The Curious Engineer

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A Neighborhood of Infinity

blog.sigfpe.com

MathHaskellScience

’05’10’15’20’25
Posts
306 from 13 May 2005 to 27 Apr 2026
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now and then (3 in the last year)
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personal blog
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2026 3

  1. Some type constructors are tensor products
  2. A Simple Switch Makes Code Differentiable
  3. "What does it take to be a hero?" revisited

2024 2

  1. What does it take to be a hero? and other questions from statistical mechanics.
  2. How to hide information from yourself in a solo RPG

2023 2

  1. What does it mean for a monad to be strong?
  2. Constructing Clifford Algebras using the Super Tensor Product

2020 1

  1. Some pointers to things not in this blog

2018 2

  1. Why is nuclear fusion so hard?
  2. Running from the past

2017 7

  1. A tail we don't need to wag
  2. What is a photon?
  3. Self-referential logic via self-referential circuits
  4. A relaxation technique
  5. Logarithms and exponentials of functions
  6. Building free arrows from components
  7. Addressing Pieces of State with Profunctors

2016 2

  1. Expectation-Maximization with Less Arbitrariness
  2. Dimensionful Matrices

2014 4

  1. Cofree meets Free
  2. Types, and two approaches to problem solving
  3. The Monad called Free
  4. Reinversion Revisited

2013 4

  1. Distributed computing with alien technology
  2. What stops us defining Truth?
  3. Why Heisenberg can't stop atomic collapse
  4. Aliasing and the Heisenberg uncertainty principle.

2012 8

  1. Shuffles, Bayes' theorem and continuations.
  2. A pictorial proof of the hairy ball theorem
  3. Generalised entropy
  4. Overloading Python list comprehension
  5. Using Lawvere theories to combine effects
  6. Lawvere theories made a bit easier
  7. Some parallels between classical and quantum mechanics
  8. Lossless decompression and the generation of random samples

2011 13

  1. Quick and dirty reinversion of control
  2. Computing errors with square roots of infinitesimals.
  3. Profunctors in Haskell
  4. The Infinitude of the Primes
  5. An elementary way to approach Fourier transforms
  6. Simulating visual artifacts with Fourier optics
  7. Fast forwarding lrand48()
  8. Perturbation confusion confusion
  9. Image-based rendering and some ancient history
  10. Generalising Gödel's Theorem with Multiple Worlds. Part IV.
  11. Build Yourself a Bluetooth Controlled Six-Legged Robot
  12. Generalising Gödel's Theorem with Multiple Worlds. Part III.
  13. Quine Central

2010 20

  1. Generalising Gödel's Theorem with Multiple Worlds. Part II.
  2. Generalising Gödel's Theorem with Multiple Worlds. Part I.
  3. Beating the odds with entangled qubits
  4. Statistical Fingertrees
  5. On Removing Singularities from Rational Functions
  6. Automatic even/odd splitting
  7. Constraining Types with Regular Expressions
  8. Divided Differences and the Tomography of Types
  9. Automatic Divided Differences
  10. Death to Hydrae (or the operational semantics of ordinals)
  11. Constructing Intermediate Values
  12. Optimising pointer subtraction with 2-adic integers.
  13. On representing some real numbers exactly
  14. A Partial Ordering of some Category Theory applied to Haskell
  15. Products, Limits and Parametric Polymorphism
  16. The Categorification of the Naturals
  17. Tagging Monad Transformer Layers
  18. Target Enumeration with the Euler Characteristic. Parts 1 & 2
  19. Counting Targets using the Euler Characteristic, Part 1
  20. Monads are Trees with Grafting

2009 21

  1. Where do monads come from?
  2. Programming with impossible functions, or how to get along without monads.
  3. Memoizing Polymorphic Functions with High School Algebra and Quantifiers
  4. Buffon's Needle, the Easy Way
  5. "What Category do Haskell Types and Functions Live In?"
  6. Vectors, Invariance, and Math APIs
  7. test, ignore
  8. Finite Differences of Types
  9. More Parsing With Best First Search
  10. A Monad for Combinatorial Search with Heuristics
  11. Automata and the A-D-E classification.
  12. Hashing Molecules
  13. Trace Diagrams with Monads
  14. The Three Projections of Doctor Futamura
  15. Faster than a speeding photon
  16. Dinatural Transformations and Coends
  17. Beyond Monads
  18. Beyond Regular Expressions: More Incremental String Matching
  19. Fast incremental regular expression matching with monoids
  20. Haskell Monoids and their Uses
  21. Rewriting Monadic Expressions with Template Haskell

