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.


Exercises:

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.

Exercises:

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.]

[E&OE]

From the horses’ mouths

My first choice for the title was: “From the Nobel Laureate’s Mouth”; I had spotted only the opinion piece by Professor David Gross in yesterday’s Indian Express [^]. Doing the ‘net search today for the URI link to provide here, I found that there also were three other Nobel laureates, also joined by one Fields Medalists. And they all were saying more or less the same thing [^].

… That way, coming from a Marathi-medium schooling background, I had always had a bit of suspicion for the phrase “from the horse’s mouth.” It seemed OK to use in the news reports when, say, a wrong-doer admits his wrong. But purely going by the usage, I could see that the phrase would also be used in the sense: “from the top-gun himself,” or “from the otherwise silent doer himself.” This guess turns out to be right [^]. Further, since there were as many as five “horses” here, the word to be used would have to be in the plural, and if you say it aloud: “From the horses’ mouths” [go ahead, say it aloud, sort of like:“horseses” mouth) it really sounds perfect (for something to be posted on the ‘net).

So, that’s how comes the title.

As to the horses’ thoughts… Ummm…

[But please, please, give me just a moment to get back to the title again, and congratulate me for not having chosen a title like: “From Dave Himself.” You see, Professor David Gross had visited COEP in 2013, and I might have been, you know, within 50 meters of where he was sitting. I mean, of all places, in the COEP campus! Right in the COEP campus!! [^]. Obviously, you must compliment me for my sense of restraint, of making understatements.]

OK. As to their thoughts… Umm….

I think these guys are being way too optimistic. Also naive.

Without substantial economic reforms, I see no possibility of the Indian Science in general undergoing any significant transformation yet again. And substantial economic reforms aren’t happening here any more. In fact, no one is even talking about it, any more. [Check out Arnab’s hours, or Sardesai’s, or Dutt’s, if you want to find out what they are talking about. [I don’t, because I know.]]

It was the 1991 that could propel, say a Mashelkar into prominence several years later, and help transform the 70+ CSIR labs from something like less than 100 patents a year, to thousands of them per year—all within a matter of a few years [less than a decade, to be sure]. If the same momentum were to be kept, the figure should have gone up to at least tens of thousands of patents by the CSIR labs alone—and with a substantial increase in the share of the international patents among them. Ditto, for the high-quality international journal papers.

Why didn’t any of it happen? Plain and clear. The momentum created by the economic liberalization of the early 1990s has been all but lost. Come on, face it, 1991 was twenty-five years ago.

To an anthropologist, 25 years is like an entire generation! More than enough of a time to lose any half-hearted momentum (which, despite the hysterical Indian press, the liberalization in the early 1990s was).

It’s been years that we entered the staleness 2.0 of the mixed economy 1.0. Even today, the situation continues “as is,” despite a change of regime in New Delhi. Yes, even under “Modiji.” [I am quoting Professor Gross—I mean the word.]

But, yes, the five gentlemen were also being realistic: Each one of them emphasized decades.

Decades of sustained efforts would have to go in, before the fruits could begin to be had. [But you know that decades isn’t a very long period—just recall what was happening to India’s economy some two decades ago—in the mid ’90s.]

Talking of how realistic they actually were being, Haroche even pointed out the lack of freedom in China [obvious to any one outside of California], and its presence in Europe [I don’t know about that] and in India [yeah, right!].

But anyway, it’s nice to hear something like this being highlighted after an Indian Science Congress, rather than, say, “vimaanshaastra.”

Both happened during “Modiji”’s tenure. So what is it that really accounts for the difference? I have no idea. (It can’t be a “pravaasi” whatever, to be sure; they would be too busy booking the next Olympics-size stadium.)

Whoever within the organizers of the Congress was responsible for the difference, compliments are due to him. (Hindi) “der se kiyaa lekin kuchh achhaa hi to kiyaa.”

In the meanwhile, bring out your non-programmable desk calculators and do some exercises: 0.8 \times \dots, 2.7 \times \dots, 4.4 \times \dots and 2.1 \times \dots. Oh well, you will have to refer to the ‘net.

