The Cartesian Cafe

About The Cartesian Cafe

The Cartesian Cafe is the podcast where an expert guest and Timothy Nguyen map out scientific and mathematical subjects in detail. This collaborative journey with other experts will have us writing down formulas, drawing pictures, and reasoning about them together on a whiteboard. If you’ve been longing for a deeper dive into the intricacies of scientific subjects, then this is the podcast for you. Topics covered include mathematics, physics, computer science, machine learning, and artificial intelligence. Content also viewable on YouTube: www.youtube.com/timothynguyen and Spotify. Timothy Nguyen is a mathematician and AI researcher working in industry. Homepage: www.timothynguyen.com, Twitter: @IAmTimNguyen Patreon: www.patreon.com/timothynguyen

Publisher

Timothy Nguyen

Category

science

Language

en

Explicit

No

First episode

17 Aug 2022

Latest episode

6 Dec 2024

Latest episodes

22 episodes in the feed.

1. 

   6 Dec 2024

   Justin Clarke-Doane | Mathematics, Reality, and Morality

   Columbia University professor Justin Clarke-Doane explores the intersections of mathematics, reality, and morality, revealing surprising analogies between these seemingly unrelated topics.

2. 

   2 Oct 2024

   Jay McClelland | Neural Networks: Artificial and Biological

   Jay McClelland is a pioneer in the field of artificial intelligence and is a cognitive psychologist and professor at Stanford University in the psychology, linguistics, and computer science departments. Together with David Rumelhart, Jay published the two volume work Parallel Distributed Processing, which has led to the flourishing of the connectionist approach to understanding cognition. In this conversation, Jay gives us a crash course in how neurons and biological brains work. This sets the stage for how psychologists such as Jay, David Rumelhart, and Geoffrey Hinton historically approached the development of models of cognition and ultimately artificial intelligence. We also discuss alternative approaches to neural computation such as symbolic and neuroscientific ones. Patreon (bonus materials + video chat):https://www.patreon.com/timothynguyen Part I. Introduction 00:00 : Preview 01:10 : Cognitive psychology 07:14 : Interdisciplinary work and Jay's academic journey 12:39 : Context affects perception 13:05 : Chomsky and psycholinguists 8:03 : Technical outline Part II. The Brain 00:20:20 : Structure of neurons 00:25:26 : Action potentials 00:27:00 : Synaptic processes and neuron firing 00:29:18 : Inhibitory neurons 00:33:10 : Feedforward neural networks 00:34:57 : Visual system 00:39:46 : Various parts of the visual cortex 00:45:31 : Columnar organization in the cortex 00:47:04 : Colocation in artificial vs biological networks 00:53:03 : Sensory systems and brain maps Part III. Approaches to AI, PDP, and Learning Rules 01:12:35 : Chomsky, symbolic rules, universal grammar 01:28:28 : Neuroscience, Francis Crick, vision vs language 01:32:36 : Neuroscience = bottom up 01:37:20 : Jay’s path to AI 01:43:51 : James Anderson 01:44:51 : Geoff Hinton 01:54:25 : Parallel Distributed Processing (PDP) 02:03:40 : McClelland & Rumelhart’s reading model 02:31:25 : Theories of learning 02:35:52 : Hebbian learning 02:43:23 : Rumelhart’s Delta rule 02:44:45 : Gradient descent 02:47:04 : Backpropagation 02:54:52 : Outro: Retrospective and looking ahead Image credits:http://timothynguyen.org/image-credits/ Further reading: Rumelhart, McClelland. Parallel Distributed Processing. McClelland, J. L. (2013). Integrating probabilistic models of perception and interactive neural networks: A historical and tutorial review Twitter: @iamtimnguyen Webpage: http://www.timothynguyen.org

3. 

   19 Jul 2024

   Michael Freedman | A Fields Medalist Panorama

   Michael Freedman is a mathematician who was awarded the Fields Medal in 1986 for his solution of the 4-dimensional Poincare conjecture. Mike has also received numerous other awards for his scientific contributions including a MacArthur Fellowship and the National Medal of Science. In 1997, Mike joined Microsoft Research and in 2005 became the director of Station Q, Microsoft’s quantum computing research lab. As of 2023, Mike is a Senior Research Scientist at the Center for Mathematics and Scientific Applications at Harvard University. Patreon (bonus materials + video chat): https://www.patreon.com/timothynguyen (https://www.patreon.com/timothynguyen) In this wide-ranging conversation, we give a panoramic view of Mike’s extensive body of work over the span of his career. It is divided into three parts: early, middle, and present day, which respectively include his work on the 4-dimensional Poincare conjecture, his transition to topological physics, and finally his recent work in applying ideas from mathematics and philosophy to social economics. Our conversation is a blend of both the nitty-gritty details and the anecdotal story-telling that can only be obtained from a living legend. I. Introduction 00:00 : Preview 01:34 : Fields Medalist working in industry 03:24 : Academia vs industry 04:59 : Mathematics and art 06:33 : Technical overview II. Early Mike: The Poincare Conjecture (PC) 08:14 : Introduction, statement, and history 14:30 : Three categories for PC (topological, smooth, PL) 17:09 : Smale and PC for d at least 5 17:59 : Homotopy equivalence vs homeomorphism 22:08 : Joke 23:24 : Morse flow 33:21 : Whitney Disk 41:47 : Casson handles 50:24 : Manifold factors and the Whitehead continuum 1:00:39 : Donaldson’s results in the smooth category 1:04:54 : (Not) writing up full details of the proof then and now 1:08:56 : Why Perelman succeeded II. Mid Mike: Topological Quantum Field Theory (TQFT) and Quantum Computing (QC) 1:10:54: Introduction 1:11:42: Cliff Taubes, Raoul Bott, Ed Witten 1:12:40 : Computational complexity, Church-Turing, and Mike’s motivations 1:24:01 : Why Mike left academia, Microsoft’s offer, and Station Q 1:29:23 : Topological quantum field theory (according to Atiyah) 1:34:29 : Anyons and a theorem on Chern-Simons theories 1:38:57 : Relation to QC 1:46:08 : Universal TQFT 1:55:57 : Witten: Donalson theory cannot be a unitary TQFT 2:01:22 : Unitarity is possible in dimension 3 2:05:12 : Relations to a theory of everything? 2:07:21 : Where topological QC is now III. Present Mike: Social Economics 2:11:08 : Introduction 2:14:02 : Lionel Penrose and voting schemes 2:21:01 : Radical markets (pun intended) 2:25:45 : Quadratic finance/funding 2:30:51 : Kant’s categorical imperative and a paper of Vitalik Buterin, Zoe Hitzig, Glen Weyl 2:36:54 : Gauge equivariance 2:38:32 : Bertrand Russell: philosophers and differential equations IV: Outro 2:46:20 : Final thoughts on math, science, philosophy 2:51:22 : Career advice Some Further Reading: Mike’s Harvard lecture on PC4: https://www.youtube.com/watch?v=TSF0i6BO1Ig (https://www.youtube.com/watch?v=TSF0i6BO1Ig) Behrens et al. The Disc Embedding Theorem. M. Freedman. Spinoza, Leibniz, Kant, and Weyl. arxiv:2206.14711 Twitter: @iamtimnguyen Webpage: http://www.timothynguyen.org

Reach and audience

Public platform figures. Ratings count people who left a rating, not total listeners.

Apple Podcasts (US)

4.8 / 5

53 ratings

Spotify

5.0 / 5

33 ratings

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Books guests

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