Morgan Arnold

PhD student in Mathematics at UBC. MSc from EPFL, graduated 2026. BSc from UBC, graduated 2024. This blog obeys the (-, +, +, +) metric signature. Luddite. Politically left, and occasionally gauche.

Doctorant en Mathématiques à UBC. MSc de EPFL, diplômé 2026. BSc de UBC, diplômé 2024. Ce blogue obéit la signature métrique (-, +, +, +). Luddite. De la gauche, et parfois gauche.

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Last Notes

2026-03-10 04:47:50 GMT

@npub1z8r…mrq6 totally out of the blue, but thanks to you and grimgrains for putting me on to seitan! i've been getting into fitness recently and it's by far the best source of plant-based protein that i've found

2026-02-20 23:16:05 GMT

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ooh, cool! i'll have to get a shirt!

2026-02-20 23:12:58 GMT

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ooh, cool! any chance you guys are in town for the plan9 conference in may? seems like the sort of thing that y'all would be into

2025-12-15 22:23:06 GMT

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ah, that's a much more valuable observation than my suspicion based on provenance

2025-12-15 20:19:10 GMT

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i wouldn't call myself an expert, but my master's degree is in mathematical general relativity. at a glance, this doesn't look like any paper i've ever seen in mathematical general relativity. the researcher also appears to be employed by the research division of a mobile phone company, which makes me doubly suspicious. i can try to take a closer look later

2025-12-07 19:20:23 GMT

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ah, i also read that current affairs article a few days ago. i think that it was one of the most thought-provoking pieces that i've read about ai. i do wonder if this stems from capitalists thinking of workers as being sort of like commodity-producing automata. the way that people who are into ai "artwork" talk about art, for instance, only makes sense if you think of artists as automata which produce a commodity, namely art. granted, proofs don't make much sense as commodities, but the way in which ai math folks often talk about math only makes sense if you think of mathematicians as automata which produce proofs

2025-12-07 13:07:42 GMT

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i find something oddly disconcerting about the way in which people and groups like this perceive and understand mathematics. it smacks of this kind of silicon valley tech-bro-ification, but seeing it applies to math feels exceptionally strange to me

2025-12-01 11:57:53 GMT

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i suspect that he has some other tricks up his sleeves that he didn't reveal to us...

2025-11-30 20:59:20 GMT

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i heard a talk by martin rees once where he said that if he's on a train and someone strikes up a conversation, he tells them he's a physicist if he's in the mood for a conversation and tells them he's a mathematician if he's not. you might be on to something!

2025-11-07 00:10:37 GMT

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in particular, i think that the 20km segment from schaan to vaduz is entirely paved

2025-11-07 00:06:07 GMT

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yeah! i'm not sure about in town (the streets might be cobblestone in places? that's fine on a bike, but i can see it not being fun on rollerblades), but there's an excellent paved cycling path following the rhône, right on the swiss border

2025-11-07 00:03:01 GMT

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they'll also stamp your passport for a couple of francs, which is the kind of kitschy tourist stuff that i love

2025-11-07 00:02:26 GMT

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not in liechtenstein, but over the summer i cycled from my home in lausanne to vienna, and passed through liechtenstein! check out the royal treasure room while you're there. it's a collection of very random expensive things that belong to the royal family. there are rocks from the moon on display right next to a fabergé egg

2025-10-07 23:07:56 GMT

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oh, i'm sure! my experience with texts in category theory has just tended to be that the examples and motivations given tend to be very algebraic in nature (this was my experience with mac lane's book and riehl's book, at least), and so my lack of fluency in algebra can make them tricky to understand. i might try looking at awodey's book? i'm mostly interested in category theory insofar as it's connected to logic and type theory, so awodey's book might be a better fit

2025-10-07 21:09:49 GMT

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granted, i might have better luck grokking category theory if my algebraic pedigree didn't end with a mediocre grade in undergraduate ring theory...

2025-10-07 21:08:50 GMT

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much as i'd love to hear about general relativity, i think that i hear enough about it while working on my thesis! i'd love to hear a bit about category theory. it's something that i've heard a lot about (hell, i even tried reading johnstone's "sketches of an elephant"), but i've never seemed to really grok it. it seems sort of magically natural to those who understand it though!

2025-09-28 14:46:13 GMT

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okay, a couple of observations from computations. most probably aren't surprising.
first of all, light is blue-shifted rather than red-shifted. naturally, because there is no event horizon, there is no infinite red-shift at the event horizon.
as for orbits, the potential has no extrema, again somewhat unsurprisingly. although the singularity is naked, it isn't physically accessible, as the potential barrier goes to infinity near the singularity. gravitational lensing also isn't terribly surprising, although i struggle somewhat to visualise it! assuming the same impact parameter, you just get a sign change in the first-order approximation of the deflection, so instead of light rays being lensed around the black hole, they tend to be dispersed outward. maybe a better term here is gravitational mirroring? as best i can imagine, this sign reversal would make the black hole appear somewhat like a sort of weird spherical mirror. i wonder if i could hack into some computer simulation to better imagine what this would look like...

