A Universe of Sorts

§ Siddharth Bhat

  1. Why quaternions work better
  2. DFA to CFG via colimits?
  3. Why pointless topology is powerful
  4. Denotational semantics in a few sentences
  5. Monge Matrix
  6. Fixpoint as decorator
  7. Combinatorial generation algorithms
  8. Perform DP on measures, not indexes.
  9. Alternative version of Myhill-Nerode
  10. Polya Enumeration
  11. Weighted Burnside Lemma
  12. Cycle index polynomial
  13. Mnemonics For Symmetric Polynomials
  14. Uses of minimal string rotation
  15. Suffix Automata
  16. Simpson's Paradox
  17. Myhill Nerode Theorem
  18. Linearity of expectation for sampling
  19. Dedekind MacNiellie
  20. Good and bad combinatorics: intro to counting
  21. Expected number of turns to generate all numbers 1..N (WIP)
  22. Diameter in single DFS (WIP)
  23. Min cost flow (WIP)
  24. Clojure: minimal makefile for REPL driven dev with Neovim
  25. Delimited continuations
  26. Never forget monic again
  27. Weird canonical example of monic and epic: left/right shift
  28. Playing guitar: being okay with incorrect chords
  29. Sparse table
  30. Duval's algorithm
  31. Amortized complexity from the verifier perspective
  32. Relationship betwee permutations and runs
  33. Brouwer's fixed point theorem
  34. XOR on binary trie
  35. Inconvergent: beautiful generative art
  36. Prefix/Border function
  37. Shortest walk versus shortest path
  38. Minimal tech stack
  39. FFT
  40. Zscoder codeforces rating
  41. Continuum TTRPG
  42. Words to know in target language
  43. DP on subarrays
  44. Vis editor cheat sheet
  45. Mean, Median and Jensen's
  46. The similarity between labellings and representations
  47. L1 norm is greater than or equal to L2 norm
  48. Z algorithm
  49. For a given recurrence, what base cases do I need to implement?
  50. Number of distinct numbers in a partition
  51. Splitting f(x)=yf(x) = y into indicators
  52. Why searching for divisors upto sqrt(n) works
  53. Heuristics for the prime number theorem
  54. Sum of absolute differences of an array
  55. GCD is at most difference of numbers
  56. implementing GCD and LCM
  57. Centroid of a tree
  58. Center of a tree
  59. Image unshredding as hamiltonian path
  60. Distance between lines in nD
  61. lower_bound binary search with closed intervals
  62. Sliding window implementation style
  63. Kawaii implementation of x = min(x, y)
  64. CSES: Counting Towers
  65. Smallest positive natural which can't be represented as sum of any subset of a set of naturals
  66. Example of RVs that are pairwise but not 3-way independent.
  67. Notes on Liam O Connor's thesis: Cogent
  68. C++ lower_bound, upper_bound API
  69. Books that impart mental models
  70. Subarrays ~= prefixes
  71. Operations with modular fractions
  72. Modular inverse calculation
  73. The number of pairs (a,b) such that ab≤x is O(xlogx)
  74. DP as path independence
  75. Binary search to find rightmost index which does not possess some property
  76. Correctness of lower_bound search with half-open intervals
  77. Greedy Coin change: proof by probing
  78. Clean way to write burnside lemma
  79. The groupoid interpretation of type theory
  80. Mnemonics for free = left adjoint
  81. Where to scratch a cat
  82. Mnemonic for Specht module actions
  83. Quotes from 'Braiding Sweetgrass'
  84. Transfinite recursion: Proof
  85. Transfinite induction: Proof
  86. Thoughts on playing Em-Bm
  87. An explanation for why permutations and linear orders are not naturally isomorphic
  88. We can't define choice for finite sets in Haskell!
  89. Geomean is scale independent
  90. Thoughts on playing Em Bm.
  91. Induction on natural numbers cannot be derived from other axioms
  92. Ordinals and cardinals
  93. Musing about Specht modules
  94. Every continuous function on [a,b][a, b] attains a maximum
  95. Invisible cities
  96. Associativity of addition in cubicaltt
  97. Etymology of fiber bundle FEBF \rightarrow E \rightarrow B
  98. Galois correspondence, functorially
  99. CubicalTT: sharpening thinking about indexed functions
  100. Functors to motivate adjuntions
  101. Madoka Magica: plot thoughts
  102. Chain rule functorially
  103. Lagrange multipliers by algebra
  104. Specht module construction