OK then. Find out also the R&D spending by, say, (i) Baba Ramdev’s pharmaceutical industries, (ii) the top or most well-established five industrial groups in India (Reliance, Tatas, Mittals, whoever…), and (iii) the top three (or five) Indian IT firms. Compare them to those in the advanced countries. Let your comparisons be comparable: pharma to pharma; oil, steel and engineering (and salt!) to oil, steel and engineering (and salt!); IT to IT [engineering IT to engineering IT]; overall (GDP) to overall (GDP).

And, never forget that bit about freedom. Don’t just count the beans “spent” on research. Think also about whether it is the government spending or the private spending, and where the expenditure occurs (in private universities, private labs, independently run government labs, public universities in a country with a past of a private control, etc., or in the in-service-pensioner’s-paradises with something like “laboratory” in their titles).


But why didn’t the “horses” cite any specific statistics about how many Indian students go abroad for their graduate studies, and choose to permanently settle there—their trends?

Obvious: Nobel and Fields laureates (and in fact any visiting dignitaries to any country (and in fact any visitors to a foreign country)) generally tend to be more polite, and so tend to make understatements when it comes to criticism (of that host country). That’s why.


A Song I Like:

(Hindi) “kahin naa jaa…”
Music: R. D. Burman
Lyrics: Majrooh Sultanpuri
Singers: Kishore Kumar, Lata Mangeshkar

[E&OE]

“They don’t even touch a good text-book!”

“They don’t even touch a good text-book!”

This line is a very common refrain that one often hears in faculty rooms or professors’ cabins, in engineering colleges in India.

Speaking in factual terms, there is a lot of truth to it. The assertion itself is overwhelmingly true. The fact that the student has never looked into a good (or “reference” or “foreign authors'”) text is immediately plain and clear to anyone who has ever graded their examination papers, or worked as an examiner on the oral/viva voce examinations.

The undergraduate Indian students these days, esp. those in Pune and Mumbai, and esp. those in the private engineering colleges, always refer to only a locally published text for all their studies.

These texts are published by a few local publishers well known to the students (and their professors). I wouldn’t mind dropping a few names: Nirali, Pragati, TechMax, etc. The books are published at almost throw-away prices (e.g. Rs. 200–300). (There also exists a highly organized market for the second-hand books. No name written, no pencil marks? Some 75% of the cost returned. Etc. There is a bold print, too—provided, the syllabus hasn’t changed in the meanwhile. In that case, there is no resale value whatsoever!)

The authors of these texts themselves are professors in these same private engineering colleges. They know the system in and out. No, I am not even hinting at any deliberate fraud or malpractice here. Quite on the contrary.

The professors who write these local text-books often are enthusiastic teachers themselves. You would have to be very enthusiastic, because the royalties they “command” could be as low as a one-time payment of Rs. 50,000/- or so. The payment is always only a one-time payment (meaning, there are no recurring royalties even if a text book becomes a “hit”), and it never exceeds Rs. 1.5 lakhs lump-sum or so. (My figures are about 5 year old.) Even if each line is copied verbatim from other books, the sheer act of having to write down (and then proof-read) some 200 to 350 pages requires for the author to invest, I have been told, between 2 to 4 months, working overtime, neglecting family and all. The monthly salary of these professors these days can easily approach or exceed Rs. 1 lakh. So, clearly, money is not the prime motivation here. It has to be something else: Enthusiasm, love of teaching, or even just the respect or reputation that an author hopes to derive in the sub-community of these local engineering colleges!

These professors—the authors—also often are well experienced (15–40 years of teaching experience is common), and they know enough to know what kind of examination questions are likely to come up on the university examinations. (They themselves have gone through the same universities.) They write these books targeting only task: writing the marks-scoring answers on those university examinations. Thus, these “text” books are more or less nothing but a student aid (or what earlier used to be called the “guide” books).

It in fact has evolved into a separate genre by itself. Contrary to an impression wide-spread among professors of private engineering colleges in India, there in fact are somewhat similar books also used heavily by the students in the USA. Thus, these local Indian books are nothing but an improvised version of the Schaums’ series in science and engineering (or the Sparks Notes in the humanities, in the US schools).

But there is a further feature here. There is a total customization thrown in here. These local books are now-a-days written (or at least adapted) to exactly match the detailed syllabus of each university separately. So, there are different books, by the same author and for the same subject, but one for Mumbai University, and the other for Pune University, etc. Students never mix up the universities.

