1801
How are PCA and SVD related?
Exploring the relationship between singular value decomposition and principal component analysis.
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
1802
What is an elliptic curve? (2019)
The informal definition of an elliptic curve is simple. The formal definition is more involved.
1803
Algorithms for making interesting organic simulations
Article explaining simulation algorithms that produce complex organic behaviours, starting with the classic physarum algorithm from Jeff Jones.
1804
Damas-Hindley-Milner inference two ways
What is Damas-Hindley-Milner?
1805
More than half of adults in U.S. say they lack basic statistical understanding
Many people in the U.S. believe that their statistical knowledge is limited, but they would rely on statistics for decision-making more if they understood statistics better, according to a new study led by a Penn State researcher.
1806
Let’s talk about PAKE
The first rule of PAKE is: nobody ever wants to talk about PAKE. The second rule of PAKE is that this is a shame, because PAKE — which stands for Password Authenticated Key Exchange — is actually o…
1807
Turing's topological proof that every written alphabet is finite (2010)
Recently one of my colleagues was reading Alan Turing’s groundbreaking 1936 article “On Computable Numbers with an Application to the Entscheidungsproblem.” This is the article in…
1808
Encoding tic-tac-toe in 15 bits
I recently stumbled upon a blog post by Alejandra González (a.k.a @blyxyas) that seeks to compress a tic-tac-toe game state into as few bits as possible. She arrived at a solution in 18 bits. This got me thinking, can we do better?
1809
Einstein-Bohr debate settled once and for all
In Steven Pinker’s guest post from last week, there’s one bit to which I never replied. Steve wrote: After all, in many areas Einstein was no Einstein. You [Scott] above all could speak…
1810
How to store a chess position in 26 bytes (2022)
Made in Notion, the connected workspace where AI agents and teams organize docs, projects and knowledge together.
1811
Calculating Pi: My Attempt at Breaking the Pi World Record
Before I go into the specifics of my record attempt, it is important for you to have some background information. Over the past few years I have been steadily acquiring server hardware to increase my knowledge of system administration and cyber security. This is not only for personal growth: it has also helped me…
1812
Three-Valued Logic
Making decision despite missing SQL data (NULL): How to avoid OR…IS NULL in the WHERE clause.
1813
Principal Component Analysis
In the previous article in this series we distinguished between two kinds of unsupervised learning (cluster analysis and dimensionality reduction) and discussed the former in some detail. In this installment we turn our attention to the later. In dimensionality reduction we seek a function $f : \mathbb{R}^n \mapsto…
1814
Zero Knowledge Proofs: An illustrated primer (2014)
One of the best things about modern cryptography is the beautiful terminology. You could start any number of punk bands (or Tumblrs) named after cryptography terms like ‘hard-core predicate&#…
1815
Solving Probabilistic Tic-Tac-Toe
This morning, I came accross Cameron Sun’s Probabilistic Tic-Tac-Toe on HN . However, the comments were disappointing, with people proposing probabilistic models, linear programming, minimax algorithms, and heuristic evaluations to develop AI approaches for the game, none of which quite correct. In this post, I’ll…
1816
Understanding the power of bitwise operators
When learning a new programming language, there is usually a table in the documentation that shows the various operators that can be used with numbers.
1817
Fast Perfect Hashing
A perfect hash function is one that is collision-free. By implication, the hash must be at least as many bytes as the key and the function is theoretically reversible, though not always tractably so. In other words, perfect hashing is a special case of encryption. Because the hash is no smaller than the key, the…
1818
How to make fake data look meaningful
If you are trying to trick somebody with your data, never share the raw data; only share the conclusions. Bonus points if you can’t share the data because it is somehow priviledged or a trade secret. The last thing you want is to allow other people to evaluate your analysis and possibly challenge your conclusions.
1819
The Strangest Book on the Theory of Computation (2009)
Based on the description of the book in the World Scientific Press catalogue, I asked my university library to order a book entitled Automat...
1820
Logic Puzzles with Prolog (2017)
Solving Logic Puzzles with Prolog
1821
Shenanigans With Hash Tables
One reason to know how your data structures work is so that when your problem has unusual constraints you can tweak how they work to fit the problem better or work faster. In this article I’ll talk about four different fun tweaks to the concept of a hash table that I made in the process of using hash tables to…
1822
1823
Consistency Models
Jepsen analyzes the safety properties of distributed systems–most notably, identifying violations of consistency models. But what are consistency models? What phenomena do they allow? What kind of consistency does a given program really need?
1824
Efficient simulation through linear algebra
I spent a lot of time working on a project in which physically plausible simulation of soft materials with pressure chambers was a key part, and in doing so, we managed to improve a part of our simulation by a significant amount. I was very happy with how this small part of the whole system turned out, and I've been…
1825
The number line freaks me out (2016)
“Welcome to math class, boys and girls! Today we’ll be drawing a picture that gestures beyond the limits of mortal comprehension.”
1826
The case against geometric algebra (2024)
Every once in a while the internet gets talking about Geometric Algebra (henceforth GA) and how it’s a new theory of math that fixes everything that’s wrong with linear algebra and multivariable calculus. When I come across this stance I am compelled to respond with something like: “wait wait, it’s not true! GA is…
1827
1828
Category Theory, Syntactically (2016)
A blog mostly on math, physics, and computer science.
1829
Lace: A New Kind of Cellular Automata Where Links Matter
This article is about a new kind of simple computational rule ("LACE rules" running on LACE, the Link Automata Computing Engine platform) which, when applied locally on a grid of cells, demonstrates fascinating emergent "artificial life" behavior.
1830
Regression to the mean is the main reason ineffective treatments appear to work
Jump to follow-up “Statistical regression to the mean predicts that patients selected for abnormalcy will, on the average, tend to improve. We argue that most improvements attributed to the p…