  105. Even and odd functions through representation theory
  106. Greg egan: Orthogonal
  107. Simplicial approximation: maps can be approximated by simplicial maps (TODO)
  108. Excision (TODO)
  109. Marshall: Andrej (TODO)
  110. Limit is right adjoint to diagonal
  111. Working out why right adjoints preserve limits.
  112. Limit/Colimit/Cone/Cocone: the arrows are consistent!
  113. Representable Functors
  114. Why terminal object is a limit
  115. Excluded middle is not false in intuitionistic logic
  116. Yoneda Lemma and embedding
  117. GHCID
  118. Character theory
  119. Cofibration
  120. Emily Riehl Contrability as uniqueness
  121. Cofactor as derivative of determinant
  122. Homology, the big picture
  123. Normaliztion by evaluation (TODO)
  124. Legal Systems very different from ours
  125. Lefschetz fixed point theorem (TODO)
  126. Shrinking wedge of circles / Hawaiian earring (TODO)
  127. Simplicial approxmation of maps (TODO)
  128. Lebesgue number lemma (TODO)
  129. Lean internals Cheat Sheet
  130. MicroUI
  131. Proof of tree having (V-1) edges
  132. Creating PDFs to read code
  133. Bias and gain
  134. Barycentric subdivision: edge length decreases
  135. Homotopic maps produce same singular homology: Intuition
  136. Singular homology: induced homomorphism
  137. Demoscene tools
  138. Binaural Beat
  139. Low pass filter by delaying
  140. Octaves are double frequency apart (TODO)
  141. Bias and gain
  142. Show, don't tell
  143. Try and think of natural transformations as intertwinings
  144. Subobject classifier measures how much we need to pay to access fact
  145. Spectral norm of Hermitian matrix equals largest eigenvalue (TODO)
  146. Penrose cohomology [TODO ]
  147. Bicycle wheel proof of Gauss Bonnet (TODO)
  148. What is Levi Cevita trying to describe (TODO)
  149. Torsion as giving monodromy of path lifts (TODO)
  150. Cartan's spiral staircase (TODO)
  151. Dupin indicatrix (TODO)
  152. Rodrigues curvature formula (TODO)
  153. Weingarten map (TODO)
  154. When maps cannot be lifted to the universal cover
  155. Nets from Munkres (TODO)
  156. Limit point compactness from Munkres
  157. Proof of Heine Borel from Munkres (compact iff closed, bounded)
  158. Alexandrov topology
  159. Zeroth singular homology group: Intuition
  160. Examples of fiber products / pullbacks
  161. Covariant derivative
  162. Clackety sounds: bucklespring
  163. Submersions and immersions
  164. Ehrsmann connection
  165. Quotes from the culture
  166. Lie bracket commutator from exponentiation (TODO)
  167. Thoughts on proof of fundamental group of unit circle
  168. Pasting lemma
  169. Tensoring with base ring has no effect
  170. Seeing the semidirect product of the dihedral group.
  171. Animating rotations with quaternion curves
  172. Mnemonic for hom-tensor and left-right adjoints
  173. Construction of tensor product: Atiyah macdonald
  174. Recovering topology from sheaf of functions: Proof from Atiyah Macdonald
  175. Urhyson's lemma
  176. Compact Hausdorff spaces are normal
  177. Stone representation theorem: Proof from Atiyah Macdonald
  178. Covariant Hom is left exact
  179. Internal versus External semidirect products
  180. Splitting of semidirect products in terms of projections
  181. Tensor is right exact
  182. Semidirect product as commuting conditions
  183. Exact sequences for semidirect products; fiber bundles
  184. Semidirect product is equivalent to splitting of exact sequence
  185. Intro to topological quantum field theory
  186. Non examples of algebraic varieties
  187. Nilradical is intersection of all prime ideals
  188. Exactness of modules is local
  189. Quotient by maximal ideal gives a field
  190. Ring of power series with infinite positive and negative terms
  191. Mean value theorem and Taylor's theorem. (TODO)
  192. Cayley Hamilton
  193. Nakayama's lemma
  194. Vector fields over the 2 sphere
  195. Learning to talk with your hands
  196. Lovecraftisms
  197. Hairy ball theorem from Sperner's Lemma (TODO)
  198. CS and type theory: Talks by vovodesky
  199. Hilbert basis theorem for polynomial rings over fields (TODO)
  200. Covering spaces
  201. Wedge Sum and Smash Product
  202. Quotient topology
  203. CW Complexes and HEP
