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- Is the golden ratio the "most irrational number"?
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- "Calculus-based physics"
- "In space, there's no up or down."
- A crash course on mathematical logic: Part I
- A curious infinite sum arising from an elementary geometric argument
- A review of "Age of Em" by Robin Hanson
- Abstracting our abstractions: "limits of cones", universal properties
- Abstracting some categorical definitions
- Age of Gen: a picture of a transhuman society
- All matrices can be diagonalised over R[X]/(X^n)
- Ancestral graphs
- ANOVA and model testing
- Backpropagation and the chain rule
- Bayes theorem, estimators and the theory of Amazon ratings
- Bayes, bias, p-hacking and the Monty Hall problem
- Causation and semi-supervised learning
- Causation, transfer and symmetry
- Central limit theorem
- Church-Turing: the "Fundamental Thesis of Computer Science"
- Classical Statistics, Confidence Regions and Hypothesis tests
- Composition of linear transformations: matrix multiplication
- Computable functions I: mu-recursion
- Computation and model theory
- Contour Integration I: Cauchy and Morera's Integral Theorems
- Contour Integration II: everything about singularities; what gives life to Pi
- Covariance matrix and Mahalanobis distance
- Covectors, conjugates, and the metric tensor
- Curvature is just the Hessian
- Dealing with eigenspaces; noncommuting variables and another postulate
- Derivations and the Jacobi Identity
- Discovering the Fourier transform
- Divide-and-conquer algorithms
- Dutch book argument for probability theory
- Engineering as the theory of airlocks
- Everything you know about history is false.
- Exogenous variables and normal linear models
- Fancy polynomials
- Finance as time traveling retail
- Financial derivatives, payoff functions and portfolios: motivation
- First-order logic and computer science
- Fourier series and Hilbert spaces
- Frequentism as a bureacuratic restriction on speech
- From flint to the industrial revolution in 2 years: rebuilding civilization (after a zombie apocalypse)
- From polarisation to quantum mechanics: states, observables, Born's law
- Further notes on causation
- Geometry, positive definiteness, and Sylvester's law of inertia
- Godel, Turing and Time Travel
- Hacking Evidential Decision Theory
- I don't believe p-hacking is a problem.
- Incredible Duals of category theory
- Information and bits
- Information theory of multiple random variables
- Internalization and value capture
- Introduction to Algebraic Geometry
- Introduction to Bayesian inference
- Introduction to category theory: a second-abstraction
- Introduction to Lie groups
- Introduction to linear transformations
- Introduction to measure
- Introduction to Projective Geometry
- Introduction to special relativity
- Introduction to symmetry
- Introduction to tensors and index notation
- Intuition behind some basic ideas of calculus
- Intuition to convergence
- Intuition, analogies and abstraction
- Invariant and generalised eigenspaces; Jordan normal form
- Inverses, determinants, column spaces, non-square matrices
- Is the golden ratio the "most irrational number"?
- Jevon's theorem and economic intuitions
- Kolmogorov complexity
- Least-squares estimator and Gauss-Markov
- Lie Bracket, closure under the Lie Bracket
- Lie group homomorphisms
- Lie group topology
- Light cones and causality
- Limiting cases I: the integral of e^(ax) and the finite-domain Fourier transform
- Limiting cases II: repeated roots of a differential equation
- Linear sums and independence, span, and linear bases
- Linguistics and causal models
- Logarithmic market scoring
- Lorentz transforms lives
- Lossless compression, invertible change of variables and entropy
- Machine learning and information theory
- Machine learning as function approximation; statistical and cognitive motivations
- Making sense of Euler's formula
- Matrix decompositions
- Minkowski everything -- invariants
- Minkowski everything -- spacetime vectors, rapidity
- Mixed states I: density matrix, partial trace, the most general Born rule
- Mixed states II: decoherence; important measures of purity and entropy
- Model diagnostics
- Moments as tensors
- Motivating ring theory, domains with integer-polynomial analogies
- Newton's laws in relativity
- Noether's theorem and convolutional nets
- Null, row spaces, transpose, fundamental theorem of linear algebra
- Number theory: Part I
- Order statistics
- Ordinals and well-founded recursion
- Original thinking and art
- Orthogonal group, indefinite orthogonal group, orthochronous stuff
- Outer and inner measure, complete measure
- Overview of neural network architectures
- Philosophy of the Efficient Market Hypothesis
- Pi and collisions (the 3blue1brown problem)
- Poisson processes: from geometric to Gamma distributions
- Polynomial interpolation and Vandermonde
- Position, momentum bases and operators, Fourier transform, uncertainty
- Positive vs normative social sciences
- Positivism as the rejection of anthropic reasoning
- Probabilistic convergence
- Probabilistic inequalities
- Probability of immortality for a transhuman being
- Projection operators, generalised Born's rule, position basis, wavefunction
- Quaternion introduction: Part I
- Random variables as vectors
- Ranking academic disciplines from science to pseudo-science
- Relativistic dynamics
- Riddles and mental models
- Sigma fields are Venn diagrams
- Statistical models; causal models
- Sufficient statistics and the Rao-Blackwell theorem
- Supplementary definitions: compactness, compactification, hemicompactness
- Supplementary definitions: connectedness, clopen sets
- Supplementary definitions: levels of abstraction
- SVD, polar decomposition, normal matrices; a re-look at transposes and FTLA
- Systems and sub-systems, the tensor product, quantum entanglement
- The "transhuman vision"
- The Cauchy Riemann Equations: what do they really mean?
- The correct multi-variate mean-value theorem (no inequality)
- The correct resolution of the twin paradox
- The Dirichlet (also Beta) distribution
- The era of Einstein
- The Hamiltonian and exactly where it comes from
- The Killing form; factorising non-Abelian Lie groups
- The mathematical definition of an image
- The three theorems of complete statistics
- Things being alienly alien
- Thoughts on Roko's basilisk
- Three domains of knowledge
- Time evolution, Schrodinger and Heisenberg pictures, Noether's theorem
- Topology I: limits, continuity and homeomorphism, the neighbourhood filter, open sets
- Topology II: Kuratowski closure topology, nets, neighbourhood basis
- Topology III: example topologies, inherited topologies, distinguishability
- Trace, Laplacian, the Heat equation, divergence theorem
- Triangular matrices: Schur, QR, Cholesky and LU/LPU decompositions
- Two ways to understand overfitting (and don't peek!)
- Two-envelopes problem: beyond the Bayes explanation
- Understanding polynomial-ish differential equations
- Understanding variable substitutions and domain splitting in integrals
- Uniform priors and Maximum Likelihood Estimation
- Walkthrough of Galois theory
- What even are pure and applied math, anyway?
- What is energy? What is physics?
- What's with e^(-1/x)? On smooth non-analytic functions: part I
- Why are calculus and linear algebra taught early?
- Why are negative temperatures hot?
- Why do we conflate philosophy with psychology?
- Why history needs to be completely reformulated
- Why is the Pythagoras theorem true anyway?
- Why matrices?
- You can't hack Bayes's theorem