2008 35

  1. The Mother of all Monads
  2. An Approach to Algorithm Parallelisation
  3. Some thoughts on reasoning and monads
  4. From Monoids to Monads
  5. Operads and their Monads
  6. What's the use of a transfinite ordinal?
  7. Untangling with Continued Fractions: part 5
  8. On writing Python one-liners.
  9. Untangling with Continued Fractions: Part 4
  10. Two Papers and a Presentation
  11. Untangling with Continued Fractions: Part 3
  12. Untangling with Continued Fractions: Part 2
  13. Untangling with Continued Fractions: Part 1
  14. Untangling with Continued Fractions: Part 0
  15. Hopf Algebra = Group + Monad
  16. The Fibonacci Numbers, Coalgebraicaly
  17. MSFP 2008
  18. A blessed man's formula for holey containers
  19. Categories of polynomials and comonadic plumbing
  20. Drugs, Kate Moss, and Intuitionistic Logic
  21. Life in a Lazy Universe
  22. The Interchange Law
  23. Desingularisation and its applications
  24. You Could Have Defined Natural Transformations
  25. Infinitesimal rotations and Lie algebras
  26. Negative Probabilities
  27. Transforming a comonad with a monad
  28. Comonadic Arrays
  29. What does topology have to do with computability? Reloaded.
  30. What is Topology?
  31. How many functions are there from () to ()? (Updated)
  32. A Third Order Quine in Three Languages
  33. Purely functional recursive types in Haskell and Python
  34. The Type that Should Not Be
  35. What does topology have to do with computability?

2007 37

  1. What's all this E8 stuff about then? Part 3.
  2. The IO Monad for People who Simply Don't Care
  3. What's all this E8 stuff about then? Part 2.
  4. What's all this E8 stuff about then? Part 1.
  5. A Small Combinatorial Library
  6. A Blobby Language
  7. Using Thermonuclear Pennies to Embed Complex Numbers as Types
  8. How can it possibly be that we can exhaustively search an infinite space in a finite time?
  9. Arboreal Isomorphisms from Nuclear Pennies
  10. Tries and their Derivatives
  11. The Antidiagonal
  12. I'll have a Buchburger with fries
  13. Data and Codata
  14. Death>Dishonour =/=> ~Dishonour>~Death
  15. Monads from Algebra and the the Gray Code from Groups
  16. How to write tolerably efficient optimzation code without really trying...
  17. Haskell Incarnate
  18. Homeland Security Threat Level Monad
  19. The Trivial Monad
  20. The curious rotational memory of the Electron, Part 2
  21. The Curious Rotational Memory of the Electron, Part 1
  22. The Angel Problem has been Solved! (Maybe)
  23. The Shor Quantum Error Correcting Code (and a Monad for Heat)
  24. Independence, entanglement and decoherence with the quantum monad
  25. Monads, Vector Spaces and Quantum Mechanics pt. II
  26. The allure of LaTeX
  27. Monads in C pt. III
  28. Monads in C, pt. II
  29. Monads for vector spaces, probability and quantum mechanics pt. I
  30. The Essence of Quantum Computing
  31. Modular arithmetic with regular expressions
  32. Exceptions, Disjunctions and Continuations
  33. Comonads and reading from the future
  34. The Monads Hidden Behind Every Zipper
  35. Fox's Ubiquitous Free Derivative pt. 2
  36. Fox's Ubiquitous Free Derivative
  37. Oriented Fish and Hairy Balls