  204. Stable homotopy theory
  205. Simply connected spaces
  206. Finitely generated as vector space v/s algebra:
  207. Weak and Strong Nullstllensatz
  208. Screen recording for kakoune pull request
  209. Intuition for why finitely presented abelian groups are isomorphic to product of cyclics
  210. Euler characteristic of sphere
  211. John Conway: The symmetries of things
  212. Semidirect product mnemonic
  213. Non orthogonal projections
  214. Why did maxwell choose his EM wave to be light?
  215. Fast string concatenation in python3
  216. Split infinitive
  217. Yoneda from string concatenation
  218. Right Kan extensions as extending the domain of a functor
  219. Non standard inner products and unitarity of representations
  220. take at most 4 letters from 15 letters.
  221. Flat functions
  222. Hopf Algebras and combinatorics
  223. Butcher group
  224. Neovim frontends
  225. A semidirect product worked on in great detail
  226. Direct and Inverse limits
  227. LEAN 4 overfrom from LEAN together 2021
  228. BLM master thesis
  229. Hololive subculture
  230. RSK correspondence for permutations
  231. Djikstra's using a segtree
  232. Markov and chebyshev from a measure theoretic lens
  233. Among any 51 integers, that are 2 with squares having equal value modulo 100
  234. 1n+2n++(n1)n1^n + 2^n + \dots + (n-1)^n is divisible by nn for odd nn
  235. 103n+110^{3n+1} cannot be written as sum of two cubes
  236. Coq-club: the meaning of a specification
  237. SQLite opening
  238. Old school fonts
  239. Stalking syzigies on hackernews
  240. Conditional probability is neither causal nor temporal
  241. Hook length formula
  242. The tyranny of light
  243. Muirhead's inequality
  244. Rearrangement inequality
  245. Triangle inequality
  246. The Heather subculture
  247. Frobenius Kernel
  248. Galois theory by "Abel's theorem in problems and solutions"
  249. Galois theory perspective of the quadratic equation
  250. Burnside lemma by representation theory.
  251. Contributing to SAGEmath
  252. Shadow puppet analogy for entanglement
  253. Books for contest math
  254. Analysing simple games
  255. Linear algebraic proof of the handshaking lemma
  256. Historical contemporaries
  257. Rota's twelvefold way
  258. Counting necklackes with unique elements
  259. Decomposition of projective space
  260. Childhood: Playing pokemon gold in japanese
  261. Tensor is a thing that transforms like a tensor
  262. Tensor Hom adjunction
  263. Schur's lemma
  264. Daughters of destiny
  265. Stuff I learnt in 2020
  266. Line bundles, a high level view as I understand them today
  267. Conversations with a wood carver
  268. Discrete Riemann Roch
  269. Conversation with Olaf Klinke
  270. Topological groups and languages
  271. The mnemonica stack (TODO)
  272. Conversation with Alok about how I read
  273. KMP (Knuth, Morris, Pratt) (TODO)
  274. Reading C declarations
  275. Make mnemonics
  276. Vandermonde and FFT
  277. Thoughts on blitz chess: 950 ELO
  278. Periodic tables and make illegal states unrepresentable
  279. questions on the structure of graphs
  280. Combinations notation in bijective combinatorics
  281. Arguments for little endian
  282. Expectiles
  283. Depth first search through linear algebra (TODO)
  284. 2-SAT
  285. Longest increasing subsequence, step by step (TODO)
  286. On reading how to rule (TODO)
  287. Strongly Connected Components via Kosaraju's algorithm
  288. Articulation points
  289. Disjoint set union
  290. Making GDB usable
  291. Bouncing light clock is an hourglass
  292. Euler tours
  293. Representation theory of the symmetric group (TODO)
  294. Maximum matchings in bipartite graphs
  295. p-adics, 2's complement, intuition for bit fiddling
  296. Diameter of a tree
  297. Catalan numbers as popular candidate votes (TODO)
  298. The chromatic polynomial (TODO)
  299. Structure theory of finite endo-functions
  300. Number of paths in a DAG
  301. Set partitions
  302. Integer partitions: Recurrence
  303. Stars and bars by direct bijection
  304. DFS and topological sorting
  305. Tournaments
  306. Matching problems (TODO)
  307. Four fundamental subspaces
  308. WHO list of essential medicines (TODO)
  309. why is int i = i allowed in C++?
