From: Freeman Craig Presson (dhr@iname.com)
Date: Sun Jul 18 1999 - 12:05:57 MDT
A few possible directions :
* Notation: obvious. It would be shocking if alien languages in general were
not radically different from the "Terran language family," so you'd certainly
expect mathematical notation, assuming the concept even applies, to be
incomprehensible. Maybe it's all geometry to them (think Feynman
diagrams).
* Philosophy: There are radically different philosophies of math on Earth,
let alone elsewhere/when. It would be telling to see how an ETSI would
deal with infinity/infinitesimals, for example.
* Abstraction level: one might expect that large parts of our math might be
special cases of an advanced alien system. I have often wondered about
the upper limits of abstraction, as I studied more and more abstract
algebra and found it more and more "empty." But that's *my* orientation
speaking, which is more concrete than I thought when I was a freshman
(as a pure math major, that was a hard fact to swallow).
* Variant axioms: If an alien system has axioms that to us are undecidable
theorems ... (what was that old saw? "The Axiom of Choice is obviously
true, Real Countability is obviously false, and Zorn's Lemma is
meaningless ... but they are all equivalent.")
* Different approaches to logic: fuzzy logic/set theory, multivalued systems
and so on are all a little kinky to most earthly minds, but they might seem
quite natural elsewhere. Or think of Spencer-Brown's calculus from Laws of
Form, which comes from somewhere quite different, but has propositional
calculus as one of its interpretations.
That's just off the top of my head. However, I think math would still be the
first thing we understand in common with ETIs, because we could compare
how each applies it to science and technology. Tell me how Qzztbkf
expresses "F = ma" and I'll have a pretty good idea how to start
deciphering everything else she sends us.
If her math and physics are so alien that it takes us years to explain
Newton and Wrrrzjl to each other, then the rest of the conversation's going
to be mighty strained as well. That'll be OK with me if the aging therapy
kicks in in time -- besides, if you're having a conversation that was almost
impossible in the first place, you shouldn't be surprised at its difficulty, enit?
-- fcp@traveller.com (Freeman Craig Presson)
-- ExI member, geek-at-large, etc.
-- http://www.bhm.tis.net/~fcp/
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