A Universe of Sorts

§ Siddharth Bhat

  1. Examples of fiber products / pullbacks
  2. Covariant derivative
  3. Clackety sounds: bucklespring
  4. Bicycle wheel proof of Gauss Bonnet
  5. What is Levi Cevita trying to describe
  6. Torsion as giving monodromy of path lifts
  7. Cartan's spiral staircase
  8. Submersions and immersions
  9. Ehrsmann connection
  10. Quotes from the culture
  11. Penrose cohomology [WIP]
  12. Lie bracket commutator from exponentiation (WIP)
  13. Thoughts on proof of fundamental group of unit circle
  14. Lefschetz fixed point theorem (WIP)
  15. Pasting lemma
  16. Tensoring with base ring has no effect
  17. Projective resolution / fundamental theorem of homological algebra (WIP)
  18. Seeing the semidirect product of the dihedral group.
  19. Animating rotations with quaternion curves
  20. Mnemonic for hom-tensor and left-right adjoints
  21. Construction of tensor product: Atiyah macdonald
  22. Dupin indicatrix (WIP)
  23. Rodrigues curvature formula (WIP)
  24. Weingarten map (WIP)
  25. Recovering topology from sheaf of functions: Proof from Atiyah Macdonald
  26. Urhyson's lemma (WIP)
  27. Compact Hausdorff spaces are normal
  28. Stone representation theorem: Proof from Atiyah Macdonald
  29. Covariant Hom is left exact
  30. Internal versus External semidirect products
  31. Splitting of semidirect products in terms of projections
  32. Tensor is right exact
  33. Semidirect product as commuting conditions
  34. Exact sequences for semidirect products; fiber bundles
  35. Semidirect product is equivalent to splitting of exact sequence
  36. Intro to topological quantum field theory
  37. Spectral norm of Hermitian matrix equals largest eigenvalue (WIP)
  38. Non examples of algebraic varieties
  39. Nilradical is intersection of all prime ideals
  40. Exactness of modules is local
  41. Quotient by maximal ideal gives a field
  42. Ring of power series with infinite positive and negative terms
  43. Mean value theorem and Taylor's theorem. (TODO)
  44. Cayley Hamilton
  45. Nakayama's lemma (WIP)
  46. vector fields over the 2 sphere (WIP)
  47. Learning to talk with your hands
  48. Lovecraftisms
  49. Hairy ball theorem from Sperner's Lemma (WIP)
  50. CS and type theory: Talks by vovodesky
  51. Hilbert basis theorem for polynomial rings over fields (WIP)
  52. Covering spaces (WIP)
  53. Van Kampen theorem (WIP)
  54. Wedge Sum and Smash Product
  55. Quotient topology
  56. CW Complexes and HEP
  57. Stable homotopy theory
  58. Tychonoff theorem (WIP)
  59. Simply connected spaces
  60. Finitely generated as vector space v/s algebra:
  61. Weak and Strong Nullstllensatz
  62. Screen recording for kakoune pull request
  63. Intuition for why finitely presented abelian groups are isomorphic to product of cyclics
  64. Alternative orderings for segtrees (WIP)
  65. Group structure of nim games (WIP)
  66. Euler characteristic of sphere
  67. John Conway: The symmetries of things
  68. Semidirect product mnemonic
  69. Non orthogonal projections
  70. Why did maxwell choose his EM wave to be light?
  71. Fast string concatenation in python3
  72. Split infinitive
  73. Yoneda from string concatenation (WIP)
  74. Right Kan extensions as extending the domain of a functor (WIP)
  75. Non standard inner products and unitarity of representations
  76. take at most 4 letters from 15 letters.
