A Universe of Sorts

§ Siddharth Bhat

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