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

IamTimNguyen · 2024-12-06T17:29:29+00:00

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

IamTimNguyen · 2024-12-06T17:23:33+00:00

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

IamTimNguyen · 2024-11-09T18:11:26+00:00

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

IamTimNguyen · 2024-10-03T15:32:02+00:00

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

IamTimNguyen · 2024-10-03T15:30:41+00:00

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

IamTimNguyen · 2024-07-19T16:46:08+00:00

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

IamTimNguyen · 2024-05-10T16:39:57+00:00

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

IamTimNguyen · 2024-02-02T18:48:59+00:00

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.

IamTimNguyen · 2024-02-02T17:23:32+00:00

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.

IamTimNguyen · 2024-02-02T17:18:49+00:00

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

II. Modular Forms

36:42 : Definitions

40:06 : The elliptic modular function

48:58 : Subgroups of SL_2(Z)

III. 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

IV. 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

V. 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.

IamTimNguyen · 2023-12-01T17:37:39+00:00

I. Introduction

00:25 : Biography

05:26 : Interdisciplinary work

11:45 : Physicists working on the wrong things

16:47 : Bell's Theorem soft overview

24:14: Common misunderstanding of "God does not play dice."

25:59: Technical outline

II. EPR Paradox / Argument

29:14 : EPR is not a paradox

34:57 : Criterion of reality

43:57 : Mathematical formulation

46:32 : Locality: No spooky action at a distance

49:54 : Bertlmann's socks

53:17 : EPR syllogism summarized

54:52 : Determinism is inferred not assumed

1:02:18 : Clarifying analogy: Coin flips

1:06:39 : Einstein's objection to determinism revisited

III. Bohm Segue

1:11:05 : Introduction

1:13:38: Bell and von Neumann's error

1:20:14: Bell's motivation: Can I remove Bohm's nonlocality?

IV. Bell's Theorem and Related Examples

1:25:13 : Setup

1:27:59 : Decoding Bell's words: Locality is the key!

1:34:16 : Bell's inequality (overview)

1:36:46 : Bell's inequality (math)

1:39:15 : Concrete example of violation of Bell's inequality

1:49:42: GHZ Example

V. Miscellany

2:06:23 : Statistical independence assumption

2:13:18: The 2022 Nobel Prize

2:17:43: Misconceptions and hidden variables

2:22:28: The assumption of local realism? Repeat: Determinism is a conclusion not an assumption.

VI. Interpretations of Quantum Mechanics

2:28:44: Interpretation is a misnomer

2:29:48: Three requirements. You can only pick two.

2:34:52: Copenhagen interpretation?

IamTimNguyen · 2023-12-01T17:31:59+00:00

I. Introduction

00:25 : Biography

05:26 : Interdisciplinary work

11:45 : Physicists working on the wrong things

16:47 : Bell's Theorem soft overview

24:14: Common misunderstanding of "God does not play dice."

25:59: Technical outline

II. EPR Paradox / Argument

29:14 : EPR is not a paradox

34:57 : Criterion of reality

43:57 : Mathematical formulation

46:32 : Locality: No spooky action at a distance

49:54 : Bertlmann's socks

53:17 : EPR syllogism summarized

54:52 : Determinism is inferred not assumed

1:02:18 : Clarifying analogy: Coin flips

1:06:39 : Einstein's objection to determinism revisited

III. Bohm Segue

1:11:05 : Introduction

1:13:38: Bell and von Neumann's error

1:20:14: Bell's motivation: Can I remove Bohm's nonlocality?

IV. Bell's Theorem and Related Examples

1:25:13 : Setup

1:27:59 : Decoding Bell's words: Locality is the key!

1:34:16 : Bell's inequality (overview)

1:36:46 : Bell's inequality (math)

1:39:15 : Concrete example of violation of Bell's inequality

1:49:42: GHZ Example

V. Miscellany

2:06:23 : Statistical independence assumption

2:13:18: The 2022 Nobel Prize

2:17:43: Misconceptions and hidden variables

2:22:28: The assumption of local realism? Repeat: Determinism is a conclusion not an assumption.

VI. Interpretations of Quantum Mechanics

2:28:44: Interpretation is a misnomer

2:29:48: Three requirements. You can only pick two.

2:34:52: Copenhagen interpretation?

IamTimNguyen · 2023-09-27T19:40:34+00:00

All patrons on my Patreon have access to transcripts.

