
US Army applying new areas of math - tacon
https://www.johndcook.com/blog/2019/03/21/us-army-math/
======
noobermin
To be very honest, count me in as one of these. I am someone who works for a
gov't lab, but I do "very pure" scientific research. It's not that our
research doesn't have "defense applications," it might eventually, but we are
definitely a few steps removed from say CFD modeling of airplane wings.

The thing is traditional sources of funding suck, and gov't labs give
researchers a much better environment than the endlessly political academia.
Moreover, while the contractor we work with has something like a 30% odd
markup for grants, the nearest university (that I got my PhD from) takes a
whopping 56% of grant money as "overhead," I imagine to pay the salaries of
the President, coaches, and superstar medical faculty salaries, as well as the
new development all along the nearby street.

I'm happy for my job, I just am embarrassed when I tell people I work for the
military because they think I make bombs or something.

~~~
geoka9
> I just am embarrassed when I tell people I work for the military because
> they think I make bombs or something.

Personally, I don't understand this, but I'm from an ex-Eastern Bloc country
which I was all too happy to escape.

I'd rather the US (and the rest of the Western world) made bombs than only
Russia and China did. Vacuums of power in the world will always be filled and
a Western invasion/expeditionary force is a much nicer alternative to a
Russian one.

~~~
bshipp
Having a military is kind of like having house insurance. you wish you didn't
have to spend the money on it, you hope you never have to actually use it, but
it would be very irresponsible not to have it.

~~~
asdffdsa
ie we spend a third of all our tax revenue on housing insurance

~~~
leetcrew
where is this "third" figure coming from?

~~~
asdffdsa
it's a poor proxy for "a lot"

~~~
leetcrew
I figured. I admit I tend to be pedantic about the US military spending figure
because, while huge, it is not nearly as large a portion of govt spending as
most people think.

------
romwell
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.

~~~
amirhirsch
Hipster Topology: I studied Algebraic Topology before it became "Applied"

~~~
bilbo0s
That would be "Old Geezer Topology".

------
wenc
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?

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

[https://arxiv.org/pdf/1607.04822.pdf](https://arxiv.org/pdf/1607.04822.pdf)

~~~
tzs
Abstract: [https://arxiv.org/abs/1607.04822](https://arxiv.org/abs/1607.04822)

------
archgoon
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...](https://johncarlosbaez.wordpress.com/2016/10/02/complex-adaptive-
system-design-part-1/)

~~~
fmihaila
> 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
Correct, I misread that paragraph. Editing original comment, thank you.

------
dannykwells
I love that new areas of math are being applied, but (as a PhD applied
mathematician) I disagree with the quote "Applied mathematics is not a subject
classification. It’s an attitude".

It has taken me years - an entire career, really - to learn to effectively
communicate my mathematical findings to other non-mathematical researchers and
effectively bridge these gaps. I know a lot of mathematicians who say "well,
sure, I could communicate my work to other fields, but ...<some excuse here>",
when the truth is, they just don't have the training or expertise for how to
do it. It's not just that they don't want to/are too good to bother/etc./etc.
(as much as they would like it to seem that way).

The fact is, translating research findings is hard. Much harder than actually
making them. And asking good questions, relevant to the scientific field you
are working in, even harder. The quote above reflects a common, damaging
hubris in mathematics research and is why most of the "best" math research
never gets used in other fields of science.

~~~
effie
> translating research findings is hard. Much harder than actually making
> them.

I think this is an indication that one is making findings in area that other
people don't care about. Not necessarily that it is bad subject to study, but
with some people, it is better not to spend the effort to explain, because
only the prepared mind can understand.

------
nabla9
DARPA was looking people with expertise in category theory, algebraic geometry
and topology, and sheaf theory few years back for the Complex Adaptive System
Composition And Design Environment (CASCADE) program
[https://www.darpa.mil/program/complex-adaptive-system-
compos...](https://www.darpa.mil/program/complex-adaptive-system-composition-
and-design-environment)

------
xorand
This recalls me a story from Stanislaw Lem' Cyberiad. The two constructors,
Trurl and Clapautius, give the same advice to the leaders of two opposing
armies:the best army, each of them explain, is the one where there is an
unique spirit in all the bodies. So, just add to all soldiers a plug in front
and a socket in the back, so that they can all connect. The armies apply the
advice and something unexpected happens.

------
tw1010
Not the first time I've stumbled into topology/homology used in military
areas:
[https://www.youtube.com/watch?v=1Id3Gu18MME](https://www.youtube.com/watch?v=1Id3Gu18MME)
(Great channel btw.)

------
ska
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".

~~~
qubex
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_.

~~~
ska
That's not quite right, in my opinion. In a past life I was an (applied)
research mathematician, but started off fairly pure.

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.

~~~
salty_biscuits
And how worried you are about rigorous proofs. You can happily hand wave your
way to some approximation in Applied Maths land (because you need the result,
not that you are trying to prove that it is true). Then you can spend the next
bit of time relaxing various assumptions about your approximation and see
where it takes you. A lot of new tools come from thinking deeply about
roadblocks to applied problems, that sort of thing tends to be the maths I am
personally most engaged by.

~~~
ska
You still need rigorous proofs at the end, if you are trying anything new. I
think I would look at it more as you might try an ugly/practical
approximation, or add a term, or whatever just to see if it will improve
things. And maybe it gets you "close enough" for the application. But if you
have a deep think about where you are stuck and come up with a new tool, then
you have to be careful.

~~~
salty_biscuits
We call them "physicists" :)

~~~
ska
hah. it's true ... there is a weird fuzzy line between theoretical physics and
applied maths. Sometimes you're on the same page, sometime you really are not.

------
xvilka
Obligatory GitHub link to UniMath project:

[https://github.com/UniMath](https://github.com/UniMath)

------
hopler
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.

~~~
sigstoat
> this sounds like some bureaucrat who likes HTT

...did you read that after you typed it? do you think there is a actually some
US federal government bureaucrat running around who has an opinion on HTT?

~~~
marshray
Well, considering that it's the official position of the U.S. Army Research
Office Aberdeen Proving Ground that

"Homotopy Type Theory and its applications are such an area that is of
significant interest in military applications",

yes.

[https://www.arl.army.mil/www/pages/8/W911NF-17-S-0002%20ARO-...](https://www.arl.army.mil/www/pages/8/W911NF-17-S-0002%20ARO-
Core-BAA-Amendment-03.PDF)

------
mlthoughts2018
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 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.

~~~
cerealbad
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.

~~~
leereeves
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.

~~~
ska
I think this is mostly unavoidable whenever your field of study bumps up
against politics and money. Economics has the same problem but perhaps worse
in some ways, as there is less rigor.

I don't know how much of the blame you should assign to the field, in that.

------
excalibur
> 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 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.

~~~
falcor84
> You could fit everyone in the Army who understands this in a single
> barracks.

Why would you need more people than that? I wouldn't be surprised if the
number of people in my University who understand this would fit in a single
barracks too, but it doesn't in any way detract from the work they're doing.

