then: still jump on to the chapter on Jainism. (It really is a very good summary of this tradition, IMHO.)

Then, browse through some more material.

Then, take a moment and think: if you have appreciated what you’ve just read, think of continuing with the rest of the text.

Else, simple: just call it a book! (It’s very inexpensive.)


No need to add anything, but looking at the tone of the comments (referring to the string “Ayn Rand”) that got generated on this above-mentioned thread, I find myself thinking that, may be, given my visitor-ship pattern (there are more Americans hits today to my blog than either Indian or British), I should explain a bit of a word-play which I attempted in that comment (and evidently, very poorly—i.e. non-noticeably). It comes near the end of my above-quoted reply.

“Let’s call it a day” is a very neat British expression. In case you don’t know its meaning, please look it up on the ‘net. Here’s my take on it (without looking it up):

Softly folding away a day, with a shade of an anticipation that a day even better might be about to arrive tomorrow, and so, softly reminding yourself that you better leave the party or the function for now, so as to be able to get ready for yet another party, yet another function, some other day, later…

A sense of something like that, is implied by that expression.

I just attempted a word-play, and so, substituted “book” for the “day”.

Anyway, good night. Do read my last post, the document attached to it, and the links therefrom.

Bye for now.

Oh, yes! There is a song that’s been playing off-and-on at the back of my mind for some time. Let me share it with you.

A Song I Like:

(Hindi) “dil kaa diyaa jala ke gayaa…”
Lyrics: Majrooh Sultaanpuri
Singer: Lata Mangeshkar
Music: Chitragupt

[PS: The order of the listing of the credits, once again, is completely immaterial here.]

Anyway, enjoy the song, and the book mentioned in the quotes (and hopefully, also my past few posts and their attachments)… I should come back soon, with a maths-related puzzle/teaser/question. … Until then, take care and bye!


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.]


(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.]


What is the soul?

I ended my last post by asking you whether you were entertaining the possibility of astrology as a valid idea. Were you?

Ummm… Regardless, I am going to write further, on more ideas of similar nature. For instance, this question:

What is the soul?

Here is an indication of the cluttered drawer that currently is my mind, concerning this question. No, I haven’t tried to put it in any order. (Why not? Possibly, it’s because I don’t care for you. I am irresponsible. I am bad.)

I will not attempt to define this term (“soul”), i.e., define it in terms of some other terms. I have over the years attempted doing so, and at last have conquered this highly alluring temptation. I conquered it by taking the soul to the most fundamental level in philosophy: at the level of axioms. [An axiom is a concept or a principle that has to be taken for granted before any thinking or discussion can ensue. A philosophical axiom is a (a) self-evident (b) fundamental (c) primary (i.e. unanalyzable concept).]

The soul is the “I” in the statement: “There is something that I am aware of”:

  • There (in space-time)
  • is (being in existence)
  • There is (Existence)
  • something (Identity)
  • that (an abstract level; contrast: “of which I am aware”)
  • that … of (Primacy of Existence)
  • I (To Ayn Rand: Consciousness qua faculty; also man the integrated being. To me: Also in addition: the Soul.)
  • am (To Objectivists: the Focus as the beginning point of knowledge and epistemology. To me: in fact also in addition the axiom of life)
  • aware (To Ayn Rand and to me: Consciousness qua a state of Awareness)
  • that—of (To me: An unnecessary appendage inserted into the English language by the British and the Americans so that people like me would continue to have difficulty with their language all their life, and so, couldn’t possibly compete with them, in any sphere of life.)

But why the hell should someone go on just being aware, in the first place? So, let’s try something more lively (and tasty).

There was a (Marathi) “peru” I wanted to eat. I saw it. I reached for it. I ate it. It tasted good. I am satiated. (The British and Americans: You try a peach or an apple.)

In this sequence of statements, wherever the term “I” came in, the Soul came in, too. (Dear Objectivist, you mean to say you had never noticed it before? (LOL!))

OTOH, it wasn’t just the soul that came in. The soul cannot see anything, it cannot grab anything, it cannot taste anything. The doer actually was the integrated being that is the individual living man that is me.

The Indian term for this metaphysical integration (in the sense I take the term) is: “yoga” (which is not pronounced as “yogaa” (and Indians are more guilty for the continued perpetration of this crime than are the Americans)).

I often differ from Indian tradition(s).

The soul has no feelings. (Dear Indians, this is the place where I most saliently differ from you.) Feelings arise only in the context of consciousness, which arises only in the context of life. The soul has no desires.

The soul is not “just a bundle of” desires. (That’s just an empiricist position—not because of the involvement of desires or feelings, but simply because: a primary being is being described via a “bundle” of its attributes. Disintegration. That’s what this position indicates.)

The soul is not even a stand-alone and integrated existing instance of desires. It is an integration, but not of anything to do with consciousness, e.g. desires.

The soul is an integration of the pre-desires (and don’t raise the issue of their origin (turtles!)) and the pre-dispositions (which, I know, are acquired by the Soul itself, during a life-time).

The soul requires life to become a metaphysically active causal agent. A soul without life is in a state of a passive kind of an existence. Not exactly passive, because there also is a dormant potential for a striving for perfection built into its state, but it is only a dormant potential. It’s in a frozen state, so to speak. It needs the warmth of the life to make its potential participate in actions—whether in the physical realm or in the spiritual realm.

To Ayn Rand, it seems, life was not an un-analyzable and self-evident primary. To me, in a certain sense, it is. (However, my thinking on this count isn’t yet clear enough.)

To the ancient Indian tradition, man—the individual living man—is an integration of soul, life and body. I accept this position (I mean, using the terms only in the respective senses in which I take them).

The soul is the soul-wise identity of a man. Repetition? Just because it’s an axiom.

The soul does have identity (and the usage is to be taken in the Objectivist sense—in the sense that each soul is an identity.)

The soul does cause life-times, but I am not sure whether it causes the principle of life itself. Is life an axiom? I don’t know. (Dear Objectivists, yes, I do entertain this question. I really am not an Objectivist.)

The soul is not the unconscious. It is the pre-conscious.

The unconscious refers to the conscious for its definition. The soul does not require consciousness to exist. It requires consciousness only in order to achieve its goals better.  In fact, to achieve its goals, it does not even metaphysically require consciousness. At the most fundamental metaphysical level, it only needs life.

By rejecting the unconscious from the soul, I think I have emptied a lot of Western garbage about it (and also the Eastern one). Allow me to continue. I also empty the sub-conscious from the soul. The sub-conscious is just a part of consciousness—with time-varying content.

The goal of a living being is not “just” to live; it is: to satiate the soul.

Life is not an end in itself (and here I again differ from Ayn Rand); the satiation of a soul is the end of life. The satiation of different desires arising due to the integrated pre-dispositions and pre-desires that the soul carries.

What is the ultimate goal for a soul? I differ once again from the Indian tradition.

  • It is not a merging with the God, or even becoming a God.
  • It also is not a mastery over Existence: How can an aspect/attribute of something ever possibly be master of that same thing of which it is just an attribute? (Try: the blueness of the ink trying to become a master of the ink.)
  • It is not even mastery over just the physical universe: How can one attribute ever be a master of another attribute? (Try: the blueness of the ink trying to be a master of its fluidity.)

The ultimate goal for a soul, I therefore think, can only be: to be the most satiated. Which means, if taken in a mathematically limiting sense, to be so satiated as not to have any possibilities of any potential for any further satiations left. (BTW, a limiting process does require a preferred direction, and thus does imply a goal.)

So the Ultimate Goal for the Soul now becomes: the metaphysically most complete state of satiation, without any element of any unsatiation in any respect ever left.

How would you describe the state of reaching of that goal? I don’t know. But I guess the answer may be: When it is one with the soul-plenum. I mean to say: If you accept the idea that there is a plenum for souls (just the way there is a plenum for physical bodies), and if it is some kind of internal tensions (or state with pre-desires) propel the soul to grow, the only state in which the tension would cease to exist is when the soul becomes one with the entire plenum. The soul doesn’t die, really speaking—it has no life. But it does have states other than the basic existential state that is only to exist. Again, on this point, I have to think further. But it is clear to me that there are only individual souls, and no super-soul, and that the soul is outside of space and time and the physical world, and that there are rebirths. Teleology is deceptive: It appears simple, but is damn difficult to deal with—correctly.