  310. Kakoune cheatsheet
  311. Assembly IDE
  312. Cohomology is like holism
  313. Flows (TODO)
  314. Amortized analysis
  315. Shelly Kegan: death --- Suicide and rationality (TODO)
  316. Sam harris and jordan peterson: Vancouver 1 (TODO)
  317. Correctness of binary search
  318. readlink -f to access file path
  319. rank/select as compress/decompress
  320. Remembering Eulerian and Hamiltonian cycles
  321. Nice way to loop over an array in reverse
  322. Dynamic Programming: Erik Demaine's lectures
  323. Accuracy vs precision
  324. Why is the gradient covariant?
  325. Politicization of science
  326. Multi ꙮ cular O: ꙮ / Eye of cthulu
  327. You can't measure the one way speed of light
  328. Show me the hand strategy
  329. Words that can be distinguished from letters if we know the sign of the permutation
  330. Easy times don't create weak people, they just allow weak people to survive.
  331. Multiplicative weights algorithm (TODO)
  332. How to fairly compare groups
  333. Bijection from (0, 1) to [0, 1]
  334. Rene Girard
  335. Noam Chomsky on anarchism (TODO)
  336. Slavoj Zizek: Violence
  337. Poverty: Who's to blame?
  338. Learn Zig in Y minutes
  339. The algebraic structure of the 'nearest smaller number' question
  340. Why loss of information is terrifying: Checking that a context-free language is regular is undecidable
  341. Sciences of the artificial
  342. Numbering nodes in a tree
  343. Number of vertices in a rooted tree
  344. Median minimizes L1 norm
  345. LISP quine
  346. A slew of order theoretic and graph theoretic results
  347. Thebes
  348. Beethoven
  349. Neko to follow your cursor around
  350. Non commuting observables: Light polarization
  351. Statement expressions and other GCC C extensions
  352. A quick look at impredicativity
  353. Data oriented programming in C++
  354. Retro glitch
  355. SSA as linear typed language
  356. Nix weirdness on small machines
  357. Autodiff over derivative of integrals
  358. Proof of projective duality
  359. Preventing the collapse of civilization
  360. Violent deaths in ancient societies (TODO)
  361. An elementary example of a thing that is not a vector
  362. Elementary probability theory (TODO)
  363. The handshaking lemma
  364. Git for pure mathematicians
  365. Mutorch
  366. Computing the smith normal form
  367. Laziness for C programmers
  368. Exact sequence of pointed sets
  369. What is a syzygy?
  370. Under the spell of Leibniz's dream
  371. Normal operators: Decomposition into Hermitian operators
  372. Readable pointers
  373. The grassmanian, handwavily
  374. Lie bracket as linearization of conjugation
  375. Computational Origami
  376. Katex in duktape
  377. Kebab case
  378. Localization: Introducing epsilons (TODO)
  379. NaN punning: Storing integers in doubles in JavaScript
  380. Offline Documentation
  381. Using Gurobi
  382. osqp: convex optimizer in 6000 LoC
  383. stars and bars by generating functions
  384. This is not a place of honor
  385. Topological proof of infinitude of primes
  386. Burnside Theorem
  387. The Ise Grand shrine
  388. Edward Kmett's list of useful math
  389. Cokernel is not sheafy
  390. Von neumann: foundations of QM
  391. Discrete schild's ladder
  392. Derivative of step is dirac delta
  393. Extended euclidian algorithm
  394. In a PID, all prime ideals are maximal, geometrically
  395. Prime numbers as maximal among principal ideals
  396. Axiom of Choice and Zorn's Lemma
  397. Local ring in terms of invertibility
  398. Nullstellensatz for schemes
  399. Perspectives on Yoneda
  400. Germs, Stalks, Sheaves of differentiable functions
  401. Connectedness in terms of continuity
  402. Intuition for limits in category theory
  403. Finite topologies and DFS numbering
  404. Categorical definition of products in painful detail
  405. Why is the spectrum of a ring called so?
  406. Ergo proxy
