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An illustrated introduction to linear algebra
Chapter 1: Row vs column picture
New
The latest blog posts to take off on Hacker News. 2,391 posts.
212
Packing the world for longest lines of sight
I have a side project to find the longest line of sight on the planet 1 using a novel Total Viewshed algorithm . At a resolution of 3 arc-seconds (~92m x 92m), the planet contains around 4.5 billion elevation samples 2 . Now obviously we don’t need to calculate the visibility between literally every single one of…
213
Memory access is O(N^[1/3])
In computer science, we often compare the efficiency of algorithms by describing their runtime as a function of the size of the input. Sorting is O(n * log(n)), meaning that sorting a list of N items takes an amount of time proportional to the number of items multiplied by its logarithm. Matrix multiplication is…
214
Lánczos Interpolation Explained (2022)
When you resize, rotate, or in any way transform an image; or more generally when you resample some discrete signal, the software you are using must _interpolate_ between the discrete points to produce a result. Linear and cubic interpolation are easy to explain, but Lánczos interpolation, one of the most popular…
215
Category Theory Illustrated – Natural Transformations
I didn’t invent categories to study functors; I invented them to study natural transformations. — Saunders Mac Lane
216
Diff Algorithms
How I overcame copying and modifying my own diff library from project to project by diving too deep into diff algorithms and coming out at the other end with new diff library in my hand.
217
Random Attractors – Found using Lyapunov Exponents (2001)
Contribution by Philip Ham: attractor.basic and Python implementation by Johan Bichel Lindegaard.
218
How has mathematics gotten so abstract?
What's the meaning of "numbers" and "arithmetic operations"? We consult Georg Cantor's turtles and look at Giuseppe Peano's code.
219
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.
220
Failing to Understand the Exponential, Again
Posts and writings by Julian Schrittwieser
221
Is Fortran better than Python for teaching basics of numerical linear algebra?
Quarto Academic Website Template adapted by Dr. Gang He
222
The Ruliology of Lambdas
Stephen Wolfram explains the rich ruliology of lambdas, made particularly significant by their connection to practical computing. Covers basic computations to undecidability to multiway graphs and evaluation strategies.
223
A dumb introduction to z3
Exploring the world of constraint solvers with very simple examples.
224
Folks, we have the best π
And some novel ideas for bicycle wheel design.
225
Language models pack billions of concepts into 12k dimensions
In a recent 3Blue1Brown video series on transformer models, Grant Sanderson posed a fascinating question: How can a relatively modest embedding space of 12,288 dimensions (GPT-3) accommodate millions of distinct real-world concepts? The answer lies at the intersection of high-dimensional geometry and a remarkable…
226
Many hard LeetCode problems are easy constraint problems
Use the right tool for the job.
227
Hashed sorting is typically faster than hash tables
Benchmarks and theoretical explanation of why and when hashed radix sort beats hash tables.
228
How many dimensions is this?
A degree in mathematics might not save you from stacking boxes for a living.
229
A Random Walk in 10 Dimensions (2021)
The geometry of random walks in high dimensions provides the power behind deep learning and may be the secret to intelligence.
230
John Coltrane's Tone Circle
An article about the John Coltrane Tone Circle, a 5-octave Circle of Fifths and a double-ring Hexatonic Circle as well. Interpretation, explanation ...
231
The maths you need to start understanding LLMs
A quick refresher on the maths behind LLMs: vectors, matrices, projections, embeddings, logits and softmax.
232
Minesweeper thermodynamics
You know how sometimes you start a game of Minesweeper and immediately get stuck?
233
Inverting the Xorshift128 random number generator
CVE-2025-7783 is a very recent vulnerability affecting a lot of applications in the Node.js ecosystem including those which use axios or the deprecated request library. In all honesty, this vulnera…
234
Why haven't quantum computers factored 21 yet?
Craig Gidney's computer science blog
235
From multi-head to latent attention: The evolution of attention mechanisms
From Multi-Head to Latent Attention: The Evolution of Attention Mechanisms What is attention? In any autoregressive model, the prediction of the future tokens is based on some preceding context …
236
God created the real numbers
W. Jherek Swanger writes in his introduction to Camillo 7 Agrippa's "A Treatise on the Science of Arms, with a philosophical Dialogue (1553)" that:
237
The Math Behind GANs (2020)
Generative Adversarial Networks refer to a family of generative models that seek to discover the underlying distribution behind a certain data generating process. This distribution is discovered through an adversarial competition between a generator and a discriminator. As we saw in an earlier introductory post on…
238
Important machine learning equations
A reference guide to fundamental machine learning equations with correct implementations and clear explanations of how they connect to each other.
239
A visual introduction to big O notation
A visual introduction to big O notation.
240
Everything is correlated (2014–23)
Anthology of sociology, statistical, or psychological papers discussing the observation that all real-world variables have non-zero correlations and the implications for statistical theory such as ‘null hypothesis testing’.