  77. Flat functions
  78. Hopf Algebras and combinatorics (WIP)
  79. Butcher group
  80. Neovim frontends
  81. A semidirect product worked on in great detail
  82. Direct and Inverse limits
  83. LEAN 4 overfrom from LEAN together 2021
  84. BLM master thesis
  85. Hololive subculture
  86. RSK correspondence for permutations
  87. Djikstra's using a segtree
  88. Markov and chebyshev from a measure theoretic lens
  89. Among any 51 integers, that are 2 with squares having equal value modulo 100
  90. 1n+2n++(n1)n1^n + 2^n + \dots + (n-1)^n is divisible by nn for odd nn
  91. 103n+110^{3n+1} cannot be written as sum of two cubes
  92. dual of applicative [WIP]
  93. The dual of traversable [WIP]
  94. Coq-club: the meaning of a specification
  95. SQLite opening
  96. Old school fonts
  97. Stalking syzigies on hackernews
  98. Conditional probability is neither causal nor temporal
  99. Hook length formula
  100. The tyranny of light
  101. Muirhead's inequality [WIP]
  102. Rearrangement inequality
  103. Triangle inequality
  104. The Heather subculture
  105. Frobenius Kernel
  106. Galois theory by "Abel's theorem in problems and solutions"
  107. Galois theory perspective of the quadratic equation
  108. Burnside lemma by representation theory.
  109. Contributing to SAGEmath
  110. Shadow puppet analogy for entanglement
  111. Books for contest math
  112. Analysing simple games
  113. Using the bound library (WIP)
  114. Linear algebraic proof of the handshaking lemma
  115. Historical contemporaries
  116. Rota's twelvefold way
  117. Counting necklackes with unique elements
  118. Decomposition of projective space
  119. Childhood: Playing pokemon gold in japanese
  120. Tensor is a thing that transforms like a tensor
  121. Tensor Hom adjunction
  122. Schur's lemma
  123. Newton polygon and simplification, blowing up (WIP)
  124. Daughters of destiny
  125. Stuff I learnt in 2020
  126. Method of types in information theory(WIP)
  127. Line bundles, a high level view as I understand them today
  128. Conversations with a wood carver
  129. Resolution and first order logic (WIP)
  130. Kruskal card trick (WIP)
  131. Discrete Riemann Roch (WIP)
  132. Conversation with Olaf Klinke
  133. Topological groups and languages
  134. Killing fields (WIP)
  135. The mnemonica stack (WIP)
  136. Conversation with Alok about how I read
  137. KMP (Knuth, Morris, Pratt) (WIP)
  138. Reading C declarations
  139. Make mnemonics
  140. Vandermonde and FFT
  141. Thoughts on blitz chess: 950 ELO
  142. Periodic tables and make illegal states unrepresentable
  143. Big list of questions on the structure of graphs
  144. Combinations notation in bijective combinatorics
  145. Arguments for little endian
  146. Expectiles
  147. Depth first search through linear algebra (WIP)
  148. 2-SAT
  149. Longest increasing subsequence, step by step (WIP)
  150. On reading how to rule (WIP)
  151. Strongly Connected Components via Kosaraju's algorithm
  152. Articulation points
  153. Disjoint set union
  154. Making GDB usable
  155. Bouncing light clock is an hourglass
  156. Euler tours
  157. Representation theory of the symmetric group (WIP)
  158. Maximum matchings in bipartite graphs
  159. p-adics, 2's complement, intuition for bit fiddling
  160. Diameter of a tree
  161. Catalan numbers as popular candidate votes (WIP)
  162. The chromatic polynomial (WIP)
  163. Structure theory of finite endo-functions
  164. Number of paths in a DAG
  165. Set partitions
  166. Integer partitions: Recurrence
  167. Stars and bars by direct bijection
  168. DFS and topological sorting
  169. Tournaments
  170. Matching problems (TODO)
  171. Four fundamental subspaces
  172. WHO list of essential medicines (WIP)
  173. why is int i = i allowed in C++?
