> So when you say that you couldn't create a universe in which Euclidian geometry doesn't hold, you're ignoring the fact that it doesn't hold in this Universe? I don't understand...
>
> wintermute

You still seem confused by my distinction between the physical geometry of the universe and the theoretic Euclidean geometry I was talking about. The first is physical structure, the second is just a bunch of axioms and theorems. It is true that these axioms were *modeled* by Euclid based on what *seemed* to be inherently true about the world. He had no way of knowing that space wasn't really a nice flat three dimensional surface unaffected by matter, energy, and time. Nevertheless, whether or not those axioms and the theorems they lead to are *useful* in the real universe is totally irrelevant. The point is that IF those axioms are assumed to be true (and if the other logical axioms you need are true, etc.,) then the conclusions are necessarily true in this universe and any universe. There might be possible universes in which, in addition, the Euclidean axioms DO represent a true model of the physical universe -- Euclid just didn't have very good luck in this one.