julesh

(This is your periodic reminder that if you ever visit the UK you should *really* use a vpn, unless you want this list of 48 government agencies to be able to see your stuff without a warrant
https://en.wikipedia.org/wiki/Investigatory_Powers_Act_2016#Authorities_allowed_to_access_Internet_connection_records

2026-06-22 20:43:24 UTC

RE: https://mstdn.social/@hkrn/116792861660199455
I have been thinking about setting up a VPS to practice in advance of a VPN ban in the UK (or a requirement to use government id, which for me is an unbreakable red line equivalent to a ban). But, perhaps it will not be necessary after all?
#note1j7r…2uhw

2026-04-01 23:48:40 UTC

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I wonder what it would take to hook up an old school mechanical typewriter as a keyboard, those take a lot of force to press

2026-03-15 17:45:45 UTC

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No doubt they will say it's impossible because a bunch of contracts are already signed, or some other thinly veiled excuse

2026-03-09 16:57:36 UTC

The greatest bamboozle that the English language ever pulled is using the same word for legal rights and actual rights. The second-greatest is using the same word for proof-objects and actual proofs

2026-02-23 21:31:25 UTC

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Quick question, why can't I find any Pythagorean triples but for cubes or higher exponents?

2026-02-19 14:44:18 UTC

Starting writing the introduction paragraph of a blog post after finishing the rest of it, and my muscle memory literally typed "In this paper" before I could stop it

2026-02-16 21:22:17 UTC

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I wonder if there's some model theoretic universality result that all finite (or not too big) commutative rings embed into one specific commutative ring that involves numbers, like the ring of rationals or something like that?

2026-02-16 20:56:15 UTC

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I wonder what this looks like for rings that have very little to do with numbers, like boolean rings or rings of functions

2026-01-24 00:22:20 UTC

Today I learned that during the ice age there was a really big river in Doggerland that included the Rhine, the Seine and the Thames as tributaries. Or I guess you could say, the Rhine continued and gained the Seine and Thames as tributaries
https://en.wikipedia.org/wiki/Channel_River

2026-01-14 12:28:52 UTC

"Lines of code" is a metric invented by languages without pattern matching, to sell more verbosity

2026-01-14 12:19:15 UTC

I thought the point of python was to sacrifice both speed and theoretical discipline in order to maximise user friendliness, but honestly it's not even very user friendly, I could do better

2025-12-26 13:07:44 UTC

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This is definitely true for keyboard instruments and most ensembles, but most non-keyboard instruments have a "natural" key (eg. G for violin, which causes the lowest string to resonate on the fundamental and the next string to resonant on the 5th), and I reckon some very pedantic people playing solo instrumental music must tune a few cents off the standard tuning to match that

2025-12-26 11:06:23 UTC

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A discrete manifold equipped with an approximate scalar field? That sounds like it could be useful for some other stuff too

2025-12-25 16:50:12 UTC

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"up to and including", you forgot to include the counts from days 1 and 2 in day 3

2025-12-25 14:41:08 UTC

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Note that this assumes that every pair of 1 partridge in 1 pair tree counts as a single gift

2025-12-25 13:32:19 UTC

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Today is the first day of Christmas so you should only expect a(1) = 1 gifts

2025-12-25 10:44:44 UTC

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Also public service announcement that today is the *first* day of Christmas. The 12th day of Christmas, aka Twelfth Night, is January 5. Advent is something different.

2025-12-25 10:39:36 UTC

The number of gifts sent to you by your true love up to and including the 𝑛th day of Christmas is
𝑛(𝑛+1)(𝑛+2)/6
https://oeis.org/A000292

2025-12-22 13:12:42 UTC

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It didn't occur to me before to switch to HAL, I'll actually think about that now

2025-12-21 21:01:43 UTC

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I'm not sure I have that much to say, especially not that you haven't already said. To be honest, I feel like doing interdisciplinary research is so difficult that if you're in a position where advice from a blog would help you, you've probably already failed

2025-12-21 14:53:35 UTC

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I had to scan back through my blog to see if I'd forgotten anything, but no, I never wrote about it. Well, pretty sure I wrote a few twitter threads about it, but it would be easier to write it again than to track those down

2025-12-21 13:58:21 UTC

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I submit {me, Philipp Zahn} (with several other people joining at various points) as a successful ACT collaboration. My experience broadly matches yours, this collaboration is more than a decade long and required very much meeting each other half way

