A Universe of Sorts
§ Siddharth Bhat
- Why quaternions work better
- DFA to CFG via colimits?
- Why pointless topology is powerful
- Denotational semantics in a few sentences
- Monge Matrix
- Fixpoint as decorator
- Combinatorial generation algorithms
- Perform DP on measures, not indexes.
- Alternative version of Myhill-Nerode
- Polya Enumeration
- Weighted Burnside Lemma
- Cycle index polynomial
- Mnemonics For Symmetric Polynomials
- Uses of minimal string rotation
- Suffix Automata
- Simpson's Paradox
- Myhill Nerode Theorem
- Linearity of expectation for sampling
- Dedekind MacNiellie
- Good and bad combinatorics: intro to counting
- Expected number of turns to generate all numbers
1..N (WIP) - Diameter in single DFS (WIP)
- Min cost flow (WIP)
- Clojure: minimal makefile for REPL driven dev with Neovim
- Delimited continuations
- Never forget monic again
- Weird canonical example of monic and epic: left/right shift
- Playing guitar: being okay with incorrect chords
- Sparse table
- Duval's algorithm
- Amortized complexity from the verifier perspective
- Relationship betwee permutations and runs
- Brouwer's fixed point theorem
- XOR on binary trie
- Inconvergent: beautiful generative art
- Prefix/Border function
- Shortest walk versus shortest path
- Minimal tech stack
- FFT
- Zscoder codeforces rating
- Continuum TTRPG
- Words to know in target language
- DP on subarrays
- Vis editor cheat sheet
- Mean, Median and Jensen's
- The similarity between labellings and representations
- L1 norm is greater than or equal to L2 norm
- Z algorithm
- For a given recurrence, what base cases do I need to implement?
- Number of distinct numbers in a partition
- Splitting f(x)=y into indicators
- Why searching for divisors upto
sqrt(n) works - Heuristics for the prime number theorem
- Sum of absolute differences of an array
- GCD is at most difference of numbers
- implementing GCD and LCM
- Centroid of a tree
- Center of a tree
- Image unshredding as hamiltonian path
- Distance between lines in nD
-
lower_bound binary search with closed intervals - Sliding window implementation style
- Kawaii implementation of
x = min(x, y) - CSES: Counting Towers
- Smallest positive natural which can't be represented as sum of any subset of a set of naturals
- Example of RVs that are pairwise but not 3-way independent.
- Notes on Liam O Connor's thesis: Cogent
- C++
lower_bound, upper_bound API - Books that impart mental models
- Subarrays ~= prefixes
- Operations with modular fractions
- Modular inverse calculation
- The number of pairs
(a,b) such that ab≤x is O(xlogx) - DP as path independence
- Binary search to find rightmost index which does not possess some property
- Correctness of
lower_bound search with half-open intervals - Greedy Coin change: proof by probing
- Clean way to write burnside lemma
- The groupoid interpretation of type theory
- Mnemonics for free = left adjoint
- Where to scratch a cat
- Mnemonic for Specht module actions
- Quotes from 'Braiding Sweetgrass'
- Transfinite recursion: Proof
- Transfinite induction: Proof
- Thoughts on playing Em-Bm
- An explanation for why permutations and linear orders are not naturally isomorphic
- We can't define choice for finite sets in Haskell!
- Geomean is scale independent
- Thoughts on playing Em Bm.
- Induction on natural numbers cannot be derived from other axioms
- Ordinals and cardinals
- Musing about Specht modules
- Every continuous function on [a,b] attains a maximum
- Invisible cities
- Associativity of addition in cubicaltt
- Etymology of fiber bundle F→E→B
- Galois correspondence, functorially
- CubicalTT: sharpening thinking about indexed functions
- Functors to motivate adjuntions
- Madoka Magica: plot thoughts
- Chain rule functorially
- Lagrange multipliers by algebra
- Specht module construction
- Even and odd functions through representation theory
- Greg egan: Orthogonal
- Simplicial approximation: maps can be approximated by simplicial maps (TODO)
- Excision (TODO)
- Marshall: Andrej (TODO)
- Limit is right adjoint to diagonal
- Working out why right adjoints preserve limits.
- Limit/Colimit/Cone/Cocone: the arrows are consistent!
