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I must have sat through a dozen of talks about how double push-out rewriting theory is going to revolutionize mathematical biology/linguistics/etc. I can give f

I must have sat through a dozen of talks about how double push-out rewriting theory is going to revolutionize mathematical biology/linguistics/etc. I can give firsthand evidence that it’s not limited to funding proposals. And there is a long tradition of category theory being applied to CS theory in PL semantics and type theory. It’s really not a new idea.

consilient 3y ago
Sure, I'm not saying there's no hype. And DPO rewriting has gone the way of all concurrent systems stuff, I agree. But good work that's hyped up as an era-defining breakthrough is ... still good work. Lenses are great. Synthetic differential geometry is imo super promising. HoTT is going to make for a beautiful failed dream. None of it is the Principia, but it shouldn't have to be. And there's plenty of space between there and crypto scams.
- wholinator2 3y ago
  You list many highly interesting sounding theories. As someone who's just entering post undergraduate academia, do you suggest any resources for learning a survey of the field currently? I'd heard of category theory and thought it was awesome but in all my looking I've never seen the number of current in development and actually applied ideas you've listed here. Thanks
  - consilient 3y ago
    Lenses: https://arxiv.org/pdf/2001.08045.pdf https://arxiv.org/pdf/2001.08045.pdf SDG: https://tildeweb.au.dk/au76680/NMOS.pdf https://tildeweb.au.dk/au76680/NMOS.pdf HoTT (good luck): https://hott.github.io/book/hott-online-1404-g79e6d60.pdf https://hott.github.io/book/hott-online-1404-g79e6d60.pdf
- catgary 3y ago
  I think you’re conflating criticism of Applied Category Theory™ with criticism of category theory. I honestly feel bad for some of the students who got swept up into it - I’m not convinced they come out with the hard programming skills of someone working in PL semantics or the flexibility to work in other fields of mathematics that an algebraic topology- or geometry-focused category theory student might have.
  - consilient 3y ago
    Maybe so. I'm not sure what the TM means, at any rate. But to my mind there's a clear distinction between the sort of stuff John Baez does, which could reasonably be called "applied", and the sort of stuff Jacob Lurie does, which absolutely is not. And there's good and valuable work in both clusters.
    - catgary 3y ago
      Maybe! I just think I was exactly the sort of industrial scientist who would be the market for something like CatLab.jl, or a lot of papers that intersected with my new-found industrial domain, and I just never found anything compelling. I feel like I wasted a fair bit of time trying to get anything out of it, so I’ve been left pretty skeptical of anything coming of California or Oxford. The lenses stuff is quite good and I think it would have been well-published/cited in PL theory even without the ACT branding.

consilient 3y ago

Sure, I'm not saying there's no hype. And DPO rewriting has gone the way of all concurrent systems stuff, I agree. But good work that's hyped up as an era-defining breakthrough is ... still good work. Lenses are great. Synthetic differential geometry is imo super promising. HoTT is going to make for a beautiful failed dream. None of it is the Principia, but it shouldn't have to be. And there's plenty of space between there and crypto scams.

wholinator2 3y ago
You list many highly interesting sounding theories. As someone who's just entering post undergraduate academia, do you suggest any resources for learning a survey of the field currently? I'd heard of category theory and thought it was awesome but in all my looking I've never seen the number of current in development and actually applied ideas you've listed here. Thanks
- consilient 3y ago
  Lenses: https://arxiv.org/pdf/2001.08045.pdf https://arxiv.org/pdf/2001.08045.pdf SDG: https://tildeweb.au.dk/au76680/NMOS.pdf https://tildeweb.au.dk/au76680/NMOS.pdf HoTT (good luck): https://hott.github.io/book/hott-online-1404-g79e6d60.pdf https://hott.github.io/book/hott-online-1404-g79e6d60.pdf
catgary 3y ago
I think you’re conflating criticism of Applied Category Theory™ with criticism of category theory. I honestly feel bad for some of the students who got swept up into it - I’m not convinced they come out with the hard programming skills of someone working in PL semantics or the flexibility to work in other fields of mathematics that an algebraic topology- or geometry-focused category theory student might have.
- consilient 3y ago
  Maybe so. I'm not sure what the TM means, at any rate. But to my mind there's a clear distinction between the sort of stuff John Baez does, which could reasonably be called "applied", and the sort of stuff Jacob Lurie does, which absolutely is not. And there's good and valuable work in both clusters.
  - catgary 3y ago
    Maybe! I just think I was exactly the sort of industrial scientist who would be the market for something like CatLab.jl, or a lot of papers that intersected with my new-found industrial domain, and I just never found anything compelling. I feel like I wasted a fair bit of time trying to get anything out of it, so I’ve been left pretty skeptical of anything coming of California or Oxford. The lenses stuff is quite good and I think it would have been well-published/cited in PL theory even without the ACT branding.