2025-12-20 15:50:04 UTC

In Soviet Russia, snoot boops you

2025-12-15 12:24:00 UTC

What the LaTeX feature of Mathstodon is supposed to be used for: Writing formulas that appear beautifully typeset (except to people on any other server and anyone using any client except the web client)
What I actually use it for: quick access to the → unicode symbol for talking about my train journeys

2025-11-18 11:17:57 UTC

It's funny how a bunch of my local mastodon discourse today is about how the "u" sound doesn't exist in American, that's a thing I've joked about for years. Waaaay back in the day my twitter display name was "Categories with Jules" and only after like 2 years I got rid of that because I suddenly discovered that anyone who learned USEn just didn't get the joke (because they would pronounce this nLab page as "categories with dools", which amuses me to this day)
https://ncatlab.org/nlab/show/category+with+duals

2025-10-23 21:51:20 UTC

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This is the orange site, if you don't expect the worst from it then you haven't been around it long enough

2025-10-23 20:33:53 UTC

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https://news.ycombinator.com/item?id=45677397
(but nothing especially worth seeing there)

2025-10-22 16:58:36 UTC

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She does have a daemon, you just can't see or interact with it

2025-10-18 19:53:07 UTC

Big shoutout to the community of people who could be developing better ballistic missiles or earning a fortune as quants but instead are saving frames in super mario 64 tool assisted speedruns
https://www.youtube.com/watch?v=_yx0eutBwII
https://media.mathstodon.xyz/media_attachments/files/115/396/904/348/980/713/original/a546437906d8786b.png
https://media.mathstodon.xyz/media_attachments/files/115/396/905/151/410/243/original/2c971f3473c99180.png
https://media.mathstodon.xyz/media_attachments/files/115/396/906/387/838/030/original/258420204396ade0.png
https://media.mathstodon.xyz/media_attachments/files/115/396/907/177/808/101/original/535ba346b61cf345.png

2025-10-07 16:22:35 UTC

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It could still work if you firmly think of them as open-ended projects with no defined endpoint

2025-10-07 15:08:21 UTC

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Is it feasible to say all of the above, all interleaved in a random order

2025-09-29 22:20:31 UTC

For some reason I was 100% convinced Wikipedia was based in Sweden, I'm actually horrified to learn that it's entirely American
So...... rest-of-world alternatives to Wikipedia?

2025-09-22 16:46:10 UTC

It's called Prolog because something something mumble profunctors

2025-09-07 12:13:30 UTC

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It's like when your cat goes missing but shows up a few days later after a mystery adventure

2025-08-29 18:49:55 UTC

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So I dug up a file where I was playing around with doubly linked list contexts like 6 months ago and it turns out that I already had a bit of lambek calculus worked out there. I should probably finish this and write up a blog post...
https://media.mathstodon.xyz/media_attachments/files/115/113/545/855/045/800/original/27f2f0b316219d72.png

2025-08-28 23:17:25 UTC

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In theory I could do lambek calculus in this style, CFGs not sure. In practice I think it would run into an annoying problem that if your monoid operation is noncommutative + left closed + right closed then to write the rules you need your context to be a doubly linked list, which is not a recursive datatype so it's probably beyond the capability of current generation type checkers
For semantics, the composition product of endofunctors turns out to be closed on one side and *coclosed* on the other side (these are called right and left kan extension and are very scary), I don't know whether it works out to be a model of lambek calculus, but it's at least very close

2025-08-28 21:34:21 UTC

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Yeah. Specifically in this case it was functor composition (ie. the monoidal product from "a monad is just a monoid in the category of endofunctors what's the problem"), which is noncommutative

2025-08-28 16:49:09 UTC

For a while I've been struggling with how "abstract syntax" means so many different things in a modern compiler pipeline, but I finally came up with a good naming scheme:
raw syntax: the character string read in from the file
rare syntax: after lexing and parsing, but no static indexing
medium rare syntax: statically well scoped
well done syntax: statically well typed
overdone syntax: the object code produced by the backend

2025-08-27 15:39:41 UTC

Me and @npub1d0d…5zz4 are mostly done with implementing a noncommutative lambda calculus where types denote endofunctors, terms denote natural transformations, tensor denotes endofunctor composition and arrow denotes right kan extension

2025-08-13 11:10:45 UTC

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In applied category theory symmetric monoidal categories are *the* unifying concept, virtually all kinds of open systems/networks/processes/etc collect into morphisms of symmetric monoidal categories
I have a low level explanation too. Operads describe patterns of compositionality, but operads are technically very difficult to work with (here I'm technically talking about 2-operads and their pseudo-algebras). In a wild coincidence, lots of useful operads turn out to be representable by structured monoidal categories, which are much more tractable to work with. An important example is hypergraph categories (symmetric monoidal categories in which every object is a special commutative frobenius algebra), which are equivalent to algebras of an operad that describes a very common sort of many-to-many composition

