I thought this said Joan Baez and was very intrigued.
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Applied Category Theory Course
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Re: Applied Category Theory Course
#72Re: Applied Category Theory Course
#73[flagged]
Re: Applied Category Theory Course
#74Earlier quoted context omitted.
All "applied category theory" books seem to be like this: they start by talking about how great the applications will be, but then instead of getting to the applications, they never stop developing the category theory for its own sake. A lot of math does similar things, to be fair, but I also don't count those as applied.
So, just to offer a few counterpoints there is Tom Leinster’s work on diversity/entropy [1], where people working in mathematical ecology have been happy with his contributions. I’ve also see the Penn robotics group start to use categorical machinery to nail down concepts like bisimulation of dynamical systems and develop a ‘type theory’ for motion plans that has its semantics in a category of dynamical systems [2].…
Semi-related: I read the first page of your second reference and really can't make any sense of it, despite having what I would have thought to be enough knowledge to at least orient:
"We aim to construct a physically-grounded compositional framework for hybrid system synthesis, particularly targeted at applications in robotics. Compositionality lies at the heart of language in general [WHM12] and its formalization underlies much of computer science in particular [Lee90]. However the behavioral modularization of physical synthesis for digital computing that arguably ushered in the information technology revolution [MC80] has proven much harder to achieve in analog computing technology [Mea89]. There are fundamental reasons for this challenge to become more severe in machines intended to perform mechanical work on their environments [Whi96]."
Since you know enough about this field to cite it, does it appear to you that this stuff could be written in a more comprehensible way, without losing expressive power? Or is this level of ornament necessary to say whatever it's saying?
Re: Applied Category Theory Course
#75Re: Applied Category Theory Course
#76I'm writing a book [1] about "bona fide" applications of mathematics to practical programming problems, where bona fide is my own personal definition [2]. I've had my eye on claims of applications of category theory for many years, and none of them have quite fit the bill (sorry, John, if you're reading this). When they talk about applications to databases it seems quite unrealistic or lacking in sufficient detail to…
This paper seems to be pretty applied, but I've only skimmed the intro:
https://arxiv.org/pdf/1504.05625.pdf
That starts to make sense to me as a sort of generalized framework for Feynman-diagram-like things. Explains why particle physicists would be drawn to category theory as well.
Feels like there's still probably a hell of a lot of dots to connect there though.
Re: Applied Category Theory Course
#77Earlier quoted context omitted.
Programming is applied algebra, the choice is not using vs not using, but understanding what you are doing vs being ignorant about it. Relevance is in the eye of the beholder. In typical business the incentive is to have a good enough code ready "yesterday", and it will be thrown away tomorrow, as the code and whatever it does are only a means to generate profit and not a goal in itself, and spending time on making i…
Programming is also applied physics. But understanding the kinetic forces behind typing is no guide to improved programming. To say that learning a field is useful is to say that knowing these abstractions is useful. Much of Haskell's "category theory" is a reuse of terms. Replace Monoid by Appendable, Monad by Composable, Functor by Runnable, etc. and most programming languages are "category theory". This says littl…
> Replace Monoid by Appendable, Monad by Composable, Functor by Runnable, etc. and most programming languages are "category theory".
I'm not sure an "Appendable" Int or IO type, or a "Runnable" / "Composable" List type is any less confusing to Joe Programmer. These descriptions do not articulate the same things implied by the Monoid, Functor, and Monad laws. Some of these aren't even correct (i.e. not all Functors are "Runnable", Monadic types do not necessarily compose directly, just via Kleisli composition).
> This says little about whether knowing the field of category theory will be useful to programming. Indeed, I think there's a good argument to say Haskell programming is much harmed by it.
> If its authors hadnt used their knowledge of category theory, but rather named the abstractions in more ordinary terms, the language would be more useful to more people.
I think this is really the least of Haskell's problems. Mystifying/poorly written monad tutorials and conflation with IO (or confusion about how IO works in the haskell runtime) is more responsible for confusing new programmers than the concept itself. I have no background in mathematics above undergrad calc 2 and I was able to understand them just fine.
Re: Applied Category Theory Course
#78Surely Baez's even in American English (yeah, I know it's a Spanish name).
British English almost always adds 's for the singular possessive, even when the name ends in s, so Dickens's and St. James's.
However, American English often uses the plural possessive suffix ' for names ending in s. One Spanish name example I have seen is Bezos' for something of Jeff's (his billions, or his wives, I forget which).
But Baez' makes no sense to me on any side of the Atlantic.
Re: Applied Category Theory Course
#79I thought this said Joan Baez and was very intrigued.
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Re: Applied Category Theory Course
#80I'm writing a book [1] about "bona fide" applications of mathematics to practical programming problems, where bona fide is my own personal definition [2]. I've had my eye on claims of applications of category theory for many years, and none of them have quite fit the bill (sorry, John, if you're reading this). When they talk about applications to databases it seems quite unrealistic or lacking in sufficient detail to…
Sorry, off-topic: can you recommend some (applied) math books for self study people can read before your book is published? I realize the question is somewhat strange and the answer depends on what people work on. Let's say it is not ML/AI. I've enjoyed e.g. 'Calculus' by G. Simmons and Niven's 'The Mathematics of Choice' even though I didn't apply any of that at work.
I can't say I've read any that I could recommend. I have heard nice things about Princeton Companion to Applied Mathematics (TOC: https://assets.press.princeton.edu/chapters/c10592.pdf) but I haven't ready it personally, and it seems to be more of a reference text and have less stuff relevant to programming specifically.