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half marathon runners
“Let's erase this here. There was a huge crowd of runners. They were there for the big race, the half marathon race. So I'm not gonna draw them all here, but they were all sort of densely ordered…” (Joel David Hamkins)
Lectures on Infinity · Lecture 8: Hilbert's Hotel Is Always Open▶︎ watch 11:43 · read ↗︎
halfway
“Then before you do that, before you go from A to B, you have to get halfway to B." Okay, so that's something that you must do before you go from here to there. But before you get halfway there, you” (Joel David Hamkins)
Lectures on Infinity · Lecture 1: Zeno's Paradox and Infinite Sums▶︎ watch 1:02 · read ↗︎
halting problem
“one being the halting problem, which are fundamentally, meaning both today and as far into the future as you care to think about, that are fundamentally unsolvable by computers. In the second…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Intro: Computation and Its Limits▶︎ watch 1:24 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 1: Is There Anything Computers Can't Do?▶︎ watch 23:28 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 2: How Algorithms Outsmart Complexity▶︎ watch 0:22 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 3: Easy Problems, Hard Problems▶︎ watch 2:43 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 50:33 · read ↗︎
Lectures on Infinity · Lecture 4: The Largest Tweetable Number▶︎ watch 43:19 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 32:36 · read ↗︎
hard electron
“way, what we wanna say is that the electron enters some state on passing through a hardness box, that is, a white electron does. A hard electron doesn't do this. A hard electron just comes out here,…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 2: When Physics Stops Making Sense▶︎ watch 10:56 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 1: The Experiment That Broke Reality▶︎ watch 4:09 · read ↗︎
hard problems
“fast algorithms, and these hard problems, problems that, as far as we can tell, appear to be unsolvable by fast algorithms. And that is exactly the P versus NP question, whether or not this dichotomy…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Intro: Computation and Its Limits▶︎ watch 4:54 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 3: Easy Problems, Hard Problems▶︎ watch 39:09 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 1:35 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 30:51 · read ↗︎
hardness
“Another of the properties we're gonna be measuring, we're gonna be talking about measurements of is we'll call the hardness of the electron. That only has two possible numerical values as well. Let's…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 1: The Experiment That Broke Reality▶︎ watch 3:05 · read ↗︎
hardness box
“magnetic fields as boxes, as measuring boxes. So, it's routine, it's easy to construct in the laboratory, something that you might wanna call a hardness box. This is a box with three apertures.” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 1: The Experiment That Broke Reality▶︎ watch 4:17 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 2: When Physics Stops Making Sense▶︎ watch 1:04 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 3: Two Laws That Can't Both Be True▶︎ watch 7:37 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 1:08:25 · read ↗︎
hardwiring
“through is all on the surface, and the really important stuff happens beneath our awareness in this hard wiring, this custom or habit. And that is not susceptible to control or change. That is not…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Recap: Making Your Beliefs Your Own▶︎ watch 3:19 · read ↗︎
harmonic series
“It's called the harmonic series. The harmonic series is one plus one-half plus... So far, it looks like the geometric series.” (Joel David Hamkins)
Lectures on Infinity · Lecture 1: Zeno's Paradox and Infinite Sums▶︎ watch 27:01 · read ↗︎
Harvey Friedman
“a conversation he had with Eisenin Volpin.... who is a famous ultrafinitist. And he put to Yacene and Volpin the question, "Well, let's consider the numbers, you know, 2, 2 squared, 2 cubed, 2 to the…” (Joel David Hamkins)
Lectures on Infinity · Lecture 5: Potential vs Actual Infinity▶︎ watch 18:15 · read ↗︎
Hegel
“you know, late 19th century European philosophical education. This is all about Hegel, okay? This is all about thesis and antithesis and so on and so forth. Yeah, this is a very elaborate way of…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 3: Two Laws That Can't Both Be True▶︎ watch 25:05 · read ↗︎
Heidegger
“Heidegger tries to say, "Well, a deeper concept of truth is the revelation, the showing of things." So only if showing happens through your assertion or your judgment is there truth. Mm-hmm. And he…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 4: The Soul Behind the Senses▶︎ watch 44:00 · read ↗︎
heliocentric
“a heliocentric model of the solar system. Meaning, you think the sun is in the center of the solar system and the earth is turning on its axis while rotating around the sun. And that's why you would…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 1: Descartes Reboots Everything▶︎ watch 7:02 · read ↗︎
Heraclitus
“Now, Heraclitus, if you haven't read Heraclitus, please do. We don't have his book, but we have a couple hundred brief quotations, fragments, quoted by later authors, and almost inevitably, they're…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 2: When Every Perception is True▶︎ watch 4:38 · read ↗︎
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 3: Does Relativism Refute Itself?▶︎ watch 1:14 · read ↗︎
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 4: The Soul Behind the Senses▶︎ watch 0:52 · read ↗︎
hexagonal wheel
“Galileo said, "Well, let's not imagine a circular wheel, but rather a hexagonal wheel." So, he drew this hexagon. Let's see if I can draw it properly here. Okay, so there's the hexagon. This is…” (Joel David Hamkins)
Lectures on Infinity · Lecture 6: Galileo's Paradox of Infinity▶︎ watch 8:33 · read ↗︎
Hilbert
