Geniuses -

genius scott aaronson

Scott Aaronson

One immediate consequence of the Completeness Theorem is the Löwenheim–Skolem Theorem: every consistent set of axioms has a model of at most countable cardinality.

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genius scott aaronson

We are given a biased coin that comes up heads with probability p. Using this coin, construct an unbiased coin.

genius scott aaronson

You haven't seen the proof of that either? Alright, alright. Let's say you have an infinite set A. We'll show how to produce another infinite set, B, which is even bigger than A.

genius scott aaronson

Model 1: But if quantum mechanics isn't physics in the usual sense – if it's not about matter, or energy, or waves – then what is it about? Model 2: Well, from my perspective, it's about information, probabilities, and observables, and how they relate to each other.

genius scott aaronson

What's the point of talking about philosophical questions? Because we're going to be doing a fair bit of it here – I mean, of philosophical bullshitting.

genius scott aaronson

Even there, something inside me (and, I suspect, inside many other computer scientists!) is suspicious of those parts of mathematics that bear the obvious imprint of physics, such as partial differential equations, differential geometry, Lie groups, or anything else that's “too continuous.

genius scott aaronson

More often than not, the only reason we need experiments is that we're not smart enough.