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December 23, 2017 ~ squarishbracket

Published by squarishbracket

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Recent Posts

  • Biblical inerrancy
  • Formal Semantics 1: Historical Prelude and Compositionality
  • Two more short and sweet proofs of propositional compactness
  • The Theory of Knots
  • A Compact Proof of the Compactness Theorem
  • ZFC, and getting the right answer by accident
  • Polish Notation and Garden-Path Sentences
  • Defining uncountability
  • Who would win in a fight, logic or computation?
  • Computing truth values of sentences of arithmetic, or: Math is hard
  • How uncomputable are the Busy Beaver numbers?
  • The Arithmetic Hierarchy and Computability
  • A Self-Interpreting Book
  • Epsilon-induction and the cumulative hierarchy
  • Nonstandard integers, rationals, and reals
  • Transfinite Nim: uncomputable games and games whose winner depends on the Continuum Hypothesis
  • A Coloring Problem Equivalent to the Continuum Hypothesis
  • No known unknowns in Peano arithmetic
  • The subtlety of Gödel’s second incompleteness theorem
  • Undecidability results on lambda diagrams
  • The Anti-Set Program
  • Pictures of some extremely large numbers
  • How to draw lambda diagrams
  • Fundamentals of Logic: Syntax, Semantics, and Proof
  • The Pictorial Mathematics of Klak-Adbmal
  • The Rise of Anti-Set Theory
  • The Transfinite Factorial
  • On Self-Hating Theories of Arithmetic
  • Updated Introduction to Mathematical Logic
  • Finiteness can’t be captured in a sound, complete, finitary proof system
  • The Mindblowing Goodstein Sequences
  • Wacky Non-Standard Models of PA
  • The Continuum Hypothesis is False
  • Kolmogorov Complexity, Undecidability, and Incompleteness
  • Constructing the Church-Kleene Ordinal
  • What ordinals can be embedded in ℚ and ℝ?
  • Visualizing the rationals
  • The order type of the rational numbers
  • Can you compute all the countable ordinals?
  • Immoral or Inconsistent?
  • Constructing ordinal numbers in ZFC
  • Meaning ain’t in the brain
  • On philosophical progress
  • Logic on Planet Zorko
  • A result on the incompleteness of mathematics
  • A Gödelian Logic Puzzle
  • Crazy conditionals
  • A Dice Puzzle
  • Proving the Completeness of Propositional Logic
  • Sum and Product Puzzle
  • Four Pre-Gödelian Limitations on Mathematics
  • A proof of the Compactness Theorem
  • A challenge to constructivists
  • Describing the world
  • The full solution to the dog puzzle
  • The Surprise-Response Heuristic
  • Three paradoxes of self-reference
  • A logic puzzle about dogs
  • A suspicious proof of God’s existence
  • Fractal Trees
  • In defense of collateralized debt obligations (CDOs)
  • Six Case Studies in Consequentialist Reasoning
  • Will we ever build a Galactic Empire?
  • Earning to give or waiting to give
  • Diversification is magic
  • Paradoxical Precommitment
  • Solving the Linear Cournot Model
  • Building an analog calculator
  • Complex numbers in physics
  • The laugh-hospital of constructive mathematics
  • Can chess be solved?
  • For Loops and Bounded Quantifiers in Lambda Calculus
  • There’s a problem with infinity
  • A Supertask Puzzle
  • Can an irrational number raised to an irrational power be rational?
  • Are the Busy Beaver numbers independent of mathematics?
  • Introduction to Mathematical Logic (Part 4: Zermelo-Fraenkel Set Theory)
  • The Weirdest Consequence of the Axiom of Choice
  • Introduction to Mathematical Logic (Part 3: Reconciling Gödel’s Completeness And Incompleteness Theorems)
  • Introduction to Mathematical Logic (Part 2: The Natural Numbers)
  • Introduction to Mathematical Logic (Part 1)
  • Thinking in first order: Are the natural numbers countable?
