I have a prototype solution to #20 and provided some runway it could, after validation by research, solve for #2. I am working a prototype distributed OS that (partially) executes in the browser. The prototype is far enough along that I can qualify some of my initial goals and assumptions.
But then those questions are for undergrads. I am just an old dumb soldier with my undergrad days long behind me.
The UI is largely the same, but the project has different design goals now and a more ambitious internal architecture. Over the next month I will be concluding end-to-end test automation in the browser across various devices which will include a text messaging component.
DARPA isn't afraid to ask the easy questions I see /s
Too bad agency, DARPA included, wants to pay enough to have people work on these problems for extended time periods. It's good to see some funding for high-risk work but there just isn't enough anymore.
That seems to show that the R part of R&D has remained static (in terms of the Federal Budget) but the D part has fallen. At the same time there have been very large tax incentives for "D" in the USA. And the R bit is the bit that I would point to in terms of this discussion.
I think the NSF funds a lot of people who are perhaps not attacking these problems directly, but are working in nearby fields that may yield insights into how to solve these problems.
Disagree, in these types of projects you want longevity over peak talent. You start paying top dollar then that talent is going to leave the second they get a better top dollar option--and then you're in an arms race you can't win.
People that want to work for the government are aware of the $$$. I think the system is working as intended
Economics, for instance, has been stuck since Marshall[1] in Newton's method of fluxions/ Liebnitz calculus. (Well, their elaborations perhaps. And leavened with a little game theory. Probability and statistics have contributed nothing significant to the core theory.)
Economics has been crying out for a better mathematical foundation since the 1960s at least.
Can someone please give us a better understanding in what's meant by this?
> Duality in mathematics has been a profound tool for theoretical understanding. Can it be extended to develop principled computational techniques where duality and geometry are the basis for novel algorithms?
It means that DARPA is cutting corners by farming their work out to unpaid "challengers". You solve these problems at your own peril. You're participating in weapons research.
Duality in mathematics is in general a principle that objects in one category can be mapped onto another category (and vice versa), that two objects are reflections of each other in some abstract sense.
It most often appears as a principle in geometry. Looking at or working with the 'dual' of something can give additional insight or allow another way of working. For example, Fourier Transform can be considered a type of duality.
I'm not clear what computational techniques are expected here - I personally don't think it's a very well-formed problem.
>Mathematical Challenge Eight: Beyond Convex Optimization
* Can linear algebra be replaced by algebraic geometry in a systematic way?
I think this is probably by far the most useful, practical and relevant challenge to be solved for science and engineering, and perhaps closely follows by the stochastic and duality challenges.
For computer science and engineering it is the popular "Gimbal lock" problem in 3-D environment in which linear algebra cannot comprehensively represent but easily represented by geometric algebra or quaternions.
Similarly in electromagnetics (EM) wave propagation, due to the prominent effect of polarization (other waves like sound does not has polarization), comprehensively modeling polarization with linear algebra is close to impossible. I kind of liken the geometric algebra unpopularity and conundrum similar to 18th mathematicians suspicious views when complex number was originally introduced and looks how far we have got now by embracing it [1]. Basically the discovery and utilization of complex number provide us with WiFi 6 and 5G. But if we want to move forward with robust and reliable wireless similar to wired (or close to wired connection reliability) we need to take control of EM polarization by embracing geometric algebra.
It seems that what it meant here by algebraic geometry is different compared to the terminology of geometric algebra. In this case geometry algebra is just one of the tools for algebraic geometry albeit a very useful one. But the points on its importance is still valid IMHO.
Any good resources on linear algebra and algebraic geometry? I think I've read about it before but when I look it up now there's few hits coming up for me for some reason.
> Brain
* Develop a mathematical theory to build a functional model of the brain that is mathematically consistent and predictive rather than merely biologically inspired.
My gut reaction to that was: that’s pie-in-the-sky outlandish.
However, with more thought, I agree it is possibly the most important in the list.
In the past year, Congress demanded a powerful general AI. (1)
Many have been and continue to be concerned that AIs will fail in the areas of ethics and morality.
An unethical and immoral AI could be chaotic and unpredictable. It could try to kill everyone (Skynet) or manipulate them for its amusement or quest for knowledge, or it could leave Earth in a spaceship never to be seen again, since it would have no obligation to us.
An ethical and moral AI on the other hand might decide that it should keep humans alive and happy in a virtual world to save us from ourselves or to better control disease, hunger, and other risks. But by doing so, would take away our actual physical freedom.
The problem with the human brain as a model is that it’s not necessarily going to be much better. For example, consider how humans treat other animal species: we let some roam free, we study some, we heal some, we feed some, we have pets, we have zoos, we milk some, we take their eggs, we eat them as food, some hunt them for sport, and some accidentally run them over with vehicles.
Perhaps if we only were to try to make AI purely just do some human jobs to save money or to act as a scalable collection of virtual human minds, that could in-theory be less risky than a hyper-intelligent general AI.
That’s not going to stop development of such a general AI. But, maybe it could help defend us better and could help those designing that AI to make dystopia less eminent.