“and actually in his era, they met with some stubborn rejection, but eventually they came to be accepted completely by all of mathematics. And Hilbert famously said, "Let no one cast us from the…” (Joel David Hamkins)
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 2:33 · read ↗︎
Hilbert's bus
“It was Hilbert's bus had arrived. And Hilbert's bus is very big bus, and it has infinitely many seats in it. So there's seat zero, seat one, seat two, seat three, seat four, and so on. And the bus…” (Joel David Hamkins)
Lectures on Infinity · Lecture 8: Hilbert's Hotel Is Always Open▶︎ watch 3:30 · read ↗︎
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 0:42 · read ↗︎
Hilbert's Hotel
“Hi, I'm Joel David Hamkins, and I'd like to tell you about the Parable of Hilbert's Hotel. I'm a New Yorker, and I noticed one day this giant hotel going up across the street. And it had infinitely…” (Joel David Hamkins)
Lectures on Infinity · Lecture 8: Hilbert's Hotel Is Always Open▶︎ watch 0:01 · read ↗︎
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 0:11 · read ↗︎
Hilbert's program
“of arriving at these proofs of true statements. So that was part of the Hilbert program, which, you know, you saw seeds of it in that 1900 address. He continued to develop it over the early 20th…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 1: Is There Anything Computers Can't Do?▶︎ watch 7:58 · read ↗︎
Hilbert's train
“Of course, it's Hilbert's train arrived. And the thing about Hilbert's train is that it has many, many train cars. So there's car zero, and car one, and car two, and car three, and so on.” (Joel David Hamkins)
Lectures on Infinity · Lecture 8: Hilbert's Hotel Is Always Open▶︎ watch 7:11 · read ↗︎
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 0:58 · read ↗︎
history of philosophy
“circumstances to improve them. This is how the history of philosophy works. It's a long, long conversation where everyone tries to make the previous ideas better by making them their own. And…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Recap: Making Your Beliefs Your Own▶︎ watch 5:14 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 0:53 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 36:09 · read ↗︎
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 3: Does Relativism Refute Itself?▶︎ watch 24:16 · read ↗︎
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 4: The Soul Behind the Senses▶︎ watch 17:37 · read ↗︎
how are a priori synthetic judgments possible
“So the question of the book is how are a priori synthetic judgments possible? Because we have them. We have two bodies of them we're known, math and science.” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 36:10 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 7:39 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 7: Nietzsche's Warning to the Future▶︎ watch 23:39 · read ↗︎
Hugh Everett
“There is a tradition going back to the thesis of a physicist named Hugh Everett, that he did at Princeton in the 1950s of hoping that, as a matter” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 36:14 · read ↗︎
human understanding
“Why do we need to emphasize that this is human understanding? Well, we do need to emphasize it. If you go back to Descartes, Descartes was actually not interested in human understanding. For…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 3: Hume's Map of the Mind▶︎ watch 2:34 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 4: Why You Can't Prove Tomorrow▶︎ watch 23:39 · read ↗︎
Hume
“and two things and put them together? Well, that's not fully good... that's not perfect evidence. As we're gonna see when we return to Hume. But for Descartes, the evidence of this is a priori.” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 2: The Birth of Modern Science▶︎ watch 4:20 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 0:11 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 1:56 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 7: Nietzsche's Warning to the Future▶︎ watch 3:08 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Recap: Making Your Beliefs Your Own▶︎ watch 2:43 · read ↗︎
Lectures on Infinity · Lecture 6: Galileo's Paradox of Infinity▶︎ watch 3:06 · read ↗︎
Husserl
“So this is a topic that a much later philosopher, 20th century German philosopher, Husserl, talked about a great deal. And so there's no way to s- in, but use sensory data to take in all aspects of…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 2: The Birth of Modern Science▶︎ watch 7:47 · read ↗︎
hyper volume
“Well, it has length two, you know. That's the relevant notion of size in dimension one, is length, area, volume, hyper volume in the higher dimensions. That's what we call it. We could call all of…” (Joel David Hamkins)
Lectures on Infinity · Lecture 3: The Paradox of Giants: Strange Consequences in High Dimension▶︎ watch 43:00 · read ↗︎
hyperbolic geometry
“are different kinds of geometry. There's Euclidean geometry and there's, you know, various kinds of non-Euclidean geometry, spherical geometry, hyperbolic space, and so on, and they're all fully real…” (Joel David Hamkins)
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 46:54 · read ↗︎
hyperbolic spiral
“be called the hyperbolic spiral, and if I use say, r equal one over theta, you know, and this one maybe I draw it something like this. It spirals around infinitely many times, but it's very kind of…” (Joel David Hamkins)
Lectures on Infinity · Lecture 3: The Paradox of Giants: Strange Consequences in High Dimension▶︎ watch 40:03 · read ↗︎
hypercube
“to three dimensions only, so. I wanna understand these hyperspheres and how they sit inside the cubes that they're naturally part of. So for example, we have the unit circle, and it,” (Joel David Hamkins)
Lectures on Infinity · Lecture 3: The Paradox of Giants: Strange Consequences in High Dimension▶︎ watch 47:52 · read ↗︎
hypersphere
“Okay, and then what about higher dimension? So we wanna talk about the concept of the hypersphere, you know? See, in the four-dimensional sphere, you know, and five-dimensional, six-dimensional. So,…” (Joel David Hamkins)
Lectures on Infinity · Lecture 3: The Paradox of Giants: Strange Consequences in High Dimension▶︎ watch 42:10 · read ↗︎