282 | Joel David Hamkins on Puzzles of Reality and Infinity

282 | Joel David Hamkins on Puzzles of Reality and Infinity

The philosophy of mathematics would be so much easier if it weren't for infinity. The concept seems natural, but taking it seriously opens the door to counterintuitive results. As mathematician and philosopher Joel David Hamkins says in this conversation, when we say that the natural numbers are "0, 1, 2, 3, and so on," that "and so on" is hopelessly vague. We talk about different ways to think about the puzzles of infinity, how they might be resolved, and implications for mathematical realism.

Blog post with transcript: https://www.preposterousuniverse.com/podcast/2024/07/15/282-joel-david-hamkins-on-puzzles-of-reality-and-infinity/

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Joel David Hamkins received his Ph.D. in mathematics from the University of California, Berkeley. He is currently the John Cardinal O'Hara Professor of Logic at the University of Notre Dame. He is a pioneer of the idea of the set theory multiverse. He is the top-rated user by reputation score on MathOverflow. He is currently working on The Book of Infinity, to be published by MIT Press.


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Episoder(398)

185 | Arvid Ågren on the Gene’s-Eye View of Evolution

185 | Arvid Ågren on the Gene’s-Eye View of Evolution

One of the brilliant achievements of Darwin’s theory of natural selection was to help explain apparently “purposeful” or “designed” aspects of biology in a purely mechanistic theory of unguided evolution. Features are good if they help organisms survive. But should we put organisms at the center of our attention, or the genetic information that governs those features? Arvid Ågren helps us understand the attraction of the “selfish gene” view of evolution, as well as its shortcomings. This biological excursion has deep connections to philosophical issues of levels and emergence.Support Mindscape on Patreon.Arvid Ågren received his Ph.D. in Ecology and Evolutionary Biology from the University of Toronto. He is currently a Wenner-Gren Fellow at the Evolutionary Biology Centre at Uppsala University. Previously he worked at Cornell and Harvard. His recent book is The Gene’s-Eye View of Evolution.Web siteGoogle Scholar publicationsAmazon author pageTwitterSee Privacy Policy at https://art19.com/privacy and California Privacy Notice at https://art19.com/privacy#do-not-sell-my-info.

21 Feb 20221h 25min

184 | Gary Marcus on Artificial Intelligence and Common Sense

184 | Gary Marcus on Artificial Intelligence and Common Sense

Artificial intelligence is everywhere around us. Deep-learning algorithms are used to classify images, suggest songs to us, and even to drive cars. But the quest to build truly “human” artificial intelligence is still coming up short. Gary Marcus argues that this is not an accident: the features that make neural networks so powerful also prevent them from developing a robust common-sense view of the world. He advocates combining these techniques with a more symbolic approach to constructing AI algorithms.Support Mindscape on Patreon.Gary Marcus received his Ph.D. in cognitive science from MIT. He is founder and CEO of Robust.AI, and was formerly a professor of psychology at NYU as well as founder of Geometric Intelligence. Among his books are Rebooting AI: Building Machines We Can Trust (with Ernest Davis).Web siteWikipediaTwitterAmazon.com author pageSee Privacy Policy at https://art19.com/privacy and California Privacy Notice at https://art19.com/privacy#do-not-sell-my-info.

14 Feb 20221h 24min

AMA | February 2022

AMA | February 2022

Welcome to the February 2022 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). I take the large number of questions asked by Patreons, whittle them down to a more manageable size — based primarily on whether I have anything interesting to say about them, not whether the questions themselves are good — and sometimes group them together if they are about a similar topic. Enjoy!Support Mindscape on Patreon.See Privacy Policy at https://art19.com/privacy and California Privacy Notice at https://art19.com/privacy#do-not-sell-my-info.

10 Feb 20224h 15min

183 | Michael Dine on Supersymmetry, Anthropics, and the Future of Particle Physics

183 | Michael Dine on Supersymmetry, Anthropics, and the Future of Particle Physics

Modern particle physics is a victim of its own success. We have extremely good theories — so good that it’s hard to know exactly how to move beyond them, since they agree with all the experiments. Yet, there are strong indications from theoretical considerations and cosmological data that we need to do better. But the leading contenders, especially supersymmetry, haven’t yet shown up in our experiments, leading some to wonder whether anthropic selection is a better answer. Michael Dine gives us an expert’s survey of the current situation, with pointers to what might come next.Support Mindscape on Patreon.Michael Dine received his Ph.D. in physics from Yale University. He is Distinguished Professor of Physics at the Santa Cruz Institute for Particle Physics, University of California, Santa Cruz. Among his awards are fellowships from the Sloan Foundation, Guggenheim Foundation, American Physical Society, and American Academy of Arts and Sciences, as well as the Sakurai Prize for theoretical particle physics. His new book is This Way to the Universe: A Theoretical Physicist’s Journey to the Edge of Reality.Web pagePublications at iNspireWikipediaAmazon author pageSee Privacy Policy at https://art19.com/privacy and California Privacy Notice at https://art19.com/privacy#do-not-sell-my-info.

