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lacunic number
“and then it has a lot of zeros until the next one in the 6 factorial place way out there and so on. So this is, this kind of number is called a lacunic, a lacunic number because it has these lakes of…” (Joel David Hamkins)
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 39:45 · read ↗︎
Ladner's theorem
“theorem from the 1970s which says if you're in world number one, okay, so if you don't have this total collapse, if you do have a separation between P and NP-complete problems, then in fact there…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 4:51 · read ↗︎
lambda calculus
“for a fact that indeed it does. So Church, he didn't invent Turing machines, but he had to invent some other model of computation, which he called the lambda calculus, which also has lots of…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 1: Is There Anything Computers Can't Do?▶︎ watch 54:14 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 3: Easy Problems, Hard Problems▶︎ watch 27:19 · read ↗︎
large cardinals
“Subsequent work showed in set theory in a deep way that actually if there are certain kinds of large cardinals, if certain kinds of extremely strong infinities exist, then in fact, Cantor's program…” (Joel David Hamkins)
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 28:58 · read ↗︎
large language models
“So, for example, large language models, generative AI, it seems to be changing everything around us. In fact, for stuff we're gonna be talking about in this series, for the nature of computation and…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Intro: Computation and Its Limits▶︎ watch 11:56 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 36:18 · read ↗︎
largest tweetable number
“Hi, I'm Joel David Hamkins, and I'd like to tell you today about the paradox of the largest tweetable number. I mean, of course it's called x.com now, but I wanna use this old terminology of tweeting…” (Joel David Hamkins)
Lectures on Infinity · Lecture 4: The Largest Tweetable Number▶︎ watch 0:01 · read ↗︎
Law Number One
“this wave function mathematical object evolves. And another law that he called the first one law number one and he called the second one law number two. Another law that tells us how these wave…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 3: Two Laws That Can't Both Be True▶︎ watch 11:51 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 5:57 · read ↗︎
Law Number Two
“Another law that tells us how these wave functions behave, how the states of these systems behave when measurements are being carried out. And the essence of that law is when you carry out a…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 3: Two Laws That Can't Both Be True▶︎ watch 12:01 · read ↗︎
law of identity
“There's no mystery as to wh- how we know relations of ideas. Couldn't be anything else. It's, it's, it's guided, guarded, guided by the law of non-contradiction, one of the most fundamental, uh,…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 3: Hume's Map of the Mind▶︎ watch 34:39 · read ↗︎
law of non-contradiction
“There's no mystery as to wh- how we know relations of ideas. Couldn't be anything else. It's, it's, it's guided, guarded, guided by the law of non-contradiction, one of the most fundamental, uh,…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 3: Hume's Map of the Mind▶︎ watch 34:39 · read ↗︎
laws of logic
“there to there, but the story violates..."... logic, okay? The story represents the first case in history of an empirical scientific discovery about the laws of logic.” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 2: When Physics Stops Making Sense▶︎ watch 6:05 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 24:32 · read ↗︎
laws of nature
“live in, really sort of laws of nature, in effect. And so, in each of the five episodes in this series, we're going to grapple with some sort of fundamental concepts and questions. In the first…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Intro: Computation and Its Limits▶︎ watch 0:31 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 4: Why You Can't Prove Tomorrow▶︎ watch 16:45 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 23:12 · read ↗︎
least number principle
Lectures on Infinity · Lecture 7: What Does Finite Really Mean?▶︎ watch 35:05
Lebesgue measure
“philosophy of probability very much, and the justification for why is it that we want our probability measures, and Lebesgue measure, and so on to be countably additive and not to be more than that.…” (Joel David Hamkins)
Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 29:59 · read ↗︎
Leibniz
“So, there were a number of figures, like Descartes, uh, Bacon, Galileo, Newton, Leibniz, who were all doing science and philosophizing about the nature of science simultaneously. They were playing…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Intro: When the Old Map Stopped Working▶︎ watch 3:51 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 18:08 · read ↗︎
Leonid Levin
“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 55:31 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 18:44 · read ↗︎
