Why not solve the paradox by dropping the expectation that infinitty works like finity? (And how does Cook solve the paradox?)
The book "solves" the paradox by stating that, yes, you can add an infinite number of guests to Hilbert's hotel, even when it was full to begin with. Again, it's only stating surprising results and if Hilbert considered it sufficiently surprising to articulate then I'm not going to argue!
It's not that infinity doesn't work, it's that it struck me that it's barren of interesting structure. Yes, infinity + infinity is still infinit...
It's interesting that you choose dividing by zero as your comparison to infinity, because there are infinite possible solutions to x/0.
I think if you ask a mathematician what x/0 is, they'll say "undefined" or "that's not a valid question". But if you ask how many natural numbers there are they'll say "infinity" (or ℵ-zero). But we could have defined x/0 as "foo" to see what resulted, like sqrt(-1) is i. But I think not much results and so people don't bother, and maybe we shouldn't have bothered with infinity either.
(I don't think the same about infini...
I don't understand what you mean by "the structure behind infinity"
I mean it in contrast to, for example, sqrt(-1). There was clearly a “hole” in polynomial equations: equations that couldn't be solved. Cardano decided to just define the thing that would fit in that hole and explored the structures that resulted. That turned out fantastically! The structure of complex numbers is incredibly rich and, with 20th century physics, turns out to be arguably more fundamental than the reals.
People tried to repeat that with higher-dimensional numbers. Quaternions...
The culture of the FDA didn't spring into being this year, of course. This book covers their failures to regulate foreign manufacturing of generic drugs and it substantially dented my previous belief that generic versions of drugs are equal to the branded. The book is, however, about twice as long as it should be and you may prefer this podcast with the author.
Don't forget that (in the US, at least) there is a fine for owing too much tax at filing time, while there's no penalty for having paid too much except for opportunity costs. Given the extremely low interest rates currently, the risk is not symmetrical.
I think that personal choices about morality are unaffected by the fact that significantly different cultures exist. Perhaps they call for a soupçon more humility, but your moral intuitions remain axiomatic for you.
Rather I think the adjustment needed in some cases is a greater weight on the idea that your moral intuitions are significantly shaped by the culture that you found yourself in, and that the scope of possibilities is wide.
Perhaps this has little practical impact because, though your axioms might be more arbitrary than supposed, you have little c...
See page six of the paper for the authors dealing with this point. It's certainly a potential explanation, but the map of obesity in the US does seem to suggest that being, say, at the mouth of the Mississippi basin is much worse than being on the west coast, despite them both being at sea level.