Posted on Thursday, 7 April 2011
The axiom of choice need not hold in a topos, and the law of the excluded middle need not hold.
John Baez
more, much more: toposes, triples and theories (full book pdf)
(Source: math.ucr.edu)
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posted 2 years ago
summary of Edward Tufte's The Visual Display of Quantitative Information
Manifolds, Metrics, StarFox, and Self-versus-Other Things I learned as an Entrepreneur. μ dt + σ dWt, my #ss Category Theory, Postmodernism, and Object-Oriented Programming. Part & Whole I Ⅱ Ⅲ Ⅳ V VI Ⅶ Ⅷ ∑i,j Change one thing and you change everything Immigrants should teach high school Spanish. Superposition of feelings. The worst thing about lawyers School maths I Ⅱ Ⅲ Ⅳ V VI Ⅶ Ⅷ sin & cos Ⅸ Ⅹ Ⅺ XII XIII XIV XV XVI XVII XVIII XIX XXX XXXI XXXII XXXIII XXXIV XXXV XXXVI XXXVII XXXVIII XXXIX XL Logic & emotion are not opposites. College majors versus industry & job title Seeing higher dimensions I Ⅱ Ⅲ Ⅳ V VI Ⅶ Ⅷ Ⅸ Ⅹ XI Trichotomy, QCD, and Dialectic Linear algebra is the main barrier between mathematicians and everyone else. What is a determinant?, a Jacobian?, how to multiply matrices, the different kinds of matrices, matrices that act like just one number, how to think about matrices as linear transformations "of an entire space". Fuzzy Thinking I Ⅱ Ⅲ Rubik's Cube and Quantum Chromodynamics When Doves Cry inside a Convex Hull 6-D Sphere, 4-D Cube, 3-D Random Walk Time is like space. Thinking with probability distributions I Ⅱ III Ⅳ V Why I Despise the MBTI. Imagination, creativity, and artistry are distinct. Why I support progressive taxation. Department of Happiness studies. Who's more moral, journalists or hedge fund managers? Our Flat Solar System Hey! I baked you some Wiener processes! Mathematics of people I Ⅱ Ⅲ Ⅳ V VI Ⅶ Ⅷ Ⅸ Ⅹ Ⅺ XII XIII XIV XV XVI XVII XVIII XVIII XIX XX XXI XXII XXIII XXIII XXIV XXV XXVI XXVII XXVIII XXIX XXX XXXI XXXII XXXIII XXXIII XXXIV XXXV XXXVI XXXVII Incomparable things. How not to draw a probability distribution. READ before you upvote. Watch a windmill go up in 1 minute. Physics 0 I Ⅱ Ⅲ Ⅳ V VI Ⅶ Ⅷ Ⅸ Ⅹ Ⅺ XII XIII XIV XV XVI XVII XVIII Logic I Ⅱ Ⅲ IV V VI Ⅶ Ⅷ Ⅸ Ⅹ Ⅺ XII Causality I II Ⅳ V Logicism, Scientism, Logocentrism I Ⅱ Ⅲ Ⅳ V VI Pizza, I like. (OSV) Probability & Statistics I Ⅱ Ⅲ Ⅳ V VI Ⅶ Ⅷ Ⅸ Ⅹ Ⅺ XII XIII XIV XV XVI XVII XVIII XIX XX Financial markets are not just an infinite time series. Fahrenheit is better than Celsius. Total variance can be split into parts. Zeno's Paradox, resolved. Business I Ⅱ Ⅲ Ⅳ V VI Ⅶ Ⅷ Ⅸ Ⅹ Ⅺ XII XIII XIV XV XVI XVII XVIII XIX Three views of Special Relativity The Hotness Scale The universe is a song, singing itself. 43252003274489856000 Philosophy I Ⅱ Ⅲ Ⅳ V VI Ⅶ Ⅷ Ⅸ Ⅹ Ⅺ XII XIII XIV XV XVI XVII XVIII XVIII XIX XX XXI A Quant in King Arthur's Court Eigenfaces, eigenbasis, eigenvectors, eigenfunctions, eigendirection, eigengraph, eigenvalue, eigentweet, eigen-hacker-news-post. Spectral Mesh Compressions of Ponies Grigory Perelman is not weird. The distribution of digits in √2's decimal expansion Polymorphism, overloading, and all that The Self I Ⅱ Ⅲ vs Other I II III Ⅳ Zeno's Paradox, Resolved Beyond Between Good and Evil Different Conceptions of Number 0 I Ⅱ Ⅲ Ⅳ V VI Ⅶ Ⅷ Ⅸ Ⅹ Ⅺ XII XIII XIV XV Something stupid that stupid magazines and blogs said is true, is not true. Your 12th Boyfriend is not Mr. Right. The Social Cost of Lawyers Unmeasurable distances. Drama in ƒ: ℤ₂ × ℤ₂ → {0,1} Shapes I Ⅱ Ⅲ Ⅳ V VI Ⅶ Ⅷ Ⅸ Ⅹ Ⅺ XII XIII XIV XV XVI XVII XVIII XIX XX XXI XXII XXIII XXIV XXV XXVI XXVII Poor Estadounidenses are rich by world standards and historical standards. Language 0 I Ⅱ Ⅲ Ⅳ V VI Ⅶ Ⅷ Ⅸ Ⅹ Ⅺ XII XIII Concepts I ">Ⅱ Ⅱ Ⅲ Ⅳ V VI Ⅶ Ⅷ Ⅸ Ⅹ Ⅺ XII XIII XIV Regression analysis is only reliable for interpolation – not extrapolation. God's gender. Where should I start learning mathematics if I didn't go very far with it in school? Correlation, cointegration, causation and OLS. Different conceptions of distance & size I Ⅱ Ⅲ Ⅳ V VI Ⅶ Ⅷ Ⅸ Ⅹ Ⅺ XII XIII XIV, XV, XVI, XVII, XVIII, XIX XX XXI Realised and unrealised "human capital" Talking in Tuples: Mathematics is the most different language. Resolving the gender wars with support vector machines and probability distributions. Zero-sum locally, positive-sum globally. Religious ∞, Math ∞, Graham's Number, and ∞+1 Farming and the volatility landscape. Do numbers exist? Meditation — invented by people without iPhones. (all the) Things You Can Do With Four Things Un-priming experimental subjects. Bad mathematical writing I Ⅱ Ⅲ 1729 is not a number; it's a method of calculation. Mexican immigrants are Native Americans. Impulse control, the hedonic treadmill, what really matters I Ⅱ Ⅲ Ⅳ V VI Ⅶ Ⅷ Ⅸ Ⅹ Ⅺ XII XIII XIV XV XVI XVII XVIII XIX XX XXI XXII XXIII XXIV XXV XXVI XXVII XXVIII Wassily Leontief's vision of the economy. Convolving life-experiences / life-paths γ I Ⅱ Ⅲ Ⅳ V Do we live in a 3-dimensional universe because that's the most interesting universe? Spatial voting theory. Noncommutative I Ⅱ Ⅲ IV Jan Koenderink on clouds. Dmitry Tymoczko's mathematical theory of Western music. 1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388 (my favourite number) What's wrong with OKCupid's matching algorithm. User-friendly search means filters. Better word association for search engines doing data mining What's half of 100℉? It's not 50℉. Affine transformations. Feminine cause ( Yin 阴) The speed of imagination. Complexity I Ⅱ Ⅲ Ⅳ V Does time pass for a photon? Oaken staff beats longsword, and other implications of the Central Limit Theorem. Rochambot is intransitive. History I Ⅱ III Ⅳ V VI Ⅶ Ⅷ Ⅸ Ⅹ Ⅺ XII The Vector Mathematics of Colour Space. Utility Theory maps ℝᴺ × ℕᴷ → ??? → ≻ Linear Combinations of Ideas The ℝeal numbers are messed up. I Ⅱ Ⅲ Ⅳ V VI Real Dynamics vs the Eternal Return: Cantor whomps Nietzsche Logical circular logic Let's ditch the ★★★★★ rating system for books (Amazon), movies (Netflix), and surveys (SurveyMonkey).
• Integration by Parts • Power Series (spectrum) • Geometric Series • Concave • Imaginary Arithmetic • Linear • Non-linear • Convex Combinations • The Differential • Phase Space • Dynamical Systems • Matrix Multiplication • Graphs (networks, not plots) • Noncommutative • Nontrivial • Outer Product • Inner Product (how to multiply matrices) • Category & Functor • Tensor • Topology • Operators • Transforms • Eigenvectors • Projective Geometry • Weighted Averages • Fuzzy Numbers • Kernels • Sigma Algebras • Autocorrelation • Convergence of series • √π • Imprecise Probability • Quantum Logic • Robust Regression • Groups • Polytopes (high-dimensional polygons) • Game Theory • Determinant of a Matrix • Jacobians • Vectors • Time Series • GARCH • Wavelet Basis • Fourier Basis • Positive Semi-Definite • The Laplace Transform • Manifolds • Metrics • Quasimetrics • Norms • Measures • Topology • Splines • Sheaves • Solitons • Forms • Groups • Semigroups • Corpora • Boundaries and flows • Vector Fields • Stereographic Projection • Geometries • Torsors • Fundamental Theorem of Algebra • Central Limit Theorem • Fundamental Theorem of Calculus • Vectors • Logarithms • Sin and Cos • The Pythagorean Theorem • Imprecision (on purpose)
explains everything 3-D √−1 4-D also explains everything free will regression β lm size politics A→B brain cli quips tale ↑
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