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radical branching
“much more radical conception of potentialism that's maybe more connected with ultra-finitism, but also with pluralist views in the foundations of mathematics and the philosophy of set theory, the…” (Joel David Hamkins)
Lectures on Infinity · Lecture 5: Potential vs Actual Infinity▶︎ watch 49:51 · read ↗︎
Rain Dogs
“one of his albums, one of his best albums is titled Rain Dogs, and he's a fantastic lyricist and... I read an interview with him one time and he explained what the title means, and he said, you know,…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 34:34 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 7: Nietzsche's Warning to the Future▶︎ watch 13:30 · read ↗︎
random choice balls in a sack
“choice balls in a sack paradox. We start with an empty sack, we're gonna do infinitely many things, you know, in this super task manner so it's all finished in a finite amount of time, we put two…” (Joel David Hamkins)
Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 18:57 · read ↗︎
rational numbers
“The natural numbers themselves, of course, are countable, but the integers are countable, as are the rational numbers, those are also countable. We saw how the union of two countably infinite sets is…” (Joel David Hamkins)
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 0:32 · read ↗︎
Lectures on Infinity · Lecture 8: Hilbert's Hotel Is Always Open▶︎ watch 12:20 · read ↗︎
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 18:12 · read ↗︎
rationalism
“This is to be contrasted with... rationalism, which, again, you can see from the title, focused on reason. Now, Descartes was the founder, sort of, of early modern rationalism.” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 3: Hume's Map of the Mind▶︎ watch 16:57 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 0:22 · read ↗︎
rationalism and empiricism
“value in each and cuts away what he sees as wrong in each to bring together these two schools of rationalism and empiricism that were warring for 200 years until they became a beautiful unified” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Recap: Making Your Beliefs Your Own▶︎ watch 4:22 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 3: Hume's Map of the Mind▶︎ watch 17:51 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 0:00 · read ↗︎
rationalist
“But somebody who's more of a, a rationalist, these are modern labels, empiricist and rationalist, would say, "No, it fundamentally doesn't come from experience. It comes from something that, that's…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 4: The Soul Behind the Senses▶︎ watch 14:04 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 11:10 · read ↗︎
real numbers
“numbers than integers. And if you've never seen this stuff before, you might think, what does that even mean? There's an infinite number of integers, right? One, two, three, as big as you want. And…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 1: Is There Anything Computers Can't Do?▶︎ watch 36:32 · read ↗︎
Lectures on Infinity · Lecture 8: Hilbert's Hotel Is Always Open▶︎ watch 50:51 · read ↗︎
Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 43:46 · read ↗︎
Lectures on Infinity · Lecture 3: The Paradox of Giants: Strange Consequences in High Dimension▶︎ watch 21:34 · read ↗︎
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 1:35 · read ↗︎
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 0:00 · read ↗︎
realistic
“the aspirations very crudely to give us a sort of straightforward, flat-footed, literal, realistic, complete account of the physical world had collapsed, and were” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Intro: The Crisis In Physics▶︎ watch 2:18 · read ↗︎
reason
“Well, this is the third faculty of the mind, which he calls reason. It is what attempts to give us” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 26:16 · read ↗︎
recollection
“Another way that Socrates talks about this, in several other dialogues is that, in fact, philosophy, since it's not a matter of new information, it's a kind of recollection. It's an attempt to…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 5: Defeat as Philosophical Victory▶︎ watch 2:48 · read ↗︎
recreating his self
“through and actually genuinely believed them. There's a sense in which he was really recreating his self, because if your body is what you eat, then your mind is what you believe. And he talks about…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Recap: Making Your Beliefs Your Own▶︎ watch 1:28 · read ↗︎
recurrence relation
“then there's a kind of recurrence relation that you can prove, and it goes like this. V sub n is equal to two pi over n times V sub n minus two.” (Joel David Hamkins)
Lectures on Infinity · Lecture 3: The Paradox of Giants: Strange Consequences in High Dimension▶︎ watch 44:16 · read ↗︎
recursion
“but the first idea is about recursion, which is, you solve a problem by first boiling it down to one or more smaller instances of the problem. Recursion. So there are examples in” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 2: How Algorithms Outsmart Complexity▶︎ watch 11:13 · read ↗︎
reduces
