/sci/ - Science & Math

>>12715117
That's ridiculous. Watch
https://www.youtube.com/watch?v=Dqj32jxOC0Y
If determinism is true, you don't have free will, since everything "you" ever do is a direct consequence of the state of the universe before you were born, none of which you're responsible for unless you go full schizo and assert eternal presence, in which case you might have an argument, but you can no longer call it "the non-schizo answer".
>>12714862
Personality type averse to thought.

>>12673918
The first monster you face is the Continuum Hypothesis. We know view it as something less-than-mathematical, something only relevant to set theorists and not-so-real mathematicians, but this was not so. It used to be an absolutely central problem in mathematics, first on the list of Hilbert's 23 problems posed to set the direction of mathematics for the next century. Mathematicians genuinely believed that it had a definite answer, and that it was a genuine problem (albeit a bit esoteric in its statement, especially for those a bit sceptical of infinities), until Cohen came along and blew it all. Now the consensus is that it's a esoteric, set-theoretic problem that we don't really have to care about.
Ok, so let's forget such artificial statements as CH, as the Godel sentences and whatnot, and move on to do some analysis (a field for which set theory was invented), and focus only on natural questions!
In Hilbert spaces, a very natural and useful structure is the ideal of compact operators. When we quotient out by this ideal, we can ask: are all the automorphisms in the resulting space inner? A very natural question which in fact turns out to have physical relevance. The answer? Independent from ZFC!
Let's take a look at algebra. A very natural algebraic questions that arose is the Whitehead problem: is every compact path-connected abelian group a product of copies of the circle group, R/Z? You can probably already guess the answer. There is none! You can take any answer you like and you will never encounter an inconsistency. Of course you could argue that this problem isn't about the real numbers per se (even though the construction of R/Z relies on them), but you cannot argue against the fact that constructions involved in the questions are inextricably linked to those or real numbers and have the same kind of vagueness.
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