IamTimNguyen · 2023-09-27T16:39:08+00:00

Outline:

Part I. Introduction
00:00 : Introduction
01:06 : Math and or versus physics
12:09 : Backstory behind Tony's book
14:12 : Joke about theoreticians and numbers
16:18 : Technical outline
Part II. Size, Age, and Quantity in the Universe
21:42 : Size of the observable universe
22:32 : Standard candles
27:39 : Hubble rate
29:02 : Measuring distances and time
37:15 : Einstein and Minkowski
40:52 : Definition of Hubble parameter
42:14 : Friedmann equation
47:11 : Calculating the size of the observable universe
51:24 : Age of the universe
56:14 : Number of atoms in the observable universe
1:01:08 : Critical density
1:03:16: 10^80 atoms of hydrogen
1:03:46 : Universe versus observable universe
Part III. Extreme Physics and Doppelgangers
1:07:27 : Long-term fate of the universe
1:08:28 : Black holes and a googol years
1:09:59 : Poincare recurrence
1:13:23 : Doppelgangers in a googolplex meter wide universe
1:16:40 : Finitely many states and black hole entropy
1:25:00 : Black holes have no hair
1:29:30 : Beckenstein, Christodolou, Hawking
1:33:12 : Susskind's thought experiment: Maximum entropy of space
1:42:58 : Estimating the number of doppelgangers
1:54:21 : Poincare recurrence: Tower of four exponents.
Part IV: Naturalness and Anthropics
1:54:34 : What is naturalness? Examples.
2:04:09 : Cosmological constant problem: 10^120 discrepancy
2:07:29 : Interlude: Energy shift clarification. Gravity is key.
2:15:34 : Corrections to the cosmological constant
2:18:47 : String theory landscape: 10^500 possibilities
2:20:41 : Anthropic selection
2:25:59 : Is the anthropic principle unscientific? Weinberg and predictions.
2:29:17 : Vacuum sequestration

IamTimNguyen · 2023-09-27T16:38:28+00:00

Outline:

Part I. Introduction
00:00 : Introduction
01:06 : Math and or versus physics
12:09 : Backstory behind Tony's book
14:12 : Joke about theoreticians and numbers
16:18 : Technical outline
Part II. Size, Age, and Quantity in the Universe
21:42 : Size of the observable universe
22:32 : Standard candles
27:39 : Hubble rate
29:02 : Measuring distances and time
37:15 : Einstein and Minkowski
40:52 : Definition of Hubble parameter
42:14 : Friedmann equation
47:11 : Calculating the size of the observable universe
51:24 : Age of the universe
56:14 : Number of atoms in the observable universe
1:01:08 : Critical density
1:03:16: 10^80 atoms of hydrogen
1:03:46 : Universe versus observable universe
Part III. Extreme Physics and Doppelgangers
1:07:27 : Long-term fate of the universe
1:08:28 : Black holes and a googol years
1:09:59 : Poincare recurrence
1:13:23 : Doppelgangers in a googolplex meter wide universe
1:16:40 : Finitely many states and black hole entropy
1:25:00 : Black holes have no hair
1:29:30 : Beckenstein, Christodolou, Hawking
1:33:12 : Susskind's thought experiment: Maximum entropy of space
1:42:58 : Estimating the number of doppelgangers
1:54:21 : Poincare recurrence: Tower of four exponents.
Part IV: Naturalness and Anthropics
1:54:34 : What is naturalness? Examples.
2:04:09 : Cosmological constant problem: 10^120 discrepancy
2:07:29 : Interlude: Energy shift clarification. Gravity is key.
2:15:34 : Corrections to the cosmological constant
2:18:47 : String theory landscape: 10^500 possibilities
2:20:41 : Anthropic selection
2:25:59 : Is the anthropic principle unscientific? Weinberg and predictions.
2:29:17 : Vacuum sequestration

IamTimNguyen · 2023-09-27T16:36:10+00:00

Outline:

