"Develop a mathematical theory to build a functional model of the brain that is mathematically consistent and predictive rather than merely biologically inspired."
Huh? As far as I'm concerned that's the wrong way to think about neuroscience. Although perhaps the goal here is to replicate parts of the brain's function without regard to the underlying structure, in which case I suppose this is a fair way to go about it.
And "The Geometry of Genome Space: What notion of distance is needed to incorporate biological utility?" is a question I work on every day!
I find many of the rest to be quite vague though. "What are the Fundamental Laws of Biology?" huh? The same fundamental laws as the rest of the universe . . .
Is it just me, or are a lot of those challenges crap? Biological quantum field theory being used to control the evolution of pathogens? WTF? Who wrote this, a Markov algorithm?
It's definitely not just you. To me, almost the entire list reads like "Figure out something how to do something frigging awesome in field X, by solving Y!" where X is any old scientific field and Y a random mathematical problem drawn from a pop math book with a picture to equation ratio greater than 1.
Mathematical Challenge 15: The Geometry of Genome Space
What notion of distance is needed to incorporate biological utility?
That was the point where I decided that I want to crawl into a hole and die [1]. The biology related "challenges" on this list drive me particularly crazy, though most of the others are pretty bad, too, since they're not well defined enough to even have much to say about.
[1] It's not that I don't think "notions of distance" are an important thing to understand, or anything like that, they certainly are, and biologists do worry about that type of stuff - I'd guess that the computational bio folks out there understand that stuff a lot better than a lot of mathematicians. But this question...it's the type of thing a philosophy major would ask after hearing about the concept of a metric space, getting stoned, and seeing a Darwin poster, not something anyone that actually knows both math and biology would (should?) ever ask.
It is phrased very poorly, and admittedly does sound pretty crazy, but it made sense to me as someone who works in the field. Gene regulation is a really complicated process, and its becoming increasingly clear that 3D interactions and chromatin remolding/confirmation are very important. Some regulatory elements act very specifically on genes that are over 1 million base pairs away. How are they targeted? Good question.
Although I suppose the probability that DARPA was thinking about gene regulation when they wrote this is slim to none :/
As I understand, this particular point is about quantum-aware molecular dynamics of the whole organism; but I agree it is a mainly a buzzword collection.
A good scientific model makes novel predictions (bonus points if unexpected), then we later confirm them through experiment. For example, Einstein's theory of relativity is continually tested in novel ways -- predictions are made using the mathematics then confirmed via experiment.
The challenge means that current computational neuroscience models by and large are mainly descriptions of the data we've gathered and seldom are able to extrapolate beyond that. Somewhat embarrassingly, perhaps the field's biggest success in achieving a deeper understanding is what bootstrapped it 60 years ago -- the Hodgkin-Huxley model. Admittedly, neuroscience is extremely challenging and our experimental techniques are still relatively primitive. However, having testable, predictive models is essential to moving the field forward.
>> I find many of the rest to be quite vague though. "What are the Fundamental Laws of Biology?" huh? The same fundamental laws as the rest of the universe . . .
Indeed. I'm not sure what they mean by that. In my view, the best way to understand biology is to develop a greater understanding of QM and then model macroscopic structures through simulation. Biology is really just an emergent phenomenon after all.
>Biology is really just an emergent phenomenon after all.
Absolutely, and it enrages me that there are many in the field who don't think like this.
I would point out, however, that the physics/chem we have is likely good enough for the representation biological systems. A more nuanced understanding of QM or fundamental physics in general, while obviously necessary in the end, is not going to do a whole lot to further the biological sciences at this moment. Unless of course, there's some sort of fundamental physics we're missing that is somehow intrinsic to protein/RNA folding, but that's a vanishingly unlikely prospect.
EDIT: oh I see, you do MD stuff, which helps explain your mindset :P I work in developmental genetics and the mindset/goals are very different.
As a (hopefully interesting!) aside, on the scale of most biological molecular dynamics simulations, quantum mechanical contributions can largely be ignored, because the mechanics of the large, heavy nuclei dominate the system. There are a few instances where a hybrid classical/quantum force field is necessary though, like any simulation involving breaking/formation of chemical bonds (where electrons must be treated explicitly).