I don’t know if that is what (at least some of the) ancient Indians have meant by terms such as the (“mahaa mahaa”) “moksha” and the (“mahaa mahaa”) “nirwaaNa”. Even if they did, there have been any number of retards—Indian, Middle-Eastern, Middle-Western, Western, Eastern, Far-Eastern, Whatever-Directionan/Place-an—to interpret terms like these in any number of irrational ways. The most salient error involves ascribing to life (and its attributes) what rests with (or is attribute of) soul. And, make an ethics and politics out of it. For example: annihilate pleasure—that’s “moksha”. Can’t do that? Suppress pleasure—that’s “moksha”. The direction from this point on can only be downhill. And these retards do go all the way down. Also throw humanity down that way.

BTW, did you know what the term “moksha” means? The easiest way to approach its true meaning is via astrology (!), even though it is not the best. But as soon as one says astrology, who really cares for anything else? Not at least initially, anyway. So, we go with the astrological approach first.

In astrology, the nature of the houses repeats, three times, this particular sequence of the four (in the order given): “dharma”, “artha”, “kaama”, “moksha”. Following my own ideas, and in brief: “dharma” (here) means: the nature, the identity, the cause, of a certain pre-desire (and note, I said, a pre-desire; not a desire—and that’s where I differ from the Indian tradition); “artha” means the act of looking around in this physical world so as to identify the physical object whose nature matches the nature of that particular pre-desire, and thus translating the pre-desire into the conscious terms as a desire; “kaama” means taking action to satisfy that desire, and to actually enjoy it; “moksha” means mentally translating the experience (mostly emotional) of the mental and bodily satiation into the soul-like (or pre-desire-some) terms, i.e. taking the experience into the soul, so to speak, thereby helping retire that pre-desire of the soul. The cycle repeats three times, with somewhat differing modulations and at different levels: the matters of the childhood and the early youth, (first four houses); those of the youth and the early mature adult (the next four); and those of a fully mature adult (the last four). So, you know what “moksha” means: it is the change of the state of the soul in different ways: “sukha” (accessible also to a child), “aShtama” (properly speaking, ”kundalini”, accessible to a man only after coming to an age), and “vyaya” (accessible only after mature adult-hood). Those are the levels in normal course and for the general case—i.e., after allowing for exceptions (like Dnyaaneshwara).

But of course, the best way to know the meaning of “moksha” would be via etymology. Here, I don’t know, but guess, that the roots could be: “mu:” + ”ksha”. “mu” means bond, and “much_” means letting go, to let fall, to let go away. (Remember “pramuchchate”?) So I guess, “mu” means that bond which is about to break or at least a bond that can be broken. “ksha” means to waste away, to pine away, and also, loss. (“kshama:” is a verb that means: to endure; “ma” means: happiness, emotional calmness, stability. “kshama:” means: to maintain mental balance or calm despite loss or damage. “kshamaa” means the quality of character that comes by following such action.) So, “moksha” (and, as usual, not “mokshaa”) should mean (though don’t take my word for it (I am careless etc.)): loss of a bond that could be broken or was about to break.

In particular, “moksha” emphatically is not the same as “mukti”; it is the latter that means freedom. “moksha” properly translates only to the breaking of a bondage.

But bondage of what? bonded to what? “moksha” by itself has no root whatsoever indicating an answer to these questions. The intelligent Indian retards have put forth “desires” as the answer. (Yes, a retard can be intelligent, esp. if he is an Indian.)

In contrast, in my thinking, the term must attach to the pre-desires.

The Ultimate Goal of a Soul, then, is to attain the Most Satiated State by retiring all the pre-desires.

I don’t know if what was described in the last sentence is metaphysically possible. I have no speculation to offer on this count either. (Yes, I am irresponsible. Also, careless.)

To me, the soul is always the individual soul. There is no metaphysical conscious being whose splinters the individual souls are. If at all you wish to entertain the idea of splinters, make sure to know that IMO the soul is not conscious, and so, what you are talking about can only be the splinters of the apersonal plenum. Why not consider them as the distinct, isolated conditions in that plenum?

Consciousness is nothing but a sophisticated means that the principle of life has caused to come into being, and a conscious being uses. How did it happen? I don’t know. Any speculation? The only way it could have happened would be under the direction of the more evolved souls—directing their own bodies, I mean. And then, passed on to the rest of us, as a faculty, via persistent modifications to the genes. (Such modifications is a very slow process but one with discretely identifiable steps. And, it is the individual soul-directed process, in my scheme.)

What does that imply? A soul can modify the physical world (including the genes), in its own “image”. Evolution refers to this fact. Nothing is random. Randomness cannot metaphysically exist (just the way a void cannot metaphysically exist). At the same time, I also reject the idea of a Supreme Commander Sitting Up There and Directing the evolution down below.

An imperfect soul must have something like a state of tension or stress built into itself; but this does not mean it even feels that. All that it means is that it, by a causal metaphysical law, this soul must take birth before it can release it. And, during those life-times, its rate of improvement should be “proportional” to how evolved he is on his (Soul-ic) perfection scale. I agree with Ayn Rand that perfection is a moral term and that perfection is achievable. I only suggest (though still have to think this thing through) that there also is a certain metaphysical sense to the term “perfection” and that the moral principle traces its root not just to life but also to the axiom of the soul.

The soul does mould life, but the moulding is not to be taken in the active, or verb-like sense. If you know calculus, the soul moulds life only via setting up the initial conditions for the system evolution (or the living being’s actions). Thus, it is the state of the soul at birth that moulds the nature of the actions of/in an individual’s life. The actions proper belong only to life, not to soul; the soul, however does have a state.

Since you don’t know my unpublished mathematical poutings, apart from the initial and boundary conditions, there also is a possibility of the continuing conditions. The soul also gets affected by life, qua its state. If not, its teleological evolution across life-times would have been impossible.

Other notes:

When I say “the” soul, I sometimes mean not a specific instance of a particular soul, but the principle of soul. I try to use “a” soul to mean the former. If I make confusing usage, the inconsistency is due to the roughness of the draft writing, as well as to my poor English. But, in any case, I never mean something Platonic (or  pre-Platonic, or post-Platonic) such as, say, the “global” soul, the “mahaa” soul that encompasses all the souls within itself.

The context should make clear the places where I borrow from others (esp. from the Indian tradition), and where I put forth my own philosophizations. If in doubt at some place, and also troubled about it: ask me!

All the philosophical debts are acknowledged, whether explicitly or not. (This is just a blog post; not a monograph.) The trouble isn’t there. The trouble is on the other hand: a philosopher may interpret some of my points in the light of some philosophical tradition that I am not even aware of, and so accuse me—not of plagiarism, but of some position that actually is not mine. Possible. They—the philosophers—are always like that. Well, not always, but mostly, anyway.

I am unreliable. I may modify my views any time. For instance, I have no clarity on whether life should be an axiom, and what exactly the relation between life and soul (in my sense of the term) is. I will continue thinking about such things off and on, the way I have for such a long time—since high-school. However, though I am unreliable and irresponsible, I will let this post stay here. I will not delete it.

OK, enough of this write-up. As usual, I may come back and edit this post a bit—but only for grammar/typos, not for altering ideas.



Am I an Objectivist?

I have deleted my previous post. It had served its purpose. No one pressured me (to delete it or to keep it either). It was my own decision. I had given a hint about the fact that it might be gone too. (What I had actually said was something like: I am going to keep this post at least for a while.) Regardless, if you are a friend, don’t put this blog on any archiving service, whether for paid or for free. If you are not, read and understand the copyright line.

And, regardless, I am now in this post going to write a bit about another controversy-prone topic. The difference for this (present) post is: I am going to keep it.

The topic is the title line: Am I an Objectivist?

