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US Army applying new areas of math (johndcook.com)
206 points by tacon 32 days ago | hide | past | web | favorite | 138 comments



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.


I am reminded of a reception at the HPC User Forum back around 2002. There were a number of people in the room from various national labs and intelligence agencies. I was part of the firm that organized and hosted these meetings. I overhear a guy from NSA kidding a guy from Lawrence Livermore Labs with the following line.

"At least I don't design weapons of mass destruction, all I do is read emails"

In truth neither one of these guys did the activities stated, both really were doing system design, optimization and resource allocation with super computers so that the intelligence analysts could rapidly search billions of emails for trigger words, cryptographers could break encryption or weapons designers could model the characteristics of nuclear weapons since we were in a weapons testing ban.

But to echo your point the amount of resources available at national labs and intelligence agencies. The supercomputing resources they had available dwarfed anything available in industry or academia at the time. Today, one might argue that industry and in particular places like Google and Facebook have computing infrastructure and support that was previously only available at national labs.

So now the Google or Facebook guy in a similar meeting will be saying "I only do the analytics that enable us to target people with ads and messages to which they are most vulnerable."


You say he is joking, but that person does know. I work at a research lab and at our yearly reviews, we have to day how our work directly contributes to a war fighting capacity. If that person thinks they do not contribute they are very seriously naïve or they are filling themselves.

Military labs do not try to make euphemisms for what they do, they want to make sure they directly contribute to a war fighting capability.


There are varying degrees of "military lab," my favorite example being the National Ignition Facility.


The NIF has a military mission too. Straight from Wikipedia:

> NIF's mission is to achieve fusion ignition with high energy gain, and to support nuclear weapon maintenance and design by studying the behavior of matter under the conditions found within nuclear weapons.

https://en.m.wikipedia.org/wiki/National_Ignition_Facility


Heh, can you say more about it?

That is true. I am military and I work in a true military lab, so I probably have a different perspective


While working in defense R&D, I did my most interesting work and met some of my best colleagues.

Eventually I moved to SV and its greener grass: a better salary and a clearer conscience.

The truth is, I miss the interesting work, the competent managers, and having an office. Working to keep people addicted to their screens didn’t do wonders for my conscience or the state of the world.


Do you think that negative attitude would change if you told them you are working on math problems? I don't think much, the attitude is there for a deep reason. If people do not identify with actions of their military, they won't like that you're helping the military. If they do identify, they would support you even if were working on actual bombs.


For the record, given I'm at a university with 56% overhead, this is:

- Often less than corporate research. I know because I've also worked with them.

- Pays for things like startup packages for new faculty, administrative support, things shared by multiple groups, etc. (as well as, without a doubt, some waste, but I mean, private research companies have that too).

- Is negotiated in advance with the government.

- Is often less than the cost of doing research.


For comparison, German federal government research grants (from the BMBF) explicitly have a 20% markup that is reserved for non-research stuff. Typically this goes to the university to cover the offices of the employees who work on the project and into a fund for other stuff (grant application overhead etc). The rest is all used for salaries and project specific investments.

Theoretically that's pretty good. However if you look at a lot of the research projects you kind of scratch your head at the actual output (which imo is the real problem).


>However if you look at a lot of the research projects you kind of scratch your head at the actual output (which imo is the real problem).

Can you elaborate? What do you mean?


Your post is very puzzling. You, on one hand, sound exceptionally well educated but on the other hand describe a social circle that seems exceedingly ignorant or uninformed. Knowing the profound disconnect why would that make you embarrassed?


This is such a non sequitur that I looked through the parent poster's comment history to see if he'd made some other post down thread that you were replying to. Do you mean "people who work in military research", "people who work at military contractors" or was there something else I didn't pick up on?

Edit: Am not a military researcher, military contractor, etc.


I don't understand your comment. What people are you speaking about?


His social circle. Apologies if I missed something, but I don't understand where that comes into the equation.


I cannot speak to the OPs social circle. To me it sounds pretty uninformed to think anybody working with the military is building bombs. The DOD (the US military) has about 2.8 million employees and there are about another 2 million people who work as defense contractors. I find it strange to think all those people could constantly be working on bombs.

By comparison the largest US commercial employer is WalMart with 1.5 million US employees. Imagine (for the sake of numbers) every WalMart employee and two of their kids constantly making bombs.


