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Jonathan_Blow's profile
Jonathan Blow
Jonathan Blow
Jonathan Blow
@Jonathan_Blow

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Jonathan Blow

@Jonathan_Blow

Designer/Programmer of Braid and The Witness. President, Thekla, Inc. Partner in IndieFund. Currently working on good new things.

San Francisco
the-witness.net/news
Joined January 2010

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    1. Jonathan Blow‏ @Jonathan_Blow Apr 1

      I have tried to read several books about category theory, but they all appear to dissolve into lists of trivial details before they ever clearly say anything new or powerful. Is category theory really just the idea "hey we can draw equations in 2D instead of 1D",

      33 replies 4 retweets 95 likes
      Show this thread
    2. Jonathan Blow‏ @Jonathan_Blow Apr 1

      and then all these books are just listing out what that looks like, or is there really a separate body of ideas about something that isn't already covered everywhere else?

      3 replies 0 retweets 18 likes
      Show this thread
    3. shachaf‏ @shachaf Apr 1
      Replying to @Jonathan_Blow

      Which books have you tried reading? I think the important ideas to take away from category theory are things like naturality and universal properties, which don't have much to do with diagrams.

      1 reply 0 retweets 1 like
    4. shachaf‏ @shachaf Apr 1
      Replying to @shachaf @Jonathan_Blow

      Those sorts of things are real ideas that don't come up that much in other contexts. But this quote (from Leinster's _Basic Category Theory_) is probably pretty true, and useful to keep in mind:pic.twitter.com/zyCdr9Fjfw

      1 reply 0 retweets 0 likes
    5. shachaf‏ @shachaf Apr 1
      Replying to @shachaf @Jonathan_Blow

      I like Leinster's book. Other than that, you might like Riehl's _Category Theory in Context_, which starts out by stating a bunch of corollaries of the theorems in the book in terms of other maths (topology, linear algebra, group theory, etc.).

      1 reply 0 retweets 1 like
    6. Jonathan Blow‏ @Jonathan_Blow Apr 1
      Replying to @shachaf

      But no, that's exactly the problem? My experience reading one of these books is, I am bored + frustrated because they are spending a long time saying things I learned 15 times already from other areas but pretending they are kind of new. Then eventually they are so mired in

      1 reply 0 retweets 1 like
      Jonathan Blow‏ @Jonathan_Blow Apr 1
      Replying to @Jonathan_Blow @shachaf

      their own obtuse terminology that I cannot proceed, but, also they never showed me anything that made it make sense to invest more energy in trying to proceed. Because all I saw was stuff I already know from other subject areas.

      10:08 AM - 1 Apr 2021
      • 3 Likes
      • orneryostrich Ivan Braidi James Giammona
      3 replies 0 retweets 3 likes
        1. New conversation
        2. shachaf‏ @shachaf Apr 1
          Replying to @Jonathan_Blow

          If you want to see things that really motivate expressing things categorically, presumably a context like algebraic topology (where categories etc. originally came up) would be better.

          1 reply 0 retweets 3 likes
        3. shachaf‏ @shachaf Apr 1
          Replying to @shachaf @Jonathan_Blow

          If you learn about categories to talk about maths you already know, it'll plausibly just be a different perspective. Perspectives are still valuable, and sometimes they can help with "asking the right questions" (what topology should products have?), rather than answering them.

          1 reply 0 retweets 2 likes
        4. Show replies
        1. New conversation
        2. sclv‏ @sclv Apr 1
          Replying to @Jonathan_Blow @shachaf

          simplicial sets are one example i know of where the categorical defn is clearer and simpler than the “longhand” one. another advantage is once you know about the framework, it is easier to transport knowledge between seemingly very different topics 1/2

          1 reply 0 retweets 1 like
        3. sclv‏ @sclv Apr 1
          Replying to @sclv @Jonathan_Blow @shachaf

          for example presheaf techniques let one perform similar constructions in vector spaces, logic, homology theory, and combinatorics (via species).

          0 replies 0 retweets 0 likes
        4. End of conversation
        1. New conversation
        2. Achim Blumensath‏ @ABlumensath Apr 1
          Replying to @Jonathan_Blow @shachaf

          That's kind of the point of category: to pile abstractions onto abstractions so that certain things become very short to state. It takes years to become familiar with all this stuff, but then you can work on a very abstract level where you can get rid of all unnecessary details.

          1 reply 0 retweets 0 likes
        3. Achim Blumensath‏ @ABlumensath Apr 1
          Replying to @ABlumensath @Jonathan_Blow @shachaf

          I would guess that it has not much to offer to you personally.

          0 replies 0 retweets 0 likes
        4. End of conversation

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