The complete answer, in principle, is: no. The partial answer is: both yes and no. Allow me to explain. [And if you are the kind to whom no explanation is necessary, please stop reading this post. It will bore you.]

A philosophic system is judged in reference to its most fundamental principles, not the derivative ideas (no matter how important or valuable in certain narrower contexts). In case of Objectivism, the case is straight-forward. Ayn Rand did write down her system in a very logical manner. So, the task of knowing what her fundamentals are, was always easy (at least relatively speaking).

I do not know whether she in her lifetime agreed to the idea that (a) Existence, Identity and Consciousness are the axioms of her system, and (b) they form the complete set of axioms for her system.

However, Dr. Peikoff had begun delivering his lectures on her philosophy right back in 1976, when she was still alive, and indeed, with her knowledge of the material and her permission (and I suppose even presence (at least during some Q&A sessions)). This course indeed had put forth this above-mentioned idea.

My interest in philosophy is only as an amateur, as a “hobby.” The latter description, of course, must have told you that I take philosophy seriously. This conclusion is true. It’s just that I have no professional interest in philosophy. I never wanted to make a career in anything other than engineering. But while “hobby” does imply seriousness, it does not imply expertise.

Within whatever understanding I have developed of philosophy in general, and Objectivism in particular, I believe that Peikoff’s presentation of the three axioms as the complete set of axioms is, indeed, valid. If you know Objectivism, there is no way you can delete any one of the three. And, if you know Objectivism, there also is no way you can think of any other ideas for the choices of its axiom.

My trouble rests right there. (I do have some serious issues with Objectivists—and God knows I continue to do—but I have enough of clarity not to confuse principles with practitioners—the “attempting” practitioners included. Here, I remain concerned only with the sin, not the sinner, so to speak [with the tongue firmly held in the cheek].

My trouble is that I agree with all the three axioms, and, simultaneously, I also do not agree that these three exhaust what, in my opinion, ought to be the fundamentals of a system of philosophy. My further trouble is that Ayn Rand herself does not show enough evidence of these other ideas that I was looking for. As a matter of fact, in my amateurish philosophical way, I can even condense down this cluster of ideas and bring it down to just one additional axiom: Soul.

But of course, you cannot slap yet another axiom on an existing philosophy and give it a better appearance—a system of philosophy is not a wall; a coating of plaster won’t help. [A true Objectivist would rather allude to the practice of painting graffiti on someone else’s wall.]

To incorporate the fourth axiom is to change everything, and to actually create an entirely new system of philosophy. And, I have neither the competence nor the desire to do so. However, I do have a good mind, and I certainly have studied general philosophy for 3+ decades, and so, I do have some inklings of how such a system might look like.

No, I haven’t tried my hand at writing anything about these inklings in a systematic manner. Neither am I likely to.

But let me tell you one thing: In just thinking of this additional axiom of Soul (and the related matters: spirituality, for instance, and the ancient Indian traditions for another thing), I always found myself getting drawn to this temptation of wanting to integrate those ideas of mine (in the sense that I took them) with Ayn Rand’s.

Initially, I didn’t care: I was just reading about these other things (the soul, re-birth, spirituality, why, even astrology!) simply because I could. (Just the way I am very talkative, and usually can talk with almost any one, similarly, I am also readative, and usually can read almost anything.)

Later on came a period of years when I thought an integration would be possible. These years have in part overlapped with my blogging years, and so, my regular readers would have some idea about it. (I also made comments at other blogs during this time.)

It’s only recently, while drawing some notes on these matters, that I realized that, no, integration of something like Soul with Ayn Rand’s system isn’t at all possible. It impacts and changes everything about her philosophy in such profound manner that you couldn’t possibly recognize the new system as Ayn Rand’s.

Consider, for instance, the axiom of Existence. What does it mean? Go through the Objectivist literature. Make sure you know what Ayn Rand means. (Take years, if you wish.)

Now, consider this idea: Do inanimate beings carry a soul-related attribute?

From whatever I know of Ayn Rand, she would have dismissed this idea out of the hand. Ditto, for Dr. Leonard Peikoff, Dr. Harry Binswanger and Mr. Peter Schwartz. [BTW, also, most physical scientists would do the same.]

However, if it is possible to entertain this idea, then take care to realize that the wording is exact: ascribing a soul-related quality to inanimate objects is not tantamount to animism, really speaking. One is not talking of the rocks and the minerals carrying life.

One is only wondering about the idea that since the soul is “outside” of space and time (and fields and everything physical), but since it exists, and since the only evidence for existence as such is what you perceive, and since you perceive yourself too, and since your own self or the soul is, at least during this life-time, associated with your body, it’s not all that radical an idea that a soul can be associated with something that exists in space and time.

Now, if the soul (by which I always mean the individual soul) must persist after death (and that’s because the soul is “outside” of space and time), what is it to which you would then ascribe it? If something is in space and time, but is no longer limited to any particular sub-region thereof (viz. the body), then it would have to be everywhere (and for all times when it has not taken a birth). It would have to be taken as being associated with the inanimate matter, too—all of it (may be with varying intensities, including possibly zero for some regions for some individual souls, but the point is, in principle, the soul would be associated with all of matter, including the inanimate matter). Why do we use a weak term like “associated”? Because, there is no direct evidence for it. It’s an inference, based on certain observations and certain premises.

Yet, the point is clear: If it is possible to think of the idea of a soul without life, it is possible to ascribe a soul-like attribute to inanimate matter. Nay, the former logically and unavoidably leads to the latter.

It does not make the universe alive, in that celebrated Californian retards’ tradition(s). It makes it soulful.

Now, go back to Ayn Rand. [Peikoff, Binswanger et al. would find exhilaration at this point; allow them that—who are we to take away some one else’s happiness?—indeed, the latter action is proscribed also in our [as yet unwritten] books!]

Existence has primacy over consciousness, says Ayn Rand. I agree. Consciousness is an attribute of living beings. I agree.

But, if I am going to integrate the idea of soul into Ayn Rand’s system, here is what happens. Since soul also is put forth as an axiom, a question arises about its hierarchical place within the existing axioms. Clearly, it is before Consciousness. Consciousness requires life, but soul can exist without life. So, the question becomes: Does it come before, or after Existence? Or is it that, just like the physical world (which is better put here as “realm”), there also is a spiritual realm?

Here, Ayn Rand would agree that the soul is an aspect of Existence. Indeed, she would maintain that it is a part of Existence. To her, if all living beings were to be annihilated, not only the principle of life but also the principle of soul, would go out of existence.

But the attempted “integration” indicates that the soul is not a part of Existence, it is an essential aspect of it. Everything that exists comes with a plenum for the soul. Ayn Rand would immediately deny that. To her, this would mark a beginning of mysticism. She would criticize me for having taken mysticism to the most fundamental level.

So, alright. The attempted integration doesn’t work out. It has to be a new system. Peikoff’s argument concerning the completeness of Objectivism is valid.

Now, does that make me a mystic? Return me the favor, please; entertain the idea, not the ideator!

Mysticism is an issue in epistemology. It concerns a purported method of gaining knowledge—a method whose nature is not accessible to any rational understanding. That’s what mysticism is. In particular, it is not an idea in metaphysics.

But we were entertaining only metaphysics. The universe is what it is. Whether you get it—the universe—via rational means or otherwise is an issue orthogonal to what is being discussed here. What you get, is the matter under consideration, not how.

Thus, if I can rationally demonstrate that the universe is soulful, I don’t actually become a mystic. Indeed, in just entertaining this idea, by this sheer fact alone, I do not at all become a mystic. (Dear Objectivists, mark the difference of emphasis in the preceding two statements.)

So, how would you refute the idea that the universe is soulful?

What was the technique that Ayn Rand used in matters like this? Not her usual method of induction, really speaking. In matters like this, what she actually used was her invention of the “arbitrary.”

But, more on it, later. Just while typing this post (on the fly, as usual), I got a telephone call regarding a promising position for an engineering professor’s job in another town (requiring yet another trip outside of Pune). Therefore, my current “avataara” of the amateur philosopher, so limited in space and time (as all “avataara”s always are) must end. Now.

