US Army applying new areas of math • Hacker News Board

Re: US Army applying new areas of math

#11

Post by leereeves » Thu, Mar 21, 2019, 7:50 PM UTC

cerealbad wrote: post #6

mlthoughts2018 wrote: post #4

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…

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.

Re: US Army applying new areas of math

#12

Post by Darmani » Thu, Mar 21, 2019, 7:54 PM UTC

wenc wrote: post #3

I 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?

One application: It makes it easier to do mechanized reasoning to optimize SQL queries.

https://arxiv.org/pdf/1607.04822.pdf

Re: US Army applying new areas of math

#13

Post by hopler » Thu, Mar 21, 2019, 7:54 PM UTC

wenc wrote: post #7

archgoon wrote: post #5

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...

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.

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.

Re: US Army applying new areas of math

#14

Post by hopler » Thu, Mar 21, 2019, 7:57 PM UTC

ska wrote: post #2

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.

Re: US Army applying new areas of math

#15

Post by hopler » Thu, Mar 21, 2019, 8:01 PM UTC

Frankly this sounds like some bureaucrat who likes HTT made up an excuse to fund it. It's a mil/gov version of a corporate engineer who decides to build a project in a language they read about on HN.

Re: US Army applying new areas of math

#16

Post by Ericson2314 » Thu, Mar 21, 2019, 8:02 PM UTC

mlthoughts2018 wrote: post #4

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 knowledge, and the statistics isn't to bad and just the last step, you definitely want to make sure you model prior to drawling statistical conclusions is sound and rich.

tl;dr there's good reason to invest in better tools, and the homotopy type theory that's being funded is as much about "how to apply math" as "what math to apply".

Re: US Army applying new areas of math

#17

Post by empath75 » Thu, Mar 21, 2019, 8:02 PM UTC

wenc wrote: post #3

I 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?

It’s basically a new foundation for math based on types rather than sets.

Re: US Army applying new areas of math

#18

Post by [deleted] » Thu, Mar 21, 2019, 8:05 PM UTC

wenc wrote: post #3

I 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?

[deleted]

Re: US Army applying new areas of math

#19

Post by fspeech » Thu, Mar 21, 2019, 8:09 PM UTC

hopler wrote: post #13

wenc wrote: post #7

Earlier quoted context omitted.

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.

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.

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). The main thing is that your subject under study has a monoidal structure (basically operations that compose associatively and have units).

Re: US Army applying new areas of math

#20

Post by mlthoughts2018 » Thu, Mar 21, 2019, 8:14 PM UTC

cerealbad wrote: post #6

mlthoughts2018 wrote: post #4

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…

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.

How is any of that related to this article? This is about applications of formal mathematics, and the criticism (not skepticism) used by the author is in no way connected to the point you’re making.