US Army applying new areas of math
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US Army applying new areas of math
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Re: US Army applying new areas of math
#2I like the characterization of pure vs. applied math being primarily about motivation. I've often said the difference is more on the "why" that the "what".
Re: US Army applying new areas of math
#3I wonder if there's anyone here working on Homotopy Type Theory that can explain what it is, and how it is used in modeling?
I skimmed the PDF of the book but am drawing blank as to its connection to an application. Perhaps it's used for verification of concepts, similar to how formal methods in CS (e.g. TLA+) are used to conceptually check algorithms?
Re: US Army applying new areas of math
#4Without more details about why homotopy type theory was mixed into that paragraph about causal inference, I call bullshit. I think this is bolstered by clicking on the link to the previous post about categorical data analysis, which offers nothing and even takes a pot shot at professional statistics (saying the field is “bad at specifying the domain and range of functions” which is a bizarre and incredibly inaccurate characterization of professional statistics).
I think someone is making a mountain out of a mole hill here. I’m sure there will be a flurry of grant money though.
Re: US Army applying new areas of math
#5In 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-adap...
Re: US Army applying new areas of math
#6Without more details about why homotopy type theory was mixed into that paragraph about causal inference, I call bullshit. I think this is bolstered by clicking on the link to the previous post about categorical data analysis, which offers nothing and even takes a pot shot at professional statistics (saying the field is “bad at specifying the domain and range of functions” which is a bizarre and incredibly inaccurate…
Statistics has become politicized through questionable interpretations of polling and crime data specifically with respect to various demographic markers. Increasing skepticism towards the field is a product of ideological division. No science is immune from its scientists and most humans are irrational creatures with emotive drivers.
Re: US Army applying new areas of math
#7In 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-adap...
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.
Re: US Army applying new areas of math
#8For anyone interested in applying traditionally pure fields, Applied Topology has been slowly gaining steam lately (as reflected in the article: "topological" is now a hot word).
Robert Ghrist of UPenn has been at the forefront of bringing topology into applied fields; and has written a good text on the subject.
Re: US Army applying new areas of math
#9In 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-adap...
> 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.
Re: US Army applying new areas of math
#10I like the characterization of pure vs. applied math being primarily about motivation. I've often said the difference is more on the "why" that the "what".
I studied applied mathematics. Roughly summarised: pure mathematicians create new math through the process of conjecture and proof. Applied mathematicians use those theorems and methods to solve simplified models of reality in order to draw conclusions about expected behaviour and/or for the sake of optimisation.