6 ms·

Note. A mathematician's idea of "applied" and a normal person's idea of the same bear little resemblance.

by btilly 8y ago

marquis-chacha 8y ago
"Applied Category Theory" almost seems a bit tongue-in-cheek to me, given Category Theory is designed to distill the concepts found in a bunch of different "applied" fields into one, theoretical, framework. (That was my impression from the intro lecture, at least)
- brianberns 8y ago
  They should call the class “Concrete Nonsense” (since category theory itself is sometimes described as “abstract nonsense”).
  - saidajigumi 8y ago
    Which phrase, I note with profound glee, has its own Wikipedia page for precisely this usage: https://en.wikipedia.org/wiki/Abstract_nonsense https://en.wikipedia.org/wiki/Abstract_nonsense
  - dizziest 8y ago
    Thank you! I couldn't verbalize it until your comment :)
  - quickthrower2 8y ago
    Maybe “Brutalist Nonsense”
neel_k 8y ago
It may be professional deformation speaking, but they seem to be using "applied category theory" in a coherent and natural sense: they mean the theory of monoidal categories, (a) viewed as a generalization of linear algebra, and (b) omitting logic and programming language semantics as applications. Given the centrality of linear algebra to applied mathematics (even in places where you wouldn't first expect, like the theory of regular expressions and finite automata), this seems like a perfectly sensible coinage. (Even though I must admit I get my back up at the omission of categorical proof theory, it's perfectly natural as a sales pitch -- type theorists don't need to be convinced of the utility of category theory!)
- luxbock 8y ago
  > Given the centrality of linear algebra to applied mathematics (even in places where you wouldn't first expect, like the theory of regular expressions and finite automata) Where can I read more about this?
  - doneata 8y ago
    Stephen Dolan's pearl "Fun with semirings" might be relevant: http://stedolan.net/research/semirings.pdf http://stedolan.net/research/semirings.pdf But I would also like to know what other resources Neel has to recommend.
    - eru 8y ago
      If you like Matlab more than Haskell, try https://www.goodreads.com/book/show/11768822-graph-algorithms-in-the-language-of-linear-algebra https://www.goodreads.com/book/show/11768822-graph-algorithm...

Note. A mathematician's idea of "applied" and a normal person's idea of the same bear little resemblance.

by btilly 8y ago

Note. A mathematician's idea of "applied" and a normal person's idea of the same bear little resemblance.

"Applied Category Theory" almost seems a bit tongue-in-cheek to me, given Category Theory is designed to distill the concepts found in a bunch of different "applied" fields into one, theoretical, framework. (That was my impression from the intro lecture, at least)

brianberns 8y ago
They should call the class “Concrete Nonsense” (since category theory itself is sometimes described as “abstract nonsense”).
- saidajigumi 8y ago
  Which phrase, I note with profound glee, has its own Wikipedia page for precisely this usage: https://en.wikipedia.org/wiki/Abstract_nonsense https://en.wikipedia.org/wiki/Abstract_nonsense
- dizziest 8y ago
  Thank you! I couldn't verbalize it until your comment :)
- quickthrower2 8y ago
  Maybe “Brutalist Nonsense”

neel_k 8y ago

It may be professional deformation speaking, but they seem to be using "applied category theory" in a coherent and natural sense: they mean the theory of monoidal categories, (a) viewed as a generalization of linear algebra, and (b) omitting logic and programming language semantics as applications. Given the centrality of linear algebra to applied mathematics (even in places where you wouldn't first expect, like the theory of regular expressions and finite automata), this seems like a perfectly sensible coinage. (Even though I must admit I get my back up at the omission of categorical proof theory, it's perfectly natural as a sales pitch -- type theorists don't need to be convinced of the utility of category theory!)

luxbock 8y ago
> Given the centrality of linear algebra to applied mathematics (even in places where you wouldn't first expect, like the theory of regular expressions and finite automata) Where can I read more about this?
- doneata 8y ago
  Stephen Dolan's pearl "Fun with semirings" might be relevant: http://stedolan.net/research/semirings.pdf http://stedolan.net/research/semirings.pdf But I would also like to know what other resources Neel has to recommend.
  - eru 8y ago
    If you like Matlab more than Haskell, try https://www.goodreads.com/book/show/11768822-graph-algorithms-in-the-language-of-linear-algebra https://www.goodreads.com/book/show/11768822-graph-algorithm...