That's not a very charitable response. Obviously the OP's social circle will know better than that because they know him (or her) and what they actually work on.

Among the general public there's a real stereotype about DOD work. When I mention to strangers that I work for a defense contractor, they more often than not assume I'm working on bombs or something like that. Not every time, but often enough that I'm used to explaining that I only work on mapping software.


> they more often than not assume I'm working on bombs

> I only work on mapping software

In fairness, those maps are likely used to ensure the bombs go where they should.


Better that they go where they should, than that they go where they shouldn't. The more accurate the mapping, the smaller the bomb can be, and the less collateral damage (presuming that the targeting information is correct).


that assumes the bomber isn't intending to maximize collateral damage


> Better that they go where they should, than that they go where they shouldn't

True, at least when you're not the one being bombed.


This is a clever point. I think, even if I am being bombed, I don’t want my neighbors to die[1]. I would care very much about why. But if the hammer is coming down on me, it’s better for everyone if it’s only me.

[1] except maybe that one across the alley that starts loud parties at 3:00 am. If I’m going down you can too guy.


To be more fair, better maps means better targeting and less collateral damage. And the software can also used for logistics, base planning, humanitarian missions, rescue missions, etc.


> Obviously the OP's social circle will know better than that because they know him (or her) and what they actually work on.

If that were true then the OP would not have to explain himself/herself in any way that made him/her feel embarrassed in the first place.


I spent two years of my life working on a technology I really hope is never used.

I think it's very hard to think about making a technology you know is to killing someone. But at the same time, you know it is necessary. You really wish the world you live in would mean there's no reason to. But that isn't the world you live in.


> I think it's very hard to think about making a technology you know is to killing someone.

That does not appear to be related to this conversation. The OP does not have those worries and instead feels embarrassed when he/she must explain such.


Yeah, traditional sources suck, in America; universities should be way more tightly controlled, in a decent society taking 56% of grant money should put some people in jail.

In the year 2019 working for the US military should feel embarrassing, after the Iraq fiasco, support to journalist-killer Saudi crown prince; support to genociders that use child soldiers such as Idriss Déby (Chad), plus many other mistakes makes it reasonable to feel ashamed of working for the US military complex.


There is danger in inaction. Note that US soil isn't often annexed.

This damned thread has triggered all my pent up jingoism.

"America makes prodigious mistakes, America has colossal faults, but one thing cannot be denied: America is always on the move. She may be going to Hell, of course, but at least she isn't standing still. " -- e.e. cummings

If you take orders for a living, your job is to be on the move. Not to be right. Ain't no one who matters who has time for being 100% in the right.


Everybody who is not self employed takes orders for a living.


The problem is that "being 100% in the right" doesn't seem to be their goal, not even a secondary one.


Let us not blame the military. The military just works for the government. And the government works for we the people.


They are however killing people. Lets not skip over that part as nice and cuddly as "just doing their job" sounds. I highly doubt the dead would care that their murderers were paid to do it.


It's nice to displace the guilt for democratically electing a government that orders your military to kill people by blaming the military instead of yourself.


I wouldnt assume that you could displace that.

But why would you assume an either or to begin with? Soldiers are certainly responsible for their actions like anyone else, no matter their orders. Just as people giving the orders are responsible for whats done on their behalf. I also dont think it would be to controversial to also see responsibility of the people who voted them into office.

I would have hoped, that the excuse of just following orders had died with the end of WW2.


>The military just works for the government.

The military is part of the government (executive branch).


"in a decent society taking 56% of grant money should put some people in jail."

A decent society made this a law because it makes the separation between "Money spent directly on research" and "Money spent on things like the copy machine, internet, keeping the lights on, etc." transparent - unlike how it works in most private industry.

Trust me, universities would love to be able to get rid of the concept of indirect costs. It's mandated by the government, and negotiated with them (at my university, at a slight loss sometimes).


But you do make bombs


> 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.


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.


Its more like buying a very expensive hammer, and “everything looks like a nail”

See: afganistan, expanding africom, iraq, etc


Sometimes my kids act up, so I smash a hole in the fence and call in my home insurance, which kills all the neighbors (and some of the kids).


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


where is this "third" figure coming from?



it's a poor proxy for "a lot"


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.


As long as you realize everyone feels that exact way.


Everyone does, we know.


You're talking to an audience that didn't see WWII, and mostly didn't see the Cold War.