2025-08-12 22:49:28 UTC

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You probably have an unreasonable number of category theorists who follow you... I consider the most important definition I know to be that of monoidal categories. Specifically the one due to Kelly, which only needs 2 coherence diagrams

2025-08-08 19:27:06 UTC

"Hey Socrates, what do you want for dinner?"
"All I know is that I know nothing"
"Goddamn it Socrates"

2025-08-06 09:50:10 UTC

My thoughts about this just clicked. I have seen a bunch of cases of professed non-programmers building pretty big things entirely by vibe-coding, and they work fine. This allows people to participate in creation without years of training, and in the end that is not a bad thing
There are a bunch of other systems like this, that allow non-experts to simulate being able to do the real thing. Playing a shooter with aimbot. Playing guitar with 3 chords. Driving automatic.
These are all perfectly good things that allow amateurs to match the performance of experts, and none of them are bad things. But if you don't take the hit and switch over to the real thing sooner or later, you'll be a novice forever.

2025-07-20 15:00:44 UTC

ibuprofunctor

2025-06-27 21:04:12 UTC

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Ah yes, UK academia
I think we only have 6. Of which I've done 0 in the last few years

2025-06-27 13:43:04 UTC

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Studying HoTT is all cool and good, but they keep trying to redefine standard terminology in nonstandard ways that don't make sense in most models

2025-06-25 19:08:59 UTC

Back in the day when someone sent you a meno they could see that your inbox is overflowing all over the desk and floor. I think we should bring back that feature

2025-06-05 10:43:13 UTC

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Here's the standard answer: the von Neuman-Morgenstern expected utility axioms are equivalent having real-valued utility, and *you* try doing any nontrivial modelling without using any calculus

2025-05-18 17:05:13 UTC

We should launch another deep space probe carrying a golden record with Never Gonna Give You Up

2025-04-23 17:29:11 UTC

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Nice! Unlike last year I'm going to make an effort to hang around for this, if I'm allowed to. Naturally I'm very interested in the economic part

2025-04-19 13:00:14 UTC

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Glad I'm not the only person who noticed, this was *obviously* written by AI

2025-04-08 15:27:06 UTC

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Incidentally the theoretically optimal way to play the chicken game is to cut off your steering wheel, for example by passing a law mandating tit-for-tat tariff escalation and now allowing politicians any discretionary choice in the matter. Whether that would actually work in the present situation is a different matter, applied game theory is hard.

2025-04-08 15:22:58 UTC

I spent 24 hours thinking people talking about "the chicken game" were talking about modelling tariff brinksmanship
https://media.mathstodon.xyz/media_attachments/files/114/303/024/553/009/589/original/0a86ce2c1dc168e4.png

2025-04-01 19:37:14 UTC

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For those who don't know, PhD positions in the UK that are not just open to UK citizens (or those with existing residence permits) are rare as hens teeth

2025-03-25 18:06:02 UTC

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My first thought is to wonder what is a "quasi-octagon", ie. what shape has this thing as its symmetry group?

2025-03-16 17:52:05 UTC

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The article I linked has a lot to say about that. One of the main underlying causes is that the Scottish government pays for Scottish students to study in Scotland, but they amount they pay hasn't been adjusted for inflation in a very very long time, so universities now make quite a big loss on every single Scottish student

2025-03-16 17:32:14 UTC

https://www.bbc.co.uk/news/articles/cddynyz9q6po
https://media.mathstodon.xyz/media_attachments/files/114/173/301/214/753/739/original/7b8dea33deb86b6f.png

2025-02-21 20:31:31 UTC

Ah yes, a letter of support for the NIH, that'll learn the bastards for sure

2025-02-18 14:20:26 UTC

Time to write a game theory test
All else fails I can go with this: "Submit a number between 0 and 100. Everybody who jointly chooses the highest number will get a mark of 0, everybody else will get the mark that they chose"

2025-02-15 18:30:52 UTC

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In practice I'm currently more worried right now about running Android on my phone than OSX on my laptop, but yeah. Gonna need to replace both of them at some point

2025-02-15 17:35:32 UTC

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I'm thinking of moving my stuff github stuff to codeberg for exactly this reason. Now arXiv, I had not thought about that until now.....