The syllabus for each university is followed literally, down to dividing the text into chapters as per the headings of the modules mentioned in the syllabus (usually six per course), and dividing each chapter into sections, with the headings and order of these sections strictly following the order and the letter of the syllabus. The text in each section is followed by a compilation of the past university examination questions (of that same university) pertaining to that particular section alone. Most of these past examination questions are solved in the text—that’s the bulk of the book. When the opening page of a chapter lists the sections in it, the list also carries, in the parentheses, whether this section is “theory” or “numericals”.

Overall, the idea is, even just looking at the “text” book, a student can easily anticipate whether a question is likely to be asked on a given section or not, and if yes, of what kind. The students also work out many logics: “Every semester, they have asked a question on this section. So we have to mug it up well.” Or, playing the “contra”: “Last three semesters, not a single question here? It’s going to come this time round.” Etc. (Yes, I followed this practice in my lectures, too—I did want my students to score well on the final university examinations, after all!)

The customization, for each revision of the syllabus of each university, is done down to that level of detail. So, for the first year course on electrical engineering, you have one text-book of title, say, Electrical Engg. (FE), Pune University, 2012 course, and another text book, now of the title, say, Basic Electrical Technology (FE), Mumbai University, 2011 course. Etc.

That’s what I mean, when I use the phrase the “local” text-books.

I certainly don’t mean the SI Units editions of American texts, or the Indian Standards-adapted editions of reputed texts (such as, say, Shigley’s on design or Thomson and Dahleh’s on vibrations). I don’t mean the inexpensive Indian editions of foreign texts (such as those by Pearson, Wiley, ELBS, etc.) I also don’t mean the text-books written by the well-known Indian authors working right in India (such as those by IIT professors, and published by, say, Universities Press, Narosa, or PHI). I don’t even mean the more general text-books written for Indian universities and/or the AMIE examinations (such as those by S. Chand, Khanna, CBS, etc.). When I say “local” text-books, I specifically mean the books of the kind mentioned above.

Undergraduate students in Pune and Mumbai these days refer only to these local books.

They (really) don’t even bother to touch a good reference text, even if it’s available on the college library shelf.

In contrast, in our times, the problem was, we simply didn’t have the “foreign authors'” texts available to us—not always even in the COEP library. In those days, sometimes, such books happened to be too expensive, even for COEP’s library. And, even back then, Shahani’s text-books anyway were available. But at least, they didn’t cater to only the Pune university (they would list problems from universities as far flung as Madras, Gorakhpur, Agra, Allahabad, etc.) And, in fact, these books were generally looked down upon. Even by the students themselves.

The contrast to today’s situation is too glaring. Naturally, professors sometimes do end up saying the title line with a tone of exasperation.

Yes, I used to sometimes say that line myself, of course with sarcasm, when I taught in the late ’80s in the Pune of those days. (The situation back then was not so acute.) Almost as if by habit, I also repeated the line when I more recently taught a course at COEP (2009, FEM). However, observing students, somehow, my line had somehow begun to lose that cutting edge it once had. First, at COEP, I had the freedom to design this course (on FEM), and they did buy at least Logan and/or Cook. (Even if I was distributing my PDF notes.) And, there was something else to it, too. I somehow got a vague feel that it somehow wouldn’t be fully right to blame students (I mean COEP students in general). However, my COEP stint was only for one semester, only for one course, and only as a visiting faculty. So, the vague feel simply remained what it was—just a vague feel.

Then, recently in 2014, when I began teaching at a private engineering college in Mumbai, I once again heard this line from the other professors. And, I used it myself too. With the usual sarcasm. I did that perhaps for the most part of my first semester there.

However, some way down the line, I once again got that vague feel that, may be, something was “wrong” somewhere, even here, in Mumbai: these kids really were trying to be sincere, and yet, for some reason unknown to me, they still wouldn’t at all refer to good texts.

