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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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The latest blog posts to take off on Hacker News. 2,851 posts.
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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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Decomposing language models into understandable components
Interpretability research decomposing a transformer layer into thousands of interpretable features that can steer model behavior.
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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 .]
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The Irish Logarithm
From the highly eclectic blog of Mark Dominus
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An easy-to-implement, arena-friendly hash map
My last article had tips for for arena allocation . This next article demonstrates a technique for building bespoke hash maps that compose nicely with arena allocation. In addition, they’re fast, simple, and automatically scale to any problem that could reasonably be solved with an in-memory hash map. To avoid…
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Inside the Matrix: Visualizing Matrix Multiplication, Attention and Beyond
Use 3D to visualize matrix multiplication expressions, attention heads with real weights, and more. Matrix multiplications (matmuls) are the building blocks of today’s ML models. This note presents mm, a visualization...
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Lean, Coq and other proof assistants: Visualising proofs as trees
This week we (me & Anton Kovsharov) published Paperproof, a Gentzen-tree-like proof interface for Lean 4. In this post I'll review proof visualisations from o...
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Circles do not exist
Many logos, drawings and other graphical designs have the following shape in it. What is this shape? If you thought: "Ah-ha! I'm smart and r...
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A mathematical formalization of dimensional analysis (2012)
Mathematicians study a variety of different mathematical structures, but perhaps the structures that are most commonly associated with mathematics are the number systems, such as the integers $late…
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Painting with math: A gentle study of raymarching
A compilation of my Raymarching and Signed Distance Field learnings and work. In it, I teach you how to leverage those techniques along with lighting models, smoothmin, soft shadows, and some math to create beautiful 3D raymarched scenes ranging from abstract shapes to infinite realistic-looking landscapes.
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What Is Dimensional Analysis?
Mathematics is famously concerned with numbers . However, most of the physical quantities that we encounter in everyday experience cannot be expressed as numbers alone.
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How large is that number in the Law of Large Numbers?
All large numbers are large, but some are larger than others
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Category Theory Illustrated – Sets
Ready, set , begin… (you don’t know how hard I tried to resist to making that pun). We begin our inquiry with the theory of sets. Set theory and category theory share many similarities. We can view category theory as a generalization of set theory. That is, it’s meant to describe the same thing as set theory…
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Towards a new SymPy
This is the first part of a series of posts on big changes for SymPy with particular focus on speed. What I am going to describe in these posts are:
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Chemists develop new way to split water
The news portal offers current information about studies, research and life at Münster University.
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Scientists use quantum device to slow chemical process by factor of 100B
In a world-first experimental result, scientists at the University of Sydney have used a quantum computer to coax an atom to behave the same way as a photo-chemical process that underpins the speed of human vision and solar energy harvesting - only at speeds 100 billion times slower than in nature.
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Bézier Curves and the logic behind them
The logic behind Bézier Curves used in CSS animations and visual elements.
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