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Imagine what Charles Babbage would think of my abilty to look at a colored piece of glass and utilize the computational resouces of the internet - he might consider it omniscient

Actually, I don't think he would.

He'd recognize it as a very impressive machine. But certainly not 'magic'.

Indeed, I have always disagreed with Arthur C. Clarke's "second law". The only people who mistake a phenomona for 'magic' are those who believe in magic. The others will always look for an explanation and try to figure out how it works.

[Billthedrill]

Ah, no, sorry - I slipped that one in on you - Babbage wouldn't consider it magic, but he might consider it omniscient, at least from the context of what he knew were the possibilities of his day. "Magic," as another poster reminded me, refers to what a primitive person might think of a technology "sufficiently advanced" according to Clarke, and I agree with you completely that this begs the question of what constitutes "sufficient." And, of course, how "primitive" the person in question is. There are, even today, those who find spoon-bending to be "magic..."

The question of whether mathematics is "invented by man" (i.e. a posteriori) or not (a priori) is one of many interesting questions addressed in Immanuel Kant's Critique of Pure Reason. It's a bit of a sticking point at that interstice between philosophy and theology, and a deep indicator of how one sees the universe: to a religious purist it doesn't matter because if man invented it, God invented man; to an atheist it doesn't matter because if God invented it, man invented God. To the rest of us it's a little more opaque.