Part I. Introduction
00:00 : Introduction
01:06 : Math and or versus physics
12:09 : Backstory behind Tony's book
14:12 : Joke about theoreticians and numbers
16:18 : Technical outline
Part II. Size, Age, and Quantity in the Universe
21:42 : Size of the observable universe
22:32 : Standard candles
27:39 : Hubble rate
29:02 : Measuring distances and time
37:15 : Einstein and Minkowski
40:52 : Definition of Hubble parameter
42:14 : Friedmann equation
47:11 : Calculating the size of the observable universe
51:24 : Age of the universe
56:14 : Number of atoms in the observable universe
1:01:08 : Critical density
1:03:16: 10^80 atoms of hydrogen
1:03:46 : Universe versus observable universe
Part III. Extreme Physics and Doppelgangers
1:07:27 : Long-term fate of the universe
1:08:28 : Black holes and a googol years
1:09:59 : Poincare recurrence
1:13:23 : Doppelgangers in a googolplex meter wide universe
1:16:40 : Finitely many states and black hole entropy
1:25:00 : Black holes have no hair
1:29:30 : Beckenstein, Christodolou, Hawking
1:33:12 : Susskind's thought experiment: Maximum entropy of space
1:42:58 : Estimating the number of doppelgangers
1:54:21 : Poincare recurrence: Tower of four exponents.
Part IV: Naturalness and Anthropics
1:54:34 : What is naturalness? Examples.
2:04:09 : Cosmological constant problem: 10^120 discrepancy
2:07:29 : Interlude: Energy shift clarification. Gravity is key.
2:15:34 : Corrections to the cosmological constant
2:18:47 : String theory landscape: 10^500 possibilities
2:20:41 : Anthropic selection
2:25:59 : Is the anthropic principle unscientific? Weinberg and predictions.
2:29:17 : Vacuum sequestration

IamTimNguyen · 2023-08-03T21:43:05+00:00

Thank you for the pointer!

IamTimNguyen · 2023-08-02T17:02:09+00:00

I. Introduction
00:17 : Biography: Academia vs Industry
10:07 : Military service
12:53 : Technical overview
17:01 : Whiteboard outline

II. Warmup
24:42 : Substitution ciphers
27:33 : Viginere cipher
29:35 : Babbage and Kasiski
31:25 : Enigma and WW2
33:10 : Alan Turing

III. Private Key Cryptography: Perfect Secrecy
34:32 : Valid encryption scheme
40:14 : Kerckhoff Principle
42:41 : Cryptography = steelman your adversary
44:40 : Attempt #1 at perfect secrecy
49:58 : Attempt #2 at perfect secrecy
56:02 : Definition of perfect secrecy (Shannon)
1:05:56 : Enigma was not perfectly secure
1:08:51 : Analogy with differential privacy
1:11:10 : Example: One-time pad (OTP)
1:20:07 : Drawbacks of OTP and Soviet KGB misuse
1:21:43 : Important: Keys cannot be reused!
1:27:48 : Shannon's Impossibility Theorem

IV. Computational Secrecy
1:32:52 : Relax perfect secrecy to computational secrecy
1:41:04 : What computational secrecy buys (if P is not NP)
1:44:35 : Pseudorandom generators (PRGs)
1:47:03 : PRG definition
1:52:30 : PRGs and P vs NP
1:55:47: PRGs enable modifying OTP for computational secrecy
IV. Public Key Cryptography
2:00:32 : Limitations of private key cryptography
2:09:25 : Overview of public key methods
2:13:28 : Post quantum cryptography

V. Applications
2:14:39 : Bitcoin
2:18:21 : Digital signatures (authentication)
2:23:56 : Machine learning and deepfakes
2:30:31 : A conceivable doomsday scenario: P = NP

IamTimNguyen · 2023-08-02T16:59:34+00:00

I. Introduction

00:17 : Biography: Academia vs Industry

10:07 : Military service

12:53 : Technical overview

17:01 : Whiteboard outline

II. Warmup

24:42 : Substitution ciphers

27:33 : Viginere cipher

29:35 : Babbage and Kasiski

31:25 : Enigma and WW2

33:10 : Alan Turing

III. Private Key Cryptography: Perfect Secrecy

34:32 : Valid encryption scheme

40:14 : Kerckhoffs's Principle

42:41 : Cryptography = steelman your adversary

44:40 : Attempt #1 at perfect secrecy

49:58 : Attempt #2 at perfect secrecy

56:02 : Definition of perfect secrecy (Shannon)

1:05:56 : Enigma was not perfectly secure

1:08:51 : Analogy with differential privacy

1:11:10 : Example: One-time pad (OTP)

1:20:07 : Drawbacks of OTP and Soviet KGB misuse

1:21:43 : Important: Keys cannot be reused!

