proof of one half of the pullback lemma in my lean4 cat theory library

person writing 10000 line PRs every day for their productivity web app that integrates with obsidian: “am I working on the modern day manhattan project?”

I gave them a zeugma and a piece of my mind

guy who knows about front end development upon using claude code: you know im something of a futurologist and labour market economist myself

venn diagrams aka semantics of logic in the propositional fragment of sheaves on ℝ²

Omg, they’re about to invent an anti-memetic division. And it has an actual purpose in this world.

guy who only ever learnt javascript: claude code really makes it so there is no point in new programming languages now

finally finished my "fun" christmas agda project that is now 2000 lines long

When I come back to NYC, I'd like to make a reading club to learn category theory, maybe by going through the Awodey CT book. Lmk if ur interested Anyone have experience booking spaces around NYC for that purpose? I'm happy to put my money down to book rooms somewhere assuming it's feasible etc.

2026 is the year to declare semantic bankruptcy on what the verb ‘to cook’ can be asked to do for us

spj said in one of his talks that anyone who gets into [rocq] goes away for a few years and then comes back with all their nerve endings burnt off

A -> B ∨ C ———————— A -> B ∨ A -> C fails constructively much like: ∀ (B[x] ∨ C[x]) ———————— ∀ (B[x]) ∨ ∀ (C[x]) fails classically and that gives a good sense of why the translation into modal logic is sensible / how constructive logic is intrinsically a logic of “types”

Slides for my HOPE 2025 presentation, "Finite Functional Programming via Graded Effects & Relevance Types": www.rntz.net/files/hope-2...

finally getting back on my bullshit

There is a certain three-valued-ness to syllogistic logic whereby we interpret the predicate symbols as subsets of some domain of discourse and the important judgments are that a subset is empty, a subset is non-empty or that a subset may be non-empty

“Well now all of them know his god damn name” - Tish James

∀ '(', ∃ ')'

There is a paper from the topologist Christopher Zeeman about modeling the brain as a neural top space and using Brouwer’s fixed point theorem to say there are inescapable thoughts [iirc] ☠️

I don’t think a long book is even primarily about plot, or character, or any of the patterned information on its pages. A long book is practicing over time a way of being in the world. Reading even a very good summary is not the same as giving over some portion of your own life to that practice.

America is in crisis. So it's a small relief that the rest of the world is actually getting remarkable stuff done with energy. We just passed a huge milestone globally! Now back to work on America. billmckibben.substack.com/p/something-...

World's worst calendar: label the 168 hours of the week by elements of PSL(2,7).

The literate ages created classes of people through possession of secret information, in the sense that “every profession is a conspiracy against the laity”. This is the reason the coming post-literate age lies concomitant with growing institutional skepticism and a loss of faith in expertise

“Commerce and manufactures can seldom flourish long in any state which does not enjoy a regular administration of justice, in which the people do not feel themselves secure in the possession of their property, in which the faith of contracts is not supported by law”

One of the harder meta-cognitive aspects to mathematics is embracing that there is, generally, no preferred metaphor or example or intuition for a given concept; there is no preferred example(s) or intuitions of a group or vector space, or matrix or category

Musing on the prototypical temperaments towards reductionism vs holism: liberal/realist: the correct unit of analysis is the individual/gene/neuron communitarian/anti-realist: let us humble ourselves before irreducible complexity marxist/structuralist: the unity of opposites

Scarcity and Evil is a book where the US Amazon page has a single 5 star review from Hilary Putnam

More people should listen to one hour of old radio a week to rid themselves of radical presentism. Episodes of ‘bookworm’ from the late 80s and early 90s will have authors regularly explain that their novel is in response to sheer over-stimulation of modern society and to our secular malaise

We used to have popular culture like Johnny Cash’s At Folsom Prison and Mailer’s The Executioner’s Song and now we have an enormous industry of stranger danger true crime/evening news nonsense as the main way of thinking about criminals

All I would really like is Maren Ade’s adaption of Middlemarch

I think this channel, including the pared-back, unfussy aesthetic and mode of delivery, speaks to a growing vibe shift against various legitimizing ritual objects and images that have become a root cause of online status anxiety

There is no longer a monolithic tv show where one set of fans watch it as devout Protestants careful to point out how they feel not one iota of libidinal desire towards the iconoclastic behaviour of the main character, and the other form a cult fandom around a dumb guy that does evil each week

Think often of this quote as it becomes ever clearer which path we have chosen: “In the year 1948 the reading of Plato’s dialogues by a large number of people could make the difference between a century of folly and a century of wisdom for the world.”

"There are no positive male role models" sure we're just gonna pretend this guy didn't exist gotcha

Despite being clearly perturbed by Lewontin’s critique of Dawkins as engaging in a form of dualism, I feel like he never adequately manages to address the point. What typifies one collection of behaviours as adaptive but another as against evolution’s relentless selfish drive

The Epimenides paradox — “all cretans are liars” — is only a paradox if one reads “liar” with universal quantification (X always lies i.e. X is a knave), an unusual reading. I’m not quite sure what the usual reading is; what is the distinction between ‘a liar’ and someone who is ‘not honest’

A nice elementary example of a category is the collection of all choices of a basis of a vector space V with morphisms given by change of basis. If you have two such categories for V and W then a linear transformation gives a natural transformation between their interpretation functor into Vect

Tentative: re-ascendancy of ‘fate’ in the form of sports betting, astrology, meme stocks, crypto, manifestation etc. should be seen as part of emerging anti-rational post-literacy culture

Should be called English logic instead of classical logic since - it was invented by George Boole - it typifies the English approach to both jury verdicts, and public life (give an answer and never a reason)

I am reading Calculus Made Easy, a popular introductory text from 1910, to prepare for a class I’m teaching and it has this immortal prologue

I love people on this site thinking their preferred way to play sim city is the only way to think about politics, and being fundamentally incurious about anything beyond market fundamentalism

This is what #ChatGPT responds when you ask it to 'make a poster for a maths classroom with all the key formulas on it that a student aged 11-14 in the UK might need'. As with most #AI responses, it looks plausible but the more you look, the worse it gets.. What's your (least) favourite part?

Has anyone drew the parallels between American pragmatism as a response to the civil war and logical positivism to WW1?

A formatted and archived version of my recent threads on post-Searlean critiques of LLMs and the question of whether their outputs are meaningful: deontologistics.co/2025/06/22/t...

Hauntology as a frame for a culture that fundamentally, constitutionally cannot understand the futures it failed to have; cannot speak of its sublimated yearnings; can only reproduce what came before; only seems a more prescient way of seeing things

A problem with all social theories — especially those that seek to overcome the subject/object distinction — from Plato, to Marx, to Nietzsche; is they tend towards a kind of ‘fallacy of the cave’; whereby one becomes convinced one speaks a final vocabulary others are too foolish to have embraced

“Interesting philosophy is rarely an examination of the pros and cons of a thesis. Usually it is, implicitly or explicitly, a contest between an entrenched vocabulary which has become a nuisance and a half-formed new vocabulary which vaguely promises great things.”

a better way to think about mathematics is not foundationalism — the notion that semantically rich concepts can be reduced to atomic components — but using Brandom’s idea of pragmatic meaning-use relations: one language specifying what capacities one needs in order to be able to speak another

Neal Stephenson story in which we invented Turing machines out of looms and a fringe sect of hacker priests figure out gödel numbering to see the mind of god in the machine

You can really grasp the enlightenment as an ideal of self-governing individuals when you look around our smol bean zero responsibility ever culture

Do your part and get Zohran through