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I feel like enough time has passed that somebody could get away with making a new sketch about the Spanish Inquisition. For sure nobody would expect it.
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julesh
@julesh@mathstodon.xyz
mastodon 4.7.2Applied Compositional Thinking
2099 Followers
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Joined October 30, 2022
In this paper we improve the bound on the value of Dylan's constant 𝐷. This value, first defined by Dylan [1963], is the number of roads that a man must walk down.
We briefly recap the history of Dylan's constant. Although it is not a priori obvious that a man must walk down a finite number of roads, a relatively elementary nonconstructive proof that 𝐷 is finite, using the pigeonhole principle, was quickly given by Yarrow, Stookey and Travers [1963]. The first explicit bound, a stack of exponentials of height 5, was found by Wonder [1966]. This bound was significantly improved by Baez [1976] to 𝐷 ≤ 420 using methods of higher category theory. Although this bound remains the best known currently, Adams [1980] conjectured that 𝐷 = 42 based on extensive computer calculations.
If you overflow the level of a bath then it wraps around to the maximum negative fill level, creating a column of water down to the floor downstairs
I don't like the term "hallucination" in the context of LLMs for multiple reasons, but the top reason is it's unnecessarily anthropomorphising for something that sometimes needs to be said during technical discussion
My suggestion is "fault", inspired by "page fault". What they have in common is that they are both unavoidable for deep technical reasons, and the best you can do is use various tricks to minimise them under normal conditions
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I grew up in the AI winter too. But my heart is in the 1960s cybernetics movement.
I have a new nsfw alt for hornyposting and nudes. I won't drop the link on main, but reply or dm me and it's very likely I'll send you the link (will happily trade alts too)
The function "curry" returns NaN which stands for "not a naan"
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Perhaps it would be more sensible and/or less controversial to create a brand new degree programme in AI, whose first year is initially frankensteined together from modules of mathematics, statistics, physics and computer science
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I think that disagreeing with "LLMs are now central to computer science" would be ahistorical, and probably held mainly by people who grew up in the AI winter. For the vast majority of the field's existence this was *the* flagship problem.
I don't see what all the fuss is about over the power consumption of AI, a perfectly good solution has been there all along
I'm getting subtwoten, just like the good old days. Have to go really over the top with unpopular takes just to mimic a fraction of the power of algorithmic content curation.
Being born gets you put on a government watchlist
The true map of London, ie. the London conurbation (population just under 9.8m)
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Recognising "wouldn't it be nice if everyone would just not play the unique dominant strategy" as a fallacy is baby stuff. You have to do *real* theory.
Train I was on replaced "where this train terminates" with "where this train finishes its journey". It's political correctness gone mad, next thing you know they'll be replacing "inclement weather" with a word that isn't made up
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@mc Literally any Firefox fork, I think they basically all committed to removing mozilla bs from upstream. Personally I use Zen which is a very opinionated fork, but there are plenty that look basically the same
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@mc@mathstodon.xyz @SvenGeier@mathstodon.xyz I'm pretty sure 99% of people in finance are not spending all day staring at data looking for patterns. There have been statistical algorithms that do that more reliably than humans since the 90s
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@mc@mathstodon.xyz This also plays into my conspiracy theory that quant finance was a decade ahead of the rest of the world in deep RL when it peaked around 2017 (aka they knew some stuff back then that nobody knows to this day), but then were completely blindsided by the transformer architecture (which for them is probably far more useful to run on raw time series data than on language)
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@johncarlosbaez@mathstodon.xyz @pigworker@types.pl I learned the same thing but the other way round (this is not a coincidence, we were in the same place when it happened). I knew this operation was a monad but didn't know it was the free monad monad
Said in terms of just polynomial functors, the operation p* defined as the least fixpoint of p*(y) = y + p(p*(y)) (that's the least fixpoint of an endofunctor on Poly) is both a monad -* on Poly, and also has the property that p* is a monad on Set for every p
Queering the binary/nonbinary binary
logic of brunch implications
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In theory a dot matrix printer could print 1 page in the time a laser printer could print like 20 pages, but in reality a dot matrix printer could print 1 page in the time that a laser printer can tell you that it's out of cyan
Attempted to result to using Debug.trace for debugging in idris; discovered that unsafePerformIO is actually broken in idris; found the issue opened by @gallais@mamot.fr 4 years ago
https://github.com/idris-lang/Idris2/issues/2306
I have a category theory question that turned into a set theory question. If you have a functor F : Setᵒᵖ → Set which I promise is representable then you can easily get the the representing set, up to unique bijection, as F(1). What about for a functor F : Set → Set?
If you do F(2) that tells you the powerset of the representing set. Is that enough to know the set? Is powerset injective on sets? If so, is it true in just ZF or do you need more?
Is there a less horrendous way to get back the representing set of a promised-to-be-representable covariant functor, other than trying to invert the powerset operation?
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@mc@mathstodon.xyz oh my god, I'd never been able to figure out why they keep funding and talking about pure maths, the best explanation I could come up with was to mumble about the rationalist cult and AGI, I don't know why I didn't think of this but suddenly everything makes sense
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@pettter Natural language communication, and associated things like common sense reasoning
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[desperately trying to remember what qbaisc syntax looks like]
DIM age%
PRINT "How old are you?"
INPUT age%
IF age% < 13 THEN GOTO jail
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@tranquillity@mastodon.minionflo.net we're gonna have to teach the kids haskell so they can use combinators and pointfree style
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@michael_ Not for any specific reason, more like a *should*, because AI has been a historical beacon in the field since the very beginning
I am personally satisfied to consider it empirically settled that symbol grounding is not necessary
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@tranquillity@mastodon.minionflo.net just saying LLMs are incredibly good at frontend, at least anything that's just styling and doesn't have complex logic, the main problem is it would look so professional and corporate nobody would trust it
Do Lithuanian catgirls come from Vilnyas
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@lisyarus@mastodon.gamedev.place Sounds plausible... I would like to extract the set of elements, I'm thinking that if you delete the bottom element of the lattice then the set of elements is given up to bijection by the set of remaining minimal elements, which are the singleton subsets
Piketty pointing out that macroeconomic growth is counterintuitive because it is exponential and measured logarithmatically: "growth rate on the order of 1% is in fact extremely rapid... in generational terms. Over a period of 30 years, a growth rate of 1% corresponds to cumulative growth of more than 35%... in practice, this implies major changes in lifestyle"
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@Andrev@types.pl It's at least not expected coming from haskell, where unsafePerformIO performs IO, even in interactive. Perhaps the idris version should be renamed to unsafeBuildFreeSyntaxButDoNotPerformIO
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@boarders None of the cs degrees I've interacted with give enough background in lower years in things like calculus and probability/information theory and data handling methods. In many places it's probably possible with students choosing a very specific combination of options
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@migratory Deep understanding is not the same thing as being able to make guarantees, except in very specific fields like physics where the universe is nice to you. For example in social sciences you can never make guarantees about anything, but that is no reason not to make a deep study of social sciences
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@MartinEscardo I'm a bit surprised you're so surprised by this, but maybe I'm biased since Paulo was my supervisor. I don't doubt this result is extremely cool if I could understand it, but instinctively I already felt that topology is related to constructivity (thanks to both topos theory and synthetic topology), whereas my mind is still blown by the cases where dialectica type methods were used to sharpen analytic bounds in ergodic theory and Ramsey theory and things like that
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@BartoszMilewski How are page faults faults? Or faults in tennis, for another example? In the latter case it's a legitimate part of the game