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By Christos H. Papadimitriou
Deals a complete and available therapy of the speculation of algorithms and complexity. Develops all of the priceless mathematical must haves from such diversified fields as computability, good judgment, quantity conception, combinatorics, and chance. DLC: Computational complexity.
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Not every branch of science was scouted out ahead of time by philosophy, but some were. And in recent history, I think quantum computing is really the poster child here. It’s atoms and the void 7 fine to tell people to “Shut up and calculate,” but the question is, what should they calculate? At least in quantum computing, which is my field, the sorts of things that we like to calculate – capacities of quantum channels, error probabilities of quantum algorithms – are things people would never have thought to calculate if not for philosophy.
First of all, who was Democritus? He was this Ancient Greek dude. He was born around 450 BC in this podunk Greek town called Abdera, where people from Athens said that even the air causes stupidity. He was a disciple of Leucippus, according to my source, which is Wikipedia. He’s called a “pre-Socratic,” even though actually he was a contemporary of Socrates. ” Incidentally, there’s a story that Democritus journeyed to Athens to meet Socrates, but then was too shy to introduce himself. Almost none of Democritus’s writings survive.
24 quantum computing since democritus No, we can’t. For then we could also prove in ZF that Con(PA) implies Con(ZF). But since ZF can prove Con(PA), this would mean that ZF can prove Con(ZF), which contradicts the Second Incompleteness Theorem. I promised to explain why the Incompleteness Theorem doesn’t contradict the Completeness Theorem. The easiest way to do this is probably through an example. Consider the “self-hating theory” PA + Not(Con(PA)), or Peano Arithmetic plus the assertion of its own inconsistency.