Ok. It has. It has gone.

But anyway, that’s an indication of the reason why, I am not an Objectivist.

More on that, later.

In the meanwhile, follow the master’s advice. (Ayn Rand was a master, esp. of method. To say that she might have limitations too, isn’t to take this quality away from her.) Check your premises and watch your implications, she advised. Let’s follow that.

Entertain the thought as to whether a soulful universe goes towards validating astrology—the very idea of it, not this system vs. that system, but just the basic idea of it. … Entertaining, no?



From this post onwards, sections at this blog would be separated by the HTML horizontal line. (The wordpress editor seems to have changed. If I type stars separated by space, it automatically creates an itemized list, and I don’t want to get into the hassle of turning that feature off. And, the horizontal line is just a button-click away, so it’s much more handy.)

It is also possible that the section on a song I like may return. Who knows? You twiddle your fingers.

[I may come back after two days or so, and edit this post a bit, though I am not likely to add a lot to it.]



Yo 6—A few interesting links, etc.

Just a few quick notes…

  • I really appreciated this reply by “John D” at Sean Carroll’s blog [^]. Prof. Hammond’s article to which he provides a link [(PDF) ^] has a superb summary of history of mechanics and electromagnetism, condensed down amazingly to just a few paragraphs.
  • This discussion [^] at iMechanica has turned pretty interesting. It began with Prof. Suo’s notes on frame indifference (in the context of his course on plasticity), but soon turned into a discussion on the exact meaning of the terms like gradient, vector, etc. … As you would expect, I have jumped in, too, but of course, with only a minor aside. For comparison, go through the clarifications by Prof. Amit Acharya of Carnegie Mellon, and Prof. Arash Yavari of Georgia Tech.
  • Dr. Harry Binswanger’s blog-like Web site has undergone a change. Now, HBL is supposed to be HBL 2.0, and in the new version it  stands for the Harry Binswanger Letter (and not the Harry Binswanger List). The HBL 2.0 is less frequently updated [^], but I gather that it now has a member’s area without any size limit for the comments. … The only reason I don’t want to join the list letter-cum-blog is that I know it would be a great time-sink for me. I am already far too pressed for time.
  • But, while we are at it, the holiday-reading season is almost around the corner. So let me tell you that Harry Binswanger’s book “How We Know” [^] is just amazing. This is one book that is making me read it    v     e     r     y         s     l     o     w     l     y. [That means that I like the book.] And, don’t wait for my review of this book; it’s never going to come. I mean, I already know by now that I won’t write one. So, just take my word for it, and just go ahead and buy it. (Lower-cost e-Versions are available.)

* * * * *   * * * * *   * * * * *

There are a few changes to my blog-roll, as well. I have deleted the links to a few blogs that anyway were more or less completely defunct, rectified the links to others (e.g. HBL), and also added a few new links. The process will continue. I would like to add a few S&T-related blogs in this list in the near future, too.

* * * * *   * * * * *   * * * * *

My next post could very well be concerning a few items about the diffusion equation (and about foundations of physics) that have now come under a much better focus and understanding for me. For instance, I think I now will be able to show that the proof for the uniqueness of solution is faulty. … [It would be relatively easy for me to do that because the existing proof is one by contradiction. These are always an easier game.]

* * * * *   * * * * *   * * * * *

A Song I Like:
[I don’t know why!]
(Hindi) “nazar naa lag jaaye… [Oh my love…]”
Singer: Mohamad Rafi
Music: Laxmikant Pyarelal
Lyrics: Anand Bakshi




What would a Platonic Word be like?

What would a Platonic Word be like?

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

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

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

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

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

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

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

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

Aha! So that did it!!

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Can we ascribe a philosophy to a product of technology?

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

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

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

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

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

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

Which then suggests another set of questions:

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

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

Over to you, dear reader!

* * * * *   * * * * *   * * * * *

A Song I Like:

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



Translation seen as an exacting process

You might have heard (or read) about this mantra from the Upanishads:

“असतोमा सद्गमय ।
तमसोमा ज्योतिर्गमय ।
मृत्योर्मामृतं गमय ॥”

It’s one of the most commonly known mantras. Typically, the second line, i.e. “tamaso maa jyotirgamay,” is often adopted as the motto of educational institutions in India. (One of the schools I attended had it, and so does the Department of Mechanical Engineering at COEP, where I did my PhD.)

How well do we (I mean the quoting Indians) know about the exact meaning of this mantra?

Here is a typical translation, coming from, what else, Wiki [^]:

“from the unreal lead me to the real,
from the darkness lead me to the light,
from the dead lead me to the immortal”

Here is another translation, with a write-up that serves to highlight the kind of trickiness that is involved in translating a brief gem like this [^]:

“Lead me from the asat to the sat.
Lead me from darkness to light.
Lead me from death to immortality.”

Here, Vedarat, the translator, simply refuses to translate the terms “sat” and “asat”! Apparently, he cannot make up his mind whether Yadnyavalkya (the Vedic seer who authored this mantra) meant “existence” or “truth” when he uttered “sat.”

It obviously would be “truth” here, but realize the extent to which an acceptance of philosophic fallacies such as the primacy of consciousness and intrinsicism [^][^] help muddy any honest attempts at proper translation.

It would be a different matter if Yadnyavalkya himself were to mean “existence” or “reality” instead of “truth.” But that’s not the case here. And, he also would not intend to deliberately keep the matter ambiguous here; no ancient Vedic sage ever did. … Yes, you can find a lot of mysticism in his other writings as well. Yet, judging from the context, it should be obvious to anyone that the meaning he clearly had in mind here was “truth,” and not “reality.”

Yet, the latter-day mystics confuse the issue.

Translation is a demanding process; it is an exacting process. It requires not just sensitivity to the various possible nuances of a word, but also the clarity of thought as to the exact shade that the original author might have meant. That kind of a clarity in turn requires, at least for translation of abstract statements or statements of general philosophic truth, a sufficient knowledge of the basic philosophical issues and ideas. Far too often, people carelessly bring their own assumptions into translations, and it is impossible to detect their insertions unless you do a bit of philosophic detection.

For example, I am sure that the above Wiki translation was done by some Western guy, not Indian. (Or at least, in case it was an Indian, he was one who had very heavy Western influence on him.) Why do I say so? Simple.

Look at the third line in his translation. The translator offers: “from the dead lead me to the immortal.” Implicit idea here is that there is a realm of the dead, and of the immortals. But this is a very Christian idea (and, possibly, Abrahamic in general).

The ancient Vedic sages never thought in terms of a soul going into a state of limbo after death, or its awaiting the day of the final judgement at the hands of a robes-wearing, electricity-carrying masculine God at some uncertain time in future. Theirs was a far more naturalistic viewpoint; sometimes, it can even be taken to be rather atheistic in nature. They did not necessarily believe in a human-like God dispensing out judgements and deciding on the fate of the soul.

The soul, to the ancient Vedic authors, was a natural phenomenon. The states of the soul, to them, were bound simply by a causal law (such as the law of karma). The very idea of some other consciousness or soul directly affecting even the future course for some time, let alone its fate for eternity, would be unacceptable to them. At the most fundamental level, nothing else in the universe, no other power in the universe except for the wilful soul itself could determine its own “gati” (progress/direction) and its own state, according to their typical viewpoint. (This does not mean that, in principle, prayers wouldn’t be useful. More on that, sometime later.)

Therefore, they simply wouldn’t think in terms such as the realm of the dead—which is, historically, a very, very  recent idea, and specifically Christian (or Abrahamic) in source. Not Vedic.

However, the point I wanted to make today was not about the meaning of “sat.” It was about the form of the statement that every English (or even Marathi/Hindi etc.) translation of this ancient Sanskrit mantra takes. It’s a very curious thing, all by itself. I mean, the form suggested by the part “lead me…”

Implicit in such a form is the idea that there is someone other than you in the picture. He would lead you from A to B, where A are all undesirable things, and B are the desirable ones. You thereby assume a more passive role. It’s his leadership that really counts. It’s almost as if your leader is capable of leading you from light to darkness, but since you have no power left over your own fate, you end up earnestly urging him to do otherwise, to lead you from darkness to light.

