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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 h

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!
- catgary 3y ago
  I would say that at that point you’re probably just digging in your heels - that’s a major group that does serious work. You can also look at Aaron Ames’s PhD thesis and how that work in hybrid dynamical systems, driven by category theory, has shaped his current output (which is 20-50 papers/year as a full professor at CalTech).

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!

catgary 3y ago
I would say that at that point you’re probably just digging in your heels - that’s a major group that does serious work. You can also look at Aaron Ames’s PhD thesis and how that work in hybrid dynamical systems, driven by category theory, has shaped his current output (which is 20-50 papers/year as a full professor at CalTech).