2025-02-11 09:46:02 UTC

Inside you there are 2 wolves, 1 goat and a cabbage, and you need to cross a river

2025-02-06 23:00:07 UTC

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Technically it's too early to say for sure that the US doesn't have a king, in order to be not-a-king it is necessary to either lose power without dying, or die but be succeeded by someone who is not your child

2025-02-05 15:14:17 UTC

Programming languages train you to not want what they don't provide, which is why programmers should learn a wide variety of different styles in order to not take any shit from language designers

2025-02-05 12:47:33 UTC

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So dependent types are types indexed by values, and if you index a type by a value that happens to be the result of a function call applied to a variable, the typechecker almost invariably chokes because it can't do even trivial equational reasoning. There are multiple different design patterns to work around the problem, but none of them are pleasant

2025-02-05 12:34:12 UTC

The crazy thing about Lean is that from a technically slightly inferior foundation they're successfully hacking stuff that's obviously decades away from being feasible to engineer properly. Like, literally nobody knows how to make a typechecker that doesn't totally shit itself as soon as you put a function call in an index, but they apparently just ignore the problem and charge forwards. It's genuinely impressive, it reminds me of Youtube videos like "Can you beat Dark Souls using only a wet pool noodle?"

2025-01-31 21:57:07 UTC

Speaking of Plato on conservatism, I just remembered Popper pointing out the common root of the words "patriot" and "patriarchy". They both mean "father", both in the sense of "fatherland"

2025-01-25 23:04:39 UTC

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possibly I should learn to read

2025-01-25 19:14:40 UTC

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I expect it to be a more complicated version of the tensor product, which in Kmett's source code looks like this:
https://media.mathstodon.xyz/media_attachments/files/113/890/589/091/297/397/original/58f1140d834a2bd9.png

2025-01-25 19:13:03 UTC

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I made what might be a bunch of progress but then got stuck. I expected it to be very hard and it did not disappoint

2025-01-25 18:36:20 UTC

I'm trying to implement the composition product of monomial endofunctors for the van Laarhoven encoding. It is very hard.

2025-01-25 12:31:52 UTC

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These are mostly not strategies, these are closer to end goals. This is the kind of uninformative writing I expect from university bureaucrats

2025-01-02 21:19:35 UTC

how come when you launder laundry people are like "good job" and "you are not depressed today" but then when you launder money people are like "you're under arrest"

2024-12-20 21:18:55 UTC

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That'll teach em to decimalise the currency, didn't have this problem when it was 12d to the shilling

2024-12-17 23:18:56 UTC

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So what's the alternative? Is there just nobody working on foundations now? Or are there people being hired instead of string theorists doing some alternative foundational things that I haven't heard of? (In other words: what are you supposed to do when there's only one game in town and it's a losing game?)

2024-12-17 17:34:26 UTC

Prediction: over the next decade or 2 the remaining basic principles of proof assistants will be figured out, and the first minimally viable language will be proudly handed over to the mathematicians, who will then look at the millions of lines of code they've already written in Lean and collectively decide to just keep building on that. Only another decade or 2 after that will they learn the meaning of "technical debt"

2024-12-15 16:03:47 UTC

Today I learned that the word "loot" was nicked from India in colonial times
https://media.mathstodon.xyz/media_attachments/files/113/657/682/424/391/468/original/4effb2ebcbda390a.jpg

2024-12-09 21:19:22 UTC

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Addendum: The alternative, if Google are not going down without a fight, is that they could start trying to end the LLM hype cycle (which they know they lost) and try to trigger a new one in which they have a head start on their main rivals
https://media.mathstodon.xyz/media_attachments/files/113/624/943/995/227/342/original/590a013cd9eaad3f.png
https://media.mathstodon.xyz/media_attachments/files/113/624/945/506/976/775/original/2566df6704ada4dc.png

2024-12-04 21:01:57 UTC

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I definitely don't expect Google to completely blow up, just to diminish and become a zombie husk of their former selves, like many equally giant tech companies have been doing since IBM. Of all the big tech companies right now, Google are the only one I actually expect this to happen to any time soon
<end of thread>

2024-12-04 20:58:50 UTC

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I have an additional thing which is even more speculative. The thing that Google's research division is most iconically known for is deep RL. And personally, I believe we're not even close to seeing the last of what deep RL can do. My conspiracy theory is that the top level of Google management basically shut down the AlphaStar project because they didn't want to enter the industries that it would be most useful for, like finance and military tech. I think that history will judge that Google in 2017 were sitting on the 2 most profitable technologies of the decade, and failed to exploit either of them

