@boarders.bsky.social
Thanks to impermanence all things are possible
Working on a book on topos theory
Working on a book on topos theory
proof of one half of the pullback lemma in my lean4 cat theory library
February 13, 2026 at 6:09 PM
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?”
February 12, 2026 at 6:20 PM
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
February 9, 2026 at 2:17 PM
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
February 6, 2026 at 2:37 PM
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
February 4, 2026 at 5:30 PM
venn diagrams aka semantics of logic in the propositional fragment of sheaves on ℝ²
Reposted
Omg, they’re about to invent an anti-memetic division. And it has an actual purpose in this world.
January 30, 2026 at 5:08 PM
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
January 30, 2026 at 5:58 AM
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
January 28, 2026 at 12:37 AM
finally finished my "fun" christmas agda project that is now 2000 lines long
Reposted
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.
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.
January 15, 2026 at 11:32 PM
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.
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
December 21, 2025 at 3:49 PM
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
December 18, 2025 at 6:04 PM
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”
————————
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”
December 9, 2025 at 1:33 AM
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”
————————
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”
Reposted
Slides for my HOPE 2025 presentation, "Finite Functional Programming via Graded Effects & Relevance Types": www.rntz.net/files/hope-2...
October 13, 2025 at 1:35 AM
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
November 25, 2025 at 4:52 AM
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
November 14, 2025 at 2:34 AM
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
November 5, 2025 at 2:51 AM
“Well now all of them know his god damn name” - Tish James
Reposted
Reposted
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] ☠️
October 22, 2025 at 1:59 AM
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] ☠️
Reposted
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.
October 13, 2025 at 8:41 PM
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.
Reposted
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-...
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-...
Something extraordinary just happened
But of course there's a but. Or two.
billmckibben.substack.com
October 8, 2025 at 11:22 PM
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-...
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-...
Reposted
World's worst calendar: label the 168 hours of the week by elements of PSL(2,7).
September 29, 2025 at 2:53 AM
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
September 24, 2025 at 1:38 PM
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”
August 26, 2025 at 2:39 AM
“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
August 13, 2025 at 9:19 PM
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
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
I like Douglas Hofstadter’s (to me) dialectical question “who pushes whom around?” — do individuals push history around or vice versa? do neurons push thoughts around or vice versa? Do formal symbols push truths around or vice versa?
August 11, 2025 at 5:12 PM
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
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