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The Halting Problem is a terrible example of NP-Harder
It's a justifiable copout, but it's still a copout.
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When would you ever want bubblesort? (2023)
There are very few universal rules in software engineering, but there are are a lot of near-universal principles. Things like "prefer composition to...
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Introduction to Digital Filters (2024)
INTRODUCTION TO DIGITAL FILTERS WITH AUDIO APPLICATIONS
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Parsing Advances
I find myself writing yet another toy parser, as one does during a Christmas break. It roughly follows Resilient LL Parsing Tutorial. Not because I need resilience, but mostly because I find producing a syntax tree and a collection of diagnostics a more natural fit for the problem than bailing out on the first error.
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Monte Carlo Crash Course: Sampling
In the previous chapter, we assumed that we can uniformly randomly sample our domain. However, it’s not obvious how to actually do so—in fact, how can a deterministic computer even generate random numbers? 1
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The exceptional Jordan algebra (2020)
In the early 1930s, Pascual Jordan attempted to formalise the algebraic properties of Hermitian matrices. In particular: Hermitian matrices form a real vector space: we can add and subtract Hermiti…
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The Hat, the Spectre and SAT Solvers (2024)
Introduction In this blog post you are going to read about two things:
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Numbering should start at zero (1982)
To denote the subsequence of natural numbers 2, 3, ..., 12 without the pernicious three dots, four conventions are open to us
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The economics behind "Basic Economy" – A masterclass in price discrimination
Basic Economy fares are ultra-restricted airline tickets that offer a lower base price in exchange for fewer benefits than standard economy class. Introduced by major U.S. carriers in the 2010s, these fares have become a widespread strategy for market segmentation - a textbook example of price discrimination in…
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Code golfing a tiny demo using maths and a pinch of insanity
The number of characters was 464 characters at first, but thanks to the community it got reduced further, and the article updated accordingly.
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Lambda Calculus and Lisp, part 1
The first of a series of envisioned blog posts on lambda calculus, and Lisp. It’s unclear exactly where to start: there is a whole heap of interesting issues, both theoretical and in terms of concrete implementations, which tangle and interconnect. A particular application of lambda calculus is a very salient…
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Transducer: Composition, abstraction, performance (2018)
Transducer: Composition, Abstraction, Performance
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Convolutions, Polynomials and Flipped Kernels
This is a post about multiplying polynomials, convolution sums and the connection between them.
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Is Fortran better than Python for teaching basics of numerical linear algebra?
Quarto Academic Website Template adapted by Dr. Gang He
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Analytic Combinatorics – A Worked Example
Chris Grossack's math blog and professional website.
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Derivation and Intuition behind Poisson distribution
Made in Notion, the connected workspace where AI agents and teams organize docs, projects and knowledge together.
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Using obscure graph theory to solve programming languages problems
Usually I write about solutions to problems I’ve worked out, but I’ve found myself increasingly becoming interesting in where solutions come from. Maybe it’s because I’ve been reading Boorstin’s excellent The Discoverers , which I’d strongly recommend.
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Derivatives and Logarithms of 3D Transforms
Understanding derivatives and logarithms of transforms
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Weighting an average to minimize variance
How would you allocate money to a set of independent assets with to minimize volatility if some assets are more volatile than others?
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Fold-... and Monoids
A blog about computers, functional languages, Lisp, and Scheme.
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Estimating Logarithms
While reading through the fantastic book *[The Lost Art of Logarithms](https://www.lostartoflogarithms.com/)* by [Charles Petzold](https://www.charlespetzold.com/) I was nerd-sniped by a [simple method](https://www.lostartoflogarithms.com/chapter04/) of estimating the logarithm of any number base 10. According to the…
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Minimal Boolean Formulas (2011)
28 . That's the minimum number of AND or OR operators you need in order to write any Boolean function of five variables. Alex Healy and I computed that in April 2010. Until then, I believe no one had ever known that little fact. This post describes how we computed it and how we almost got scooped by Knuth's Volume 4A…
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Entropy Attacks
The conventional wisdom is that hashing more entropy sources can't hurt: if H is any modern cryptographic hash function then H(x,y,z) is at least as good a random number as H(x,y), no matter how awful z is. So we pile one source on top of another, hashing them all together and hoping that at least one of them is good.
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Collatz's Ant
This is a brief continuation of a previous post ( Repo ), which introduced such visualization for collatz sequences based on Langton’s Ant .
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Solving LinkedIn Queens Using Haskell
Solving LinkedIn Queens in the LogicT monad
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A cute proof that makes e natural
Po-Shen Loh explains why Euler's number e is natural using only precalculus: one exponential curve has tangent slope 1 at the y-axis, which leads to the compound interest limit.
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Reflections on Sudoku, or the Impossibility of Systematizing Thought
I reflect on the Entscheidungsproblem how it relates to Sudoku solvers. It's a little weird. .