This is an aside, but I can tell you that it’s very easy to read the faces of the insincere people, esp. when they are young. There are some insincere students too. But, at least going by my own experience, they are in a minority. (It is a headache-some minority. Yet, by numerical magnitude alone, it certainly is in a small minority.) I am not saying this to be politically correct, or to win points from students. What I said is the factual case. In fact, my experience is that when it comes to in-sincerity, parents easily outperform their children. May be because, the specific parents that we mostly end up seeing in college are those whose kids have some problem—low attendance, fee payments, other issues, etc. The parents with whom we get to interact really well, thus, happens to be a self-selected sub-group. They aren’t necessarily representative of all parents… Yet, I am also sure that that’s not the real reason why I think parents can easily be more insincere. I think the real reason is that, at their age, the kids are actually unable to fake too much. It’s far easier for them to be sincere than to be a fake and still get away with it. They just can’t manage it, regardless of their desire. And, looking at it in a better light, I here remember what Ayn Rand had once said in a somewhat similar context, “one doesn’t start out in life by spitting on one’s own face—it’s not in the essential nature of life” or something like that. (Off-hand, I think, it was in the preface to the 25th anniversity edition of The Fountainhead.) So, the kids, by and large, are sincere. … By the time they themselves become parents—well, let’s leave that story right here. (We need them to make all those fee payments, anyway…)

So, coming back to the main thread, I would anyway generally chat with the students, and so, I started asking, esp. some of the more talkative students, the reason why they might not be referring to good texts. After all, in my lectures, I would try to provide very specific references: specific section numbers or even page numbers, in a specific edition of a specific reference text. (And these texts were available in the college library.) Why, I once had even distributed an original research paper. (It was Griffth’s seminal 1920 paper starting the field of fracture mechanics. Griffith’s argument here is rather conceptual, and the paper has surprisingly very little maths. Whatever the maths there is, it is very easily accessible to the SE students, too.)

The result of my initial attempts to understand the reason (why students don’t read good texts) was not so encouraging. The talkative students began dropping by my cabin once in a while, asking which section to use while answering a certain assignment question or so. However, they still only rarely used those better texts, when it came to actually completing their assignments. And, in the unit tests (and in the final end-sem examination), they invariably ended up quoting only the local text books (whether verbatim or not).

The exercise was, thus, futile. And yet, the students’ sincerity—at least the sincerity of their desire, as in contrast to their actions—could not be put in doubt.

So, I took it as a challenge. I set this as a problem for myself: To discover the main reason(s) why my students don’t refer to good text-books. The real underlying reason(s), regardless of whatever they otherwise did to impress me.

It took a while for me to crack the problem. I would anyway generally chat with them, enquiring where they lived, what their parents did, about their friends and brothers and sisters, etc. In addition, I would also observe, now with this new challenge somewhere at the back of my mind, how they behaved (or rushed around) in college: in hallways, labs, canteen, college ground, even at the bus-stop just outside the college, etc.

…Finally, I got it! At least one reason, a main reason, a systemic reason that applied even to those who otherwise were good, talented, curious, or just plain sincere.

As soon as I discovered the reason, I shared it with every one. In fact, I first shared it with my students, before I did with my colleagues or superiors. The answer lies in an Excel spreadsheet, here [^]. (It actually was created in OpenOffice Calc, on Windows 7.)  Go ahead, download it, and play with it a bit. The embedded formulae should be self-explanatory.

The numbers used in the spreadsheet may differ. The specific numbers I have used in the spreadsheet refer to my estimates while working at a college in Mumbai, in particular, in Navi Mumbai. In Mumbai, the time lost commuting is really an issue. If a student lives in Thane or Andheri and attends a college in Navi Mumbai, he easily spends about 3–4 hours in the daily commute (home->bus->railway station/second bus/metro–>another bus or six-seater, all of it taking about 1.5 hours one way, or more). In Pune, the situation is much more heterogeneous. One student could be spending 3 hours commuting both ways (think: from Nigdi to VIT) whereas some other student could be just happily walking to the college campus (think: Paud Phata residents, and MIT). It all depends. In Pune, many students would be using two-wheelers. In any case, for a professor, the only practical guideline for the entire class that he can at all use, would have to be statistical in nature. So, it’s the class average for the daily commute time that matters. For Mumbai in general, it could be 2–3 hours, for Pune students, it could be, say, between 1 to 2 hours (both ways put together).