And that’s why, I often thought, that the prayer was laughable.

If you don’t have any independent means to figure out whether the journey is occurring from bad to good, and not from good to bad, and, further, if you also essentially need an external agency, a leadership, for that journey, then, these two facts put together, leave you completely at the mercy of the leader. Essentially, it makes a spiritual slave out of you.

From my readings of the Upanishads over the past decade or so, I knew that they could be sometimes completely mystic, but not always so. And, they could easily go to the highest reaches of abstraction, the most fundamental philosophic matters. But precisely because they are so abstract and so lofty in terms of the subject matter and the goals, they therefore wouldn’t be capable of creating a prayer of such a form, I thought. Certainly not when what they were aiming for was the “peace of the soul.”

After all, this is one of the Upanishadic “shaanti mantras”. It is not a mantra for propitiation of whimsical Gods as in the main Vedas; Upanishads come after the Vedas. And, this is one of the mantras that are supposed to be recited either before the commencement of studies or meditations, or at the end of it all—the rituals, or studies, or meditations, so as to consolidate it all, via a moment of peace.

And, so, I decided to look more closely at this mantra.

And, I figured out that my suspicion was right. There is no hint of someone else leading you at all, contained in that mantra. The whole idea is an extraneous, parasitical idea that some translator initially inserted, and then, all the latter-day translators picked up this habit. Obviously, out of some interesting underlying philosophic motivations!

Let me take just one line for illustration, viz., “tamaso maa jyotirgamay.”

First, let us split up the “sandhi” (or jointed) words into their components, and note the forms of the nouns and the verbs.

“tamas” means things such as the inactivity or dullness of the soul, or (the literal) darkness, or the darkness of the soul. “tamaso” has “tam” at its root, and “tam” means darkness. “tamas” is a derived word that means something that derives from or issues from or is a byproduct of, darkness. “tamaso,” in turn, is the modification to “tamas;” such a modification implies that a “from” kind of a relationship applies in this context. So, “tamaso” means: “from darkness dullness [literally, or from darkness or dullness of the soul].”

“maa” simply means “no” or “not”. Think of the modifiers like “un-” “non-“, “in-” etc. in English. They all are negators in various senses. Similar is the “maa” in sanskrit. It is a modifier that serves to negate. (And, if I recall my Sanskrit correctly, it is a strong form of a negation. “Don’t at all!” is the sense conveyed by “maa.”)

What is being negated here? Of course the “tamas.” No “tamas!” That’s what “tamaso maa” means.

The next word is “jyotirgamaya.” It’s a compound word made from two components: “jyoti” and “gamaya”.

When the form assumed by “jyoti” is such that it has the “visarg” (or what is denoted by a colon), resulting in “jyotihi”, and when it combines with something beginning with a vowel like “ga” then the “hi” is to be replaced by “r-.”

“jyoti” is a noun that means things such as: flame, light, brightness, etc. Now, “jyotihi” is the first person (or case) singular form of this noun which would makes “jyoti” the subject, or alternatively, “jyoteehee” would be the second case plural form, which would make it the object. I would rather rely on context than the knowledge of today’s Sankrit typists, and thereby conclude that here it is the first case singular, and so, the “jyot-” here has the “rhasva” (or short) “i”, not the “deergha” (or long) “ee”.

“gamay” is a modified form of the verb “gama.”

“gama” itself means: “to go.” The well-known usages of this root-verb appear in “gaman,” which means “departure” or “going away,” and “aagaman” which means “arrival.” (“aagaman,” literally speaking, only means: “anti-departure;” it is derived by applying the “a” modifier, another negator, to the more basic “gaman.” Now, anti-departure, of course, means: arrival. Sanskrit sometimes seems to work in a funny way, at least initially, but then, realize that if you keep man at the epistemological center of the universe, then from the viewpoint, going is more natural than coming. The actor in coming is someone else—not you. The actor in going, however can be you, yourself. And, thus, departure is not defined as anti-arrival; it is arrival that is defined as anti-departure.)

Now, the modification implicit in “gamay” is all that is left to discuss, and so, you can easily see that the particular form of this modification (as got after starting from the root “gama”) could be the real game-settler.

Unfortunately, my knowledge of Sanskrit is not at all good; in fact, it is barely elementary. (I just had two years of Sanskrit in the 8th and 9th standard, and that too, only as half of one language subject—the other half being Hindi.) And, unfortunately, I could not easily locate from an Internet search any easily traceable document or a text-book that shows a verb similar to “gama” going to the modified form “gamay.” A lot of material is easily found that shows “gama” –> “gachchati” etc., but not “gama” –> “gamaya.” The Spoken Sanskrit dictionary  [^] has “gamayati” but not “gamaya.”

From the best guess that I can make, “gamay” could be something like the “bhaave prayog” implied probably for the plural in Sanskrit, i.e. for many persons (more than two persons) in general. Or, it could be something like a “bhaave prayod” but for a single person. Thus, it would mean something like “may I/we go”

So, “jyotirgamay” simply means: “may I/we go towards brightness.”

Putting it all together, the translation should read something like:

“From darkness, may I/we go towards brightness.”

That’s it. That’s all there is to it. … There is no dark world let alone the world of the dead, and there is no bright world for eternity. And, there is no leader either, not even implicitly.

The words—the roots, their modifiers, the resultant modifications (i.e. the sense of the grammatical person, etc.) and the rules of “sandhi” i.e. of joining parts of words—all put together, go on to state only this much. “From darkness may I/we go towards brightness.” A sense of “being lead” is not even hinted at. There is no leader, not even implicitly, and there is no action of being lead—not even implicitly.

Yet, every English translation goes like “Lead me from…”

The psychology and philosophy of these translators might make for an interesting thought, wouldn’t it? They want to insert something that Yaadnyavalkya (or whoever first wrote that mantra) didn’t obviously have in mind, in the first place. And they do so with a philosophic viewpoint that is mystical, passiveness-primary, and implying of a leader—i.e. mystical, action-negating and therefore virtue-negating, and collectivist.

All the authors and commentators—whether Western or Indian—are guilty of exactly this crime. Via a faulty translation, they at least passively and implicitly further the axis of mysticism, amoralism and collectivism.

And, that kind of an interpretation is smeared on Yaadnyavalkya’s original hymn expressing the exalted human soul’s earnest desire for its own betterment—and, by implication, on its own.

On the occasion of this Diwali, let’s earnestly resolve to reach for the truth from any state of ignorance; to go towards the brightness of gaining knowledge from a state of the inactivity of the soul; and to go from every position or principle (or actions) that is destructible or un-maintenable in the long run (or any position that carries contradiction) towards the positions or principles that are insusceptible to destruction—the positions or principles that are enduring or permanent. Let’s resolve to do that.

And, let’s resolve to do it as a matter of our individual responsibility, and without being dependent on any other person—i.e. independently.

[For obvious reasons, there won’t be “A Song I Like” section—this prayer itself, if said with a proper understanding the meaning of its words, and with sufficient solemnity, is a song. And, it is a song that I do like.]


Coming back to the second “world”…

[Four updates added on September 24, 2013.]

0. Coming back to the second “world,” I would like to briefly note a few points concerning it. … But before coming to these points, first, in case you have joined late and so don’t know what I mean by the term “second ‘world’,” let me tell you that in brief.

1. The term “second ‘world'” means: a view of the physical world which would correspond, roughly speaking, with the Newtonian physics. In particular, it refers to a broad, objective view of the physical world as is implied by, or is implicit in, the state of physics as it existed after Galileo and Newton, but before the discovery of the laws of electromagnetism. Roughly speaking, the mid-17th century to, say, the early 19th century.

This “world” consists of uncharged bodies not only colliding with each other but also sucking up the gravity field-fluid. The first “world,” in contrast, would be this second world, minus the phenomenon of gravity. I had written about these ideas in my recent post here [^].