  174. Kakoune cheatsheet
  175. Assembly IDE
  176. Cohomology is like holism
  177. Flows (WIP)
  178. Amortized analysis
  179. Shelly Kegan: death --- Suicide and rationality (WIP)
  180. Sam harris and jordan peterson: Vancouver 1 (WIP)
  181. Correctness of binary search
  182. readlink -f to access file path
  183. rank/select as compress/decompress
  184. Remembering Eulerian and Hamiltonian cycles
  185. Nice way to loop over an array in reverse
  186. Dynamic Programming: Erik Demaine's lectures
  187. Accuracy vs precision
  188. Why is the gradient covariant?
  189. Politicization of science
  190. Multi ꙮ cular O: ꙮ / Eye of cthulu
  191. You can't measure the one way speed of light
  192. Show me the hand strategy
  193. Words that can be distinguished from letters if we know the sign of the permutation
  194. Easy times don't create weak people, they just allow weak people to survive.
  195. Multiplicative weights algorithm (TODO)
  196. How to fairly compare groups
  197. Z algorithm (TODO)
  198. Bijection from (0, 1) to [0, 1]
  199. Rene Girard
  200. Noam Chomsky on anarchism (WIP)
  201. Slavoj Zizek: Violence
  202. Poverty: Who's to blame?
  203. Learn Zig in Y minutes
  204. The algebraic structure of the 'nearest smaller number' question
  205. Why loss of information is terrifying: Checking that a context-free language is regular is undecidable
  206. Sciences of the artificial
  207. Numbering nodes in a tree
  208. Number of vertices in a rooted tree
  209. Median minimizes L1 norm
  210. LISP quine
  211. A slew of order theoretic and graph theoretic results
  212. Thebes
  213. Beethoven
  214. Neko to follow your cursor around
  215. Non commuting observables: Light polarization
  216. Statement expressions and other GCC C extensions
  217. A quick look at impredicativity
  218. Data oriented programming in C++
  219. Retro glitch
  220. SSA as linear typed language
  221. Nix weirdness on small machines
  222. Autodiff over derivative of integrals
  223. Proof of projective duality
  224. Preventing the collapse of civilization
  225. Violent deaths in ancient societies (WIP)
  226. An elementary example of a thing that is not a vector
  227. Elementary probability theory (WIP)
  228. The handshaking lemma
  229. Git for pure mathematicians
  230. Mutorch
  231. Computing the smith normal form
  232. Laziness for C programmers
  233. Exact sequence of pointed sets
  234. What is a syzygy?
  235. Under the spell of Leibniz's dream
  236. Normal operators: Decomposition into Hermitian operators
  237. Readable pointers
  238. The grassmanian, handwavily
  239. Lie bracket as linearization of conjugation
  240. Computational Origami
  241. Katex in duktape
  242. Kebab case
  243. Localization: Introducing epsilons (WIP)
  244. NaN punning: Storing integers in doubles in JavaScript
  245. Offline Documentation
  246. Using Gurobi
  247. osqp: convex optimizer in 6000 LoC
  248. stars and bars by generating functions
  249. This is not a place of honor
  250. Topological proof of infinitude of primes
  251. Burnside Theorem
  252. The Ise Grand shrine
  253. Edward Kmett's list of useful math
  254. Cokernel is not sheafy
  255. Von neumann: foundations of QM
  256. Discrete schild's ladder
  257. Derivative of step is dirac delta
  258. Extended euclidian algorithm
  259. In a PID, all prime ideals are maximal, geometrically
  260. Prime numbers as maximal among principal ideals
  261. Axiom of Choice and Zorn's Lemma
  262. Local ring in terms of invertibility
  263. Nullstellensatz for schemes
  264. Perspectives on Yoneda
  265. Germs, Stalks, Sheaves of differentiable functions
  266. Connectedness in terms of continuity
  267. Intuition for limits in category theory
  268. Finite topologies and DFS numbering
  269. Categorical definition of products in painful detail
  270. Why is the spectrum of a ring called so?