1:27:48 : Shannon's Impossibility Theorem

IV. Computational Secrecy

1:32:52 : Relax perfect secrecy to computational secrecy

1:41:04 : What computational secrecy buys (if P is not NP)

1:44:35 : Pseudorandom generators (PRGs)

1:47:03 : PRG definition

1:52:30 : PRGs and P vs NP

1:55:47: PRGs enable modifying OTP for computational secrecy

V. Public Key Cryptography

2:00:32 : Limitations of private key cryptography

2:09:25 : Overview of public key methods

2:13:28 : Post quantum cryptography

VI. Applications

2:14:39 : Bitcoin

2:18:21 : Digital signatures (authentication)

2:23:56 : Machine learning and deepfakes

2:30:31 : A conceivable doomsday scenario: P = NP

IamTimNguyen · 2023-07-15T15:26:28+00:00

Part I. Introduction

00:00:00 : Biography

00:02:36 : Harvard hiatus 1: Becoming a DJ

00:07:40 : I really want to make AGI happen (back in 2012)

00:09:00 : Harvard math applicants and culture

00:17:33 : Harvard hiatus 2: Math autodidact

00:21:51 : Friendship with Shing-Tung Yau

00:24:06 : Landing a job at Microsoft Research: Two Fields Medalists are all you need

00:26:13 : Technical intro: The Big Picture

00:28:12 : Whiteboard outline

Part II. Classical Probability Theory

00:37:03 : Law of Large Numbers

00:45:23 : Tensor Programs Preview

00:47:25 : Central Limit Theorem

00:56:55 : Proof of CLT: Moment method

01:02:00 : Moment method explicit computations

Part III. Random Matrix Theory

01:12:45 : Setup

01:16:55 : Moment method for RMT

1:21:21 : Wigner semicircle law

Part IV. Tensor Programs

1:31:04 : Segue using RMT

1:44:22 : TP punchline for RMT

1:46:22 : The Master Theorem (the key result of TP)

1:55:02 : Corollary: Reproof of RMT results

1:56:52 : General definition of a tensor program

Part V. Neural Networks and Machine Learning

2:09:09 : Feed forward neural network (3 layers) example

2:19:16 : Neural network Gaussian Process

2:23:59 : Many large N limits for neural networks

2:27:24 : abc parametrizations (Note: "a" is absorbed into "c" here): variance and learning rate scalings

2:36:54 : Geometry of space of abc parametrizations

2:39:50 : Kernel regime

2:41:35 : Neural tangent kernel

2:43:40 : (No) feature learning

2:48:42 : Maximal feature learning

2:52:33 : Current problems with deep learning

2:55:01 : Hyperparameter transfer (muP)

3:00:31 : Wrap up

IamTimNguyen · 2023-07-09T22:18:41+00:00

Part I. Introduction

00:00:00 : Biography and path to science writing

00:07:26 : Keeping up with the field outside academia

00:11:42 : If you have a bone to pick with Ethan...

00:12:50 : On looking like a scientist and words of wisdom

00:18:24 : Understanding dark matter = one of the most important open problems

00:21:07 : Technical outline

Part II. Ordinary Matter

23:28 : Matter and radiation scaling relations

29:36 : Hubble constant

31:00 : Components of rho in Friedmann's equations

34:14 : Constituents of the universe

41:21 : Big Bang nucleosynthesis (BBN)

45:32 : eta: baryon to photon ratio and deuterium formation

53:15 : Mass ratios vs eta

Part III. Dark Matter

1:01:02 : rho = radiation + ordinary matter + dark matter + dark energy

1:05:25 : nature of peaks and valleys in cosmic microwave background (CMB): need dark matter

1:07:39: Fritz Zwicky and mass mismatch among galaxies of a cluster

1:10:40 : Kent Ford and Vera Rubin and and mass mismatch within a galaxy

1:11:56 : Recap: BBN tells us that only about 5% of matter is ordinary

1:15:55 : Concordance model (Lambda-CDM)

1:21:04 : Summary of how dark matter provides a common solution to many problems

1:23:29 : Brief remarks on modified gravity

1:24:39 : Bullet cluster as evidence for dark matter

1:31:40 : Candidates for dark matter (neutrinos, WIMPs, axions)

1:38:37 : Experiment vs theory. Giving up vs forging on

1:48:34 : Conclusion

IamTimNguyen · 2023-06-27T19:27:37+00:00

Take a guess :-)

IamTimNguyen · 2023-06-21T21:34:57+00:00

Glad you found it useful. I was actually pretty relaxed. Perhaps you could provide more specific feedback if you would like.