So Pune is a bit easier on students. In contrast, for many of my Mumbai students, the situation was bad (or even very bad), and they were trying hard (or very hard) to make the best of it. It must have been at least a bit frustrating to them when professors like me, on the top of everything, were demanding making references to good foreign texts, and openly using a sarcastic tone—even if generously laced with humor—if they didn’t. It must have been frustrating to at least 40–60% of them. (The number is my estimate of those who were genuinely interested in referring to good books, even if only for the better-drawn and colorful diagrams, photographs, and also mathematical proofs that came without errors or without arbitrary replacement of \partial by d.)

And why do I say that it must have been frustrating? Why didn’t I say it might have been frustrating?

Because, I cannot ever forget that look of that incredibly honest appreciation which slowly appeared on all their faces (including the faces of the “back-benchers”), as I shared my discovery in detail with them.

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How about your college? Your case?

Do you have the time to read good, lengthy, or conceptually clarifying “reference” texts? Say, Timoshenko (app. mech. and strength of materials); Shames, or Popov (strength of materials); White, or Fox & McDonald, or Som & Biswas (Fluid Mech.); Holman, or Nag, or Sukhatme (Heat Transfer)?

And, if you do, do you spend time reading these texts? If yes, did you complete them (I mean only the portion relevant to the syllabus) in the same semester that you were learning or teaching the subject for the first time? Could you have?

And yes, in my last sentence, I have included “teaching” too. My questions are directed to the professors too. In fact, my questions are directed, first and foremost, only at them.

After all, it is the professors—or at least some of us—who are in the driver’s seat here; the students never are. It is the professors who (i) design the syllabii as well as the examination schemes (including the number of tests to have and their nature), (ii) decide on the number of assignments (and leave no opportunity to level criticism in our capacity as External Examiners, if the length or difficulty of an assignment falls short), (iii) decide on the course text-books (and take due care to list more than 5 prescribed text-books, and more than 10 reference books per course) (iv) decide on the student attendance criteria in detail, up to the individual course level, and report on the defaulting students (and follow through with the meetings with their parents) every two weeks or at least once a month, (v) set the examination papers according to the established pattern—after all, it’s only us who is going to check the papers!, (vi) sometimes, write those local text-books!, and (vii) also keep the expectation that students should somehow show in their final university examination answer books, some evidence of having gone through some good, thick, reference texts, too. Whether we ourselves had managed to do that during our own UG years or not!

And, yes, I also want the IIX professors to ponder over these matters. All their students enjoy a fully residential program; these kids from these private engineering colleges mostly don’t. They at IIXs always get to design all their course syllabii and decide on the examination patterns, and they even get to enjoy the sole responsibility to grade their students. The possibility of adopting a marks normalization scheme, after the examination, always lies at hand, with them, just in case a topic took too long with a certain class or so… Are they then being reasonable in their request demand that the students of these “other” engineering colleges in India be well-read enough, at least by the time the students join them at IIXs for ME/MTech studies?

As to me, no, as I indicated in my earlier posts, while being a professor, I could not always find the time to do that—referring to good text-books. I tried, but basically my situation wasn’t much different from that of my students—we both were short on the available time. So, I didn’t always succeed.

[As to my own UG years, it was mixed: I did hunt for months, and got my hands on, the books like Reed-Hill, White, Holman, etc. However, I would be dishonest if I claimed that it was right during my UG years that I had got whatever I did, from books like these. In my case, the learning continued for years. Yes, I even bought and religiously studied once again even Thomas & Finney’s calculus, when I was in my PhD program at UAB. Despite my attempts during the UG years, I really cannot ascribe a large part, or even a significant part of my current understanding to my UG years. Your case may be different; I was just narrating my own experience.]

… And, as far making references to good books goes, now that I do have time at my hand these days, there is another problem: I don’t know what course in particular I will be teaching the next semester, and where—or for that matter, whether some college will even hire me in the first place, or not.

So, I end up “wasting” my time writing blog posts like this one. Thus, I, too, end up not touching a good reference text!

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A Song I Like:

(Hindi) “aane waalaa pal, jaane waalaa hai…”
Lyrics: Gulzaar
Singer: Kishor Kumar
Music: R. D. Burman

[I will go over this post once again, editing it, and may be adding a bit here and there. Done. This post is already too long. So, I will write another post—a brief one—to jot down some tips to make the best possible use of the student’s time—including my suggestions to the engineering colleges as to what they can do to help the students. Also, my take on whether the system as noted above has diluted the quality of education or not—esp. as in contrast to what we had as UG students at COEP more than three decades ago.]

