My posts assume a fairly wide range of levels of background knowledge. For that reason, I’ve labeled posts by the estimated amount of background knowledge you’ll need to be able to make it through the post (+ means little to no background knowledge assumed, +++ means lots).

My posts also tend to vary in length a fair amount, so I’ve also included length information for each post.

(This page is usually not totally up-to-date. You can see most recent posts on the sidebar on the home page.)

# Favorites

Somehow ended up here and not sure where to start? Here are some suggestions:

On Self-Hating Theories of Arithmetic

Consistently reflecting on decision theory

Matter and interactions in quantum mechanics

Pascal’s mugging

Hyperreal decision theory

Dialogue on Newcomb’s problem

Cults, tribes, states, and markets

Two-envelopes paradox

Societal failure modes

A failure of Bayesian reasoning

Infinite ethics

Bayesian experimental design

A simple explanation of Bell’s inequality

Bayesian Occam’s razor

Simpson’s paradox

# All posts

## Interactive

Mandelbrot Exploration

Exploring Julia Sets

Hopping Midpoints

The Most Irrational of Numbers

## Epistemology

### Bayesian

Logic, Theism, and Boltzmann Brains: On Cognitively Unstable Beliefs

A Cognitive Instability Puzzle, Part 2

Anti-inductive priors (++) (short)

The Problem of Logical Omniscience (+) (short)

Deciphering conditional probabilities (++) (short)

Two principles of Bayesian reasoning (+) (short)

Predicting changes in belief (++) (moderate)

Some simple probability puzzles (long)

Query sensitivity of evidential updates (++) (moderate)

Variational Bayesian inference (++) (short)

Priors in the supernatural (+) (short)

Objective Bayesianism and choices of concepts (+) (short)

Regularization as approximately Bayesian inference (++) (short)

Why minimizing sum of squares is equivalent to frequentist inference (++) (short)

Simple induction (++) (short)

Overemphasizing disagreement (+) (short)

A failure of Bayesian reasoning (++) (short)

Gibbs’ inequality (+) (super short)

Bayesianism as natural selection of ideas (++) (short)

Noisy Evidence (++) (short)

Why you should be a Bayesian (+) (short)

Consistency and priors (++) (short)

Dutch book arguments (+) (short)

Cox’s theorem (+++) (moderate)

### Slightly less Bayesian

Firing Squads and The Fine Tuning Argument (+) (short)

Rationality in the face of improbability (+) (short)

How to Learn From Data, Part 2: Evaluating Models (++) (long)

How to Learn From Data, Part I: Evaluating Simple Hypotheses (+) (long)

Making sense of improbability

A simple probability puzzle

The end goal of epistemology (+) (moderate)

Clarifying self-defeating beliefs (++) (moderate)

Seeing, Doing, Imagining (+) (super short)

Summarizing conscious experience (++) (short)

The value of the personal (+) (short)

Confirmation bias, or different priors? (+) (moderate)

Explanation is asymmetric (+) (moderate)

Patterns of inductive inference (+) (short)

If all truths are knowable, then all truths are known (+) (short)

Galileo and the Schelling point improbability principle (+) (long)

What is bias? (+) (short)

Why systematize epistemology? (+) (short)

Against falsifiability (+) (short)

Nature’s Urn and Ignoring the Super Persuader (+) (long)

More on random sampling from Nature’s Urn (+) (short)

Anthropic argument for common priors (+) (super short)

## Logic

Introduction to Mathematical Logic (Part 1)

Introduction to Mathematical Logic (Part 2: The Natural Numbers)

Introduction to Mathematical Logic (Part 3: Reconciling Gödel’s Completeness And Incompleteness Theorems)

Introduction to Mathematical Logic (Part 4: Zermelo-Fraenkel Set Theory)

Are the Busy Beaver numbers independent of mathematics?

Thinking in first order: Are the natural numbers countable?

The laugh-hospital of constructive mathematics

For Loops and Bounded Quantifiers in Lambda Calculus

Can an irrational number raised to an irrational power be rational?

