Ursula K. Le Guin is my favorite science fiction writer. She is, quite possibly, the greatest science fiction writer ever. In this video, I tell the story of her career and discuss some of the philosophy behind it all.

→ Links

→ Reading Guide

The best place to start with Le Guin is either The Dispossessed (my favorite) or The Left Hand of Darkness. Library of America has a two volume set of all of Le Guin’s Hainish Cycle, and that includes both books: https://amzn.to/46JIbuM

There is a fresh documentary about Le Guin. I consulted it heavily for this video. It can be rented or purchased from Amazon: https://amzn.to/3LVlyvE

To understand Le Guin thought process, the collection ‘The Language of the Night’ is indispensable. It is out of print and expensive, sadly. You may be able to find a PDF somewhere: https://www.isfdb.org/cgi-bin/pl.cgi?151671

Even if you don’t love fantasy, Earthsea is essential: https://amzn.to/46H2XLB

For a sample of Le Guin’s later writing, I recommend the Library of America’s edition of Always Coming Home: https://amzn.to/3Q9PvKW

For the philosophical background to engage with Le Guin, check out the following books.

Kropotkin’s Mutual Aid: https://amzn.to/3PMLc6Y

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These are affiliate links with Amazon. The channel earns a commission from each purchase — but it doesn't cost you anything.

00:00 - Introduction

Over the course of my PhD, I watched hundreds of students write parsers, and distilled transferable parser combinator design patterns to fix their biggest pain-points. Not satisfied with just identifying the patterns, however, I figured out how to provide first-class support for the patterns in the Parsley Scala parser combinator library (https://github.com/j-mie6/parsley), making it easy to start using these ideas and helping guide the parser writer to make use of them from the outset. In this talk, we’ll explore Parsley with some live-coding, and see how it can be used to create clean and maintainable parsers that can evolve straightforwardly by following the patterns. Parsley “compiles” itself to an abstract machine, which is executed, so the high-level abstractions introduced have a minimal impact on the overall running of the parser – the result is something much more efficient than the classic scala-parser-combinators library.

Jamie is a (quite possibly former!) PhD student at Imperial College London interested in Scala, parser combinators, and metaprogramming. His research was to use staged metaprogramming to implement fast non-monadic parser combinator libraries in Haskell: though he hopes to soon port this work back to Scala. This is not the subject of the talk however; he also takes an interest in teaching, and how to teach parser combinators as well as how to best to write them in a maintainable way.

Parsley is a parser combinator that foregoes monadic operations so that it can be processed at compile-time — with staging (via typed template haskell) — to produce very fast parsers. Instead it adopts selective operations.

In this talk, I will briefly describe what parser combinators are, describe the high-level design of the library, as well as outlining its current and future capabilities. I will discuss how staging works to optimise the parsers themselves.

Speaker: Jamie Willis

Explaining the origin of Latin's principal parts through comparative linguistics. Analysis of Sanskrit verbs shows why Latin's verb system is so unpredictable and sometimes hard to learn. Personally, I don't think I can consider myself as having been truly alive before witnessing my own creation.

FURTHER READING RECOMMENDATIONS:

It all makes sense from the Proto-Indo-European point of view. 🤨

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In this video I build a classic vapourwave scene from scratch using C++ and raw OpenGL. No game engines, no shortcuts—just direct graphics programming. The scene features the iconic retro grid floor, distant mountains, and a glowing neon sunset sky inspired by 80s aesthetics.

I walk through the full process of how the scene works, including the C++ code structure, how the shaders create the vapourwave look, and how the geometry is rendered using OpenGL. Along the way I also show some of the mistakes and debugging steps that happened during development, which helps illustrate how real graphics programming problems get solved.

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Topos Institute Colloquium, 4th of December 2025.

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00:00 Setting the parameters of the question

Pain is Salvation from the Europa Universalis V Original Soundtrack with added Lyrics and Translation

Music by: Håkan Glänte

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=== Nerd Notes ===

There are a number of comments asking "But what if I use [something] in my quintic formula?" One such [something] being the Bring radical, which I will take as an example here. The Bring radical is defined as the solution of a particular quintic, which can then be used to solve quintics in the general case. (Aside: I'm not sure this can be called a formula because even by invoking the Bring radical in the general case requires casework, per all of the sources I have found. If you know of one which does not, leave a comment.)

But as far as I am concerned, this yields a larger question of what can be called a formula in the first place. If I say that an oracle which yields the solutions of the quintic is a valid symbol in my "formula", then the formula is merely the identity statement that the solution to the quintic is the solution to the quintic. I think this sidesteps the question- and furthermore, in such a world, the halting problem would even be solvable, by merely invoking such an oracle. The idea of a formula, if you ask me, is that we represent a complex behavior with simpler constituent symbols which we accept as atomic computations. Where the line is drawn is, of course, arbitrary, (although there is certainly interesting things to be learned by accepting alternate symbols,) but in this video we consider the arithmetic operators and traditional radicals.

=== Errata ===

Found by @samuelwaid: at 12:26 I said "we define i as being the [square root of -1]" but the actual convention is to define i as being an element such that i^2 = -1. As mentioned in the video, there are various valid definitions of the square root function, and for some of them, the "definition" of i mentioned in the video would not be respected.

=== Sources and References ===

This video was primarily inspired by a paper by Leo Goldmakher. It covers the main proof of this video in a more academic fashion. https://web.williams.edu/Mathematics/lg5/394/ArnoldQuintic.pdf

The proof itself is by Vladimir Arnold: https://en.wikipedia.org/wiki/Vladimir_Arnold

While I was interested in Leo's paper, I saw this post about fractals of polynomial solutions. The images were somewhat low-resolution, which inspired me to make my own in conjunction with the topic of the video. https://les-mathematiques.net/vanilla/discussion/2335252/images-des-entiers-algebriques / https://web.archive.org/web/20240530132413/https://les-mathematiques.net/vanilla/discussion/2335252/images-des-entiers-algebriques

This excellent talk by Andrej Bauer was recommended to me while making my video. It goes much deeper into detail about the fractals of roots seen here. His talk prompted the comment about the dragon curve in this video. https://www.youtube.com/watch?v=8wrYPqEU1x0

Here are some other resources about the Abel-Ruffini theorem which I found along the way that helped with my own understanding: