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Death of the sampling theorem?
tl;dr: A team from Columbia University led by Ken Shepard and Rafa Yuste claims to beat the 100 year old Sampling Theorem [1,2]. Apparently anti-aliasing filters are superfluous now because one can…
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
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General Theory of Neural Networks
From gene regulatory networks to artificial neural networks
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Category Theory Illustrated – Natural Transformations
I didn’t invent categories to study functors; I invented them to study natural transformations. — Saunders Mac Lane
724
The Two Egg Problem
Analysis of the classic "dropping two eggs from a building" interview question
725
Sierpiński Triangle? In My Bitwise and?
Exploring a peculiar bit-twiddling hack at the intersection of 1980s geek sensibilities.
726
Markov Chains for programmers
Materials for book: “Markov Chains for programmers”
727
Eller’s Algorithm (2012)
Eller's algorithm creates 'perfect' mazes, having only a single path between any two cells, one row at a time. The algorithm itself is incredibly fast, and far more memory efficient than other popular algorithms (such as Prim's and Kruskal's) requiring storage proportional to only a single row. This makes it possible…
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SQL is syntactic sugar for relational algebra
This idea is particularly sticky because it was more or less true 50 years ago, and it's a passable mental model to use when learning sql. But it's an inadequate mental model for building new sql frontends, designing new query languages, or writing tools likes ORMs that abstract over sql.
729
Entropy explained, with sheep (2016)
An explorable blog post about entropy, with sheep.
730
Why is the Quintic Unsolvable?
In this article, I hope to convince you that the quintic equation is unsolvable, in the sense that I can’t write down the solution to the equation \[ ax^5 + bx^4 + cx^3 + dx^2 + ex + f = 0 \] using only addition, subtraction, multiplication, division, raising to an integer power, and taking an integer root. In fact, I…
731
Mr. Baby Paint and accidentally discovering a new cellular automata
On building Mr. Baby Paint, a radically simple co-op drawing app for toddlers & accidentally discovering a flood-fill cellular automata, plus developing pixel-fattening algorithms for bitmap fonts.
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The stack monoid revisited
This is a followup to my previous post on the stack monoid, but is intended to be self-contained.
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The Bitter Prediction
The Ivory Tower is a blog about software engineering and development philosophy by Anders Sundman.
735
Infinite Grid of Resistors
There is a well-known puzzle based on the premise of an �infinite� grid of resistors connecting adjacent nodes of a square lattice. A small portion of such a grid is illustrated below.
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100 Years to Solve an Integral (2020)
The integral of sec(x) is well known to any beginners calculus student. Yet this integral was once a major outstanding maths problem. It was first introduced...
737
500 days of math
I recently crossed 500 days of practicing math daily with Math Academy. I wrote about my experience after 100 days here. TL;DR: I am still very impressed by the Math Academy system and highly…
738
Solving Fizz Buzz with Cosines
Fizz Buzz is a counting game that has become oddly popular in the world of computer programming as a simple test of basic programming skills. The rules of the game are straightforward. Players say the numbers aloud in order beginning with one. Whenever a number is divisible by 3, they say 'Fizz' instead. If it is…
739
Ramanujan's Easiest Formula
A while ago I decided to figure out how to prove one of Ramanujan’s formulas. I feel this is the sort of thing every mathematician should try at least once. I picked the easiest one I could f…
740
A Better Strategy for Hangman
Learn the optimal strategy for playing Hangman.
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Kalman filters and functional programming
A paper on Kalman filtering and functional folds that I alluded to previously has been split into several papers and posted online.
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It's OK to compare floating-points for equality
NB: The title of this post is an intentional clickbait. Even though I do stand for its statement, a more honest one would be something like: It's NOT OK to compare floating-points using epsilons.
745
Dynamic Programming vs. Divide-and-Conquer (2018)
In this article I’m trying to explain the difference/similarities between dynamic programing and divide and conquer approaches based on two examples - binary search and minimum edit distance (Levenshtein distance)
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The unreasonable effectiveness of conditional probabilities
I have been steeping myself in probabilistic exercises recently, because it’s an area where I feel like I could benefit from building better intuition. I have found a recurring key to solving many of them: conditioning on an intermediary state, and then computing the value of that intermediary state separately. This…
748
Diffusion Forcing: Next-Token Prediction Meets Full-Sequence Diffusion
Official Website of Diffusion Forcing
749
OpenAI, the Partition Principle, and Mathematics
By the time I got out of bed yesterday, I had three people ask me if I'd seen the OpenAI announcement that the Partition Principle does not (...)
750
Why there is no Hitchhiker’s Guide to Mathematics for Programmers
For those who aren’t regular readers: as a followup to this post, there are four posts detailing the basic four methods of proof, with intentions to detail some more advanced proof techniques in the future. You can find them on this blog’s primers page. Do you really want to get better at mathematics? Remember when…