2025-09-28 10:52:00 GMT

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i'm pretty sure that there aren't any event horizons. in schwarzschild, the event horizon is the surface along which the killing field generating time translations is null, but it's easy enough to see that if the mass is negative this killing field is always timelike, so there shouldn't be any sort of "interior" or "exterior". i'll have a look at the computations for geodesics later. i'm curious to see how gravitational lensing would look for a negative-mass black hole. of course, you still have a singularity at 0, like john mentioned. the kretschmann scalar is unchanged by a change in the sign of the mass

2025-08-13 04:52:26 GMT

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since you consider it to be the most important definition that you know, is there a reason that monoidal categories are especially important in the work that you do, beyond their importance in category theory in general?

2025-02-14 08:26:46 GMT

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the more callous sales pitch for the idea is perhaps that this presents us with an opportunity to boost the global status of canadian institutions. i care a hell of a lot more about making sure that academics are able to continue their work free from political interference, but "do xyz to boost the status and influence of canadian universities" is probably an easier sell

2025-02-14 08:24:18 GMT

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even if he doesn't succeed in cancelling existing grants, i can't imagine the chaos created by the fear and uncertainty. being canadian, i would really like to see our government move to make it easier for academics concerned about the trump administration interfering with their work to come to canada. i'm thinking about writing an op-ed to a large newspaper to try to advance the idea, although i feel woefully underinformed to try to write such a thing

2025-02-14 07:29:35 GMT

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this is enraging. i applied to the phd program at john's hopkins university last year (i was rejected, mind you, but anyway) specifically because i wanted to work with emily riehl. she's an incredible mathematician (and, i might add, an incredible asset to the american mathematical community)
i hope that she either finds a way to prevent the new administration from interfering with her work, or else is able to find a post as a university in a country in which ted cruz, who presumably hasn't has sat in a math class in thirty years, does not feel so confident as to claim that a grant supporting one of the foremost category theorists in the world is "government waste"

2024-12-11 19:10:36 GMT

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i'm guessing that you're aware of it, but there's a 3blue1brown video about borwein integrals: https://youtu.be/851U557j6HE

2024-12-03 23:16:54 GMT

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funnily enough, i am only aware of greene's gâchis of a preface for "the meaning of relativity" because of another angela collier video! she talks about it in her video on string theory and popular science communication

2024-10-31 00:05:38 GMT

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i read a book while i was on vacation over the summer called "the pillars of the earth", which was set in the 1100's or so, in what is now england. for some reason, the part of that book that stuck with me was one of the characters, an architect, wondering aloud to himself how levers work! somehow, it had never occurred to me that someone actually had to invent the notion and mathematical formalism of torque! it's kind of astonishing the things that humans were able to build (such as the cathedrals which are the subject of that book) without a formalized understanding of even these most basic physical principles
i recently moved to lausanne for school, and i just found out that the cathedral in town began construction in 1170! it's quite an impressive building, and it's made all the more impressive when i consider how much of physics at the time would have completely lacked the sort of mathematical formalism that we take for granted today

2024-10-04 07:56:20 GMT

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i went around quite a lot while i was travelling. the rough itinerary was arriving in tōkyō in early may, then heading south to kyūshū through may and maybe half of june so that i could visit before the summer heat got too oppressive, and then heading north to hokkaidō around the end of june to beat the summer heat. i made it as far south as yakushima (spent a week there, and it rained for the entire week!), and as far north as wakkannai. i spent a lot of time hiking, which was sort of funny since i'm not normally a super big hiker by any means. some of the most interesting places that i visited were kaichu onsen on the south coast of yakushima, fugen-dake near unzen, ishinomaki (a small town that was badly damaged by the 2011 tsunami), and rishiri-zan, on rishiri-tō.
you've been to japan, right? did you have any favourite spots that you visited while you were there? for having spent three months there, i'm surprised that i still feel like there are places that i would like to have seen but didn't!

2024-10-03 20:42:40 GMT

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ah, what a shame! i don't really expect anyone else to pick up on (my) ilo, but if this is quite famous, it might be a good idea to rename. i'm taking the names for everything from toki pona (the assembler is "pali", the relocatable binary format is "poki", and the linker is probably going to be called "wan"), but even then, "ilo" is a bit of an awkward name for an isa, since an isa isn't really a "machine" or a "tool" in its own right, so much as it is a specification or a set of rules. "lawa" might actually be a better name for the isa itself!
as a side note, uxn was a huge inspiration for me to start thinking about isa design. the implementation of uxn's isa that i wrote was actually the first emulator that i ever wrote! i spent three months this summer backpacking in japan, and i kept a little notebook for scribbling ideas in, and ilo ended up kind of coalescing in that notebook out of ideas that i assimilated from uxn, risc-v, and a bunch of other isas. i suppose that what i'm trying to say is thank you for the inspiration that uxn provided!

2024-10-03 12:49:30 GMT

wanted to share a little project i've been working on for a bit. i've been tinkering with isa design for quite a while now, and i've been developing a 16-bit isa called "ilo". i've recently been working on a suite of binary utilities and, while it's unfinished, i have a working assembler and a relocatable binary format. my next goals are to write a "readelf"-like program to examine binaries, as well as a linker. both should probably be much less work than the assembler. once this is done, i think that i'm going to return to working on my emulator. i have a working emulator for ilo, but i would like to develop something a bit more sophisticated. if anyone is curious, the binary utilities are under development at https://codeberg.org/mra/ilo-binutils