# Alien math

Freeman Craig Presson (dhr@iname.com)
Sun, 18 Jul 1999 13:05:57 -0500

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?