giovedì 12 maggio 2011

Epic rap battles of Advanced Mathematics

Video un po’ trash…non c’è che dire. Eppure, i due goliardi che si divertono a interpretare queste strane battaglie a suon di rap non sono poi così poco seri come potrebbe sembrare a prima vista. La loro “fonte di ispirazione” è un racconto: “A Madman Dreams of Turing Machines”, scritto dalla polivalente Janna Levin, un personaggio straordinario che rappresenta il connubio perfetto tra lo scienziato e l’artista. Avrei voluto dilungarmi su A Madman Dreams of Turing Machines ma dato che se ne è già discusso qua mi limito a riportare un brano tratto da qui:

Moritz joined him at the board, quietly adding a fine comment on the infinite list of integers that might participate in the reasoning off the middle rib of the fish's spine. And in this smooth manner he eased Gödel into conversation. Everyone either knows by instinct or learns by plain experiment to meet Gödel with mathematics first. And so Moritz approached with the right words about infinity and integers and earned that look of gratitude and trust. As he shook Kurt's hand and his own head in grateful amazement, they talked:
"Herr Professor, I have been thinking about the Liar's Paradox where the liar says,this sentence is false."
"Ah, the antinomy of the liar. Yes, that liar who says, this sentence is false."
"The sentence cannot be false."
"Because if it is false as claimed, then it must be true. A contradiction." Studying his young student for a time Moritz stroked his lip dry and concluded his motion with the reply, "And it cannot be true. Because if it is true, then it is false which is again a contradiction. It is a paradox and an artifact of our careless use of language. Mathematics will never allow such a paradox. Mathematical propositions will either be true or false with no contradictions."
"What if mathematics is not free of such propositions?"
"It must be. Mathematics must be complete. There are no unsolvable problems.""

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