  271. Ergo proxy
  272. Satisfied and frustrated equations
  273. Combinatorial intuition for Fermat's little theorem
  274. An incorrect derivation of special relativity in 1D
  275. The geometry and dynamics of magnetic monopoles
  276. Sanskrit and Sumerian
  277. Writing Cuneiform
  278. The code of hammurabi
  279. The implicit and inverse function theorem
  280. Whalesong hyperbolic space in detail
  281. Motivating Djikstra's
  282. Intuitions for hyperbolic space
  283. Product of compact spaces in compact
  284. Hyperbolic groups have solvable word problem
  285. Elementary uses of Sheaves in complex analysis
  286. Snake lemma
  287. Kernel, cokernel, image
  288. The commutator subgroup
  289. Simplicity of A5 using PSL(2, 5)
  290. A5 is not solvable
  291. Complex orthogonality in terms of projective geometry
  292. Arithmetic sequences, number of integers in a closed interval
  293. The arg function, continuity, orientation
  294. Odd partitions, unique partitions
  295. Continued fractions, mobius transformations
  296. Permutations-and-lyndon-factorization
  297. Graphs are preorders
  298. Crash course on DCPO: formalizing lambda calculus
  299. Parallelisable version of maximum sum subarray
  300. Thoughts on implicit heaps
  301. Discriminant and Resultant
  302. Polynomial root finding using QR decomposition
  303. A hacker's guide to numerical analysis
  304. Mobius inversion on Incidence Algebras
  305. Finite differences and Umbral calculus
  306. Permutahedron
  307. Lyndon + Christoffel = Convex Hull
  308. Geometric proof of e^x >= 1+x, e^(-x) >= 1-x
  309. Ranking and Sorting
  310. Proof of minkowski convex body theorem
  311. Burrows Wheeler
  312. Intuitionstic logic as a Heytig algebra
  313. Edit distance
  314. Evolution of bee colonies (WIP)
  315. Best practices for array indexing
  316. Algebraic structure for vector clocks
  317. Networks are now faster than disks
  318. Einstein-de Haas effect
  319. Rank-select as adjunction
  320. Bounding chains: uniformly sample colorings
  321. Coupling from the past
  322. Word problems in Russia and America
  323. Encoding mathematical hieararchies
  324. Learning code by hearing it
  325. Your arm can be a spinor
  326. Self modifying code for function calls: Look ma, I don't need a stack!
  327. Adjunctions as advice
  328. Reversible computation as groups on programs
  329. Blazing fast math rendering on the web
  330. VC dimension
  331. Symplectic version of classical mechanics
  332. Theorems for free
  333. How to reason with half-open intervals
  334. How does one build a fusion bomb?
  335. Christoffel symbols, geometrically
  336. A natural vector space without an explicit basis
  337. Cache oblivious B trees
  338. Krohn-Rhodes decomposition
  339. Proving block matmul using program analysis
  340. Why I like algebra over analysis
  341. using for cleaner function type typedefs
  342. A walkway of lanterns (WIP)
  343. Natural transformations
  344. The hilarious commentary by dinosaure in OCaml git
  345. How to link against MLIR with CMake
  346. Energy as triangulaizing state space
  347. The cutest way to write semidirect products
  348. My Favourite APLisms
  349. Proof of chinese remainder theorem on rings
  350. monic and epic arrows
  351. The geometry of Lagrange multipliers
  352. Efficient tree transformations on GPUs (WIP)
  353. Things I wish I knew when I was learning APL
  354. Every ideal that is maximal wrt. being disjoint from a multiplicative subset is prime
  355. Getting started with APL
  356. SpaceChem was the best compiler I ever used
  357. Mnemonic for Kruskal and Prim
  358. Legendre transform
  359. Cartesian Trees
  360. DFS numbers as a monotone map
  361. Self attention? not really
  362. Coarse structures
  363. Matroids for greedy algorithms (WIP)
  364. Grokking Zariski