The Weirdest Consequence of the Axiom of Choice

Gödel’s Second Incompleteness Theorem: Explained in Words of Only One Syllable (+) (short)

## Group Theory

Galois’ Unsolvable Polynomials

x^5 – x – 1

Group Theory: The Mathematics of Symmetry?

Symmetries of Platonic Solids

Some Curious Group Isomorphisms

Extending Cauchy’s Theorem

Strong Induction Proofs of Cauchy’s Theorem and Sylow’s First Theorem

Table of Small Finite Groups

Some Group Factoids

Group Theory Toolkit (+++)

The sweet spot on the structure spectrum

Proving Cauchy’s Theorem

Group Theory: Lagrange’s Theorem and the Sudoku Principle

## Model Selection

The basics of information divergence (+) (super short)

Why “number of parameters” isn’t good enough (+) (short)

Bayesian Occam’s Razor (++) (moderate)

A model selection puzzle: Why is BIC ≠ AIC? (++) (super short)

Bayes and overfitting (+) (super short)

More model selection visualizations (+) (short)

On complexity and information geometry (+++) (short)

A note of ambiguity regarding model selection (+) (short)

Akaike, epicycles, and falsifiability (++) (short)

Some simple visual comparisons of model selection techniques (++) (short)

Bayes and beyond (++) (long)

Inference as a balance of accommodation, prediction, and simplicity (+) (moderate)

Fun with Akaike (+++) (moderate)

## Entropy

Bayesian experimental design (++) (short)

Why relative entropy (++) (short)

A survey of entropy and entropy variants (++) (moderate)

Entropy is expected surprise (++) (short)

Entropy vs relative entropy (+++) (short)

Maximum Entropy and Bayes (+++) (moderate)

Principle of Maximum Entropy (++) (short)

## Anthropics

Anthropic reasoning in everyday life (+) (short)

Adam and Eve’s Anthropic Superpowers (+) (moderate)

Sleeping Beauty Problem (+) (short)

Infinities in the anthropic dice killer thought experiment (++) (moderate)

Not a solution to the anthropic dice killer puzzle (++) (moderate)

Pushing anti-anthropic intuitions (++) (short)

A closer look at anthropic tests for consciousness (+++) (short)

Explaining anthropic reasoning (+) (moderate)

In favor of anthropic reasoning (+) (short)

Getting empirical evidence for different theories of consciousness (++) (moderate)

The Anthropic Dice Killer (++) (moderate)

## Decision Theory

Paradoxical Precommitment

Backwards induction and rationality (+) (short)

Consistently reflecting on decision theory (+) (long)

Decision Theory (+) (short)

An expected value puzzle (+) (short)

The Monty Hall non-paradox (+) (moderate)

Taxonomy of infinity catastrophes for expected utility theory (+) (moderate)

Pascal’s mugging (+) (short)

Timeless decision theory and homogeneity (+) (short)

Timeless ethics and Kant (+) (long)

Dialogue on Newcomb’s problem (++) (long)

Hyperreal decision theory (++) (moderate)

Paradoxes of infinite decision theory (+) (moderate)

Infinite ethics (+) (short)

Free will and decision theory (++) (moderate)

Free will and decision theory (Part 2) (+) (short)

Two envelopes paradox (++) (moderate)

Advanced two-envelopes paradox (++) (short)

## Quantum Computing

- Quantum Computing in a Nutshell (+) (short)
- More on quantum gates (short) (++)
- Deutch-Josza Algorithm (short) (++)
- Grover’s algorithm (short) (+++)
- Building the quantum oracle (super short) (+++)
- Building the diffusion operator (super short) (+++)

How will quantum computing impact the world? (short) (+)

## Physics

Building an analog calculator

Complex numbers in physics

The Central Paradox of Statistical Mechanics: The Problem of The Past

Is The Fundamental Postulate of Statistical Mechanics A Priori?

