15 ms·

US Army applying new areas of math

206 points by tacon 8y ago

ska 8y ago
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 8y ago
  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 8y ago
    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 8y ago
      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 8y ago
        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 8y ago
        We call them "physicists" :)
        ska 8y ago
        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.
  - opportune 8y ago
    I would say in my applied math degree we didn't really solve most problems (maybe an easy problem on a test) but we did work more directly with actual numbers in our proofs, and we usually proved theorems focused on solving computational problems. But mostly, no, we were not solving problems computaitonally
- hopler 8y ago
  "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.
  - Pamar 8y ago
    Maybe you would prefer "what for" vs. "what"?
  - ska 8y ago
    You misread my intent, I'm sure I could have been more clear. "Why" in this case is not the subject of study, but the motivation (to repeat the OPs phrasing). Wearing an "applied" hat or "pure" hat I might end up studying the same objects, but for different reasons. 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.
- bradford 8y ago
  A common joke among students when I was in my computer-science program: when asked a how-many or how-much question that involved basic arithmetic, one would reply: "Yeah, I can't do that. That's applied math".
  - ska 8y ago
    The math equivalent was "I'm a mathematician, not an arithmetician", or a variant. It's true though, lots of mathematicians are lousy at arithmetic.
wenc 8y ago
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 8y ago
  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 8y ago
    Abstract: https://arxiv.org/abs/1607.04822 https://arxiv.org/abs/1607.04822
- empath75 8y ago
  It’s basically a new foundation for math based on types rather than sets.
  - galaxyLogic 8y ago
    What is the basic difference between types and sets? From the software engineering point of view a type is something of which you can say whether something is a member of the type. And the same thing can be set about sets.
    - empath75 8y ago
      https://golem.ph.utexas.edu/category/2013/01/from_set_theory_to_type_theory.html https://golem.ph.utexas.edu/category/2013/01/from_set_theory...
    - fmihaila 8y ago
      The difference lies in the means you have at your disposal to settle the membership question. Even within "Set Theory" (as an umbrella term), there are several axiomatizations of sets that define in different ways what a set is, how sets come into existence, what it means for an element to belong to a set, and what are the allowed ways to conclude that it does or does not. The link posted in a sibling comment by @empath75 goes into more detail.
mlthoughts2018 8y ago
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 8y ago
  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 8y ago
    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 8y ago
      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.
  - mlthoughts2018 8y ago
    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.
archgoon 8y ago
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.
romwell 8y ago
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 8y ago
  Hipster Topology: I studied Algebraic Topology before it became "Applied"
  - bilbo0s 8y ago
    That would be "Old Geezer Topology".
  - Qworg 8y ago
    To borrow from AI, Good Old Fashioned Algebraic Topology?
  - jjtheblunt 8y ago
    ditto
- 2dollars27cents 8y ago
  Dr. Ghrist is awesome. He is also doing a lot of great work opening up learning materials to his undergrad students. https://www.math.upenn.edu/~ghrist/calculus.html https://www.math.upenn.edu/~ghrist/calculus.html
  - romwell 8y ago
    I recommended that book as a source when I was teaching calculus, and still do :) It's a very opinionated book, but that's no a bad thing. And, unlike the Stewart doorstop, it's compact, as a text should be.
- wenc 8y ago
  Topological Data Analysis was the next big thing a couple of years ago, and it certainly has its applications [1], but the breadth of its applicability may have been overhyped and the energy has fizzled somewhat. [1] https://en.wikipedia.org/wiki/Topological_data_analysis#Applications https://en.wikipedia.org/wiki/Topological_data_analysis#Appl...
hopler 8y ago
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 8y ago
  > 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 8y ago
    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-Core-BAA-Amendment-03.PDF https://www.arl.army.mil/www/pages/8/W911NF-17-S-0002%20ARO-...
  - Fomite 8y ago
    ...I know some US federal government bureaucrats who have opinions on things like that.
excalibur 8y ago
> 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.
- jonathanyc 8y ago
  Please don’t post non-substantive comments.
- falcor84 8y ago
  > 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.
tw1010 8y ago
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.)
nabla9 8y ago
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-composition-and-design-environment https://www.darpa.mil/program/complex-adaptive-system-compos...
noobermin 8y ago
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 8y ago
  > 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 8y ago
    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.
    - awakeasleep 8y ago
      Its more like buying a very expensive hammer, and “everything looks like a nail” See: afganistan, expanding africom, iraq, etc
    - acct1771 8y ago
      As long as you realize everyone feels that exact way.
xorand 8y ago
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.
dannykwells 8y ago
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 8y ago
  > 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.
xvilka 8y ago
Obligatory GitHub link to UniMath project: https://github.com/UniMath https://github.com/UniMath
wereanempirenow 8y ago
as an aside, Isaac Newton first invented Calculus in 1666, and he was such a paranoid weirdo sperg Autist NEET that he jealously kept it secret from the world for 20 years. i fervently hope that if another Newton lived and discovered some new Earth shattering mathematical breakthrough, that he too would Do The Right Thing and trust no one and tell no one, especially not the Pentagon, who are too wicked to deserve to possess the Ark.

