plan space from outer nine
What a fun book ! I came for the history of vectors, hoping to get interesting linear algebra background. I got more interesting stories about the history of quaternions and quite a lot more on tensors and general relativity than I'd seen before. Possibly a narrow audience will enjoy it, but I was in that audience. i 2 = j 2 = k 2 = ijk = -1 Tensors vs. n-dimensional arrays of numbers Ever since…
Here's an interactive widget, made quickly with Claude, that let's you play around with different 2x2 matrices. You can see what they do to points (as a transform, multiplying on the left) and the Singular Value Decomposition, and eigenvalues and eigenvectors (and of course determinant). 2×2 Matrix Playground --> This page needs JavaScript to compute and draw. A = A ● = ● ⓘ SVD: A = U Σ V T…
For at least six years, I've been collecting quotes about what mathematics is. Here are some of them. “... mathematics is not an empirical science, ...” (Von Neumann, The Mathematician ) “Mathematics is not a deductive science—that's a cliché.” (Halmos, I want to be a mathematician ) “Pure mathematics is, in its way, the poetry of logical ideas.” (Einstein, epitaph for Noether) “... mathematics is…
Complex numbers are usually introduced by inventing the "imaginary number" i as a new entity. Both historical mathematicians and modern students are not always quick to get on board with this. A subset of 2-by-2 real matrices can be identified that has all the properties of complex numbers, without introducing any new entities or operations, and also making it easier to understand some of the…
I finally read my copy of The Dispossessed . I hadn't realized how it relates to other things I've read on post-scarcity; apparently it was heavily inspired by Post-Scarcity Anarchism . I also hadn't known that Le Guin originated the "ansible" in scifi. The book was subtitled "an ambiguous utopia," but Le Guin pretty clearly prefers the anarchist society. Perhaps the least realistic aspect was the…
Kevin Hartnett , that prolific writer for Quanta Magazine , has written the first book published by Quanta Books . It's a solid human-oriented history of Lean and its increasing importance in formalizing mathematics and in connection with AI. I'm excited for the next two books coming out from Quanta: Six Math Essentials from Terry Tao, and Everything Is Fields from David Tong. In the latter case,…
Keeping these here for convenient reference... 2018-12-28: The Equation of a Plane 2021-09-15: The flow metaphor for matrix multiplication 2021-09-15: You can derive the formula for the determinant 2024-06-16: Linear Algebra Done Right, by Axler 2024-06-24: A brief development of matrix multiplication 2026-07-20: Outline for Fundamental Linear Algebra 2026-07-24: One-dimensional Linear Algebra…
It may not have won a Pulitzer, but Cheng's book reminds me of nothing quite so much as Gödel, Escher, Bach . It's committed to its gimmick, it's fun to read, it's self-involved, its success as an argument is incomplete, there's some math but there could have been more. GEB had better editing. Just as I was most interested in the incompleteness theorem bits of GEB, How to bake π is ostensibly…
Linear Algebra is the mathematics of linear transformations . It can handle lots of dimensions, but let's explore the one-dimensional case with real numbers. A linear transformation is called linear because it behaves like a straight line that goes through the origin. In one dimension, linear transforms are just multiplication. For example, let's consider a transform \( M \) that multiplies by 4.…
Scott Young's first book came out in 2019. It's okay, and it was reasonably successful. "Intense learning" is at least as good a name. There are some good ideas. I worry about everyone (Young) needing to release content constantly and be an "influencer" with goofy hooks; that culture permeates the book. But I do support diving in and learning things. Young motivates the book too much, in my…
Those "rationalists" are even weirder than I thought! Becker (who also wrote What is Real? ) delivers an impassioned humanist history ( e.g. ), exposé, and analysis of a modern trend in the over-empowered misusing their power. It comes out (as Becker notes) very similar to the " TESCREAL bundle " analysis of Gebru and Torres. A lot of the book is of the form "so-and-so says X is good and…
We must give our all in the struggle to unify the entire society with the revolutionary ideology of the Great Leader Kim Il Sung. We must honor the Great Leader comrade Kim Il Sung with all our loyalty. We must make absolute the authority of the Great Leader comrade Kim Il Sung. We must make the Great Leader comrade Kim Il Sung's revolutionary ideology our faith and make his instructions our…
I'm thinking about how to make linear algebra so simple that it could be taught much earlier than it usually is. I think it's often presented with some mix of excessive abstraction (proofs, symbols-only) and excessive concreteness (obsession with Gaussian elimination and manipulating matrices by hand) and often with things (matrix multiplication) that should be explained introduced as if they…
As a Man Thinketh is a 1903 self-help "book" (you can print it on eleven sheets of paper) that was part of what William James called "the mind-cure movement." It's an ancestor of The Secret . "The soul attracts that which it secretly harbors; that which it loves, and also that which it fears; ..." Why do these books on literally magical thinking get anything other than laughs? They encourage a…
Beauty and Strength Power and Compassion Honor and Humility Mirth and Reverence Like the Quakers , Wiccans don't really have official central texts, but a lot of Wiccans seem to be into The Charge of the Goddess , which was written by Doreen Valiente around 1953-54. This list of eight virtues in particular seems to be widely recognized. The eight virtues are four pairs of opposites, which is…
Broadly safe Broadly ethical Compliant with Anthropic’s guidelines Genuinely helpful These are "Claude’s core values" from the "Constitution" for Claude that Anthropic published early in 2026. "In cases of apparent conflict, Claude should generally prioritize these properties in the order in which they’re listed." One interesting comparison is to Asimov's laws of robotics . Law one on not harming…
Temperance Silence Order Resolution Frugality Industry Sincerity Justice Moderation Cleanliness Tranquility Chastity Humility Franklin famously (thanks to his autobiography) wrote his list of 13 virtues at age 20, in 1726, and focused on one per week, allowing four cycles per year. Franklin is one of the virtue-listers in After Virtue , in which MacIntyre points out that his list is different (and…
Modesty, between Diffidence and Shamelessness Temperance, between Insensitiveness and Profligacy Righteous Indignation, between Malice and Envy The Just, between Loss and Profit Liberality, between Meanness and Prodigality Sincerity, between Self-depreciation and Boastfulness Friendliness, between Surliness and Flattery Dignity, between Stubbornness and Subservience Hardiness, between Endurance…
There's something zeitgeisty about Perkins' carpe diem advice, focused on experiences over possessions and fatalistic about the future. I expect writing and promoting the book is a good experience for him. But his advice is not good in general and it doesn't seem like he takes it all that seriously. Perkins several times criticizes the "but I love my job" viewpoint, suggesting that people are…
Dr. Topol offers his adult-in-the-room response to such books as Attia's Outlive and Sinclair's Lifespan . He specifically recommends against taking rapamycin, for example, and doesn't (as far as I could tell) use misleading graphs the way Attia did. He does throw around words like "sequelae" and "senolytics" and narrate the audio book himself. He pronounces GLP-1 as "glip one" and really likes…