  407. Satisfied and frustrated equations
  408. Combinatorial intuition for Fermat's little theorem
  409. An incorrect derivation of special relativity in 1D
  410. The geometry and dynamics of magnetic monopoles
  411. Sanskrit and Sumerian
  412. Writing Cuneiform
  413. The code of hammurabi
  414. The implicit and inverse function theorem
  415. Whalesong hyperbolic space in detail
  416. Motivating Djikstra's
  417. Intuitions for hyperbolic space
  418. Product of compact spaces in compact
  419. Hyperbolic groups have solvable word problem
  420. Elementary uses of Sheaves in complex analysis
  421. Snake lemma
  422. Kernel, cokernel, image
  423. The commutator subgroup
  424. Simplicity of A5 using PSL(2, 5)
  425. A5 is not solvable
  426. Complex orthogonality in terms of projective geometry
  427. Arithmetic sequences, number of integers in a closed interval
  428. The arg function, continuity, orientation
  429. Odd partitions, unique partitions
  430. Continued fractions, mobius transformations
  431. Permutations-and-lyndon-factorization
  432. Graphs are preorders
  433. Crash course on DCPO: formalizing lambda calculus
  434. Parallelisable version of maximum sum subarray
  435. Thoughts on implicit heaps
  436. Discriminant and Resultant
  437. Polynomial root finding using QR decomposition
  438. A hacker's guide to numerical analysis
  439. Mobius inversion on Incidence Algebras
  440. Finite differences and Umbral calculus
  441. Permutahedron
  442. Lyndon + Christoffel = Convex Hull
  443. Geometric proof of e^x >= 1+x, e^(-x) >= 1-x
  444. Ranking and Sorting
  445. Proof of minkowski convex body theorem
  446. Burrows Wheeler
  447. Intuitionstic logic as a Heytig algebra
  448. Edit distance
  449. Evolution of bee colonies (TODO)
  450. Best practices for array indexing
  451. Algebraic structure for vector clocks
  452. Networks are now faster than disks
  453. Einstein-de Haas effect
  454. Rank-select as adjunction
  455. Bounding chains: uniformly sample colorings
  456. Coupling from the past
  457. Word problems in Russia and America
  458. Encoding mathematical hieararchies
  459. Learning code by hearing it
  460. Your arm can be a spinor
  461. Self modifying code for function calls: Look ma, I don't need a stack!
  462. Adjunctions as advice
  463. Reversible computation as groups on programs
  464. Blazing fast math rendering on the web
  465. VC dimension
  466. Symplectic version of classical mechanics
  467. Theorems for free
  468. How to reason with half-open intervals
  469. How does one build a fusion bomb?
  470. Christoffel symbols, geometrically
  471. A natural vector space without an explicit basis
  472. Cache oblivious B trees
  473. Krohn-Rhodes decomposition
  474. Proving block matmul using program analysis
  475. Why I like algebra over analysis
  476. using for cleaner function type typedefs
  477. A walkway of lanterns (TODO)
  478. Natural transformations
  479. The hilarious commentary by dinosaure in OCaml git
  480. How to link against MLIR with CMake
  481. Energy as triangulaizing state space
  482. The cutest way to write semidirect products
  483. My Favourite APLisms
  484. Proof of chinese remainder theorem on rings
  485. monic and epic arrows
  486. The geometry of Lagrange multipliers
  487. Efficient tree transformations on GPUs (TODO)
  488. Things I wish I knew when I was learning APL
  489. Every ideal that is maximal wrt. being disjoint from a multiplicative subset is prime
  490. Getting started with APL
  491. SpaceChem was the best compiler I ever used
  492. Mnemonic for Kruskal and Prim
  493. Legendre transform
  494. Cartesian Trees
  495. DFS numbers as a monotone map
  496. Self attention? not really
  497. Coarse structures
  498. Matroids for greedy algorithms (TODO)
  499. Grokking Zariski
  500. My preferred version of quicksort
  501. Geometric proof of Cauchy Schwarz inequality
