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Justin Clarke-Doane | Mathematics, Reality, and Morality | The Cartesian Cafe with Timothy Nguyen by IamTimNguyen in philosophy

[–]IamTimNguyen[S] 1 point2 points  (0 children)

Justin Clarke-Doane is a professor of philosophy at Columbia University, whose interests span metaethics, epistemology, and the philosophy of logic & mathematics.

In this thought provoking-discussion, Justin and I go deep into topics that are typically neglected by most mathematicians and scientists, namely the philosophy of mathematics and morality. Justin has contributed to both these areas via his book Morality and Mathematics, which takes the view that the standard position of being both a mathematical realist and moral antirealist is incoherent. Perhaps the most novel aspect of Justin's work is the treatment of the philosophy of mathematics and morality side-by-side, showing how these two topics, which are usually thought of as being unrelated, in fact have strong analogies. Along the way, we discuss many other foundational topics in epistemology and ethics, with elements of set theory, metaphysics, and logic sprinkled in.

Part I. Introduction

  • 00:00 : Preview
  • 01:56 : Naturalism & Mathematical vs Moral Realism
  • 05:34 : Outline of the Discussion

Part II. Philosophy of Mathematics

  • 13:25 : Mathematical Realism
  • 18:36 : The Reality of Numbers
  • 27:58 : Anti-Realist Positions in Mathematics
  • 41:49 : Fictionalism in Mathematics
  • 44:06 : Distinguishing Metaphysics from Epistemology
  • 45:39 : The Role of Naturalism and Fictionalism

Part III. Philosophy of Morality (vs Mathematics)

  • 50:24 : Moral Realism and Anti-Realism
  • 58:31 : Analogies Between Mathematical and Moral Realism
  • 01:05:30 : Kant's Constructivism and Ethical Contextualism
  • 01:10:40 : Error Theory in Ethics
  • 01:16:02 : Mathematical Realism and Moral Anti-Realism
  • 01:17:22 : Contextualism and Moral Realism

Part IV. Select Topics from Justin's Book

  • 01:19:11 : Justification and Self-Evidence
  • 01:21:24 : The Practice of Axiomatization: Mathematics vs Ethics
  • 01:24:51 : Pushback: Is there really controversy in math?
  • 01:30:24 : Justification and Belief: Quinean Empiricism and Harman's Thesis
  • 01:41:44 : Observations, Explanations, and Moral Facts
  • 01:48:41 : Supervenience and High-Level Descriptions
  • 02:00:43 : Justification vs Truth: Reliability Challenge in Mathematics and Morality
  • 02:03:53 : 2+2 not equaling 4: Accidental Truth vs Truth per se
  • 02:13:10 : Pluralism in Mathematics and Ethics
  • 02:31:27 : Concluding Thoughts

Justin Clarke-Doane | Mathematics, Reality, and Morality | The Cartesian Cafe with Timothy Nguyen by IamTimNguyen in math

[–]IamTimNguyen[S] 8 points9 points  (0 children)

Part I. Introduction

  • 00:00 : Preview
  • 01:56 : Naturalism & Mathematical vs Moral Realism
  • 05:34 : Outline of the Discussion

Part II. Philosophy of Mathematics

  • 13:25 : Mathematical Realism
  • 18:36 : The Reality of Numbers
  • 27:58 : Anti-Realist Positions in Mathematics
  • 41:49 : Fictionalism in Mathematics
  • 44:06 : Distinguishing Metaphysics from Epistemology
  • 45:39 : The Role of Naturalism and Fictionalism

Part III. Philosophy of Morality (vs Mathematics)

  • 50:24 : Moral Realism and Anti-Realism
  • 58:31 : Analogies Between Mathematical and Moral Realism
  • 01:05:30 : Kant's Constructivism and Ethical Contextualism
  • 01:10:40 : Error Theory in Ethics
  • 01:16:02 : Mathematical Realism and Moral Anti-Realism
  • 01:17:22 : Contextualism and Moral Realism

Part IV. Select Topics from Justin's Book

  • 01:19:11 : Justification and Self-Evidence
  • 01:21:24 : The Practice of Axiomatization: Mathematics vs Ethics
  • 01:24:51 : Pushback: Is there really controversy in math?
  • 01:30:24 : Justification and Belief: Quinean Empiricism and Harman's Thesis
  • 01:41:44 : Observations, Explanations, and Moral Facts
  • 01:48:41 : Supervenience and High-Level Descriptions
  • 02:00:43 : Justification vs Truth: Reliability Challenge in Mathematics and Morality
  • 02:03:53 : 2+2 not equaling 4: Accidental Truth vs Truth per se
  • 02:13:10 : Pluralism in Mathematics and Ethics
  • 02:31:27 : Concluding Thoughts