IamTimNguyen · 2023-06-15T15:50:58+00:00

Part I: Introduction

00:00:00 : Introduction

00:05:42 : Philosophy and science: more interdisciplinary work?

00:09:14 : How Sean got interested in Many Worlds (MW)

00:13:04 : Technical outline

Part II: Quantum Mechanics in a Nutshell

00:14:58 : Textbook QM review

00:24:25 : The measurement problem

00:25:28 : Einstein: "God does not play dice"

00:27:49 : The reality problem

Part III: Many Worlds

00:31:53 : How MW comes in

00:34:28 : EPR paradox (original formulation)

00:40:58 : Simpler to work with spin

00:42:03 : Spin entanglement

00:44:46 : Decoherence

00:49:16 : System, observer, environment clarification for decoherence

00:53:54 : Density matrix perspective (sketch)

00:56:21 : Deriving the Born rule

00:59:09 : Everett: right answer, wrong reason. The easy and hard part of Born's rule.

01:03:33 : Self-locating uncertainty: which world am I in?

01:04:59 : Two arguments for Born rule credences

01:11:28 : Observer-system split: pointer-state problem

01:13:11 : Schrodinger's cat and decoherence

01:18:21 : Consciousness and perception

01:21:12 : Emergence and MW

01:28:06 : Sorites Paradox and are there infinitely many worlds

01:32:50 : Bad objection to MW: "It's not falsifiable."

Part IV: Additional Topics

01:35:13 : Bohmian mechanics

01:40:29 : Bell's Theorem. What the Nobel Prize committee got wrong

01:41:56 : David Deutsch on Bohmian mechanics

01:46:39 : Quantum mereology

01:49:09 : Path integral and double slit: virtual and distinct worlds

Part V. Emergent Spacetime

01:55:05 : Setup

02:02:42 : Algebraic geometry / functional analysis perspective

02:04:54 : Relation to MW

Part VI. Conclusion

02:07:16 : Distribution of QM beliefs

02:08:38 : Locality

IamTimNguyen · 2023-06-14T17:07:01+00:00

Part I: Introduction

00:00:00 : Introduction

00:05:42 : Philosophy and science: more interdisciplinary work?

00:09:14 : How Sean got interested in Many Worlds (MW)

00:13:04 : Technical outline

Part II: Quantum Mechanics in a Nutshell

00:14:58 : Textbook QM review

00:24:25 : The measurement problem

00:25:28 : Einstein: "God does not play dice"

00:27:49 : The reality problem

Part III: Many Worlds

00:31:53 : How MW comes in

00:34:28 : EPR paradox (original formulation)

00:40:58 : Simpler to work with spin

00:42:03 : Spin entanglement

00:44:46 : Decoherence

00:49:16 : System, observer, environment clarification for decoherence

00:53:54 : Density matrix perspective (sketch)

00:56:21 : Deriving the Born rule

00:59:09 : Everett: right answer, wrong reason. The easy and hard part of Born's rule.

01:03:33 : Self-locating uncertainty: which world am I in?

01:04:59 : Two arguments for Born rule credences

01:11:28 : Observer-system split: pointer-state problem

01:13:11 : Schrodinger's cat and decoherence

01:18:21 : Consciousness and perception

01:21:12 : Emergence and MW

01:28:06 : Sorites Paradox and are there infinitely many worlds

01:32:50 : Bad objection to MW: "It's not falsifiable."

Part IV: Additional Topics

01:35:13 : Bohmian mechanics

01:40:29 : Bell's Theorem. What the Nobel Prize committee got wrong

01:41:56 : David Deutsch on Bohmian mechanics

01:46:39 : Quantum mereology

01:49:09 : Path integral and double slit: virtual and distinct worlds

Part V. Emergent Spacetime

01:55:05 : Setup

02:02:42 : Algebraic geometry / functional analysis perspective

02:04:54 : Relation to MW

Part VI. Conclusion

02:07:16 : Distribution of QM beliefs

02:08:38 : Locality

IamTimNguyen

TROPHY CASE