2006 92

  1. Tying Knots Generically
  2. Evaluating cellular automata is comonadic
  3. Why isn't ListT [] a monad?
  4. A Yonedic Addendum
  5. How Telescopes Really Work and What You Can See Through Them
  6. From Löb's Theorem to Spreadsheet Evaluation
  7. Oliver Heaviside
  8. Reverse Engineering Machines with the Yoneda Lemma
  9. Variable substitution gives a...
  10. The Poincare Conjecture on the Radio
  11. Monads, a Field Guide
  12. Games, Strategies and the Self-Composition of the List Monad.
  13. Negative Databases
  14. Infinitesimal Types
  15. You can fire me, but you can't stop me working!
  16. Practical Synthetic Differential Geometry
  17. Local and global side effects with monad transformers
  18. More Low Cost Geometric Algebra
  19. Learn Maths with Haskell
  20. Geometric Algebra for Free!
  21. Algebraic Topology in Haskell
  22. What can we measure? Part II
  23. What can we measure? Part I
  24. You Could Have Invented Monads! (And Maybe You Already Have.)
  25. SIGGRAPH, 2B0ST0N6
  26. Using markets to aggregate information
  27. "I love the Hahn-Banach Theorem"
  28. What is a Saros?
  29. Do Particles Exist?
  30. Iannis Xenakis and Formalized Music
  31. Even More Numb3rs
  32. Laws of Form: An Opinion
  33. k-calculus and Special Relativity
  34. How to Divide by Three
  35. A Taylor Series for Types
  36. Fun with Derivatives of Containers
  37. Monads, Kleisli Arrows, Comonads and other Rambling Thoughts
  38. A Monadic Lightswitch
  39. Solar Astronomy
  40. Defining the Reals
  41. Exceptional Objects
  42. Quantum Mechanics and Probability Theory
  43. Two Kinds of Mathematics
  44. Monads Without Types
  45. Writing a pure functional lazy call-by-name compiler
  46. Grok Haskell Monad Transformers
  47. The Most Amazing Development Environment Ever
  48. The Solar Corona Problem
  49. Zog, The Devil and Me.
  50. S4 and Partial Evaluation
  51. A Modal Logic of Near Certainty?
  52. Mongruences
  53. The Minority Game
  54. Anti-Foundation and Strong Extensionality
  55. SIGFPE's Law
  56. Quantum Probability
  57. A Neat Proof Technique
  58. The General Theory of Self-Reproducing Programs
  59. Stanislaw Lem has Passed Away
  60. The Most Amazing and Mysterious Thing in All of Mathematics
  61. 6
  62. Sets, Classes and Voodoo
  63. The Representation of Integers by Quadratic Forms
  64. Category Theory Screws You Up!
  65. What can I do with adjoints? And Lemma 28.
  66. Answers and questions
  67. Homotopies between proofs and between programs
  68. Cellular automaton puzzle
  69. Coalgebras and Automata
  70. Hyperfun!
  71. It's a square, square world!
  72. Blind Games
  73. When is one thing equal to some other thing?
  74. An Actual Application of Fractal Dimension
  75. A Cautionary Tale for Would-Be Generalisers
  76. Counter-counterfactual Computation
  77. The ambiguous operator, pt.2
  78. The ambiguous operator, pt. 1
  79. The cut rule and reading seminars
  80. Mathematics has Competition
  81. Young babies count
  82. What's the most implausible but true mathematical proposition?
  83. Is Mathematics too Easy?
  84. An End to Coding Theory
  85. The Flyspeck Project
  86. Biggest Test of Benford's Law?
  87. De Rham Cohomology and Computer Algebra
  88. Geometry is Innate
  89. Eleven Reasons to use Haskell as a Mathematician
  90. You're needed!
  91. General Relativity for Dummies
  92. Self-Reference in the Real World

2005 53

  1. Theorem Proving and Code Generation
  2. Rant: Just for kids?
  3. Bees can fly after all!
  4. A Game of Logic
  5. Opinion: A Farewell to Angles
  6. Quadratic Residues and Acoustics
  7. A Fabulous Biplane
  8. This post brought to you by the number six...
  9. Alternative Logic
  10. Quantum Mechanics and the Fourier-Legendre Transform over a Semiring
  11. Are Men Innately Better than Women at Mathematics?
  12. Tetris and matrices over semirings
  13. The 100 Greatest Theorems
  14. A Certain 24th Root
  15. Of Partitions and Primes
  16. Adjoints
  17. Infinitesimals
  18. Caustics and Catastrophes
  19. The Unnatural Naturals
  20. The Alternative Numbers
  21. Toric Varieties
  22. Absence of Evidence is Evidence of Absence
  23. A Neighbourhood of Infinity
  24. ars mathematica
  25. The Use and Abuse of Godel's Theorem
  26. The Resurrection of God Incarnate
  27. Wavelet Noise
  28. The Product of All Primes is 4π2
  29. The Sleeping Beauty Problem
  30. Automatic Differentiation
  31. Exact Markov Chain Monte Carlo
  32. Calculators are Bad
  33. Black Hole Information Loss
  34. Mathematics Sighting
  35. The Quantum Computer Condition
  36. An Unfortunate Legacy
  37. Formal Power Series and Haskell
  38. Rithmomachia
  39. Who Invented That Symbol?
  40. Heaviside Operators and Umbral Calculus
  41. Quantum Systems are Big
  42. Oh! To live forever!
  43. Two Papers
  44. More Laws of Form
  45. Primer
  46. Laws of Form
  47. I'm a descendant of Bessel and Gauss
  48. Dual Photography Part II
  49. Derivatives of Regular Expressions
  50. Fermat's Last Theorem 'Disproved'
  51. Dual Photography Part I
  52. Diagram Chasing
  53. The Neighbourhood of Infinity is now Open