@julesh@mathstodon.xyz
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julesh

@julesh@mathstodon.xyz

Applied category theorist
Games, learning, control, complex systems, diagrams, syntax
Affiliations: MSP Group / 20squares / CyberCat Institute

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julesh, to random
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von Neumann & Morgenstern's observation that moves of nature can always be floated up to the top of an extensive form game tree using information sets is definitely a distributive law wearing a false moustache

julesh, to random
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Haskell hot take: Prelude should make Float and Double non-instances of Eq, and then provide functions unsafeFloatEq and unsafeDoubleEq for those cases when you really do want to compare them for equality

julesh, to random
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Thing that just came up in teaching: Num used to be a subclass of Eq in the 2010 Haskell Prelude, but isn't any more

julesh, to random
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Academia is when you sacrifice your research time in order to get more research time later, until you retire

julesh, to random
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Society seems to have somehow implicitly converged on using both terms "artificial intelligence" and "machine learning" in parallel for the same systems viewed at different levels of abstraction, a bit like neuroscience vs cognitive science. Roughly, if you only care about what the system does then you say AI, if you also care about how it works then you say ML

julesh,
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@SvenGeier This is just my observation of how people seem to use the terms currently

julesh, to random
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Just realised there's an off-by-1 error where musical intervals are 0-indexed but violin hand positions are 1-indexed, so 1st position you have an open string, 3rd position you stop a 4th above the string, 4th position a 5th above etc

julesh,
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This feels a lot like how 0 is the 1st number, 1 is the 2nd number, etc

johncarlosbaez, (edited ) to random
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The mathematics of harmony is full of small glitches. There's no way to eliminate them. There are even meta-glitches, arising when two glitches are almost the same size... but not quite.

And it doesn't stop there. Around 1775, Bach's student Kirnberger discovered an amazingly small meta-meta-glitch in the mathematics of harmony. It's now called 'Kirnberger's atom'.

It relies on a mathematical miracle: a coincidence so eye-popping that in 2009 a famous expert in black hole physics wrote a paper trying to explain it!

Read on:

https://johncarlosbaez.wordpress.com/2024/01/25/well-temperaments-part-3/

julesh,
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@johncarlosbaez But can 2 meta-glitches be almost the same but not quite?

Clearly somebody needs to write a paper about the gauge theory of harmony

typeswitch, to random
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"i'm not five years old anymore" tired cliche, not constructive

"i'm at least six years old" same meaning but confuses listener (positive), constructive

julesh,
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@typeswitch I sometimes say "I wasn't born yesterday", but it's more constructively useful to say the classically equivalent “I was either born today or I am at least 2 days old”

julesh, to random
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Of course it's very easy to not become the very thing you swore to destroy, if you don't become anything at all

julesh, to random
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The fact that quantum algebra was originally developed without string diagrams is no less mind blowing to me than what mathematicians did in the Islamic Middle Ages without having algebraic notation

julesh,
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@johncarlosbaez By "quantum algebra" I meant the study of things like Hopf algebras and Frobenius algebras, as in "quantum groups are neither quantum nor groups”

julesh,
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@johncarlosbaez This is fair. To me that stuff seems nightmarishly complicated, not that I've tried extremely hard to get into it (I tried and gave up a few times to figure out what cohomology is, last time I did any number theory was baby high school stuff). I vaguely wish there were sources that had the same extreme level of care and work put into clarity of explanation as, say, ZX calculus

julesh,
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@johncarlosbaez @dimpase As an applied category theorist, I sometimes look at whole fields like algebraic topology and algebraic geometry, and think...... surely all that crazy machinery has got to be useful for something

julesh,
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@johncarlosbaez @Joemoeller I don't doubt that! But there's a whole lot of very powerful looking machinery designed by a whole lot of extremely smart people, and we have hard problems that need solutions

julesh, to random
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Teaching starts today, got 2nd year haskell in half an hour and then game theory later this afternoon. It's a bit chilly out, a balmy -7 degrees this morning

julesh,
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@johncarlosbaez A little bit in the last couple of weeks, but never simultaneously cold enough and heavy enough to settle

zanzi, to random
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Do dependent lenses have a van laarhoven representation?

julesh,
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@zanzi My first guess would be the obvious thing, replace 2 of the 3 function arrows in the definition with Pi

More gnarly question, what about profunctor encoding? What's a "dependent profunctor"?

julesh, to random
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Yes, reminder that what most people call "a job done by a human" is better known by computer scientists as "a problem we haven't figured out how to solve yet"

So we're 40% of the way to the major goal of eliminating all work. Can the macroeconomists catch up and do their bit please?

julesh, to random
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Important clarification on a twoot I wrote yesterday: Max Kanovich was jointly supervised by the famous probability theorist Kolmogorov together with the famous constructive logician Andrey Andreyevich Markov, who definitely should not be confused with the famous probability theorist Andrey Andreyevich Markov (who was his father)
https://en.wikipedia.org/wiki/Andrey_Markov
https://en.wikipedia.org/wiki/Andrey_Markov_Jr.

julesh, to random
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"Markov kernel" is an exact synonym for "conditional probability distribution" that sounds far more fancy but, crucially, contains only 30% as many syllables

julesh, to random
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Today's hell journey: Basingstoke -🚍-> Reading -🚄-> London -🚄-> Glasgow

julesh,
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@BartoszMilewski Yeah those are not too bad, getting to Glasgow from London is much much slower

julesh,
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@BartoszMilewski The worst thing is the terrible system they have for security screening on the St Pancras side, which can easily take an hour

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