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In a similar vein, John Baez was given an opportunity, funded under a grant from DARPA, to use Category Theory for modeling systems. https://johncarlosbaez.wor

In a similar vein, John Baez was given an opportunity, funded under a grant from DARPA, to use Category Theory for modeling systems. https://johncarlosbaez.wordpress.com/2016/10/02/complex-adaptive-system-design-part-1/ https://johncarlosbaez.wordpress.com/2016/10/02/complex-adap...

wenc 8y ago
Fascinating. Category theory sounds like a promising approach to analyze systems of systems. But being a deterministic approach, I wonder how it handles stochastic interactions between systems though, which in a complex system results in unpredictable emergent behavior.
- hopler 8y ago
  Category theory operates at a far more abstract level than that. A whole dynamical system would just be a dot in a category theory analysis.
  - fspeech 8y ago
    You can be as abstract or concrete as you want. For example you can embed set theory inside a category (see Lawvere, Rosebrugh: Sets for Mathematics or https://ncatlab.org/nlab/show/ETCS https://ncatlab.org/nlab/show/ETCS). The main thing is that your subject under study has a monoidal structure (basically operations that compose associatively and have units).
fmihaila 8y ago
> In a similar vein, John Baez was considering (ultimately declining) an opportunity [...] But did he ultimately decline? The link you posted has this content at the very end: > Something tipped the scales and I said yes. We applied for the grant, and we got it. > And so, an interesting adventure began. It will last for 3 years, and I’ll say more about it soon. And further down, this is his reply to a reader comment: > As I said at the end of my post, I am working with Metron on this CASCADE project, and I’ll be doing it for 3 years. My decision was not predicated on the hope that the US will do anything in particular. It’s predicated on the hope that I’ll make faster progress in my research if I team up with some more practical people and use my math skills to tackle a concrete problem in network theory: namely, optimizing search and rescue missions. I’ll get lots of new ideas which I wouldn’t get otherwise, and I’ll publish papers on these ideas. > If I were only searching for mathematical beauty in the word I wouldn’t feel the need to work on this project, because beauty is so easy to find. Instead, I’m trying to develop network theory into a useful set of tools.
- archgoon 8y ago
  Correct, I misread that paragraph. Editing original comment, thank you.

wenc 8y ago

Fascinating. Category theory sounds like a promising approach to analyze systems of systems. But being a deterministic approach, I wonder how it handles stochastic interactions between systems though, which in a complex system results in unpredictable emergent behavior.

hopler 8y ago
Category theory operates at a far more abstract level than that. A whole dynamical system would just be a dot in a category theory analysis.
- fspeech 8y ago
  You can be as abstract or concrete as you want. For example you can embed set theory inside a category (see Lawvere, Rosebrugh: Sets for Mathematics or https://ncatlab.org/nlab/show/ETCS https://ncatlab.org/nlab/show/ETCS). The main thing is that your subject under study has a monoidal structure (basically operations that compose associatively and have units).

fmihaila 8y ago

> In a similar vein, John Baez was considering (ultimately declining) an opportunity [...] But did he ultimately decline? The link you posted has this content at the very end: > Something tipped the scales and I said yes. We applied for the grant, and we got it. > And so, an interesting adventure began. It will last for 3 years, and I’ll say more about it soon. And further down, this is his reply to a reader comment: > As I said at the end of my post, I am working with Metron on this CASCADE project, and I’ll be doing it for 3 years. My decision was not predicated on the hope that the US will do anything in particular. It’s predicated on the hope that I’ll make faster progress in my research if I team up with some more practical people and use my math skills to tackle a concrete problem in network theory: namely, optimizing search and rescue missions. I’ll get lots of new ideas which I wouldn’t get otherwise, and I’ll publish papers on these ideas. > If I were only searching for mathematical beauty in the word I wouldn’t feel the need to work on this project, because beauty is so easy to find. Instead, I’m trying to develop network theory into a useful set of tools.

archgoon 8y ago
Correct, I misread that paragraph. Editing original comment, thank you.