levels of infinity
“What do you mean there's more real numbers than integers? But there are, in a meaningful sense, okay? So there are different levels of infinity, if you like. And the set of real numbers is a higher…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 1: Is There Anything Computers Can't Do?▶︎ watch 36:50 · read ↗︎
Levin
“And Levin, Leonid Levin, so I mentioned that he was doing his work behind the Iron Curtain, I don't think I mentioned that his first PhD, he got a second one when he came to the States at MIT, his…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 18:44 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 14:21 · read ↗︎
Lévy-Collot theorem
“So, regarding Godel's hope to settle the continuum hypothesis on the basis of the large cardinal axioms, these hopes were basically dashed by the Lévy-Collot theorem, which shows that none of the…” (Joel David Hamkins)
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 37:32 · read ↗︎
LIGO Nobel Prize
“disturbances propagating outwards, okay? And, indeed, two or three years ago, a bunch of people won the Nobel Prize for a sort of spectacularly beautiful and sensitive experiment where, for the first” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 4: Bell's Impossible Proof▶︎ watch 57:50 · read ↗︎
Lilliputians
“in the sky and tricked that giant as well. But then again, there's also Jonathan Swift's character, Gulliver, who travels to distant lands and finds the Lilliputians, these tiny human beings to whom…” (Joel David Hamkins)
Lectures on Infinity · Lecture 3: The Paradox of Giants: Strange Consequences in High Dimension▶︎ watch 0:53 · read ↗︎
limit model
“are sort of if I'm an actualist, I can union up all of those worlds to have this sort of limit model. So there's a limit model, M, you know, they're, they're converging to this limit model. In the…” (Joel David Hamkins)
Lectures on Infinity · Lecture 5: Potential vs Actual Infinity▶︎ watch 53:38 · read ↗︎
limitations
“What are your limitations? That's the question that Hume and Kant asked. What will you do to overcome those limitations? That is Nietzsche's question. And Kant wanted us to grow up.” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Recap: Making Your Beliefs Your Own▶︎ watch 11:18 · read ↗︎
limitations of computation
“efficient computation, and then, on the other hand, the limitations of computation, okay? So both of those themes are obviously already there in Turing's 1936 paper, the introduction of Turing…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 4:19 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 2: How Algorithms Outsmart Complexity▶︎ watch 0:01 · read ↗︎
linear programming
“don't know if you wanna say discovered, up to you. So the simplex method for linear programming. So that was discovered by George Dantzig. And even if you think you haven't heard of George Dantzig,…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 2: How Algorithms Outsmart Complexity▶︎ watch 50:13 · read ↗︎
linear programming duality
“and then realizes in real time that the min-max theorem he's been working with corresponds to what we would now call the theory of linear programming duality, and that's something that Dantzig had…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 2: How Algorithms Outsmart Complexity▶︎ watch 55:02 · read ↗︎
linear time algorithm
“you can search through networks that are twice as big. And that would be the case if you are talking about what's known as a linear time algorithm. That would correspond to a polynomial, just like…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 3: Easy Problems, Hard Problems▶︎ watch 20:29 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 1:05 · read ↗︎
linearly finite
Lectures on Infinity · Lecture 7: What Does Finite Really Mean?▶︎ watch 10:05
linearly ordered
“cardinals are linear, that the sizes are linearly ordered, and that's a principle, actually, that's equivalent to the axiom of choice, which we'll discuss in a later lecture. But then finally, it was…” (Joel David Hamkins)
Lectures on Infinity · Lecture 6: Galileo's Paradox of Infinity▶︎ watch 32:48 · read ↗︎
Lectures on Infinity · Lecture 5: Potential vs Actual Infinity▶︎ watch 36:14 · read ↗︎
Liouville
“Does every real number satisfy a polynomial equation over the integers, is the question. And the answer is no, and this was proved by Liouville in 1844. He introduced a specific real number that is…” (Joel David Hamkins)
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 38:54 · read ↗︎
Liouville constant
“specific real number, it's now called the Liouville constant, and he proved that this number is not algebraic. It's a transcendental real number. So the Liouville constant is the number 0.110. Let's…” (Joel David Hamkins)
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 39:14 · read ↗︎
listing the elements
“And that is listing the elements of a thing. Now, that sounds more impressive. What's an element? It's the simplest possible unit from which something is built up. So, if you could break things down” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 5: Defeat as Philosophical Victory▶︎ watch 15:41 · read ↗︎