  • 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
  • A Cognitive Instability Puzzle, Part 2
  • Logic, Theism, and Boltzmann Brains: On Cognitively Unstable Beliefs
  • Philosophers of religion are religious. Why?
  • Why do prediction markets work?
  • A Talmudic Probability Puzzle
  • 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
  • The Most Irrational of Numbers
  • All About Adultery, BDSM, and Divorce
  • Collatz Tree
  • Record-breaking Collatz chains!
  • Producing all numbers using just four fours
  • A sequence prediction puzzle
  • Buddhabrot, Mandelbrot’s older sibling
  • Hopping Midpoints
  • Exploring Julia Sets
  • Mandelbrot Exploration
  • How will quantum computing impact the world?
  • Hopping Midpoints and Mathematical Snowflakes
  • Backwards induction and rationality
  • Firing Squads and The Fine Tuning Argument
  • The EPR Paradox
  • Measurement without interaction in quantum mechanics
  • Is the double slit experiment evidence that consciousness causes collapse?
  • Decoherence is not wave function collapse
  • On decoherence
  • The problem with the many worlds interpretation of quantum mechanics
  • Consistently reflecting on decision theory
  • Decision Theory
  • Rationality in the face of improbability
  • A probability puzzle
  • Solving the common knowledge puzzle
  • A common knowledge puzzle
  • The history of lighting technology
  • Kant’s attempt to save metaphysics and causality from Hume
  • Deriving the Lorentz transformation
  • Swapping the past and future
  • Visualizing Special Relativity
  • Fractals and Epicycles
  • How to Learn From Data, Part 2: Evaluating Models
  • How to Learn From Data, Part I: Evaluating Simple Hypotheses
  • The Match Problem
  • Gödel’s Second Incompleteness Theorem: Explained in Words of Only One Syllable
  • Anti-inductive priors
  • Making sense of improbability
  • A simple probability puzzle
  • The end goal of epistemology
  • Deciphering conditional probabilities
  • The Problem of Logical Omniscience
  • Sapiens: How Shared Myths Change the World
  • Anthropic reasoning in everyday life
  • Adam and Eve’s Anthropic Superpowers
  • Sleeping Beauty Problem
  • Infinities in the anthropic dice killer thought experiment
  • Not a solution to the anthropic dice killer puzzle
  • Pushing anti-anthropic intuitions
  • An expected value puzzle
  • Dialogue from Kafka On The Shore
  • A closer look at anthropic tests for consciousness
  • Two principles of Bayesian reasoning
  • Explaining anthropic reasoning
  • Predicting changes in belief
  • In favor of anthropic reasoning
  • Clarifying self-defeating beliefs
  • Getting empirical evidence for different theories of consciousness
  • Bad Science Reporting
  • The Anthropic Dice Killer
  • What do I find conceptually puzzling?
  • More on quantum entanglement and irreducibility
  • Ramanujan’s infinite radicals
  • Communication through entanglement
  • Quantum mechanics, reductionism, and irreducibility
  • Building the diffusion operator
  • Building the quantum oracle
  • Grover’s algorithm
  • Deutch-Josza Algorithm
  • More on quantum gates
  • Quantum Computing in a Nutshell
  • Matter and interactions in quantum mechanics
  • 100 prisoners problem
  • Some simple probability puzzles
  • Deriving the Schrodinger equation
  • On existence
  • Concepts we keep and concepts we toss out
  • Seeing, Doing, Imagining
  • Against moral realism
  • Explanation is asymmetric
  • Wave function entropy
  • Query sensitivity of evidential updates
  • Summarizing conscious experience
  • Simple induction
  • The North Korea problem isn’t solved
  • Priors in the supernatural
  • Patterns of inductive inference
  • If all truths are knowable, then all truths are known
  • Variational Bayesian inference
  • The value of the personal
  • Confirmation bias, or different priors?
