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For 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.
Without 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…
I think "bad at specifying the domain and range of functions" was somebody trying to describe type safety in more pedestrian terms. I think the actually idea is while the theory of statistics (like all math) is well typed, professional statisticians tend to use shitty tools/programming languages without good type systems. People scoff that type errors are easy, but when most of the work is encoding the domain knowled…
The idea that statistics is a field with poor software tools is just plain crazy.
I 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".
"Why" does not exist in science. "Why" is metaphysics. Pure math is increasing abstraction, moving away from physical reality, from examples to patterns. Applied math is the reverse direction. No matter which direction is your personal preference, sometimes switching direction helps you reach your goal.
I 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 .
Wearing both hats you can find yourself creating new mathematics, but there is a difference in why you are doing it, and what you consider progress to mean.
Good on them, that long division can be tricky.
> Modeling frameworks are desired that are able to eschew the usual computational simplification assumptions and realistically capture … complexities of real world environments and phenomena, while still maintaining some degree of computational tractability. Of specific interest are causal and predictive modeling frameworks, hybrid model frameworks that capture both causal and predictive features, statistical modeling frameworks, and abstract categorical models (cf. Homotopy Type Theory).
You could fit everyone in the Army who understands this in a single barracks.
I 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".
"Why" does not exist in science. "Why" is metaphysics. Pure math is increasing abstraction, moving away from physical reality, from examples to patterns. Applied math is the reverse direction. No matter which direction is your personal preference, sometimes switching direction helps you reach your goal.
For what it's worth I find your characterization awkward; an attempt to map onto a simple spectrum that seems to miss something important. I'll have to think about why that is.
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-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:…
> US Army applying new areas of math Good on them, that long division can be tricky. > Modeling frameworks are desired that are able to eschew the usual computational simplification assumptions and realistically capture … complexities of real world environments and phenomena, while still maintaining some degree of computational tractability. Of specific interest are causal and predictive modeling frameworks, hybrid m…
Earlier quoted context omitted.
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.
There certainly has been widespread misuse (and probably intentional abuse) of statistics, but is it fair to blame the field for that? It's very often an outsider misusing statistics, while professional statisticians who point out the mistakes are ignored.
I don't know how much of the blame you should assign to the field, in that.