  365. My preferred version of quicksort
  366. Geometric proof of Cauchy Schwarz inequality
  367. Dataflow analysis using Grobner basis
  368. Fenwick trees and orbits
  369. Dirichlet inversion
  370. Incunabulum for the 21st century: Making the J interpreter compile in 2020
  371. An example of a sequence whose successive terms get closer together but isn't Cauchy (does not converge)
  372. Krylov subspace method
  373. Good reference to the Rete pattern matching algorithm
  374. Leapfrog Integration
  375. Comparison of forward and reverse mode AD
  376. An invitation to homology and cohomology, Part 1 --- Homology
  377. An invitation to homology and cohomology, Part 2 --- Cohomology
  378. Stuff I learnt in 2019
  379. A motivation for p-adic analysis
  380. Line of investigation to build physical intuition for semidirect products
  381. Topology is really about computation --- part 2
  382. Topology is really about computation --- part 1
  383. PSLQ algorithm: finding integer relations between reals
  384. Geometric characterization of normal subgroups
  385. Handy characterization of adding an element into an ideal, proof that maximal ideal is prime
  386. Radical ideals, nilpotents, and reduced rings
  387. My disenchantment with abstract interpretation
  388. Computing equivalent gate sets using grobner bases
  389. The janus programming language --- Time reversible computation
  390. A = B --- A book about proofs of combinatorial closed forms
  391. Generating k bitsets of a given length n:
  392. Bondi k-calculus
  393. Topology as an object telling us what zero-locus is closed:
  394. Vivado toolchain craziness
  395. What the hell is a Grobner basis? Ideals as rewrite systems
  396. Lie bracket versus torsion
  397. Blog post: Weekend paper replication of STOKE, the stochastic superoptimizer
  398. Collapsing BlockId, Label, Unique:
  399. Spatial partitioning data structures in molecular dynamics
  400. Vector: Arthur Whitney and text editors
  401. Representing CPS in LLVM using the @coro.* intrinsics
  402. Bug in the LLVM code generator: Lowering of MO_Add2 and MO_AddWordC
  403. Discrete random distributions with conditioning in 20 lines of haskell
  404. Everything you know about word2vec is wrong
  405. Hamiltonian monte carlo, leapfrog integrators, and sympletic geometry
  406. Small Haskell MCMC implementation
  407. The smallest implementation of reverse mode AD (autograd) ever:
  408. Timings of passes in GHC, and low hanging fruit in the backend:
  409. Varargs in GHC: T7160.hs
  410. Debugging debug info in GHC
  411. GHC LLVM code generator: Switch to unreachable
  412. Concurrency in Haskell
  413. Handy list of differential geometry definitions
  414. Lazy programs have space leaks, Strict programs have time leaks
  415. Presburger arithmetic can represent the Collatz Conjecture
  416. Using compactness to argue about covers
  417. Japanese Financial Counting system
  418. Stephen wolfram's live stream
  419. Cleave as a word has some of the most irregular inflections
  420. McCune's single axiom for group theory
  421. Word2Vec C code implements gradient descent really weirdly
  422. Arthur Whitney: dense code
  423. How does one work with arrays in a linear language?
  424. Linear optimisation is the same as linear feasibility checking
  425. Quantum computation without complex numbers
  426. Linguistic fun fact: Comparative Illusion
  427. Long-form posts:
  428. Big list of emacs
  429. Big list of Coq
  430. Big list of writing
  431. Big list of Latex
  432. Big list of Architecture
  433. Big list of Recipes
  434. Big list of history
  435. Big list of words
  436. Big list of Music
  437. Big list of Social Science
  438. Big list of clojure
  439. Big list of quotes
  440. Empathy
  441. Big list of Vim
  442. Big list of Chess
  443. Big list of shitposting
  444. Cardistry
  445. Poems to memorize
  446. X86