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It’s a bit tough, on one hand John Baez is a great messenger because he’s such a fantastic communicator. But on the other hand, he’s a pretty horrible spokesper

It’s a bit tough, on one hand John Baez is a great messenger because he’s such a fantastic communicator. But on the other hand, he’s a pretty horrible spokesperson for ACT because the man did theoretical physics and higher category theory for 30 years and now has decided to do “applied” work. It’s pretty evident in this course, he’s just setting up the frameworks people talk about using but isn’t going for any actual results that demonstrate the claimed application. I don’t think he’s ever actually done any applied work before he decided to revolutionize the field. I once watched John talk down to some sort of research electrical engineer at a conference because his diagrammatic calculus didn’t line up with John’s approach, when anyone with a lick of sense would want to understand why their approach didn’t suffice and how these changes addressed its shortcomings - this person was a subject matter expert and Baez condescended to him about his own field! I think his attitude has, unfortunately, rubbed off on a lot of the people in his orbit.

j2kun 3y ago
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.
- catgary 3y ago
  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]. [1] https://arxiv.org/abs/2012.02113 https://arxiv.org/abs/2012.02113 [2] http://www.tac.mta.ca/tac/volumes/35/45/35-45.pdf http://www.tac.mta.ca/tac/volumes/35/45/35-45.pdf I can’t stress enough that Koditschek group are serious people who are using this stuff because it addresses problems they’ve been grappling with.
  - shanusmagnus 3y ago
    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?
    - catgary 3y ago
      It’s basically just saying notions of compositionality from software doesn’t really translate over to analogue computers, and by extension robots that interact with their environment. It seems like they’re being careful to make atomic statements that are supported by the individual papers they’re citing. They may have been dealing with some particularly obstinate reviewers and adopted a defensive writing style (it can be a tough habit to kick, I’ve definitely given overly precise seminar talks because someone brought up size issues the week before and I just didn’t want to deal with any pedantry).
  - j2kun 3y ago
    And then the difficult part becomes, how could I verify that this is used in practical robotics products? There are a handful of citations to [2], many of which are more category theory. One non-category-theory citation seems to say, "there is this formalization that's still a work in progress, and go read that paper if you're interested", hard to tell as an outsider how much they use it. Unless I can prove it is used, then it doesn't meet my bar. Maybe it's too new, but that means it still has to prove itself. Good luck to them!

j2kun 3y ago

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.

catgary 3y ago
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]. [1] https://arxiv.org/abs/2012.02113 https://arxiv.org/abs/2012.02113 [2] http://www.tac.mta.ca/tac/volumes/35/45/35-45.pdf http://www.tac.mta.ca/tac/volumes/35/45/35-45.pdf I can’t stress enough that Koditschek group are serious people who are using this stuff because it addresses problems they’ve been grappling with.
- shanusmagnus 3y ago
  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?
  - catgary 3y ago
    It’s basically just saying notions of compositionality from software doesn’t really translate over to analogue computers, and by extension robots that interact with their environment. It seems like they’re being careful to make atomic statements that are supported by the individual papers they’re citing. They may have been dealing with some particularly obstinate reviewers and adopted a defensive writing style (it can be a tough habit to kick, I’ve definitely given overly precise seminar talks because someone brought up size issues the week before and I just didn’t want to deal with any pedantry).
- j2kun 3y ago
  And then the difficult part becomes, how could I verify that this is used in practical robotics products? There are a handful of citations to [2], many of which are more category theory. One non-category-theory citation seems to say, "there is this formalization that's still a work in progress, and go read that paper if you're interested", hard to tell as an outsider how much they use it. Unless I can prove it is used, then it doesn't meet my bar. Maybe it's too new, but that means it still has to prove itself. Good luck to them!