- Representable Functors
- Why terminal object is a limit
- Excluded middle is not false in intuitionistic logic
- Yoneda Lemma and embedding
- GHCID
- Character theory
- Cofibration
- Emily Riehl Contrability as uniqueness
- Cofactor as derivative of determinant
- Homology, the big picture
- Normaliztion by evaluation (TODO)
- Legal Systems very different from ours
- Lefschetz fixed point theorem (TODO)
- Shrinking wedge of circles / Hawaiian earring (TODO)
- Simplicial approxmation of maps (TODO)
- Lebesgue number lemma (TODO)
- Lean internals Cheat Sheet
- MicroUI
- Proof of tree having (V-1) edges
- Creating PDFs to read code
- Bias and gain
- Barycentric subdivision: edge length decreases
- Homotopic maps produce same singular homology: Intuition
- Singular homology: induced homomorphism
- Demoscene tools
- Binaural Beat
- Low pass filter by delaying
- Octaves are double frequency apart (TODO)
- Bias and gain
- Show, don't tell
- Try and think of natural transformations as intertwinings
- Subobject classifier measures how much we need to pay to access fact
- Spectral norm of Hermitian matrix equals largest eigenvalue (TODO)
- Penrose cohomology [TODO ]
- Bicycle wheel proof of Gauss Bonnet (TODO)
- What is Levi Cevita trying to describe (TODO)
- Torsion as giving monodromy of path lifts (TODO)
- Cartan's spiral staircase (TODO)
- Dupin indicatrix (TODO)
- Rodrigues curvature formula (TODO)
- Weingarten map (TODO)
- When maps cannot be lifted to the universal cover
- Nets from Munkres (TODO)
- Limit point compactness from Munkres
- Proof of Heine Borel from Munkres (compact iff closed, bounded)
- Alexandrov topology
- Zeroth singular homology group: Intuition
- Examples of fiber products / pullbacks
- Covariant derivative
- Clackety sounds:
bucklespring - Submersions and immersions
- Ehrsmann connection
- Quotes from the culture
- Lie bracket commutator from exponentiation (TODO)
- Thoughts on proof of fundamental group of unit circle
- Pasting lemma
- Tensoring with base ring has no effect
- Seeing the semidirect product of the dihedral group.
- Animating rotations with quaternion curves
- Mnemonic for hom-tensor and left-right adjoints
- Construction of tensor product: Atiyah macdonald
- Recovering topology from sheaf of functions: Proof from Atiyah Macdonald
- Urhyson's lemma
- Compact Hausdorff spaces are normal
- Stone representation theorem: Proof from Atiyah Macdonald
- Covariant Hom is left exact
- Internal versus External semidirect products
- Splitting of semidirect products in terms of projections
- Tensor is right exact
- Semidirect product as commuting conditions
- Exact sequences for semidirect products; fiber bundles
- Semidirect product is equivalent to splitting of exact sequence
- Intro to topological quantum field theory
- Non examples of algebraic varieties
- Nilradical is intersection of all prime ideals
- Exactness of modules is local
- Quotient by maximal ideal gives a field
- Ring of power series with infinite positive and negative terms
- Mean value theorem and Taylor's theorem. (TODO)
- Cayley Hamilton
- Nakayama's lemma
- Vector fields over the 2 sphere
- Learning to talk with your hands
- Lovecraftisms
- Hairy ball theorem from Sperner's Lemma (TODO)
- CS and type theory: Talks by vovodesky
- Hilbert basis theorem for polynomial rings over fields (TODO)
- Covering spaces
- Wedge Sum and Smash Product
- Quotient topology
- CW Complexes and HEP
- Stable homotopy theory
- Simply connected spaces
- Finitely generated as vector space v/s algebra:
- Weak and Strong Nullstllensatz
- Screen recording for kakoune pull request
- Intuition for why finitely presented abelian groups are isomorphic to product of cyclics
- Euler characteristic of sphere
- John Conway: The symmetries of things
- Semidirect product mnemonic
- Non orthogonal projections
- Why did maxwell choose his EM wave to be light?
- Fast string concatenation in python3
- Split infinitive
- Yoneda from string concatenation
- Right Kan extensions as extending the domain of a functor
- Non standard inner products and unitarity of representations
- take at most 4 letters from 15 letters.