The first world really speaking doesn’t pose much of a conceptual problem to any one, because it is a local theory, and a relatively simpler one at that. The only kind of entities making it up are all definite objects—either discrete objects like apples and planets, or such continua that their defining properties always are defined in reference to a definite portion of that continuum, as in the classical fluid and solid mechanics. Further, all entities in this world are material (i.e. mass-possessing) ones. And, all the interactions are via a common surface between the directly touching bodies.

The second world, as I indicated in my earlier post, posed conceptual problems back then (and it continues to stump people even today—if they at all care to think about it) because gravity adds two difficult features: (i) forces acting through a “void,” and (ii) instantaneous action at a distance (IAD).

I had then sketched a possible solution involving a hypothetical, massless, gravity field-fluid.

In the follow-up post [^], I had referred you to Wang’s papers, and had asked if scientific papers like these would be enough. And, also what additional input would be necessary for you to be convinced that a hypothetical massless fluid indeed makes for a first-class object of physics.

2. The main paradox:

For convenience, let me now more or less fully reproduce, paraphrasing only a bit here and there, what I said by way of the question, right in that first post about the conceptual trouble with that kind of a “fluid.”

The first issue that arises in the second world, viz., forces being transmitted through a void, is a more serious challenge, because it spoils the neat view otherwise built for our first world—a view of localized, definite objects exchanging momenta/energy through direct contact via a common surface (collisions or fluxes).

So, now, a question arises: Where do we place the field of gravity? Is gravity an attribute of the distinct material objects (such as apples or planets), or is it an attribute of the “void” in between them.

The issue is not as simple as it might sound to you.

If you say that gravity is an attribute of the void, then an immediate next question is: does gravity exist in a world devoid of the material objects like apples and planets? If so, what does the field do? Forcing nothing is a contradiction in terms—the definition of force involves the change of momentum of a material object like an apple or a planet.

There cannot be a force in a field if there is nothing to force from/to. Assuming unit masses for all entities, mathematically, “forcing” is nothing but another name for “accelerating.” Even if you hypothesize the existence of a definite, lawful, but massless physical object for the Newtonian gravitational field, i.e. one with identity, a question still remains: how do you define forces (i.e. accelerations) within this object? A massless forcing object can make sense but only when there is some mass to be accelerated.

Naturally, you have to attribute the phenomenon of gravity to the usual material objects: the stars and planets, for example. If so, you have come back to square one: you can no longer explain interactions via simple direct contacts between material bodies. If gravity is to be attributed to the material bodies themselves, then no mechanism is left to explain how it can act over the “void” (or “free space” or whatever).

This theoretical complication is what Newton himself should have commented upon. But, he didn’t. His shortcoming.

3. The (other) candidate solutions:

My further ‘net searches threw quite a few fascinating ideas. I will note down just a few of them (i.e. apart from Wang’s papers that I have noted earlier in this series).

First, the obligatory Wiki articles, and the references therein: Aether the Classical Element [^], Aether Theories [^], Mechanical Explanations of Gravitation [^], and, though meant for electromagnetism, if you wish to use similar ideas also for gravity, Luminiferous Aether [^]. …

BTW, the coverage of the aether-related ideas on the Internet in general, and on Wiki in particular, has improved a significantly great deal since the time not so long so—around 2004/05 times, when I was doing my PhD. At that time, most pages were amateur or even worse—crackpot! The only exceptions were a few groups like a nonlinear studies center in an Austrian university, or so. [Update on September 24, 2013: Link, here[^]]. BTW, my PhD papers had assumed an aether hypothesis, but quite different from what people meant about it. Which brings us to the next set of material.

  • The “MountainMan” collection of links [^]. Very comprehensive. (They didn’t miss Dirac’s surprisingly pro-aether viewpoint either!)
  • The “Cellular Universe” Web site, with an excellent summary of the views of the aether idea, throughout history (right in the format of a table/timeline!) [^]. You may want to spend some time exploring some related material (like that on cosmology) on this site; consult the links given in the side bar of that site.
  • There were quite a few others too, though the links already given would cover pretty much the entire territory one way or the other. … For instance, see this blog post [^]. Its presentation is good, but all those points are one or the other already covered in the links (and the sub-links) given above.

Comment: Realize that none of these solutions, IMO, fully satisfactorily resolve the main paradox which I have noted above.

For many of these aether theories, if you wish to use a simple heuristic to expedite your reading (though I wouldn’t advise you to outright dismiss any idea out of hand), just ask yourself this simple question:

If it is a continuum aether, is it massive or massless? If the former, how does the theory account for Newton’s three laws for the massive objects? Are they modified too? Must they? And, if the latter, then what specific characteristics of aether are proposed here that would go on to provide a mechanism for the gravity force?

For certain other, particles-based theories (i.e. particles of aether), always ask yourself: Is this theory philosophically satisfactory? What exists in between those aether particles? void?

Have fun.

4. “But why should I pursue it in the first place? What is the fallout?”

You may now wonder, of course, where the fun is, in all this “back-dated” enterprise.

You may perhaps say something like: “All we seem to be doing here is to dig through the errors of the other people, and, that too, of those who are long dead. There is no fun in going through the wrong theories of the ancient people [like Newton and all!], how they thought. Einstein proved them all wrong, and the 20th century—including all the finest and costliest experiments performed till date—has proved Einsten right.” And, continuing, you may then ask me: “How is your paradox relevant to solving the really important problems (or even paradoxes) facing today’s physics? Why dig up old paradoxes when new ones are available, and old ones are already resolved?”

I won’t argue a lot here. By way of my answer, I will only note down a couple of points. [Many other smart people, I am sure, would have already noted these by now, without me having to tell them about that…. But still…].

(i) The second world is important because it is the simplest toy world that still carries an important, defining feature of the standard model of the modern particle physics: viz., the division of all things (they call it “particles”) into two mutually exclusive and collectively exhaustive classes: the massive particles (i.e. the fermions) and the massless particles (i.e. the bosons). If you know how to (properly) quantize a continuum (the way I have done in my published papers and also writings on the blogs etc.), then, in solving the toy problem of the gravity-fluid, you create a platform that would be very directly useful in solving some of the really difficult conceptual riddles concerning the modern standard model. … I won’t name them. You should know what those are. [LOL! Why? Because you were concerned with the modern standard model, that’s why!]

(ii) If you can resolve the main paradox, by giving a logically consistent and complete (i.e. fully satisfactory) aether-based description even if only for the second world, then, that accomplishment, by itself, would mean that you had overcome the greatest hurdle in resolving the most difficult paradoxes related to the relativity theory as well. They would go out the door in one go. Web pages like, e.g., this excellent set [^], would be taken down, though the Web sites themselves (including that Web site) will still continue to thrive—by focusing on other, better, more authentic problems of physics. Why?

Because, this way, you would be able to give an “engineer’s” description for the physical world, a description that, at its most fundamental level, requires only a 3D Euclidean geometry for space, and a basically separate scalar for time. (Time would no longer be a “dimension” in the theory; it would be just a parameter, really speaking.)

Imagine what kind of a simplification in the conceptual structure of physics that would represent.

… And, yes, if you wished, you would still be free to play with the “spacetime” continuum, manifolds, their contortions… all those concepts as well, though you wouldn’t have to use them. You may find reasons (perhaps even good reasons) to continue using them for mathematical convenience in (some, not all) applications, that’s all. [For instance, you may find some convenience in error analysis of some numerical analysis code, or in presenting a more concise deductive formulation.] But not in the basic physics theory.

[Update on September 24, 2013:

This update on September 24, 2013, over.]

Of course, your intermediate step would still consist of first resolving a similar riddle for the third world (that of EM) as well. Yet, the nature of the issues is such that if you can resolve the paradox even if only in the second world, then that by itself would be a great step forward. You see, the paradox concerning the third world (i.e. the one concerning the EM field) is only mathematically a bit more complicated—conceptually, not so much, though some conceptual advancements would still be necessary, too (other than what I have already explicitly noted or hinted at).

3. One more reason why you can give it try. It’s because… the paradox—at least that in the second world—most certainly is resolvable.