  • Objective Bayesianism and choices of concepts
  • A shameful history
  • “Beating the drum for justice”
  • Overemphasizing disagreement
  • Regularization as approximately Bayesian inference
  • Against the status quo
  • Why minimizing sum of squares is equivalent to frequentist inference
  • History is Lamarckian
  • Short and sweet proof of the f(xy) = f(x) + f(y) logarithmic property
  • Constructing the world
  • Moving Naturalism Forward: Eliminating the macroscopic
  • Some social justice factoids
  • What is integrated information?
  • How to sort a list of numbers
  • Defining racism
  • Utter confusion about consciousness
  • Getting evidence for a theory of consciousness
  • The Scourge of Our Time
  • The problem with philosophy
  • Argument screens off identity
  • Facts about guns
  • “You don’t believe in the God you want to, and I won’t believe in the God I want to”
  • Galileo and the Schelling point improbability principle
  • Why “number of parameters” isn’t good enough
  • Bayesian Occam’s Razor
  • All about IQ
  • A model selection puzzle: Why is BIC ≠ AIC?
  • Bayes and overfitting
  • The basics of information divergence
  • More model selection visualizations
  • Where I am with utilitarianism
  • The Monty Hall non-paradox
  • Akaike, epicycles, and falsifiability
  • On complexity and information geometry
  • A note of ambiguity regarding model selection
  • Gibbs’ inequality
  • Some simple visual comparisons of model selection techniques
  • Bayes and beyond
  • Racism and identity
  • What is bias?
  • Value beyond ethics
  • Taxonomy of infinity catastrophes for expected utility theory
  • Two-factor markets for sex
  • A simple explanation of Bell’s inequality
  • Cults, tribes, states, and markets
  • Bayesian experimental design
  • Why relative entropy
  • A survey of entropy and entropy variants
  • Entropy is expected surprise
  • The Rival-Expert Heuristic
  • Inference as a balance of accommodation, prediction, and simplicity
  • Pascal’s mugging
  • Those who have forgotten words
  • Why systematize epistemology?
  • Journey into abstraction
  • Timeless decision theory and homogeneity
  • Timeless ethics and Kant
  • A failure of Bayesian reasoning
  • Bayesianism as natural selection of ideas
  • Against falsifiability
  • Metaphysics and fuzziness: Why tables don’t exist and nobody’s tall
  • Is [insert here] a religion?
  • Hyperreal decision theory
  • Infinite ethics
  • More on random sampling from Nature’s Urn
  • Free will and decision theory (Part 2)
  • Paradoxes of infinite decision theory
  • Does fine-tuning give evidence for God?
  • Noisy Evidence
  • Nature’s Urn and Ignoring the Super Persuader
  • Entropy vs relative entropy
  • Fun with Akaike
  • Anthropic argument for common priors
  • Why you should be a Bayesian
  • Consistency and priors
  • Dutch book arguments
  • Cox’s theorem
  • Maximum Entropy and Bayes
  • Advanced two-envelopes paradox
  • Sam Harris and the is-ought distinction
  • Two envelopes paradox
  • Principle of Maximum Entropy
  • Consciousness
  • Inequality and free markets
  • 40 papers on inequality in one sentence each
  • Gregory Watson (and how to change the world)
  • Statistical mechanics is wonderful
  • Solution: How change arises in QM
  • TIMN view of social evolution
  • Race, Ethnicity, and Labels
  • Is quantum mechanics simpler than classical physics?
  • Iterated Simpson’s Paradox
  • Causal decision theory
  • Free will and decision theory
  • Simpson’s paradox
  • Screening off and explaining away
  • Societal Failure Modes
  • Dialogue: Why you should one-box in Newcomb’s problem
  • Opt-out organ donation
  • The spiritual and the scientific
  • Comprehensibility of the Complex
  • Correlation and causation
  • Causal Intervention
  • Causal Arrows
  • Causality: Preliminaries
  • Low-hanging policy fruit

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