- Flat functions
- Hopf Algebras and combinatorics
- Butcher group
- Neovim frontends
- A semidirect product worked on in great detail
- Direct and Inverse limits
- LEAN 4 overfrom from LEAN together 2021
- BLM master thesis
- Hololive subculture
- RSK correspondence for permutations
- Djikstra's using a segtree
- Markov and chebyshev from a measure theoretic lens
- Among any 51 integers, that are 2 with squares having equal value modulo 100
- 1n+2n+⋯+(n−1)n is divisible by n for odd n
- 103n+1 cannot be written as sum of two cubes
- Coq-club: the meaning of a specification
- SQLite opening
- Old school fonts
- Stalking
syzigies on hackernews - Conditional probability is neither causal nor temporal
- Hook length formula
- The tyranny of light
- Muirhead's inequality
- Rearrangement inequality
- Triangle inequality
- The Heather subculture
- Frobenius Kernel
- Galois theory by "Abel's theorem in problems and solutions"
- Galois theory perspective of the quadratic equation
- Burnside lemma by representation theory.
- Contributing to SAGEmath
- Shadow puppet analogy for entanglement
- Books for contest math
- Analysing simple games
- Linear algebraic proof of the handshaking lemma
- Historical contemporaries
- Rota's twelvefold way
- Counting necklackes with unique elements
- Decomposition of projective space
- Childhood: Playing pokemon gold in japanese
- Tensor is a thing that transforms like a tensor
- Tensor Hom adjunction
- Schur's lemma
- Daughters of destiny
- Stuff I learnt in 2020
- Line bundles, a high level view as I understand them today
- Conversations with a wood carver
- Discrete Riemann Roch
- Conversation with Olaf Klinke
- Topological groups and languages
- The mnemonica stack (TODO)
- Conversation with Alok about how I read
- KMP (Knuth, Morris, Pratt) (TODO)
- Reading C declarations
- Make mnemonics
- Vandermonde and FFT
- Thoughts on blitz chess: 950 ELO
- Periodic tables and make illegal states unrepresentable
- questions on the structure of graphs
- Combinations notation in bijective combinatorics
- Arguments for little endian
- Expectiles
- Depth first search through linear algebra (TODO)
- 2-SAT
- Longest increasing subsequence, step by step (TODO)
- On reading how to rule (TODO)
- Strongly Connected Components via Kosaraju's algorithm
- Articulation points
- Disjoint set union
- Making GDB usable
- Bouncing light clock is an hourglass
- Euler tours
- Representation theory of the symmetric group (TODO)
- Maximum matchings in bipartite graphs
- p-adics, 2's complement, intuition for bit fiddling
- Diameter of a tree
- Catalan numbers as popular candidate votes (TODO)
- The chromatic polynomial (TODO)
- Structure theory of finite endo-functions
- Number of paths in a DAG
- Set partitions
- Integer partitions: Recurrence
- Stars and bars by direct bijection
- DFS and topological sorting
- Tournaments
- Matching problems (TODO)
- Four fundamental subspaces
- WHO list of essential medicines (TODO)
- why is
int i = i allowed in C++? - Kakoune cheatsheet
- Assembly IDE
- Cohomology is like holism
- Flows (TODO)
- Amortized analysis
- Shelly Kegan: death --- Suicide and rationality (TODO)
- Sam harris and jordan peterson: Vancouver 1 (TODO)
- Correctness of binary search
-
readlink -f to access file path - rank/select as compress/decompress
- Remembering Eulerian and Hamiltonian cycles
- Nice way to loop over an array in reverse
- Dynamic Programming: Erik Demaine's lectures
- Accuracy vs precision
- Why is the gradient covariant?
- Politicization of science
- Multi ꙮ cular O: ꙮ / Eye of cthulu
- You can't measure the one way speed of light
- Show me the hand strategy
- Words that can be distinguished from letters if we know the sign of the permutation
- Easy times don't create weak people, they just allow weak people to survive.
- Multiplicative weights algorithm (TODO)
- How to fairly compare groups
- Bijection from
(0, 1) to [0, 1] - Rene Girard
- Noam Chomsky on anarchism (TODO)
- Slavoj Zizek: Violence
- Poverty: Who's to blame?
- Learn Zig in Y minutes
- The algebraic structure of the 'nearest smaller number' question
- Why loss of information is terrifying: Checking that a context-free language is regular is undecidable
- Sciences of the artificial
- Numbering nodes in a tree
- Number of vertices in a rooted tree
- Median minimizes L1 norm
- LISP quine
- A slew of order theoretic and graph theoretic results
- Thebes
- Beethoven
- Neko to follow your cursor around
- Non commuting observables: Light polarization
- Statement expressions and other GCC C extensions
- A quick look at impredicativity
- Data oriented programming in C++
- Retro glitch
- SSA as linear typed language
- Nix weirdness on small machines
- Autodiff over derivative of integrals
- Proof of projective duality
- Preventing the collapse of civilization
- Violent deaths in ancient societies (TODO)
- An elementary example of a thing that is not a vector
- Elementary probability theory (TODO)
- The handshaking lemma
- Git for pure mathematicians
- Mutorch
- Computing the smith normal form
- Laziness for C programmers
- Exact sequence of pointed sets
- What is a syzygy?