2024-12-04 20:58:33 UTC

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Add to this that generative transformers were literally invented at Google, and they completely failed to see the potential and they've been just another imitator for the entire hype cycle. The big hype battle right now is between GPT and Claude, nobody gives a shit about Gemini, I guess including investors

2024-12-04 20:58:20 UTC

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Compare this to Facebook. The whole metaverse thing is probably one of the biggest wastes of money in the entire history of business, but the whole thing came and went without it ever touching their core products: Facebook, Instagram and Whatsapp. So they write off the loss, pick themselves up and jump onto the next hype cycle (LLMs) much poorer but still fundamentally healthy as a business

2024-12-04 20:57:59 UTC

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In short: every big corp has to constantly play whatever is the current hype cycle in order to keep the money rolling from investors. It's irrelevant whether their management actually believe the tech du jour is important or not, this is just the game that they have to play to stay ahead. I think that Google's fundamental mistake is that they have compromised their core product in service of the LLM hype cycle. Yes, the "product" is really Adwords, but the search service is what actually drives it. Yes, they have other products like Android, Youtube, Gmail and Chrome, but search is the biggest of them all

2024-12-04 20:57:46 UTC

I believe that Google are in the process of the biggest corporate fuckup of recent times (ok ok, not counting Intel who might match them, but I don't even pretend to understand what's happening there). No "they're ruining the internet" here, this is me trying to think in purely corporate terms
<thread>

2024-11-29 20:28:32 UTC

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MLEM

2024-11-28 18:55:58 UTC

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Yes, exactly... but I expect things not to work so nicely because -* on the category of lenses is not functorial, so it's a pleasant surprise when it has any nice properties

2024-11-28 18:50:30 UTC

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The part that didn't go how I expected is how function types operate on kinds. For context of this, here's my blog post on the bizarre kind system of Aptwe: https://cybercat.institute/2024/09/12/bidirectional-programming-iii/
It transpires that 𝑝 ⊸ 𝑞 is covariant when 𝑝 is contravariant and 𝑞 is covariant, and 𝑝 ⊸ 𝑞 is contravariant when 𝑝 is covariant and 𝑞 is contravariant

2024-11-28 18:43:58 UTC

I just implemented function types in Aptwe, aka the monoidal closed structure of lenses. Here's the interpreter cases corresponding to hom introduction and elimination, which correspond to the bidirectional semantics of (linear) lambda abstraction and function application
https://github.com/CyberCat-Institute/Aptwe/blob/main/src/Interpreter/Terms.idr
https://media.mathstodon.xyz/media_attachments/files/113/562/046/542/391/376/original/21da8de43dbbda98.png

2024-11-27 17:58:59 UTC

" scare quotes "
《 square quotes 》

2024-11-08 14:40:30 UTC

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I won't be going to ACT25, but I also wouldn't if it was held in a different US state. I also didn't go to ACT23 partly because I didn't have the energy and partly because I didn't want to go to the USA in particular

2024-11-06 12:26:28 UTC

Basic question but I'm not 100% sure: it's not possible to have a "reasonable" syntax that captures exactly the total computable functions N → N, right?

2024-10-14 15:33:00 UTC

Because I don't have a clear mental timeline of most research that happened before I was in the business, I didn't realise until now that the machine learning research that got the physics Nobel was published over 40 years ago. It happened much closer to the time Turing was working in AI than to the present.

2024-10-13 14:29:03 UTC

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I saw the original in passing, I did not see the argument but I'm not surprised it happened
My own take went in my own feed instead of your replies: https://mathstodon.xyz/@julesh/113276332265442477

2024-10-13 12:54:31 UTC

Normally I'm very on top of my mastodon feed, but last week I was too busy. I just scrolled back through almost 3 days worth before the feed crashed and stopped loading more, so anything from the couple of days before that goes into the void

2024-10-03 16:25:45 UTC

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Perhaps... I'd point to the theory of 4 humours which was universally accepted in the West as the most important idea in medicine for like 2000 years, and now is of basically zero interest except for understanding why people behaved the way they did in the past

2024-10-03 15:54:11 UTC

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I'm 50/50 whether this kind of thing is old superstition that's only of historical interest, or if one day in the future building on machinery like information geometry there'll be a serious theory that amounts to "something flows out after death"

2024-09-30 18:04:29 UTC

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It's like the old joke: I had a problem, so I tried using Haskell. Now I have a monoid in the category of problems.