Danny Wood

You know that thing where the farther something is, the smaller it looks? That doesn’t quite work in an expanding universe. It’s true for a while but after a certain point, more distant things (of the same size) start to look BIGGER because their light has been traveling since the cosmos was small 🙃

YouTube video by suckerpinch Badness 0 (Apostrophe‛s version)

This post was inspired by a video by @tomvii.bsky.social, where he uses paraphrasing by large language models as part of an entirely new typesetting system based around his own programming language

I highly recommend checking it out:
www.youtube.com/watch?v=Y65F...

Image showing the transformation of the intro paragraph to the Hot Fuzz Wikipedia page into perfectly justified monospace text

Can we get LLMs to generate text that is perfectly typeset down to the very last character?

In a new blog post, I show how using a constrained beam search, LLMs can efficiently generate perfect blocks of monospace text

echostatements.net/posts/2026/0...

GitHub - EchoStatements/Voronoi-Generator: A library for creating random Voronoi diagrams A library for creating random Voronoi diagrams. Contribute to EchoStatements/Voronoi-Generator development by creating an account on GitHub.

The library is open source, so feel free to play with it:

github.com/EchoStatemen...

I've added the ability to create Delaunay triangulations to my Voronoi diagram generation Python library.

The image generation takes a few seconds but I'm pleased with how easy it is to make pretty and varied outputs with it

TIL if you do Miller-Rabin with the first 12 prime bases, you have a fast, exact primarily test for all 64-bit integers.

Cf. oeis.org/A014233 which gives the upper bound on the two-sided correctness of Miller-Rabin given that you tested on the first k bases.

The lego logo

A lego forklift

And an honourable mention:

Lego: Lego

Lego supposedly are the world's largest manufacturer of tyres (at least according to the Guinness*). Sure, tyres aren't their main focus, but that doesn't seem so unusual for a tyre company!

* While we're at it: yes, Guinness the brewery/word record authority

The good year logo

The Goodyear blimp

Goodyear: Blimps

Unbelievably left-field. In the 20th century, they at least built the blimps themselves, but now their sideline seems to just be being the world's most famous owner of a fleet of airships

The Michelin logo

A fancy looking meal

Michelin: Restaurant reviews

This clearly got out of hand for them. It started as a more general guide for motorists, (even that is a slightly eccentric thing for a tyre company) but getting your tyres from the world's foremost authority on restaurant quality is odd

The Dunlop logo

A Dunlop tennis ball

Dunlop: Sports equipment

If you're working with rubber anyway, I can see how you get into making tennis balls and how that might spiral into sporting goods more generally

Fair enough

Tyre companies and their increasingly unhinged side projects, a thread:

Suddenly, the explanation in Solo for how Han Solo got his full name doesn't seem quite so far-fetched

'No-phone rave went well until people broke rules' People at Warehouse-project's phone-free event couldn't keep off their mobiles, one raver says.

New tragedy of the commons just dropped

www.bbc.com/news/article...

Hahaha, I want to get that on a t-shirt

It was definitely one of the things that got me hooked on bias-variance decompositions, and more generally on information geometry... Even if I'm not especially active in either any more

I guess you never know what's going to resonate with people!

I had always wondered why you hadn't done more with it. FWIW, we didn't find Buja et al's result until long after yours, so having it there was a huge boon to us

I'm really glad to see this on arXiv after all these years!

As David points out, he wasn't the first to discover this result, though he certainly deserves a great deal of credit both for its rediscovery and for (apparently somewhat accidentally) popularising it with a punchy paper/note containing clear and succinct proofs

This result was one of the foundational ideas built upon by what has since become by far my most cited paper, so I'm really happy to see a version on arXiv where it can hopefully be preserved for posterity

You could say that having chosen a reference distribution, the KL divergence tells you how far away another distribution is in the particular way that you care most about

It's vaguely distance flavoured, but in a way that we don't (as far as I know) have a general word to describe

I disagree slightly that it's not just semantics: when deciding how to generalise the notion of distance, we get to decide which attributes have to be retained in order to retain the "distance" label

Requiring symmetry is perhaps the most reasonable choice but it's not the only possible choice

I think there's a divide between those who use "distance" synonymously with "metric" and those who use it for any function with a more general sense of dissimilarity-ness.

I wonder if the former group want to say KL isn't a distance whenever possible to make their definition the more prevalent one

Why Busy Beaver Hunters Fear the Antihydra In which I explore the biggest barrier in the busy beaver game. What is Antihydra, what is the Collatz conjecture, how are they connected, and what makes them so daunting?

I published a new post on my rarely updated personal blog! It's a sequel of sorts to my Quanta coverage of the Busy Beaver game, focusing on a particularly fearsome Turing machine known by the awesome name Antihydra.

Alexander horned sphere - Wikipedia

The video is a fun watch but if you don't check it out, the counterexample I'm referring to is the Alexander horned sphere

en.wikipedia.org/wiki/Alexand...

YouTube video by Metamorphic The Most Obvious Theorem in All of Mathematics

I'm a big fan of when counterexamples to intuitive sounding theorems are so convoluted that outside of mathematics, the kind of rules-lawyering needed to construct them would be considered pedantic or even rude

youtu.be/pLgcZLysOFk?...

It's interesting that its blend of coherence and unexpected nonsense capture a dreamy quality that most things described as "dreamlike" don't quite match for me

Blocky Planet — Making Minecraft Spherical Discover the unique design challenges of creating a spherical planet out of Minecraft-like blocks.

How do you make Minecraft spherical? A really fun read about all the problem solving that goes into transferring Minecraft gameplay onto a spherical world

www.bowerbyte.com/posts/blocky...

YouTube video by Welch Labs What the Books Get Wrong about AI [Double Descent]

Really nice primer on double-descent and the bias-variance trade-off

I'm impressed by the depth that Welch Labs consistently manages to pack into their videos without sacrificing the storytelling for a popular science audience

www.youtube.com/watch?v=z64a...

How best to define "open problem" depends largely on whether you start off with a problem metric or just a problem topology

Since @spmontecarlo.bsky.social shared a post about Crinkled Arcs a couple of weeks ago, I've spent a fair bit of time digging into them

This new blog post attempts to collect what I found into an interactive introduction to crinkled arcs and their relationship to Brownian Motion