Here's something triggered by New Prof's post on her experience with a recent counseling session at her institution.
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Place: A high profile science and engineering institution in India.
Time: Eons of internet time. Maybe a year ago.
Occasion: Counseling session for the in-coming undergrad students.
A part of the session is devoted to informing the students about what they can expect to study and learn in different streams of specialization. Typically, someone from each stream makes a short presentation, with an overview of the curriculum and the philosophy behind its design.
For the math stream, the professor used the pitch that learning at the undergrad level would be significantly different from what they did at high school -- in that it's not just about learning new concepts, but also about rigorous proofs. The experience, he suggested, might even be a bit like learning a new language.
He then went on to describe all the exciting courses designed for the math students by the department.
During the Q&A, a parent commented that while the curriculum is all great and fine, it still lacked something very, very important: a course on Vedic Mathematics. He wondered how the learned faculty at this great institution could neglect this important field of knowledge, developed by the great sages of ancient India.
The temperature in the hall dropped by a few degrees in anticipation of how the professor was going to handle this tricky question -- a bouncer from the right field [pardon the mixed metaphor].
The professor's answer is what I call an Epic Win (I'm relying on my memory here, so this is not an exact quote):
You remember what I said about our curriculum -- that it's a bit like learning a new language? You see, when you learn a new language, you learn the prose first, before getting to the great poems in that language!
8 Comments:
Looks like these mathematicians aren't very up to date, in terms of the metaphors they should or should not be using today in presenting their own field of knowledge. And, looks like the students themselves also weren't very smart (or at least outspoken). Any student of their age, and living in today's times in India, should have asked the mathematician this question that should have been obvious to a lot of them: "And how does the language of mathematics differ from the computer languages?" (You could phrase that question a bit more precisely, but here I am trying to put it the way a freshly minted XII standard guy might put it.)
The metaphor of mathematics as a language is well-known, but, as I always thought, it is a bit too overstretched. It misses the real point.
The crucial question is this: What is it to which the "words," "grammar," "phrases," "statements," and "paragraphs," etc. of this language refer?
In answer: Mathematics is unique among all sciences in that its ultimate referent objects (i.e. also the ultimate source of all the mathematical relationships) are mental and abstract---they cannot be found in the reality out there. All you can directly show/point out in reality are, e.g., two oranges, two apples, etc., but not the number "2" itself. Similarly, for every other mathematical object/process (the same thing, in a way!).
On the other hand, most common languages carry words (i.e. concepts) that ultimately refer to the objects concretely existing in this world. Whether languages like English and Sanskrit, or special languages like engineering graphics and the sign languages.
Pity, these mathematicians don't even know this much about their own field. ... Of course, what else can you expect when they in principle give up (even rational) philosophy as the integrating context and tool?
BTW, finding the ultimate referents of programming languages is being left as an exercise for the reader. (Pretty simple, that one. The difficult part was getting the nature of _mathematical_ concepts right.)
Ajit
[E&OE]
It is a pity that no one told her that what the students will learn supersedes and is far more advanced than what was known 5000 years ago.
Awesome! Being a mathematician and having faced this question couple times, I have often wondered what to answer without offending the questioner. Great thinking on the feet too!
Maybe the parent was thinking of things like the following?!
Lectures on the beginnings of calculus in Kerala and in Europe
www.math.ucla.edu/~vsv/LectureApril5-19.pdf - Cached
The School of Mādhava in Kerala, c.1350-1600 CE....
Neither Newton nor Leibnitz:
www.pas.rochester.edu/~rajeev/canisiustalks.pdf - Cached
The Pre-History of Calculus in Medieval Kerala. A Colloquium ... email: rajeev@ pas.rochester.edu. Canisius ..... •Of course this modern notation was not used.
The fault lies with the NCERT which tried to to introduce Vedic Mathematics in the school curriculum. It seems people WANT to believe that there is something known as vedic maths and no amount of convincing will work.
gnaanamaargi: Vedas were not written in the Kerela school. Nor is that time frame accurate. Indeed, it may be useful to teach some real mathematics which was developed in the Kerela school rather than the arbitrary and hollow grandiloquence that passes for "knowledge" in the Vedas.
zizou: the fundamental fault is with the millenia-old Brahmin rumour mill which started and propagated the rumour that there is something in the Vedas that is factual, and worth believing, remembering and preserving.
@Ankur Kulkarni: While I have no patience for advocates of "Vedic mathematics" or those who ascribe serious mathematical works of later mathematicians such as Aryabhataa, Madhava and Brahmagupta to the Vedas, I find it hard to agree with your position that there is noting worth preserving in the Vedas. While it is true there is nothing factual in them, they are a great source of historical information about the cultural evolution of Indo-Aryans, and also of the evolution of the Sanskrit language. The very fact that the "rumor mill" succeeded in keeping parts of them unchanging for about three millenia is by itself remarkable enough to get them included in the cultural heritage of humanity. The same goes for other surviving religious texts from the same period, such as the older parts of the Bible.
On another note, parts of the Vedic literature (though I guess not the Vedas themselves) do contain serious, and for the tome, revolutionary, mathematical knowledge. See the Shulba Sutras for example.
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