7 Feb 20221h 39min

182 | Sally Haslanger on Social Construction and Critical Theory

182 | Sally Haslanger on Social Construction and Critical Theory

Reality is just out there — but how we perceive reality and talk about it depends on choices we human beings make. We decide (consciously or not) to conceptualize the world in certain ways, whether it’s because those ways provide elegant predictive descriptions or because they serve a more subtle political purpose. To get at the true nature of reality, therefore, it’s important to think about which aspects of it are socially constructed, and why. I talk with Sally Haslanger about these issues, and the techniques we can use to understand the world and make it a better place.Update (22 March): Our discussion here could have (and did) leave some listeners with the wrong impression of how Sally and I feel about trans rights -- we are entirely for them! My fault for not making things more clear during the conversation. So I have added a brief note during the podcast intro to make our position perfectly explicit. Thanks to everyone who commented.Support Mindscape on Patreon.Sally Haslanger received her Ph.D. in philosophy from the University of California, Berkeley. She is currently the Ford Professor of Philosophy at the Massachusetts Institute of Technology. Among her awards are the Carus Lectureship, the Distinguished Woman Philosopher award, and a Guggenheim Fellowship. She is the author of several books, including Resisting Reality: Social Construction and Social Critique.Web siteMIT faculty pagePhilPeople profileGoogle Scholar publicationsAmazon author pageWikipediaSee Privacy Policy at https://art19.com/privacy and California Privacy Notice at https://art19.com/privacy#do-not-sell-my-info.

31 Jan 20221h 37min

181 | Peter Dodds on Quantifying the Shape of Stories

181 | Peter Dodds on Quantifying the Shape of Stories

A good story takes you on an emotional journey, with ups and downs along the way. Thanks to science, we can quantify that. Peter Dodds works on understanding the structure of stories and other strings of words (including Twitter) by analyzing the valence of individual words, then studying how they are strung together in different kinds of stories. Understanding these structures offers powerful insight into how people communicate and how to reach them. As Peter says, “Never bring statistics to a story fight.”Support Mindscape on Patreon.Peter Dodds received his Ph.D. in mathematics from the Massachusetts Institute of Technology. He is currently a professor of computer science at the University of Vermont and Director of the Vermont Complex Systems Center. He has won multiple teaching awards, and was elected a Fellow of the Network Science Society.Web siteUniversity of Vermont faculty pageComputational Story LabGoogle Scholar publicationsWikipediaTwitterSee Privacy Policy at https://art19.com/privacy and California Privacy Notice at https://art19.com/privacy#do-not-sell-my-info.

24 Jan 20221h 16min

180 | Camilla Pang on Instructions for Being Human

180 | Camilla Pang on Instructions for Being Human

Being a human is tricky. There are any number of unwritten rules and social cues that we have to learn as we go, but that we ultimately learn to take for granted. Camilla Pang, who was diagnosed with autism spectrum disorder at age eight, had a harder time than most, as she didn’t easily perceive the rules of etiquette and relationships that we need to deal with each other. But she ultimately figured them out, with the help of analogies and examples from different fields of science. We talk about these rules, and how science can help us think about them.Support Mindscape on Patreon.Camilla Pang received her Ph.D. in computational biology from University College London. She is currently a postdoctoral researcher in pharmaceuticals and a volunteer cancer researcher at the Francis Crick Institute. She was awarded the Royal Society Prize for Science Books in 2020 for her book Explaining Humans: What Science Can Teach Us about Life, Love, and Relationships (US title: An Outsider’s Guide to Humans: What Science Taught Me about What We Do and Who We Are).Web siteWikipediaTwitterAmazon author pageSee Privacy Policy at https://art19.com/privacy and California Privacy Notice at https://art19.com/privacy#do-not-sell-my-info.

17 Jan 20221h 3min

179 | David Reich on Genetics and Ancient Humanity

179 | David Reich on Genetics and Ancient Humanity

Human beings like to divide themselves into groups, and then cooperate, socialize, and reproduce with members of their own group. But they’re not very absolutist about it; groups tend to gradually (or suddenly) intermingle, as people explore, intermarry, or conquer each other. David Reich has pioneered the use of genetic data in uncovering the history of ancient humanity: what groups existed where and when, and how they interacted. The result is a picture of churning populations in constant flux, including “ghost populations” that no longer exist today.Support Mindscape on Patreon.David Reich received his Ph.D. in zoology from the University of Oxford. He is currently a professor of genetics at Harvard Medical School. Among his awards are the Dan David Prize, the National Academy of Sciences Award in Molecular Biology, the Wiley Prize, the Darwin-Wallace Medal, and the Massry Prize. He is the author of Who We Are and How We Got Here: Ancient DNA and the New Science of the Human Past.Lab web pageHarvard faculty pagePublicationsWikipediaSee Privacy Policy at https://art19.com/privacy and California Privacy Notice at https://art19.com/privacy#do-not-sell-my-info.

10 Jan 20221h 13min

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