The ugly truth is that there are plenty of bad guys or people who would be bad guys (some of them in the U.S. admittedly), and a lot of them won't stop without force or threat of force.

I know this isn't a universal opinion but I believe that smarter military technology has a better chance of ending/stopping/preventing war than starting it.


Good vs. bad does not usually fit the narrative in war. WWI and earlier major wars are hard to figure who was the "bad guy". Many of them lack any clear moral authority and fit more as teams competing for resources.


> smarter military technology has a better chance of ending/stopping/preventing war

A global surveillance network and insect-sized drones that precisely assasinate "enemy" leaders.

Why bother with infantry and big guns etc.?


I think it is better for exercises of large power to be noticeable, because if it can be noticed, then there is at least some hope that misuse could be opposed.


As someone who also is a military researcher, I may be able to help. I have worked on things that if the USA went to war, I know that I have directly contributed to that war.

I truly hate that my research will contribute to killing. I wish that it wasn't necessary. But as events like Crimea annexation and the South China Sea shows, if the USA is not there, then other nations are very happy to use their might to boss others around. I truly do think the USA is a force for good, and I want that to be there for my following generations.


> if the USA is not there, then other nations are very happy to use their might to boss others around.

This is kind of the same logic that often makes me wish for an extraterrestrial invasion.

An alien species has a much higher chance of treating us all equally, than we do ourselves.


Funny. I wrote a blog post sometime back claiming that an external real or perceived threat is a unifying factor for societies and nations.

So if we want to unite the earth, we need an extra terrestrial threat. It could be asteroid or alien invasion. Now these are less probable, hence we should set up Martian colonies and then just allow the earthlings to do their thing. They will eventually treat Mars humans as a threat. This is our only option to unify the earth.


Simply having an "exit" from the complications on Earth, the possibility of relocating to Mars and starting from scratch, would give a lot of people hope, something to look forward to.

It could also end up being an exclusive resort for the elite of our society to escape to, so they may no longer have to pretend to care about Earth at all.


Sounds eerily similar to concepts in the Sci Fi novel https://en.wikipedia.org/wiki/The_Three-Body_Problem_(novel)


> This is our only option to unify the earth

Why do we think that a unified earth will be a good thing? It seems too utopian to me...


Unified as in: Nobody trying to harm each other, or other species, or prevent them from doing their thing.

Why would anybody think that's not a good thing?


> Why would anybody think that's not a good thing?

It sounds boring...


I agree with you, but it's not so black and white.

The atomic bomb is a notable example, and consider Eisenhower and many other military leaders said "there was no reason to use that awful thing." I realize my high school education, and most othet's, led me to believe this wasn't the case.

I'm not trying to say it's wrong, but it deserves a lot of skepticism.


Reading a biography of Oppenheimer explores much of this. One thing is clear, the bomb was used on an essentially defeated enemy. From another angle though, it was necessary to push back Stalin and could be considered not as the last blow of WWII but the first blow in the cold war.

It is difficult to question the possible outcomes if different choices were made but you can be sure that the last 80 years could have been much different and much worse. The bomb did make certain kinds of war impossible, and it is not clear if that would be true if they had not been used when they were.


> One thing is clear, the bomb was used on an essentially defeated enemy.

The bomb were used on an enemy that was sooo defeated that there was a coup attempt by the military between the two bombs to prevent the emperor from capitulating.


I am from the same boat and tottaly agree with you. Many people dont understand how real Russian threat is.


I used to work for a defense contractor and I remember the boogie man of the Soviet Union and how the intelligence community was constantly saying there was likely to be a breakout in new Soviet technology. So our budgets remained fat to fund lots of new spook technology programs. Right up to the day that the Soviet Union collapsed. I started looking with a more critical eye at the supposed threats.


> 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.

In this case you're only speaking for yourself.

Most Asians, from the Middle East through to the South East, would kindly disagree.


Good to know you speak for “most asians”.


I think the political situation in many of those countries speaks volumes. There are very few countries or peoples which have a genuinely positive view of Western occupation. Most countries that have a positive view of "Western" nations above Russia are the ones that are bribed (weapon contracts, free defense, release of political pressure) or bullied (application of political pressure) to have it.

If you spend some time looking at the divisive, genocidal campaigns of the Americans, British and French across Western, Southern and South-Eastern Asia it's not hard to see why.


While Germany isn't an Asian country, my Grandpa was German.

As you can imagine, he had a far more positive view of Western occupation than Russian occupation.

