Aleph0 Quotes & Sayings

Cattle die, kinsmen die, you yourself must also die, but he who wins word fame lives forever — Havamal - The Sayings Of The High One

That is, for a mathematical Platonist, what the C.H. proofs really show is that set theory needs to find a better set of core axioms than classical ZFS, or at least it will need to add some further postulates that are-like the Axiom of Choice-both "self-evident" and Consistent with classical axioms. If you're interested, Godel's own personal view was that the Continuum Hypothesis is false, that there are actually a whole (Infinity Symbol) of Zeno-type (Infinity Symbol)s nested between (Aleph0) and c, and that sooner or later a principle would be found that proved this. As of now no such principle's ever been found. Godel and Cantor both died in confinement, bequeathing a world with no finite circumference. One that spins, now, in a new kind of all-formal Void. Mathematics continues to get out of bed. — David Foster Wallace

Rock 'n' roll is meant to entertain. Hippie folk singers are supposed to be singing about leftist views, but I don't think rock 'n' roll was ever that way. I don't remember the early rock 'n' rollers ever expressing any political views. — Johnny Ramone

I used to have a recurring dream where I was at a party in a country house, surrounded by the same people each evening. Everyone would be singing and dancing and after a while I came to know the people; though, of course, they never really existed. — Marina Abramovic

I believe in the human form; let me find something, some method, by which that form may achieve the utmost beauty. — Richard Jefferies

God has a celebration meal with us not after we finally get out of the dark valley but in the middle of it, in the presence of our enemies. He wants us to rejoice in him in the midst of our troubles. — Timothy Keller

It's specifically this Z = 2^(Aleph0) that he couldn't prove. Ever. Despite years of unimaginable doodling. Whether it's what unhinged him or not is an unanswerable question, but it is true that his inability to prove the C.H. caused Cantor pain for the rest of his life; he considered it his great failure. This too, in hindsight, is sad, because professional mathematicians now know exactly why G. Cantor could neither prove nor disprove the C.H. The reasons are deep and important and go corrosively to the root of axiomatic set theory's formal Consistency, in rather the same way that K. Godel's Incompleteness proofs deracinate all math as a formal system. Once again, the issues here can be only sketched or synopsized (although this time Godel is directly involved, so the whole thing is probably fleshed out in the Great Discoveries Series' Godel booklet). — David Foster Wallace