  502. Dataflow analysis using Grobner basis
  503. Fenwick trees and orbits
  504. Dirichlet inversion
  505. Incunabulum for the 21st century: Making the J interpreter compile in 2020
  506. An example of a sequence whose successive terms get closer together but isn't Cauchy (does not converge)
  507. Krylov subspace method
  508. Good reference to the Rete pattern matching algorithm
  509. Leapfrog Integration
  510. Comparison of forward and reverse mode AD
  511. An invitation to homology and cohomology, Part 1 --- Homology
  512. An invitation to homology and cohomology, Part 2 --- Cohomology
  513. Stuff I learnt in 2019
  514. A motivation for p-adic analysis
  515. Line of investigation to build physical intuition for semidirect products
  516. Topology is really about computation --- part 2
  517. Topology is really about computation --- part 1
  518. PSLQ algorithm: finding integer relations between reals
  519. Geometric characterization of normal subgroups
  520. Handy characterization of adding an element into an ideal, proof that maximal ideal is prime
  521. Radical ideals, nilpotents, and reduced rings
  522. My disenchantment with abstract interpretation
  523. Computing equivalent gate sets using grobner bases
  524. The janus programming language --- Time reversible computation
  525. A = B --- A book about proofs of combinatorial closed forms
  526. Generating k bitsets of a given length n:
  527. Bondi k-calculus
  528. Topology as an object telling us what zero-locus is closed:
  529. Vivado toolchain craziness
  530. What the hell is a Grobner basis? Ideals as rewrite systems
  531. Lie bracket versus torsion
  532. Blog post: Weekend paper replication of STOKE, the stochastic superoptimizer
  533. Collapsing BlockId, Label, Unique:
  534. Spatial partitioning data structures in molecular dynamics
  535. Vector: Arthur Whitney and text editors
  536. Representing CPS in LLVM using the @coro.* intrinsics
  537. Bug in the LLVM code generator: Lowering of MO_Add2 and MO_AddWordC
  538. Discrete random distributions with conditioning in 20 lines of haskell
  539. Everything you know about word2vec is wrong
  540. Hamiltonian monte carlo, leapfrog integrators, and sympletic geometry
  541. Small Haskell MCMC implementation
  542. The smallest implementation of reverse mode AD (autograd) ever:
  543. Timings of passes in GHC, and low hanging fruit in the backend:
  544. Varargs in GHC: T7160.hs
  545. Debugging debug info in GHC
  546. GHC LLVM code generator: Switch to unreachable
  547. Concurrency in Haskell
  548. Handy list of differential geometry definitions
  549. Lazy programs have space leaks, Strict programs have time leaks
  550. Presburger arithmetic can represent the Collatz Conjecture
  551. Using compactness to argue about covers
  552. Japanese Financial Counting system
  553. Stephen wolfram's live stream
  554. Cleave as a word has some of the most irregular inflections
  555. McCune's single axiom for group theory
  556. Word2Vec C code implements gradient descent really weirdly
  557. Arthur Whitney: dense code
  558. How does one work with arrays in a linear language?
  559. Linear optimisation is the same as linear feasibility checking
  560. Quantum computation without complex numbers
  561. Linguistic fun fact: Comparative Illusion
  562. Long-form posts:
  563. Emacs Cheat Sheet
  564. Coq Cheat Sheet
  565. Writing Cheat Sheet
  566. Latex Cheat Sheet
  567. Architecture Cheat Sheet
  568. Recipes Cheat Sheet
  569. History Cheat Sheet
  570. Words Cheat Sheet
  571. Clojure Sheat Sheet
  572. Big list of quotes
  573. Empathy
  574. Vim Cheat Sheet
  575. Big list of Chess
  576. Big list of shitposting
  577. Cardistry
  578. Poems to memorize
  579. X86 Cheat Sheet
  580. Common Lisp Cheat Sheet
  581. Agda Cheat Sheet
  582. Big list of Hacker news
  583. Favourite Demoscenes