He was not a member of the Nazi party, but was in the military. The story, as best as I can recall: After they ran out of gas, the soldiers were given bicycles and panzerfaust, and told to head East, because the Russians were invading.

He hid in a hole as Russian tanks drove past. He deserted, and went West as fast as he could, deliberately getting himself captured by the invading US forces.

He said he was treated better by the Americans as a prisoner of war than he was by the Nazis as a soldier. I don't think any soldiers captured by the Russians would say the same.

Not long thereafter, the war in Germany ended. While the soviets plundered East Germany, the Americans with the Marshall plan helped rebuild West Germany. My grandfather, having not been a member of the Nazi party, was also treated very well during this period.

Even though allied bombs destroyed 80% of his home city, this earned the US enough goodwill in his eyes (and probably many of his generation) that throughout the rest of his life, he supported the US (even while he didn't agree with everything they did). His daughter ended up marrying an American.

If enemy soldiers thought you'd treat them better after they surrender than they're being treated now, they're not likely to fight very hard. Unfortunately, I think we have an instinctual urge to punish enemies. We like negative sum games.


> There are very few countries or peoples which have a genuinely positive view of Western occupation.

On the other hand, let's consider how popular inter-Asian occupation was.


It depends. If you are comparing it to the one that nearly wiped out the native population on two continents and plundered two more, even the occupation of Korea and China by Japan suddenly starts looking rather attractive, which is a very scary thought, btw


Or let's not, because this discussion doesn't have anything to do with how they view each other as neighbors - it's about perceptions towards "Western" occupation vs. Russian occupation.


Well, it felt like a complaint about Western vs non-Western occupation. Let's restrict non-Western to Russian as you suggest. You go first. How about you opine on Russian vs Western occupation?


eastern block expat also, agree whole heartedly. People who complain about the US have no idea how much worse it would be to have Russia in such a position of power instead.


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.


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#Appl...


I have a book on the subject on my desk (several, in fact), and I'm still not sold I'll get to use any of that.

Really hope to, though.


Kinda like AI is now? I use Graph Theory a lot in my every day job (nothing fancy, but it is useful for visualization, shortest path, and other things). You start to see it show up everywhere too.


Graph theory applies to social networks, and those are the viaducts of foreign propaganda. Good choice


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


That would be "Old Geezer Topology".


To borrow from AI, Good Old Fashioned Algebraic Topology?


ditto


> Robert Ghrist of UPenn has been at the forefront of bringing topology into applied fields; and has written a good text on the subject.

Found this on Dr. John D. Cook's blog.

https://www.johndcook.com/blog/2010/09/13/applied-topology-a...


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


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.


Everything within Math can be described Topologically. Topology is gaining a lot of traction. It's pretty remarkable.


I don't know much about it, but isn't Topology just one Category?


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



Personally I don't think it has any practical applications, but rather that this continues the trend of using the military to fund fundamental research. The main interest would probably be that HoTT allows for automatic theorem proving of more interesting theorems compared to other axiomatisations. It was originally designed to be able to do higher homotopy theory synthetically. The Lean theorem prover has actually dropped HoTT support. There is a certain chance that interest will vane after the founder Voevodsky died.


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


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.



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.


This is interesting https://www.youtube.com/watch?v=E9RiR9AcXeE a bit of the history and why it was needed.


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:

> 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.


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


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).


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.


> 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.


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...


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.


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


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".


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".


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.


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.


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.


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.


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.


We call them "physicists" :)


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.


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


"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.


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.


Maybe you would prefer "what for" vs. "what"?


Obligatory GitHub link to UniMath project:

https://github.com/UniMath


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.


> 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?


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-...


...I know some US federal government bureaucrats who have opinions on things like that.


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.


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".


No, it is not about static typing or the general use of typed data structures for describing statistical software. Statistical software has been among some of the best software around for a long time. In fact, I frequently revisit aspects of the C++ implementation of STAN and the interface design of pymc as inspiration for effective software design in other domains.

The idea that statistics is a field with poor software tools is just plain crazy.


> Stan interfaces with the most popular data analysis languages (R, Python, shell, MATLAB, Julia, Stata) and runs on all major platforms (Linux, Mac, Windows).

None of those languages have good type systems.

And like I said, this is about modelling more generally than just statistics.


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 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.


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.


> 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.


> 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.


Please don’t post non-substantive comments.




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