206 points by tacon 8y ago

ska 8y ago

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 8y ago
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 8y ago
  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 8y ago
    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 8y ago
      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 8y ago
        We call them "physicists" :)
        ska 8y ago
        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.
- opportune 8y ago
  I would say in my applied math degree we didn't really solve most problems (maybe an easy problem on a test) but we did work more directly with actual numbers in our proofs, and we usually proved theorems focused on solving computational problems. But mostly, no, we were not solving problems computaitonally
hopler 8y ago
"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.
- Pamar 8y ago
  Maybe you would prefer "what for" vs. "what"?
- ska 8y ago
  You misread my intent, I'm sure I could have been more clear. "Why" in this case is not the subject of study, but the motivation (to repeat the OPs phrasing). Wearing an "applied" hat or "pure" hat I might end up studying the same objects, but for different reasons. 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.
bradford 8y ago
A common joke among students when I was in my computer-science program: when asked a how-many or how-much question that involved basic arithmetic, one would reply: "Yeah, I can't do that. That's applied math".
- ska 8y ago
  The math equivalent was "I'm a mathematician, not an arithmetician", or a variant. It's true though, lots of mathematicians are lousy at arithmetic.

wenc 8y ago

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 8y ago
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 8y ago
  Abstract: https://arxiv.org/abs/1607.04822 https://arxiv.org/abs/1607.04822
empath75 8y ago
It’s basically a new foundation for math based on types rather than sets.
- galaxyLogic 8y ago
  What is the basic difference between types and sets? From the software engineering point of view a type is something of which you can say whether something is a member of the type. And the same thing can be set about sets.
  - empath75 8y ago
    https://golem.ph.utexas.edu/category/2013/01/from_set_theory_to_type_theory.html https://golem.ph.utexas.edu/category/2013/01/from_set_theory...
  - fmihaila 8y ago
    The difference lies in the means you have at your disposal to settle the membership question. Even within "Set Theory" (as an umbrella term), there are several axiomatizations of sets that define in different ways what a set is, how sets come into existence, what it means for an element to belong to a set, and what are the allowed ways to conclude that it does or does not. The link posted in a sibling comment by @empath75 goes into more detail.

mlthoughts2018 8y ago

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 8y ago
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 8y ago
  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 8y ago
    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.
- mlthoughts2018 8y ago
  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.

archgoon 8y ago

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.

romwell 8y ago

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 8y ago
Hipster Topology: I studied Algebraic Topology before it became "Applied"
- bilbo0s 8y ago
  That would be "Old Geezer Topology".
- Qworg 8y ago
  To borrow from AI, Good Old Fashioned Algebraic Topology?
- jjtheblunt 8y ago
  ditto
2dollars27cents 8y ago
Dr. Ghrist is awesome. He is also doing a lot of great work opening up learning materials to his undergrad students. https://www.math.upenn.edu/~ghrist/calculus.html https://www.math.upenn.edu/~ghrist/calculus.html
- romwell 8y ago
  I recommended that book as a source when I was teaching calculus, and still do :) It's a very opinionated book, but that's no a bad thing. And, unlike the Stewart doorstop, it's compact, as a text should be.
wenc 8y ago
Topological Data Analysis was the next big thing a couple of years ago, and it certainly has its applications [1], but the breadth of its applicability may have been overhyped and the energy has fizzled somewhat. [1] https://en.wikipedia.org/wiki/Topological_data_analysis#Applications https://en.wikipedia.org/wiki/Topological_data_analysis#Appl...

hopler 8y ago

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 8y ago
> 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 8y ago
  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-Core-BAA-Amendment-03.PDF https://www.arl.army.mil/www/pages/8/W911NF-17-S-0002%20ARO-...
- Fomite 8y ago
  ...I know some US federal government bureaucrats who have opinions on things like that.

excalibur 8y ago

> 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.

jonathanyc 8y ago
Please don’t post non-substantive comments.
falcor84 8y ago
> 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.

tw1010 8y ago

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.)

nabla9 8y ago

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-composition-and-design-environment https://www.darpa.mil/program/complex-adaptive-system-compos...

noobermin 8y ago

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 8y ago
> 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 8y ago
  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.
  - awakeasleep 8y ago
    Its more like buying a very expensive hammer, and “everything looks like a nail” See: afganistan, expanding africom, iraq, etc
  - acct1771 8y ago
    As long as you realize everyone feels that exact way.

xorand 8y ago

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.

dannykwells 8y ago

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 8y ago
> 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.

xvilka 8y ago

Obligatory GitHub link to UniMath project: https://github.com/UniMath https://github.com/UniMath

wereanempirenow 8y ago

as an aside, Isaac Newton first invented Calculus in 1666, and he was such a paranoid weirdo sperg Autist NEET that he jealously kept it secret from the world for 20 years. i fervently hope that if another Newton lived and discovered some new Earth shattering mathematical breakthrough, that he too would Do The Right Thing and trust no one and tell no one, especially not the Pentagon, who are too wicked to deserve to possess the Ark.