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The largest number representable in 64 bits
A rewrite of this blog post with many new insights and updates appeared in Jan 2026
New
The latest blog posts to take off on Hacker News. 2,391 posts.
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Q* Hypothesis: Enhancing Reasoning, Rewards, and Synthetic Data
Emergency special: The information we need to understand what Q* is was right in front of us, but the memes are more fun than reality.
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How does Cave/Glade Generator Work
Watabou’s Cave Generator is one in a series of RPG-ready map generators that Watabou has created over the years. All his work oozes style, but the cave generator was always the one I found mo…
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Lindenmayer systems
A Lindemayer system or LSystem for short consists of an alphabet of symbols that can be used to make strings, a collection of production that expand each symbol into some larger string of symbols, an initial “axiom” string from which to begin construction, and a mechanism for translating the generated strings into…
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Stable Fiddusion: Frequency-domain blue noise generator
Frequency-domain blue noise generator
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B-trees in Factorio
learning about B-Trees...in factorio
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My primality testing code is faster than Sir Roger Penrose's
But, I guess he did win the Nobel Prize for Physics in 2020 so I can't really brag. However, it was a great surprise when looking at two pa...
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Is the reversal curse in LLMs real?
A recent paper The Reversal Curse points out an apparent failure in large large language models like GPT-4. From the abstract: We expose a surprising failure of generalization in auto-regressive large language models (LLMs). If a model is
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Four Kinds of Optimisation
Premature optimisation might be the root of all evil, but overdue optimisation is the root of all frustration. No matter how fast hardware becomes, we find it easy to write programs which run too slow. Often this is not immediately apparent. Users can go for years without considering a program’s performance to be an…
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37, the median value for the second prime factor of an integer
Chris Grossack's math blog and professional website.
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A linear algebra trick for computing Fibonacci numbers fast
Fast Fibonacci Computations With a Linear Algebra Twist
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Formalising modern research mathematics in real time
(This is a guest post by Bhavik Mehta) On March 16, 2023, a paper by Campos, Griffiths, Morris, and Sahasrabudhe appeared on the arXiv, announcing an exponential improvement to the upper bound on R…
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When to Shut Up: A Visual Guide (With Included Algorithm)
Use these rules to avoid boring your audience
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What do we mean by "the foundations of mathematics"?
The phrase “foundations of mathematics” is bandied about frequently these days, but it’s clear that there is widespread confusion about what it means. Some say that a proof assistant must be based on a foundation of mathematics, and therefore that the foundations of mathematics refers to some sort of formal system…
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π in Other Universes
How the value of π depends on the definition of distance.
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When gradient descent is a kernel method
Suppose that we sample a large number N N N of independent random functions f i : R → R f_i \colon \R \to \R f i : R → R from a certain distribution F \Fc F and propose to solve a regression problem by choosing a linear combination f ˉ = ∑ i λ i f i . \bar{f} = \sum_i \lambda_i f_i. f ˉ = i ∑ λ i f i . For…
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The convolution empire strikes back
ConvNets Match Vision Transformers at Scale
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Lindenmayer Systems
Originally developed by Aristid Lindenmayer in 1968, an L-System is a formalism to generate self-similar structures. Although, L-Systems are capable of generating famous fractals like the Sierpinski Triangle (Axiom: FXF--FF--FF, F → FF , X → --FXF++FXF++FXF-- , angle = 60 ) or the Gosper Curve (Axiom: FX, X →…
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Why we don’t generate elliptic curves every day
Elliptic curves are standardized, instead of being generated like Diffie-Hellman parameters. There's good reasons!
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Marvelous Arithmetics of Distance
No reckoning allowed save the marvelous arithmetics of distance (from Smelling the Wind by Audre Lorde) Suppose a child comes up to you and says “I know 1 is odd and 2 is even, but I think 4 is mor…
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Higher quality random floats
Much has been written about how to generate random 64-bit integers; people might argue over which particular (CS)PRNG is best suited for a given task, but there is agreement on the general shape of the solution: keep some state around, and then extract 64 bits of randomness at a time, where each bit is equally likely…
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Fractional Factorial Experiment Design: There Are Too Many Experiments to Do
Have you ever found yourself in a situation where you had a bunch of parameters to tune for a better result, but there were just too many to exhaustively search all possibilities? I recently saw a …
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Circulant Matrices, Eigenvectors, and the FFT
The eigenvectors of a circulant matrix do not depend on the matrix itself, only on the size, and the eigenvectors are columns of the FFT matrix.
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BB(3, 3) is Hard
I’m excited to share a 3 state, 3 symbol Turing Machine that cannot be proven to halt or not (when starting on a blank tape) without solving a Collatz-like problem. Therefore, solving the \(BB(3, 3)\) problem is at least as hard as solving this Collatz-like problem, a class of problem for which Paul Erdős famously…
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Bounty to Recover NIST's Elliptic Curve Seeds
This is a fun challenge: The NIST elliptic curves that power much of modern cryptography were generated in the late ’90s by hashing seeds provided by the NSA. How were the seeds generated? Rumor has it that they are in turn hashes of English sentences, but the person who picked them, Dr. Jerry Solinas, passed away in…
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Subtraction is functionally complete
To be precise, IEEE-754 floating point subtraction is functionally complete . That means you can construct any binary circuit using nothing but floating point subtraction.
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Role of Algorithms
This is lobste.rs comment as an article, so expect even more abysmal editing than usual.
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NIST Elliptic Curves Seeds Bounty
Announcing a $12,288 bounty (tripled to charity) for cracking the five seeds selected by the NSA in the '90s for the NIST elliptic curve standard.
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Debunking NIST's calculation of the Kyber-512 security level
[Sidney Harris cartoon used with permission. Copyright holder: ScienceCartoonsPlus.com .]