[E&OE]

 

A second comment about appointments to academic posts

I won’t take chances. This was a comment I just made this morning at Prof. Dheeraj Sanghi’s blog, here [^]. Comments at his blog are moderated. And, I don’t know if he will allow it in. (There could perhaps even be some valid reasons for this comment not to be run there.) So, I have decided to go right ahead and note my comment here, too. (On second thoughts, as I have often said earlier on this blog, I anyway think that I should be bringing here many other comments I have made over a period of time at many other blogs, too.)

Here is the comment I have just made at Sanghi’s blog:

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Quote:

Dear Dheeraj,

You write interestingly, even engagingly. Well, at least, you write—as in contrast to mostly just excerpting from Internet links!

I don’t mean to fully defend the practice that has been adopted. I just wish to note down out a few points that seem to be contrary to the flow of your argument, a few points that passed through my mind.

When you recruit a lower-level employee, a PhD student, or a professor, you do follow the meticulous process you mentioned; it involves lengthy interviews, too. Why might someone not follow a similarly long interview while recruiting IIT directors?

I think that some at least plausible answer may be hidden right in that question.

For the starters, when it comes to the candidates for the director’s post, as against the other posts you mentioned, simply because all the candidates have already been subjected to a meticulous process, throughout their prior career, typically spanning over decades.

They have been observed and evaluated at the senior and responsible positions for at least a decade or more by multiple, disparate, parties. … Any comments they make at professional conferences, any viewpoints they offer at the industry-institute interactions, the quality of the documents they write for obtaining funding, etc. Also, the blogs they write [ 😉 ]. And, they have been continuously evaluated by various parties: h-Index (certainly), student evaluations (if these are taken seriously at IITs)—and, certainly, via the annual reviews from their seniors, which includes mandatory remarks from the viewpoint of their potential as leaders. The CRs (annual confidential reports), made over a decade+ times (through various political dispensations, under many different HoDs and Deans and Directors) do have some purpose, you know—i.e., if these are taken seriously at IITs!

They also have been short-listed by the formal selection committees. Presumably, the committee’s role does not end only with providing an unordered list of names. Presumably, the short-listing committee takes its job seriously.

IITs are not private institutes. The top decision makers here, by explicit organization structure, are the concerned ministry/ministries. Whether you like it or not, they do have their regular input channels, too—channels other than the selection committees. In India, in case you have happened to overlook it, we have more than 10 central agencies for internal intelligence gathering. When the body called the Planning Commission got dismantled, another one stepped in to fill the vacuum.

Another point: At the director’s level, IITs also typically do not go for rank outsiders. Most, if not all, of what I say would remain valid even if the candidate is an outsider.

The cumulative input from multiple sources thus is already there. It is distilled, and available, just in case not already factored in, by the time the short-list is made. And, then, there are internal reviews.

The final interview, thus, is more or less just a formality. Shocking? Why should it be, to you?

Dheeraj, since you are a senior IIT professor, I must ask you: If similarly detailed and well-processed inputs were available personally to you, for all the candidates applying for a post-doc position you had in your group, would you ever bother talking with each of them for 30+ minutes? … Please concretize the situation; it is unlike what actually happens when you select your post-docs. When you select your post-docs, you mostly don’t know about all of them. … Suppose if you or your IITK/other IITs colleagues that you trust, themselves had personally seen all your post-doc candidates right from their fifth standard (if not the first standard), and suppose you had maintained your own reports about them, including from the viewpoint of their potential as post-doc researchers, and if you had had the opportunity to go through everything about every one of them, how much time would you want to allocate for merely chatting with them?

And, doesn’t this happen in the USA anyway—and I mention this point, because I know that at IITs, esp. at IITK, a top-10 US PhD is routinely valued better than a PhD that COEP graduated after a failure at a PhD program in a 50+ USA school. Thus, mentioning the US practice should be perfectly acceptable.