The Necessity of Statistical Mechanics for Getting Macro From Micro

The EPR Paradox (++) (medium)

Measurement without interaction in quantum mechanics (++) (short)

Is the double slit experiment evidence that consciousness causes collapse? (++) (short)

Decoherence is not wave function collapse (+++) (short)

On decoherence (+++) (short)

The problem with the many worlds interpretation of quantum mechanics (+) (moderate)

Deriving the Lorentz transformation (++) (moderate)

Swapping the past and future (+) (short)

Visualizing Special Relativity (+) (short)

Fractals and Epicycles (+) (short)

More on quantum entanglement and irreducibility (++) (moderate)

Communication through entanglement (++) (short)

Quantum mechanics, reductionism, and irreducibility (++) (long)

Matter and interactions in quantum mechanics (++) (long)

Deriving the Schrodinger equation (++) (short)

Wave function entropy (+++) (short)

A simple explanation of Bell’s inequality (+) (moderate)

Statistical mechanics is wonderful (++) (long)

Is quantum mechanics simpler than classical physics? (++) (moderate)

Solution: How change arises in QM (++) (short)

## Metaphysics

Concepts we keep and concepts we toss out (+) (short)

Kant’s attempt to save metaphysics and causality from Hume (++) (way too long)

On existence (+) (short)

Against moral realism (+) (short)

Utter confusion about consciousness (+) (moderate)

Getting evidence for a theory of consciousness (+) (moderate)

Constructing the world (+) (short)

Moving Naturalism Forward: Eliminating the macroscopic (+) (short)

Consciousness (+) (moderate)

Metaphysics and fuzziness: Why tables don’t exist and nobody’s tall (+) (short)

## Morality

The Scourge of Our Time (+) (short)

Where I am with utilitarianism (+) (short)

Value beyond ethics (+) (super short)

Sam Harris and the is-ought distinction (+) (short)

## Economics

Diversification is magic

Solving the Linear Cournot Model

Inequality and free markets (+) (super long)

One-sentence sketches of 40 papers on inequality (+) (moderate)

## Politics

All About Adultery, BDSM, and Divorce (+) (long)

The North Korea problem isn’t solved (+) (short)

A shameful history (+) (moderate)

“Beating the drum for justice” (+) (long)

Against the status quo (+) (short)

Some social justice factoids (+) (moderate)

Racism and identity (+) (moderate)

Facts about guns (+) (short)

Cults, tribes, states, and markets (+) (moderate)

TIMN view of social evolution (+) (long)

Low-hanging policy fruit (+) (moderate)

Societal Failure Modes (+) (super long)

Opt-out organ donation (+) (short)

## Causality

1. Preliminaries (+) (moderate)

2. Causal arrows (++) (short)

3. Causal intervention (++) (short)

4. Correlation and causation (++) (short)

5. Screening off and explaining away (++) (short)

6. Simpson’s paradox (+++) (moderate)

7. Iterated Simpson’s paradox (++) (short)

8. Causal decision theory (++) (short)

## Puzzles

There’s a problem with infinity

A Supertask Puzzle

A Talmudic Probability Puzzle

The Match Problem (+) (short)

100 prisoners problem (+) (moderate)

## Random

Philosophers of religion are religious. Why?

Why do prediction markets work?

Buddhabrot, Mandelbrot’s older sibling (+) (short)

Hopping Midpoints and Mathematical Snowflakes (+) (short)

Sapiens: How Shared Myths Change the World (+) (moderate)

Bad Science Reporting (+) (short)

Dialogue from Kafka On The Shore (+) (short)

What do I find conceptually puzzling? (+) (moderate)

Ramanujan’s infinite radicals (+) (short)

What is integrated information? (+) (long)

History is Lamarckian (+) (short)

Short and sweet proof of the f(xy) = f(x) + f(y) logarithmic property (++) (short)

How to sort a list of numbers (+) (short)

Defining racism (+) (short)

The problem with philosophy (+) (short)

Argument screens off identity (+) (short)

All about IQ (+) (long)

Two-factor markets for sex (+) (short)

Those who have forgotten words (+) (super short)

Journey into abstraction (++) (moderate)

Is [insert here] a religion? (+) (short)

Gregory Watson (and how to change the world) (+) (super short)

Race, ethnicity, and labels (+) (long)

Comprehensibility of the complex (+) (moderate)

The spiritual and the scientific (+) (moderate)