31 comments
[ 2.6 ms ] story [ 79.5 ms ] threadHere are some links about them:
https://www.hpe.com/us/en/insights/articles/the-toughest-mat...
http://www.math.utk.edu/~vasili/refs/darpa07.MathChallenges....
The first link talks about results for some of the challenges.
https://web.archive.org/web/20090407054314/http://www.darpa....
https://en.wikipedia.org/wiki/Hilbert%27s_problems
Wikipedia notes that they "ranged greatly in topic and precision". :-)
https://golem.ph.utexas.edu/category/2007/12/challenges_for_...
But then those questions are for undergrads. I am just an old dumb soldier with my undergrad days long behind me.
http://mailmarkup.org/sharefile/demo1.mp4
The UI is largely the same, but the project has different design goals now and a more ambitious internal architecture. Over the next month I will be concluding end-to-end test automation in the browser across various devices which will include a text messaging component.
The blog post title is misleading - these are some of the toughest questions/challenges currently known, they're not geared towards undergrads.
Too bad agency, DARPA included, wants to pay enough to have people work on these problems for extended time periods. It's good to see some funding for high-risk work but there just isn't enough anymore.
What is the scale of funding over time ? My guess is that there is more money in fundamental research than ever before....
Total RD spending as % of GDP has been falling since the 60s
https://www.aaas.org/sites/default/files/2020-10/RDGDP.png
And also falling as percent of Total Federal Budget
https://www.aaas.org/sites/default/files/2020-05/Budget.png
https://www.aaas.org/programs/r-d-budget-and-policy/historic...
People that want to work for the government are aware of the $$$. I think the system is working as intended
> * Address Mumford’s call for new mathematics for the 21st century. Develop methods that capture persistence in stochastic environments.
This is interesting, what did Mumford asked for, and what does persistence in stochastic systems stands for?
https://www.dam.brown.edu/people/mumford/beyond/papers/2000b...
Economics, for instance, has been stuck since Marshall[1] in Newton's method of fluxions/ Liebnitz calculus. (Well, their elaborations perhaps. And leavened with a little game theory. Probability and statistics have contributed nothing significant to the core theory.)
Economics has been crying out for a better mathematical foundation since the 1960s at least.
1. https://en.wikipedia.org/wiki/Principles_of_Economics_(Marsh...
> Duality in mathematics has been a profound tool for theoretical understanding. Can it be extended to develop principled computational techniques where duality and geometry are the basis for novel algorithms?
Duality in mathematics is in general a principle that objects in one category can be mapped onto another category (and vice versa), that two objects are reflections of each other in some abstract sense.
https://en.wikipedia.org/wiki/Duality_(mathematics)
It most often appears as a principle in geometry. Looking at or working with the 'dual' of something can give additional insight or allow another way of working. For example, Fourier Transform can be considered a type of duality.
I'm not clear what computational techniques are expected here - I personally don't think it's a very well-formed problem.
I think this is probably by far the most useful, practical and relevant challenge to be solved for science and engineering, and perhaps closely follows by the stochastic and duality challenges.
For computer science and engineering it is the popular "Gimbal lock" problem in 3-D environment in which linear algebra cannot comprehensively represent but easily represented by geometric algebra or quaternions.
Similarly in electromagnetics (EM) wave propagation, due to the prominent effect of polarization (other waves like sound does not has polarization), comprehensively modeling polarization with linear algebra is close to impossible. I kind of liken the geometric algebra unpopularity and conundrum similar to 18th mathematicians suspicious views when complex number was originally introduced and looks how far we have got now by embracing it [1]. Basically the discovery and utilization of complex number provide us with WiFi 6 and 5G. But if we want to move forward with robust and reliable wireless similar to wired (or close to wired connection reliability) we need to take control of EM polarization by embracing geometric algebra.
[1]https://en.m.wikipedia.org/wiki/Complex_number#History
[1]https://www.reddit.com/r/math/comments/ddqt6f/algebraic_geom...
My gut reaction to that was: that’s pie-in-the-sky outlandish.
However, with more thought, I agree it is possibly the most important in the list.
In the past year, Congress demanded a powerful general AI. (1)
Many have been and continue to be concerned that AIs will fail in the areas of ethics and morality.
An unethical and immoral AI could be chaotic and unpredictable. It could try to kill everyone (Skynet) or manipulate them for its amusement or quest for knowledge, or it could leave Earth in a spaceship never to be seen again, since it would have no obligation to us.
An ethical and moral AI on the other hand might decide that it should keep humans alive and happy in a virtual world to save us from ourselves or to better control disease, hunger, and other risks. But by doing so, would take away our actual physical freedom.
The problem with the human brain as a model is that it’s not necessarily going to be much better. For example, consider how humans treat other animal species: we let some roam free, we study some, we heal some, we feed some, we have pets, we have zoos, we milk some, we take their eggs, we eat them as food, some hunt them for sport, and some accidentally run them over with vehicles.
Perhaps if we only were to try to make AI purely just do some human jobs to save money or to act as a scalable collection of virtual human minds, that could in-theory be less risky than a hyper-intelligent general AI.
That’s not going to stop development of such a general AI. But, maybe it could help defend us better and could help those designing that AI to make dystopia less eminent.
(1) https://www.intelligence.senate.gov/publications/intelligenc...