Would a colleague of yours in the USA—one who values your word—even bother to talk with someone you strongly recommend, i.e., with a personal touch of yours? Do they? actually? even for just five minutes? Especially if they themselves know someone trustworthy other than you, who personally knows the post-doc applicant? Do you find their practice offensive? Did you find it offensive when Manindra Agarwal’s students received offers for post-docs etc., even before submitting their PhD theses at IITK? Did you begin blogging something about the fact that there was no 30 minute interview, not even 5 minute interview for them? Do you hasten to wear your skeptical glasses if an IUCAA PhD student gets a post-doc offer at Princeton or CalTech even before submitting his thesis?

At this point, you should be a bit bemused, perhaps even a bit agitated, but you would still not be convinced. There is a bit of valid reason for it, too. I can understand and sympathize with your viewpoint.

You see, I myself have undergone a similar kind of a process—the kind that you criticize. When I applied for a professor’s position at COEP, what actually happened was that, apart from submitting my application (manually making sure that it was duly entered into the inwards register), I then dropped by a few professor’s cabins in the department, and then, also the Director’s cabin. I broached the metallurgy-to-mechanical branch-jumping issue with him, and sought his opinion about it. To cut a long story short, he bluntly told me that he has had no objection on that count (it was he who had given me an opportunity to teach an FEM course before my PhD thesis was defended), but that, as a director, what the department thinks, he said, was more important to him. And, while the department had thought differently earlier, when my PhD guide was still in it (or had just left it), now the department had begun “thinking” some “different” way.

I was duly short-listed, called for the interview, and it became evident to me within the first 1–2 minutes the nature of what to expect. (Doesn’t it, if you are past your 40?… In my case, I could tell right when I was in my 20s.) The interview did last for about 30 minutes—I stretched it, because I wanted to tell them in sufficient detail—while all along, they were just wanting to hurry it up and wrap up it all. … To cut a long story short, in the end, they selected someone whose thesis had been examined by a low-ranked NIT’s low-ranked professor, whereas every one in COEP knew that my guide had, on my informal remarks, dared contacting people from top 5 univs in the USA for examination of my thesis (including Frank Wilczek). That none of them bothered to examine it is a different story. The end result was that after almost 1.5 years, my thesis was finally picked up for examination by two senior professors from one of the five old IITs—both of whom had been HoDs and Deans, and one later on was a Director of a central lab. Now regardless of this difference, COEP showed me the door. As expected and made clear right during the interview process. (“Are you now casting aspersions that we don’t know what is good for this institute?” etc. When I say I had stretched them to 30 minutes, I mean it. After taking the decision, they did not take care to inform me of the outcome. I saw the director. He managed to sympathize with me. Though he didn’t say a thing, I knew that he knew that I knew that I should have known that I would not get selected.

Just a COEP professor’s post and an IIT director’s post, there is a difference, you say?

Well, Dheeraj, you then speak more like a typical IAS officer or a second-rate corporate MBA, than like a professor. If a director directly impacts some 500 faculty members over his entire term(s), a professor impacts some 500 students every year. And the impactees in the second case are both far more sensitive and powerless. And, with far longer period of their future at the stake.

If there were to be betting rackets for IIT Directors’ positions, the going rates would almost consistently get the selections right, regardless of change of political dispensations, and without the benefit of even a one minute interview. Why is a five minute interview so difficult to get by top ranked IIT professors, cognitively speaking.

And if you still say that the five minutes interviews still are not acceptable because the process can result in wrong/bad selections, well, you only join me, my argument—you cast doubts on the short-listing and the real reviewing processes, on the grounds that some people who could easily become second-rate directors, too, had got short-listed by the selection committee. Exactly similar to what happened to many other candidates in the COEP process. Not just short-listing, but the internal reviews before the interviews even began.

But then, who blogs about a non-JPBTI anyway—let alone for him? Who defends him? Answer: None—if his PhD guide is dead.

These are some of the things that passed by my mind, while thinking about this directors’ selection issue. I don’t pretend to know or understand the full situation. But I do know that what I said is, in many important ways, relevant.

Best,

–Ajit
[E&OE]

Unquote

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A Song I Like:
(Hindi) “aayaa hai mujhe phir yaad wo zaalim…”
Singer: Mukesh
Music: Roshan
Lyrics: Anand Bakshi

[E&OE]