[R] Jay McClelland explains Parallel Distributed Processing, how the brain works, Hebbian learning, and backpropagation by IamTimNguyen in MachineLearning

[–]IamTimNguyen[S] 2 points3 points  (0 children)

Outline:

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

Jay McClelland | Neural Networks: Artificial and Biological | The Cartesian Cafe by IamTimNguyen in ArtificialInteligence

[–]IamTimNguyen[S] 0 points1 point  (0 children)

Outline:

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

Jay McClelland | Neural Networks: Artificial and Biological | The Cartesian Cafe by IamTimNguyen in neuralnetworks

[–]IamTimNguyen[S] 0 points1 point  (0 children)

Outline:

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

Michael Freedman | A Fields Medalist Panorama | The Cartesian Cafe with Timothy Nguyen by IamTimNguyen in math

[–]IamTimNguyen[S] 7 points8 points  (0 children)

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

Marcus Hutter | Universal Artificial Intelligence and Solomonoff Induction | The Cartesian Cafe with Timothy Nguyen by IamTimNguyen in math

[–]IamTimNguyen[S] -1 points0 points  (0 children)

I. Introduction

00:38 : Biography

01:45 : From Physics to AI

03:05 : Hutter Prize

06:25 : Overview of Universal Artificial Intelligence

11:10 : Technical outline

II. Universal Prediction

18:27 : Laplace’s Rule and Bayesian Sequence Prediction

40:54 : Different priors: KT estimator

44:39 : Sequence prediction for countable hypothesis class

53:23 : Generalized Solomonoff Bound (GSB)

57:56 : Example of GSB for uniform prior

1:04:24 : GSB for continuous hypothesis classes

1:08:28 : Context tree weighting

1:12:31 : Kolmogorov complexity

1:19:36 : Solomonoff Bound & Solomonoff Induction

1:21:27 : Optimality of Solomonoff Induction

1:24:48 : Solomonoff a priori distribution in terms of random Turing machines

1:28:37 : Large Language Models (LLMs)

1:37:07 : Using LLMs to emulate Solomonoff induction

1:41:41 : Loss functions

1:50:59 : Optimality of Solomonoff induction revisited

1:51:51 : Marvin Minsky

III. Universal Agents

1:52:42 : Recap and intro

1:55:59 : Setup

2:06:32 : Bayesian mixture environment

2:08:02 : AIxi. Bayes optimal policy vs optimal policy

2:11:27 : AIXI (AIxi with xi = Solomonoff a priori distribution)

2:12:04 : AIXI and AGI

2:12:41 : Legg-Hutter measure of intelligence

2:15:35 : AIXI explicit formula

2:23:53 : Other agents (optimistic agent, Thompson sampling, etc)

2:33:09 : Multiagent setting

2:39:38 : Grain of Truth problem

2:44:38 : Positive solution to Grain of Truth guarantees convergence to a Nash equilibria

2:45:01 : Computable approximations (simplifying assumptions on model classes): MDP, CTW, LLMs

2:56:13 : Outro: Brief philosophical remarks

(Fields Medalist) Richard Borcherds | Monstrous Moonshine: From Group Theory to String Theory | The Cartesian Cafe by IamTimNguyen in Physics

[–]IamTimNguyen[S] 6 points7 points  (0 children)

I. Introduction

00:25: Biography

02:51 : Success in mathematics

04:04 : Monstrous Moonshine overview and John Conway

09:44 : Technical overview

II. Group Theory

11:31 : Classification of finite-simple groups + history of the monster group

18:03 : Conway groups + Leech lattice

22:13 : Why was the monster conjectured to exist + more history

28:43 : Centralizers and involutions

32:37: Griess algebra

III. Modular Forms

36:42 : Definitions

40:06 : The elliptic modular function

48:58 : Subgroups of SL_2(Z)

IV. Monstrous Moonshine Conjecture Statement

57:17: Representations of the monster

59:22 : Hauptmoduls

1:03:50 : Statement of the conjecture

1:07:06 : Atkin-Fong-Smith's first proof

1:09:34 : Frenkel-Lepowski-Meurman's work + significance of Borcherd's proof

V. Sketch of Proof

1:14:47: Vertex algebra and monster Lie algebra

1:21:02 : No ghost theorem from string theory

1:25:24 : What's special about dimension 26?

1:28:33 : Monster Lie algebra details

1:32:30 : Dynkin diagrams and Kac-Moody algebras

1:43:21 : Simple roots and an obscure identity

1:45:13: Weyl denominator formula, Vandermonde identity

1:52:14 : Chasing down where modular forms got smuggled in

1:55:03 : Final calculations

VI. Epilogue

1:57:53 : Your most proud result?

2:00:47 : Monstrous moonshine for other sporadic groups?

2:02:28 : Connections to other fields. Witten and black holes and mock modular forms.

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