# Math, lingusitics, fuzzy logic etc.

Vidhyanath K. Rao vidynath at MATH.OHIO-STATE.EDU
Wed Nov 11 16:28:10 UTC 1998

I thought that philology and mathematics had some affinity for each
other, because of the number of mathematicians who seemed to have a
done a bit of philology. H. Grassmann is perhaps the only one who is
widely known. But there were others: Gauss and Carl Gustav Jacobi both
studied philology as ``undergrads'' and later decided to go into math.
In more recent times, there was Andre Weil, who says that he attended
lectures by Jules Bloch (and Meillet?) to pass time (!).

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And please leave mathematicians out of the list of those who try to fit
everything into a one dimensional linear scale. People from other
departments, especially social sciences, when on hiring committees,
seem to think that we can rate people on a numerical scale and then
average them. Mathematicians, in my experience, prefer to partial
orders (denying the possibility of comparing every pair).

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The same goes for limiting ourselves to metric spaces. If one metric is
always enough, why do people, and not just topologists like me, study
topology? What is a round ball in one metric may look like a loaf of
french bread in another. And that is a minor change of metrics. Reading
``Semantics: primes and universals'' by A. Wierzbicka led me think that
it is the idea of connectedness that matters for semantic evolution.

Let me try to inject some Indology here. It is usually assumed that the
root `yu' can mean both join and separate in RV. But the latter meaning
occurs only when there is another word in ablative (the case of separation)
or with the preverb `vi'. Should we use the view of modern languages to
assign `yu' a semantic region of large extent or should be assign a
neutral meaning, with the actual connotation to be determined by
adverbs/case endings around it? How can we handle this with >one<
metric?

Another example is na"sati vs na"syati. Again they seem to have
completely opposite meanings. But na"syati is probably to be considered
a reflexive/passive used as an euphemism (obtained by powers better left
unsaid). Such developments do not seem to be systamatic enough to be
captured even by a metric evolving in time (but applicable to all
languages over a wide area like the Old World).

[There are of course may other examples of this kind, such as
gam vs aa+gam, daa vs aa+daa etc. But these depend on a preverb whereas
yu and na"s do not.]

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Fuzzy logic is not the only ``new logic''. There is also ``topos
logic'', where the truth values have nothing to do with numbers. Fuzzy
logic may be more useful where decisions need to be made >now<. In the
scholarly world, hasty decisions between competing theories is a bad
idea. They tend to become dogmas which require strong evidence to
dislodge, much stronger then what used in the first place to
``establish'' them. An example close to home is the common picture of
the Vedic verb. This is taken from Bopp and Whitney who had other axes
to grind. But people think that there is a complete system of moods of
aorist and perfect and a pluperfect etc in RV.

The proposal for semantic metric to be used with currently popular
methods seem to be the same idea as ``data mining''. Many of us do that
often, whether on WWW or on combined catalogs such as WorldCAT. I will
start believing in ``automated data mining'' when these searches become
easy. This thought hit me in fact when I was searching for books on
data warehousing and data mining for my wife.

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-Nath