LLMs
“and of course, LLMs, large language models, generative AI. All of these technologies would seem to, at least superficially, outperform the conventional expectations that we would have of computers.…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Intro: Computation and Its Limits▶︎ watch 6:06 · read ↗︎
local
“the world must work at a fundamental level, is that it's- is in a so-called local way. So, those are the two large topics that I'm thinking about discussing in future lectures.” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 2: When Physics Stops Making Sense▶︎ watch 44:43 · read ↗︎
locality
“and Rosen regarding the question of locality. Very briefly, we have always approached the world, and I mean always, by always I mean prior to modern science, prior to science per se, this is a…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Intro: The Crisis In Physics▶︎ watch 11:14 · read ↗︎
localize
“do is to localize particles in space, okay? And to localize any other particles that those particles may be entangled with, in the way that's implied by the nature of the entanglement. But you're…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 17:07 · read ↗︎
Locke
“And this debate between rationalism and empiricism is one of the defining, uh, debates of this early modern period, 1600 to 1800. Uh, Hume wasn't the founder of empiricism. Uh, Locke is often, uh,…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 3: Hume's Map of the Mind▶︎ watch 17:59 · read ↗︎
logarithmic spiral
“increases, this number becomes very tiny, and so it spirals very rapidly into the origin, yeah? This is called a logarithmic spiral. And you can prove that even though the curve goes around the…” (Joel David Hamkins)
Lectures on Infinity · Lecture 3: The Paradox of Giants: Strange Consequences in High Dimension▶︎ watch 38:42 · read ↗︎
logical empiricists
“to some 20th century movements in philosophy. So, some logical empiricists tried to describe the very basic given sense perceptions and then construct reality on the basis of that. Or, you might…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 5: Defeat as Philosophical Victory▶︎ watch 21:16 · read ↗︎
logical fallacy
“that's a logical fallacy. That, by the way, is what begging the question means, not bringing up a question. That's a little irritation to me. I'm sorry, it's a pet peeve. You don't beg the question.…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 4: Why You Can't Prove Tomorrow▶︎ watch 21:07 · read ↗︎
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 1:27:40 · read ↗︎
logical independence
“And so when you're talking about judging the largest number contest, maybe you have in mind that, well, we should be looking for sort of proofs from a formal system” (Joel David Hamkins)
Lectures on Infinity · Lecture 4: The Largest Tweetable Number▶︎ watch 45:55 · read ↗︎
logically coherent
“stake isn't whether or not we can actually do a supertask in physical reality, but rather, is it even logically coherent? Is it intelligible to understand a supertask of, a task involving infinitely…” (Joel David Hamkins)
Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 3:06 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 3: Two Laws That Can't Both Be True▶︎ watch 20:54 · read ↗︎
logicism
“was undertaking his program of logicism, which aimed to reduce all of mathematics to logic. This monumental work. And so he wanted to identify the most fundamental logical principles that would be…” (Joel David Hamkins)
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 1:24:39 · read ↗︎
logicist program
Lectures on Infinity · Lecture 7: What Does Finite Really Mean?▶︎ watch 18:02
logos
“So an irrational number cannot be expressed as a ratio of two whole numbers. And the fact that these numbers, that these numbers, these quantities exist was rather mind-blowing for the Greeks because…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 1: Is Knowledge Just Perception?▶︎ watch 25:33 · read ↗︎
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 3: Does Relativism Refute Itself?▶︎ watch 26:47 · read ↗︎
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 4: The Soul Behind the Senses▶︎ watch 44:02 · read ↗︎
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 5: Defeat as Philosophical Victory▶︎ watch 10:41 · read ↗︎
Löwenheim-Skolem theorem
Lectures on Infinity · Lecture 7: What Does Finite Really Mean?▶︎ watch 52:56
lower bounds
“or negative results, and those researchers might self-identify as complexity theorists or as lower bounds researchers, because they're focused on sort of you know, difficulty, okay, proving levels of…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 7:44 · read ↗︎
lowest terms
Lectures on Infinity · Lecture 7: What Does Finite Really Mean?▶︎ watch 31:33
Lucas-Penrose interpretation
“different episode, to talk about its implications not just in mathematics, but it resonated much more broadly. You know, for example in philosophy, you know, most famously maybe the Lucas-Penrose…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 1: Is There Anything Computers Can't Do?▶︎ watch 9:26 · read ↗︎