“problem is as hard as another. It means the same thing it meant back in episode one when we were talking undecidability. It means that one problem reduces to another, okay? If all you need to do to…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 2:35 · read ↗︎
reduction
“which was the halting problem. And so this transfer, this is an idea known as a reduction. And reductions are one of the most central concepts in the foundations of computer science. We will see them…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 1: Is There Anything Computers Can't Do?▶︎ watch 41:21 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 3: Easy Problems, Hard Problems▶︎ watch 49:24 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 2:15 · read ↗︎
Computation as a Universal and Fundamental Concept · Intro: Computation and Its Limits▶︎ watch 1:13 · read ↗︎
redundant work
“algorithm, where the clever idea is to basically expose redundant work, and the usual way you multiply two numbers, the one you learned, expose redundant work, and instead reuse it, thereby arriving…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Intro: Computation and Its Limits▶︎ watch 2:46 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 2: How Algorithms Outsmart Complexity▶︎ watch 17:54 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 3: Easy Problems, Hard Problems▶︎ watch 7:18 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 9:59 · read ↗︎
reference and intentionality
“would fit into such a picture. There are worries about what kind of sense one can make of reference and intentionality in the context of the picture of the world that physics seems to be presenting…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Intro: The Crisis In Physics▶︎ watch 4:33 · read ↗︎
reflexive order
“larger than X if and only if. Well, when you have a reflexive order or relation like this, then the corresponding strict order would be defined by saying, "Well, this should mean that X is less or…” (Joel David Hamkins)
Lectures on Infinity · Lecture 6: Galileo's Paradox of Infinity▶︎ watch 27:58 · read ↗︎
regulative
“for, we can treat it as regulative. Regulative means we know it's not out there. We know the wall isn't pink. We know that we can never actually” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 41:46 · read ↗︎
regulative and not constitutive
“science as regulative and not constitutive." Right? That the idea of having complete final answers once and for all, complete answers, you can't ever get that. If you think you can, that's…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 7: Nietzsche's Warning to the Future▶︎ watch 31:42 · read ↗︎
regulative self
“become who you really are, but a regulative self. Who can you become? What else is out there? What new thoughts can you have? I hope that thinking these thoughts of these four philosophers has opened…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Recap: Making Your Beliefs Your Own▶︎ watch 12:00 · read ↗︎
relations of ideas
“Because all we're doing is we're taking ideas and r- and putting them into relationships. Relationships of identity. Relations of ideas are absolutely certain, we'll give Descartes that, but that…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 3: Hume's Map of the Mind▶︎ watch 28:09 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 4: Why You Can't Prove Tomorrow▶︎ watch 0:32 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 6:34 · read ↗︎
relativism
“Well, we nearly defeated relativism last time. There were several interesting arguments against it. One was the self-refutation argument. You know, if everybody's right, then people who disagree with…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 4: The Soul Behind the Senses▶︎ watch 0:11 · read ↗︎
relativism of Protagoras
“knowledge is the same thing as perception. And Socrates immediately linked that to the relativism of Protagoras. "Man is the measure of all things," which he takes to mean that each individual” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 2: When Every Perception is True▶︎ watch 2:56 · read ↗︎
relativist
“Can't be wrong. But seriously, when you, when you meet a relativist, and you may have met one, often, you know, sometime around sophomore year of college you meet some relativists, sophomoric…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 3: Does Relativism Refute Itself?▶︎ watch 8:05 · read ↗︎
Rene Descartes
“And one philosopher, at the very beginning of this movement, who insisted on thinking everything through for himself was Rene Descartes. And when I say everything, I mean everything. He wanted to go…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Intro: When the Old Map Stopped Working▶︎ watch 5:14 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 1: Descartes Reboots Everything▶︎ watch 0:01 · read ↗︎
repeatable
“these measurements are repeatable in the way you would expect a measurement of a bonafide physical variable to be. That is, if I measure the color of an electron and I find it to be white” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 1: The Experiment That Broke Reality▶︎ watch 6:00 · read ↗︎
replacement axiom
