K

“Kant, who is, will be our next thinker, is number two. Nietzsche was 17. Our last one, Descartes, poor Descartes was only number 18, but that's still, still not bad. We're going to be talking…” (Lee Braver)

“If we go back to multiplying two numbers, right? Forget about Karatsuba, right? Even just the way we were learn- we were taught to multiply two numbers in grade school, that kind of feels like a…” (Tim Roughgarden)

“a different method, Karatsuba's method for multiplying integers, which believe it or not, is fundamentally more efficient, fundamentally faster method, a completely different method of multiplying…” (Tim Roughgarden)

“gonna see that the answer is, in fact, yes. I'm gonna show you a famous algorithm known as Karatsuba's multiplication algorithm, where the clever idea is to basically expose redundant work, and the…” (Tim Roughgarden)

“about Cook and Levin, who independently on either side of the Iron Curtain came up with the theory of NP completeness. And then we talked about how it was really Karp who, with his list of 21 NP…” (Tim Roughgarden)

“list of 21 NP-complete problems. Okay? So Cook had two, and Karp had enlarged that list to 21. And very satisfyingly for him, among those 21 indeed was the traveling salesman problem. Okay? So Karp…” (Tim Roughgarden)

“Think about these decisions." We kill time. What a horrible expression, "killing time." Right? I mean, you really are killing, but it's your time, it's your life that you're slicing off and throwing…” (Lee Braver)

“How do you know things? How do you know that you know what you think you know? What is knowledge? How does it work? How do we achieve it? These are the questions of the branch of philosophy known as…” (Lee Braver)

“So his first real answer, according to Socrates, was that knowledge is perception. And then quickly, Socrates links that to the saying of Protagoras, "Man is the measure of all things. Each perceiver…” (Richard Polt)

“when Theaetetus says..."It seems to me that a man who knows something perceives what he knows, and the way it appears at present, at any rate, is that knowledge is simply perception." Doesn't he also…” (Richard Polt)

“a man who knows perceives what he knows, and so knowledge is the same thing as perception." We also saw that that's bad logic, right? If you know it, then you perceive it. Well, maybe, but it doesn't…” (Richard Polt)

“So, in 145e, he says, "Isn't it the things which they know that men are wise about?" Well, yes. So, knowledge and wisdom will be the same thing. Now, does this logically follow? It's the things you…” (Richard Polt)

“the Knuth Prize, which is the sort of lifetime achievement award in theoretical computer science, in 2012. Presumably, he would have shared the Turing Award with Cook, I would imagine, if his work…” (Tim Roughgarden)

“The Koch snowflake curve. And the way it works is, you start with a line segment of a certain length and you chop it in thirds, and you replace the middle third with sort of two versions. Let's see,…” (Joel David Hamkins)

“And we talked about how Karatsuba was attending a research seminar by Andrei Kolmogorov. So let's put Kolmogorov on here. So this would've been ballpark 1960. And so at this point, really computers…” (Tim Roughgarden)

“more abstractly about the nature of these tweetable numbers by introducing the concept of Kolmogorov complexity. Maybe you have the idea that when you tweet a number, really what you're doing is…” (Joel David Hamkins)

“axiom known as K, for Kripke. It says that if you have an implication being necessary and you have the antecedent being necessary, then the conclusion is necessary, yeah?” (Joel David Hamkins)

“from the 20th century. So, names like David Hilbert, Kurt Godel, John von Neumann, George Dantzig, Andrei Kolmogorov, Jack Emmons, Stephen Cook, Leonid Levin, Richard Karp, Don Knuth, all of those…” (Tim Roughgarden)