- Under the spell of Leibniz's dream
- Normal operators: Decomposition into Hermitian operators
- Readable pointers
- The grassmanian, handwavily
- Lie bracket as linearization of conjugation
- Computational Origami
- Katex in duktape
- Kebab case
- Localization: Introducing epsilons (TODO)
- NaN punning: Storing integers in doubles in JavaScript
- Offline Documentation
- Using Gurobi
- osqp: convex optimizer in 6000 LoC
- stars and bars by generating functions
- This is not a place of honor
- Topological proof of infinitude of primes
- Burnside Theorem
- The Ise Grand shrine
- Edward Kmett's list of useful math
- Cokernel is not sheafy
- Von neumann: foundations of QM
- Discrete schild's ladder
- Derivative of step is dirac delta
- Extended euclidian algorithm
- In a PID, all prime ideals are maximal, geometrically
- Prime numbers as maximal among principal ideals
- Axiom of Choice and Zorn's Lemma
- Local ring in terms of invertibility
- Nullstellensatz for schemes
- Perspectives on Yoneda
- Germs, Stalks, Sheaves of differentiable functions
- Connectedness in terms of continuity
- Intuition for limits in category theory
- Finite topologies and DFS numbering
- Categorical definition of products in painful detail
- Why is the spectrum of a ring called so?
- Ergo proxy
- Satisfied and frustrated equations
- Combinatorial intuition for Fermat's little theorem
- An incorrect derivation of special relativity in 1D
- The geometry and dynamics of magnetic monopoles
- Sanskrit and Sumerian
- Writing Cuneiform
- The code of hammurabi
- The implicit and inverse function theorem
- Whalesong hyperbolic space in detail
- Motivating Djikstra's
- Intuitions for hyperbolic space
- Product of compact spaces in compact
- Hyperbolic groups have solvable word problem
- Elementary uses of Sheaves in complex analysis
- Snake lemma
- Kernel, cokernel, image
- The commutator subgroup
- Simplicity of A5 using PSL(2, 5)
- A5 is not solvable
- Complex orthogonality in terms of projective geometry
- Arithmetic sequences, number of integers in a closed interval
- The arg function, continuity, orientation
- Odd partitions, unique partitions
- Continued fractions, mobius transformations
- Permutations-and-lyndon-factorization
- Graphs are preorders
- Crash course on DCPO: formalizing lambda calculus
- Parallelisable version of maximum sum subarray
- Thoughts on implicit heaps
- Discriminant and Resultant
- Polynomial root finding using QR decomposition
- A hacker's guide to numerical analysis
- Mobius inversion on Incidence Algebras
- Finite differences and Umbral calculus
- Permutahedron
- Lyndon + Christoffel = Convex Hull
- Geometric proof of
e^x >= 1+x, e^(-x) >= 1-x - Ranking and Sorting
- Proof of minkowski convex body theorem
- Burrows Wheeler
- Intuitionstic logic as a Heytig algebra
- Edit distance
- Evolution of bee colonies (TODO)
- Best practices for array indexing
- Algebraic structure for vector clocks
- Networks are now faster than disks
- Einstein-de Haas effect
- Rank-select as adjunction
- Bounding chains: uniformly sample colorings
- Coupling from the past
- Word problems in Russia and America
- Encoding mathematical hieararchies
- Learning code by hearing it
- Your arm can be a spinor
- Self modifying code for function calls: Look ma, I don't need a stack!
- Adjunctions as advice
- Reversible computation as groups on programs
- Blazing fast math rendering on the web
- VC dimension
- Symplectic version of classical mechanics
- Theorems for free
- How to reason with half-open intervals
- How does one build a fusion bomb?