And, how do I know that?

…[Suppresses laughter] …

Time to run through the description of the main paradox, again? See the main point 2. above. (… It could be put in a better, more precise way, but what I have already noted down seems to be enough. At least to me, and at least for a blog-post, and at least for the time being. It puts the issue directly enough. … So, there!)

* * * * *   * * * * *   * * * * *

Updates on September 24, 2013:

Update 1. Why the classical fluid mechanics belongs to the first world:

In the classical fluid mechanics, there also is a flux of mass (in addition to that of momentum) which, at the first sight, seems unlike the first world, because with the solid colliding balls of the first world, there is a transfer of only momentum, not of mass.

However, we can still regard the classical fluid as belonging to the first world, because mass of the fluid is a property defined for both the parts of the material continuum sharing their common surface, and both these defining parts are definite material objects.

The classical fluid is nothing but just a limiting case, obtained by applying a mathematical homogenization (or “squishing” i.e. “continuum-ization”) procedure to a collection of what otherwise are only discrete material objects occupying a defining volume in the first world. For instance, a grosser-scale volume of air is taken as the classical fluid material, even though the reference volume itself is made up of a large number of tiny, discrete, gas “molecules” which themselves can be taken as the usual solid objects of the first world; ditto, for water and other liquids.

Left as an exercise for you: Figure out why also friction (e.g. Newton’s law of friction) does not pose any deep conceptual issue in the first world.

Update 2: A link to the Austrian university which was doing research on aether-based descriptions in the mid-naughties, has been inserted inline; it was the AINS [^]. BTW, I had made a reference to Prof. Gr\”{o}ssing’s papers, in one of my PhD research papers, too.

Update 3:  The additional beneficial fallouts of a new conceptual perspective:

Another point. I wish to note a bit more on the beneficial fallouts of a new conceptual perspective such as the resolution of the main paradox concerning the second world, as noted in these blog posts.

Though the final quantitative predictions of both the mainstream theory of Newtonian gravitation and an aether-based theory may outwardly seem to remain quantitatively the same, it still is not proper to dismiss the aether-viewpoint.

A plain epistemological fact is that with a new (objectively valid) conceptual viewpoint, new progress into the as-yet-not-even-imagined territory also becomes at all possible.

The progress of physics does not always depend only on new experimental observations; crucial to the inductive process of discovery also is the advancement in the conceptual perspective. (Claiming otherwise is a direct case of MBD—the mind-body dichotomy.)

Remember, consciousness is finite, not infinite. In other words, we have limitations to how much of a further progress we can make, given an already existing level of knowledge, and, given a particular conceptual vantage point that goes with it (at least implicitly).

Due to the finitude of our consciousness, given a particular conceptual viewpoint (implicit in a particular state of knowledge), some as-yet unknown facts, even if logically not inconsistent with that older viewpoint, still become so conceptually distant as to fall out of the limited range of any possible mental grasp, and hence, out of the range of any possible application involving them—or even the more basic discoveries of those facts.

For instance, Newton’s original formulation of the laws of dynamics, which is essentially a formulation in terms of vector mechanics (though the concept of a vector had not yet been explicitly grasped in his time) does remain applicable, in principle, to every dynamical problem of the first world. Yet, a very large range of problems become tractable only via the variational/energy-based approaches (or the Lagrangian/Hamilton reformulations). [BTW, Newton was also the first person to correctly pose and solve a variational problem.] In the classical physics, the law of conservation of energy does not add anything new to the already known dynamics at its most fundamental level.  [Incidentally, I still remember how discovery of this fact had come as a shock to me!] But try to use the original Newtonian mechanics in calculations of, say, the heat of a chemical reaction!

And, my point here is deeper than that. Among two or more conceptual viewpoints explaining the same set of facts, the most fundamental among them is the most crucial—abandoning it affects the scope of any new possible discoveries the worst. Physical observation is basic to mathematics—and not vice versa. Hence, abandoning a more fundamental physics viewpoint affects the new discoveries the worst.

Thus, not only inventions of new mathematical principles, but also new physical discoveries themselves become at all possible only when you actively adopt a new conceptual perspective—even if its initial scope seemingly refers to the same old set of facts.

As an example of this latter fact right in our present context, see the ease with which Wang’s paper suggests the possibility that the exponent “2” in the inverse-square law may not be a constant—and the ease with which you can understand it, too! Otherwise, precisely due to the much-prized mathematical “tightness” of the Poisson-Laplace equation—and, if you want, you can also throw in here any supposed beauty of the harmonic analysis, the beauty of its symmetry, et cetera—the very idea of a variable exponent in a law verified in as many separate instances as Newton’s Law of Universal Gravitation, would look wacky and crackpot to any one—especially if the paper were not written using LaTeX! …

When Dirac in fact made a similar suggestion concerning the possible variability of the universal “constants” of physics, he was rightly held in high regard and admiration for that idea. Understandably so. Abandoning aether, it would take a genius to think of varying just that part of, say, the “spacetime” (i.e. without using even the hyphenation mark [whether using LaTeX or not]). Since most physicists by then had abandoned that idea of the aether, the suggestion did look awesome to many of them. From their viewpoint, it would take not just a normal genius but, say a genius^genius, to conceive of so “bold” and such “daring” an idea.

Well, there is some boldness and daring in here, but it’s not in the detail of suggesting the possible variability of what we take as universal constants—I mean to say, it’s not an issue limited to making a variable out of a constant; it does not concern an apparently marvellous piece of a mathematical thought. Instead, the boldness and daring is in trying to keep a more fundamental physics hypothesis, that of aether, in the physics theory, despite its denials by the authorities of the day. Once you put aether back into the physics theory (or never fully abandon it as probably was the case with Dirac—at least privately to his own mind), it then looks a plain and relatively simpler consequence of that theory.

Now, you can always put such a consequence in precise mathematical terms, which, taken out of context, is guaranteed to look unbelievably awesome. [Morally lesser professors at the world’s leading universities have always employed this trick.] Further, once the concrete suggestion comes out, you can always go back into the woodwork (or near your blackboard), deduce—in part using the new suggestion—and then, come out of the woodwork and say that it was already deducible even from the plain old mathematics, and use that claim both to make the new advancement look lesser, and to continue justifying your dogma. [Morally lesser professors at the world’s leading universities are known to employ also this trick.]

…And, this variability of the supposed universal constants was just an example. .

.. New conceptual perspectives, even if based on the same set of observational referents, enable new discoveries that would otherwise remain out of the reach of the human mind that uses only an existing conceptual framework which contains some unresolved “merely philosophical” paradoxes. Every fundamentally new field of mathematics—i.e., if it is authentically new (and not just a deductive avatar of an existing one) has, in fact, depended precisely on such conceptual advancements coming from physics (or the “physical” thinking).

The Objectivist epistemology even has terms for such things: the DC [not that one!], the CCD [and now you believe me, don’t you?], the rule of fundamentality, and all that. … OK. More, later.

Update 4: Added the usual section about a song I like.

* * * * *   * * * * *   * * * * *

A Song I Like:

(Marathi) “hari bhajanaaviN kaaL ghaalavu nako re…”
Singer [of the version I like]: Dashrath Pujari
Music [of the version I like]: Dashrath Pujari (?)
Lyrics: Sant Sohirobaanaath

[PS: Just a stray thought…. Should I have put these updates in a separate post? … May be I will… I will think about that later on… For the time being, enough is enough!]


Where the Mind Stops—Not!

The way people use language, changes.

In the mid- and late-1990s, when the Internet was new, when blogs had yet to become widespread, when people would often use their own Web sites (or the feedback forms and “guestbooks” at others’ Web sites) to express their own personal thoughts, opinions and feelings—in short, when it still was Web 1.0—one would often run into expressions of the title sort. For example: XYZ is a very great course—NOT! XYZ university has a very great student housing—NOT! XYZ is a very cute product—NOT! … You get the idea—you really do! (NO not!!)… That’s the sense in which the title of this post is to be taken.