“using here, is the replacement axiom. Because for each one of these sets, I have this sequence of sets that I can define, and to know that I can take them all together and union them up is exactly…” (Joel David Hamkins)
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 1:15:04 · read ↗︎
Richard Dedekind
“the real line and the real plane are equinumerous. They have the same size. And when he discovered this, he wrote immediately a letter to Richard Dedekind, in which he said... This is 1877, "I see…” (Joel David Hamkins)
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 5:42 · read ↗︎
Richard Karp
“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)
Computation as a Universal and Fundamental Concept · Intro: Computation and Its Limits▶︎ watch 8:04 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 3: Easy Problems, Hard Problems▶︎ watch 56:12 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 20:53 · read ↗︎
Riemann
“And there's a profound theorem about this kind of situation, and it's called Riemann... Oh my god, am I spelling it right? Is it E-I or I-E? Okay, I have to look up. It's I-E, okay. So, there's a…” (Joel David Hamkins)
Lectures on Infinity · Lecture 1: Zeno's Paradox and Infinite Sums▶︎ watch 36:47 · read ↗︎
Riemann hypothesis
“Like, you might have heard of some of the other ones, like the Riemann hypothesis, or Navier–Stokes equations, or the one that has been solved actually, the Poincaré conjecture. So those are other…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 34:52 · read ↗︎
Riemann rearrangement theorem
“And there's a profound theorem about this kind of situation, and it's called Riemann... Oh my god, am I spelling it right? Is it E-I or I-E? Okay, I have to look up. It's I-E, okay. So, there's a…” (Joel David Hamkins)
Lectures on Infinity · Lecture 1: Zeno's Paradox and Infinite Sums▶︎ watch 36:47 · read ↗︎
Robertson-Seymour theory
“meaning polynomial-time algorithm, that checks whether or not you can find those 10 disjoint paths. It's a consequence, this algorithm, is a consequence of something known as Robertson-Seymour…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 28:19 · read ↗︎
Robinson Crusoe
“and effect, a causal relationship. His example, he gives the example of Robinson Crusoe, a novel that was very popular at the time, of this guy stuck on a desert island, a deserted island, and he…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 4: Why You Can't Prove Tomorrow▶︎ watch 2:19 · read ↗︎
row of dominoes
“it must be that there's a row of dominoes in between them. I mean, maybe they're hard to see, where one is knocking the next one over, and one is knocking the next one over. And another thing that…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 2: When Physics Stops Making Sense▶︎ watch 44:13 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 4: Bell's Impossible Proof▶︎ watch 2:22 · read ↗︎
RSA encryption
“And the most, one of the most common forms of public key encryption known as RSA encryption, in fact the security of RSA encryption actually is dependent on there not being any fast algorithm to…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 7:56 · read ↗︎
Rule One
“which applies under other circumstances." He called them Rule One and Rule Two, okay? He said Rule One is given by these differential equations, the Schrodinger equation, which tells you smoothly how…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 2: When Physics Stops Making Sense▶︎ watch 36:28 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 1:33 · read ↗︎
Rule Two
“which applies under other circumstances." He called them Rule One and Rule Two, okay? He said Rule One is given by these differential equations, the Schrodinger equation, which tells you smoothly how…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 2: When Physics Stops Making Sense▶︎ watch 36:28 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 1:33 · read ↗︎
running around the hearth
“So, now we do the rite of running around the hearth, which is some sort of rite you did with a newborn baby to initiate it into the family. Some sources say that at this point the father had the…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 2: When Every Perception is True▶︎ watch 36:05 · read ↗︎
running time
“a polynomial-time algorithm, it's crucial to think about the running time of an algorithm, meaning how long it takes to complete its task, the running time of an algorithm as you make the problems…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 3: Easy Problems, Hard Problems▶︎ watch 18:07 · read ↗︎
Russell
“we'll move through Galileo, and then we'll see Frege, and Dedekind, and Cantor, and the 20th century thinkers of Godel and Tarski, Russell, and so on, the contemporary ideas. To my way of thinking,…” (Joel David Hamkins)
Lectures on Infinity · Intro: Infinity Has a Story to Tell▶︎ watch 0:31 · read ↗︎
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 1:23:11 · read ↗︎
Russell set
“R is the set of all sets X, such that X is not a member of itself. So the Russell set is the set of all sets X that are not self-membered. Now being non-self-membered is” (Joel David Hamkins)
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 1:26:13 · read ↗︎