- Christoffel symbols, geometrically
- A natural vector space without an explicit basis
- Cache oblivious B trees
- Krohn-Rhodes decomposition
- Proving block matmul using program analysis
- Why I like algebra over analysis
-
using for cleaner function type typedefs - A walkway of lanterns (TODO)
- Natural transformations
- The hilarious commentary by dinosaure in OCaml git
- How to link against MLIR with CMake
- Energy as triangulaizing state space
- The cutest way to write semidirect products
- My Favourite APLisms
- Proof of chinese remainder theorem on rings
- monic and epic arrows
- The geometry of Lagrange multipliers
- Efficient tree transformations on GPUs (TODO)
- Things I wish I knew when I was learning APL
- Every ideal that is maximal wrt. being disjoint from a multiplicative subset is prime
- Getting started with APL
- SpaceChem was the best compiler I ever used
- Mnemonic for Kruskal and Prim
- Legendre transform
- Cartesian Trees
- DFS numbers as a monotone map
- Self attention? not really
- Coarse structures
- Matroids for greedy algorithms (TODO)
- Grokking Zariski
- My preferred version of quicksort
- Geometric proof of Cauchy Schwarz inequality
- Dataflow analysis using Grobner basis
- Fenwick trees and orbits
- Dirichlet inversion
- Incunabulum for the 21st century: Making the J interpreter compile in 2020
- An example of a sequence whose successive terms get closer together but isn't Cauchy (does not converge)
- Krylov subspace method
- Good reference to the Rete pattern matching algorithm
- Leapfrog Integration
- Comparison of forward and reverse mode AD
- An invitation to homology and cohomology, Part 1 --- Homology
- An invitation to homology and cohomology, Part 2 --- Cohomology
- Stuff I learnt in 2019
- A motivation for p-adic analysis
- Line of investigation to build physical intuition for semidirect products
- Topology is really about computation --- part 2
- Topology is really about computation --- part 1
- PSLQ algorithm: finding integer relations between reals
- Geometric characterization of normal subgroups
- Handy characterization of adding an element into an ideal, proof that maximal ideal is prime
- Radical ideals, nilpotents, and reduced rings
- My disenchantment with abstract interpretation
- Computing equivalent gate sets using grobner bases
- The janus programming language --- Time reversible computation
-
A = B --- A book about proofs of combinatorial closed forms - Generating
k bitsets of a given length n: - Bondi k-calculus
- Topology as an object telling us what zero-locus is closed:
- Vivado toolchain craziness
- What the hell is a Grobner basis? Ideals as rewrite systems
- Lie bracket versus torsion
- Blog post: Weekend paper replication of STOKE, the stochastic superoptimizer
- Collapsing
BlockId, Label, Unique: - Spatial partitioning data structures in molecular dynamics
- Vector: Arthur Whitney and text editors
- Representing CPS in LLVM using the
@coro.* intrinsics - Bug in the LLVM code generator: Lowering of
MO_Add2 and MO_AddWordC - Discrete random distributions with conditioning in 20 lines of haskell
- Everything you know about word2vec is wrong
- Hamiltonian monte carlo, leapfrog integrators, and sympletic geometry
- Small Haskell MCMC implementation
- The smallest implementation of reverse mode AD (autograd) ever:
- Timings of passes in GHC, and low hanging fruit in the backend:
- Varargs in GHC:
T7160.hs - Debugging debug info in GHC
- GHC LLVM code generator: Switch to unreachable
- Concurrency in Haskell
- Handy list of differential geometry definitions
- Lazy programs have space leaks, Strict programs have time leaks
- Presburger arithmetic can represent the Collatz Conjecture
- Using compactness to argue about covers
- Japanese Financial Counting system
- Stephen wolfram's live stream
-
Cleave as a word has some of the most irregular inflections - McCune's single axiom for group theory
-
Word2Vec C code implements gradient descent really weirdly - Arthur Whitney: dense code
- How does one work with arrays in a linear language?
- Linear optimisation is the same as linear feasibility checking
- Quantum computation without complex numbers
- Linguistic fun fact: Comparative Illusion
- Long-form posts:
- Emacs Cheat Sheet
- Coq Cheat Sheet
- Writing Cheat Sheet
- Latex Cheat Sheet
- Architecture Cheat Sheet
- Recipes Cheat Sheet
- History Cheat Sheet
- Words Cheat Sheet
- Clojure Sheat Sheet
- Big list of quotes
- Empathy
- Vim Cheat Sheet
- Big list of Chess
- Big list of shitposting
- Cardistry
- Poems to memorize
- X86 Cheat Sheet
- Common Lisp Cheat Sheet
- Agda Cheat Sheet
- Big list of Hacker news
- Favourite Demoscenes