For quite some time, I had been thinking of a problem, a deceptively simple problem, from engineering sciences and mechanics. Actually, it’s not a problem, but a way of modeling problems.

Consider a body or a physical object, say a piece of chalk. Break it into two pieces. Easy to do so physically? … Fine. Now, consider how you would represent this scenario mathematically. That is the problem under consideration. … Let me explain further.

The problem would be a mere idle curiosity but for the fact that it has huge economic consequences. I shall illustrate it with just two examples.

Example 1: Consider hot molten metal being poured in sand molds, during casting. Though “thick,” the liquid metal does not necessarily flow very smoothly as it runs everywhere inside the mold cavity. It brushes against mold-walls, splashes, and forms droplets. These flying droplets are more effective than the main body of the molten metal in abrading (“scrubbing”) the mold-walls, and thereby dislodging sand particles off the mold walls. Further, the droplets themselves both oxidize fast, and cool down fast. Both the oxidized and solidified droplets, and the sand particles abraded or dislodged by the droplets, fall into the cooling liquid metal. Due to oxidized layer the solidified droplets (or due to the high melting point of silicates, the sand particles) do not easily remelt once they fall into the main molten metal. The particles remain separate, and thus get embedded into the casting, leading to defective castings. (Second-phase particles like oxidized droplets and sand particles adversely affect the mechanical load-carrying capacity of the casting, and also lead to easier corrosion.) We need the flow here to be smooth, not so much because laminar flow by itself is a wonderful to have (and mathematically easier to handle). We need it to remain smooth mainly in order to prevent splashing and to reduce wall-abrasion. The splashing part involves separation of a contiguous volume of liquid into several bodies (the main body of liquid, and all the splashed droplets). If we can accurately, i.e. mathematically, model how droplets separate out from a liquid, we would be better equipped to handle the task of designing the flow inside a mold cavity.

Example 2: Way back in mid-1980s, when I was doing my MTech at IIT Madras, I had already run into some report which had said that the economic losses due to unintended catastrophic fractures occurring in the US alone were estimated to be some $5 billion annually. … I quote the figure purely from my not-so-reliable memory. However, even today, I do think that the quoted figure seems reasonable. Just consider just one category of fractures: the loss of buildings and human life due to fractures occurring during earthquakes. Fracture mechanics has been an important field of research for more than half a century by now. The process of fracture, if allowed to continue unchecked, results in a component or an object fragmenting into many pieces.

It might surprise many of you (in fact, almost anyone who has not studied fluid mechanics or fracture mechanics) that there simply does not exist any good way to mathematically represent this crucial aspect of droplets formation or fracture: namely, the fact of one body becoming several bodies. More accurately, no one so far (at least to my knowledge) has ever proposed a neat mathematical way to represent such a simple physical fact. Not in any way that could even potentially prove useful in building a better mechanics of fluids or fracture.

Not very surprising. After all, right since Newton’s time, the ruling paradigm of building mathematical models has been: differential equations. Differential equations necessarily assume the existence of a continuum. The region over which a given differential equation is to be integrated, may itself contain holes. Now, sometimes, the existence of holes in a region of space by itself leads to some troubles in some areas of mechanics; e.g., consider how the compatibility criteria of elasticity lose simplicity once you let a body carry holes. Yet, these difficulties are nothing once you theoretically allow the original single body to split apart into two or more fragments. The main difficulty is the following:

A differential equation is nothing but an equation defined in terms of differentials. (That is some insight!) In the sense of its usage in physics/engineering, a differential equation is an equation defined over a differential element. A differential element (or an infinitesimal) is a mathematical abstraction. It begins with a mathematically demarcated finite piece of a continuum, and systematically takes its size towards zero. A “demarcated finite piece” here essentially means that it has boundaries. For example, for a 1D continuum, there would be two separate points serving as the end-points of the finite piece. Such a piece is, then, subjected to the mathematical limiting process, so as to yield a differential element. To be useful, the differential equation has to be integrated over the entire region, taking into consideration the boundary and initial values. (The region must be primarily finite, and it usually is so. However, sometimes, through certain secondary mathematical considerations and tricks involving certain specific kinds of boundary conditions, we can let the region to be indefinitely large in extent as well.)

Since the basic definition of the differential element itself refers to a continuum, i.e. to a continuous region of space, this entire paradigm requires that cuts or holes not existing initially in the region cannot at all be later introduced. A hole is, as I said above, mostly acceptable in mathematical physics. However, the hole cannot grow so as to actually severe a single contiguous region of space into two (or more) separate regions. A cut cannot be allowed to run all the way through. The reason is: (i) either the differential element spanning the two sides of the cut must be taken out of the model—which cannot be done under the differential equations paradigm, (ii) or the entire model must be rejected as being invalid.

Thus, no cut—no boundary—can be introduced within a differential element. A differential element may be taken to end on a boundary, in a sense. However, it can never be cut apart. (This, incidentally, is the reason why people fall silent when you ask them the question of one of my previous posts: can an infinitesimal carry parts?)

You can look at it as a simple logical consistency requirement. If you model anything with differential elements (i.e. using the differential equations paradigm), then, by the logic of the way this kind of mathematics has been built and works, you are not allowed to introduce a cut into a continuum and make fragments out of it, later on.  In case you are wondering about a logically symmetrical scenario: no, you can also not join two continua into one—the differential equation paradigm does not allow you to do that either. And, no, topology does not lead to any actual progress with this problem either. Topology only helps define some aspects of the problem in mathematically precise terms. But it does not even address the problem I am mentioning here.

Such a nature of continuum modeling is indeed was what I had once hinted at, in one of my comments at iMechanica [^]. I had said (and none contradicted me at that forum for it) that:

As an aside, I think in classical mathematics there is no solution to this issue, and there cannot be—you simply cannot model a situation like “one thing becomes two things” or “two infinitesimally close points become separated by a finite distance” within any continuum theory at all…

In other words, this is a situation where, if one wishes to think about it in mathematical terms, one’s mind stops.

Or does it?

Today, I happened to idly go over these thoughts once again. And then, a dim possibility of appending a NOT appeared.

The reason I say it’s a dim possibility is because: (i) I haven’t yet carefully thought it through; (ii) and so, I am not sure if it really does not carry philosophic inconsistencies (philosophy, here, is to be rather taken in the sense of philosophy of science, of physics and mathematics); (iii) I already know enough to know that this possibility would not in any way help at least that basic fracture mechanical problem which I have mentioned above; and (iv) I think an application simpler than the basic problem of fracture mechanics, should be possible—with some careful provisos in place. May be, just may be. (The reason I am being so tentative is that the idea struck me only this afternoon.)

I still need to go over the matter, and so, I will not provide any more details about that dim possibility, right here, right today. However, I think I have already provided a sufficiently detailed description of the problem (and the supposed difficulty about it) that, probably, anyone else (trained in basic engineering/physics and mathematics) could easily get it.

So, in the meanwhile, if you can think of any solution—or even a solution approach—that could take care of this problem, drop me a line or add a comment.  … If you are looking for a succinct statement of the problem out of this (as usual) verbose blog-post, then take the above-mentioned quote from my iMechanica comment, as the problem statement. … For years (two+ decades) I thought no solution/approach to that problem was possible, and even at iMechanica, it didn’t elicit any response indicating otherwise. … But, now, I think there could perhaps be a way out—if I am consistent by basic philosophic considerations, that is. It’s a simple thing, really speaking, a very obvious one too, and not at all a big deal… However, the point is, now the (or my) mind no longer comes to a complete halt when it comes to that problem…

Enough for the time being. I will consider posting about this issue at iMechanica after a little while. … And, BTW, if you are in a mode to think very deeply about it, also see something somewhat related to this problem, viz., the 2011 FQXi Essay Contest (and what its winners had to say about that problem): [^]. Though related, the two questions are a bit different. For the purpose of this post, the main problem is the one I mentioned above. Think about it, and have fun! And if you have something to say about it, do drop me a line! Bye for now!!

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

[PS: Perhaps, a revision to fix simple errors, and possibly to add a bit of content here and there, is still due.]