Topic Index: U

ultrafinitism

“position in mathematics known as ultrafinitism. So ultrafinitism is the philosophical view that it is only the comparatively small or accessible numbers that actually exist. So according to the…” (Joel David Hamkins)

Lectures on Infinity · Lecture 5: Potential vs Actual Infinity▶︎ watch 16:11 · read ↗︎

Un-American Activities Committee

“It was completely ignored at the time. Part of what facilitated ignoring it was the Un-American Activities Committee that hounded Bohm out of the country. Anyway, long story. Another book I…” (David Albert)

Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 1:06:19 · read ↗︎

uncaused cause

“And you know what we call that? God. God is the uncaused cause. Cause, God is the creator of the universe that was never created. And that's metaphysics.” (Lee Braver)

From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 33:58 · read ↗︎

uncertainty principle

“Yeah. Or the uncertainty principle on some interpretations means there is no such thing as the position and velocity, and mass of a subatomic particle that co-exist at the same time.” (Richard Polt)

Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 1: Is Knowledge Just Perception?▶︎ watch 38:44 · read ↗︎

Quantum Mechanics and the Crisis of Scientific Realism · Lecture 1: The Experiment That Broke Reality▶︎ watch 33:10 · read ↗︎

uncertainty relation

“this electron is both black and soft," okay? And that got stuck with the name uncertainty relation. The word uncertainty makes it sound like this is a question of knowledge, this is a question of our…” (David Albert)

Quantum Mechanics and the Crisis of Scientific Realism · Lecture 2: When Physics Stops Making Sense▶︎ watch 16:09 · read ↗︎

Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 1:13:53 · read ↗︎

uncountable

“work with equinumerosity in the infinite and even the uncountable case that we'll come to in some future lectures. So the concept of equinumerosity also figures in Galileo's work, particularly in his…” (Joel David Hamkins)

Lectures on Infinity · Lecture 6: Galileo's Paradox of Infinity▶︎ watch 3:58 · read ↗︎

uncountable infinity

“points in the dart board is an uncountable infinity. And it's part of the theory of probability theory that the countable sums of measure zero events, they are still measure zero The probability…” (Joel David Hamkins)

Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 29:18 · read ↗︎

Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 1:43 · read ↗︎

Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 0:11 · read ↗︎

uncountably additive

“So when we have countably many, when we have a list of countably many probability zero events, then we can say it's probability zero for any of them to happen, whereas we can't make that move in this…” (Joel David Hamkins)

Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 29:39 · read ↗︎

uncountably creative

“Okay. Well, what about the case where the chocolatier is uncountably creative? Maybe there's a different chocolate for every real number. Like, maybe the width of the glazing or the density of the…” (Joel David Hamkins)

Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 43:46 · read ↗︎

uncountably infinite

“between the countably infinite and the uncountably infinite, a profound idea due to Cantor. We'll start with Zeno and the classical ideas of Aristotle and Archimedes, but eventually, we'll move…” (Joel David Hamkins)

Lectures on Infinity · Intro: Infinity Has a Story to Tell▶︎ watch 0:21 · read ↗︎

undecidable problems

“there are problems known as undecidable problems which computers will never be able to solve. And not just kind of weird, artificial problems we'd never care about. Problems we actually really would,…” (Tim Roughgarden)

Computation as a Universal and Fundamental Concept · Lecture 1: Is There Anything Computers Can't Do?▶︎ watch 20:14 · read ↗︎

Computation as a Universal and Fundamental Concept · Lecture 3: Easy Problems, Hard Problems▶︎ watch 9:10 · read ↗︎

Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 50:28 · read ↗︎

understanding

“And instead of forms, the intuition has forms, the understanding has concepts. And instead of two, it's got 12 of them, and we're not gonna get into them. We're only gonna talk about one of” (Lee Braver)

From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 22:06 · read ↗︎

Unicode

“that you could make is N to the 280. Actually, the reality is a little more complicated than that, because if you look into it, then in fact, some characters in the Unicode character set are sort of…” (Joel David Hamkins)

Lectures on Infinity · Lecture 4: The Largest Tweetable Number▶︎ watch 3:16 · read ↗︎

unicorn

“Because an easy response is, "Well, hold on, Hume, I've got all kinds of ideas in my head that I've never had an impression of. I've got the idea of a unicorn. I've never seen one." And here's where…” (Lee Braver)

From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 3: Hume's Map of the Mind▶︎ watch 21:15 · read ↗︎

From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 2: The Birth of Modern Science▶︎ watch 14:35 · read ↗︎

uniform distribution

“a kind of uniform distribution of where the dart would land somewhere on the dart board. Okay? So, I'm not paying attention to the case when the dart doesn't land on the dart board, so I'm just…” (Joel David Hamkins)

Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 25:08 · read ↗︎

uniqueness of the prime factorization

“precisely because of the uniqueness of the prime factorization, but there's a very subtle point that happens right at this moment in this argument, because in fact, it's not a one-to-one map as I…” (Joel David Hamkins)

Lectures on Infinity · Lecture 8: Hilbert's Hotel Is Always Open▶︎ watch 46:59 · read ↗︎

Lectures on Infinity · Lecture 5: Potential vs Actual Infinity▶︎ watch 9:05 · read ↗︎

unit square

“So let me show you another way of seeing this infinite summation. If we take, say, the whole unit square, the one-by-one square. So this is a one-by-one square. The total area is one. And if I take…” (Joel David Hamkins)

Lectures on Infinity · Lecture 1: Zeno's Paradox and Infinite Sums▶︎ watch 6:39 · read ↗︎

Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 35:55 · read ↗︎

universal problems

“That's what NP-complete problems are. It is a single problem like the traveling salesman problem which simultaneously encodes thousands of other problems. Every other problem with easily checked…” (Tim Roughgarden)

Computation as a Universal and Fundamental Concept · Lecture 3: Easy Problems, Hard Problems▶︎ watch 38:41 · read ↗︎

universal Turing machine

“Turing machine, call it M, okay? And then this is going to be a universal Turing machine, call it M sub U, okay? So the universal Turing machine is expecting to be told a description, a description…” (Tim Roughgarden)

Computation as a Universal and Fundamental Concept · Lecture 1: Is There Anything Computers Can't Do?▶︎ watch 30:09 · read ↗︎

Computation as a Universal and Fundamental Concept · Lecture 3: Easy Problems, Hard Problems▶︎ watch 38:19 · read ↗︎

universality

“to diagonalization, to reductions, to show you Turing's original argument that indeed, there are problems, even natural problems you'd really like to solve, like the famous one being the halting…” (Tim Roughgarden)

Computation as a Universal and Fundamental Concept · Intro: Computation and Its Limits▶︎ watch 1:13 · read ↗︎

Computation as a Universal and Fundamental Concept · Lecture 3: Easy Problems, Hard Problems▶︎ watch 38:09 · read ↗︎

universe view

“theory is that there is a unique set theoretic reality for mathematics that we are trying to axiomatize with our axioms of set theory. There is a unique cumulative hierarchy of sets that one achieves…” (Joel David Hamkins)

Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 39:29 · read ↗︎

upper bounds

“what algorithms can do, you know, sometimes they focus on what they call possibility results or, you know, or upper bounds, and they might say they're algorithms researchers. That's how they might…” (Tim Roughgarden)

Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 7:23 · read ↗︎