The computational power needed for the treatment of a very large system (e.g. whole-organism, or even whole-cell) using fundamental physical laws (like QM, and probably even a classical approximation) will be out of reach for at least the next few decades (probably :)). So I would argue that while it's technically true that biology is a phenomenon which emerges from fundamental physical laws, it's sufficient for the time being to treat biology as a field distinct from, but ultimately dependent on, physics.
Yeah, I largely agree. My comment was more to indicate that when Xcelerate thinks about simulating a biological process, he thinks on the level of simulating individual atoms, which is much more likely to make someone think about the fundamental physics of the problem. When I simulate biological processes, I think in terms of chemistry or stat mech. Rather than one molecule I'm dealing with collections of many types of molecules whose interactions are often ill defined anyway, so I'm much more likely to think "eh, the chemistry we have is good enough, let's just get on with it"
Reductionist thinking like this is tempting but not really helpful in the real world, in my experience, and I'm a physicist. More is different, and even though it might be possible to simulate the emergent properties, this is really not feasible at scale. Calculating the wave function of a mole of unordered matter numerically is not possible for example.
I'm not saying that biologists should have to think about QM, just than biologists should think about chemistry. Our understanding of gene regulatory networks (which are definitely an emergent phenomenon), for example, has, until relatively recently been very qualitative, but we're now reaching the point where they can be simulated with relative accuracy from chemical principles. This is great, as it allows us to ground our assumptions about gene function and ask "Could this system really work the way we think it does?" Sometimes the answer is no and models have to be revised.
> Biology is really just an emergent phenomenon after all.
Is that a settled question? I can see that the laws may be well defined, but what about the initial conditions? Can we determine the initial conditions precisely enough, assuming there are fundamental limits on what we can measure?
I guess that is equivalent to the question of whether if the initial conditions are approximately right, is there an in-built stability in the system, which makes a biological simulation converge to a to a meaningful result. Do errors get magnified or eliminated? (Presumably the latter, otherwise thermal noise would make us fall apart, but is this confirmed?)
As an aside, since you are in the molecular dynamics field, can you recommend a starting point for a novice that is interested in getting involved? Books? Open source software? I've always thought it would be fun to program an FPGA with the relevant equations, let it run, and see what happens.
I think the point is to really get a handle on emergent phenomenon. Really, this ties into the parents musings on mathematical model of the mind. Really, I think your views are entirely compatible with the stated goal (which is vague for a reason). The entire point is I believe is to be able to describe this emergent behavior without having to invoke all the underlying lower level processes. For example, looking at pharmacology, perhaps one day we can actually have meaningful models of what a molecule will do, without 'brute forcing' every single possible interaction.
Which kind of ties into the parent's musings into the mathematical model of thought. The point is to create models that avoid invoking as much of the underlying low-level processes as possible. It would be -amazing- if we could create a mass of DEs that would -think-, especially if those DEs weren't just a straight representation of a massive neural network that happened to be copied right out of our brains.
Maybe a better response, but I put the "just" there for a reason. That's really all there is too it. Simple laws lead to incredibly complex behavior. Of course emergent phenomena can be incredibly hard to study -- I'm not implying in any way that biology is easy (it's probably one of the hardest fields out there). Instead, I'm trying to point out than many people entirely miss the fact that there is a lower level to it. Enzymes and viruses don't have desires and I've heard it described/analogized this way by far too many biology professors. (Just bump the pH up a little and the enzyme goes and does such and such...)
> Enzymes and viruses don't have desires and I've heard it described/analogized this way by far too many biology professors.
But it's such a useful mental model. It allows you to gloss over irrelevant low-level details while focusing on the aspects of the complex emergent system that are actually relevant.
> I'm not implying in any way that biology is easy
This is what saying it's 'just' emergent behavior comes off as, though. I understand (and agree with) your perspective, but being a little more tactical with your word use can head off pointless (as opposed to interesting) arguments.
Sure thing. When I posted that, I didn't even consider the possibility that it might be interpreted the way you stated, so I will attempt to assess my future posts in advance for potentially unfriendly perspectives.
Oh I see, perhaps I misread. In any case, from what I understand neuroscience needs better experimental methods, not better math, so still sort of an odd challenge—unless the point is have "brain-like" function without regard to how human brains actually work, which is something I could imagine DARPA being very interested in.
Mathematical Challenge 6: Computational Duality
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?
Mathematical Challenge 7: Occam’s Razor in Many Dimensions
As data collection increases can we “do more with less” by finding lower bounds for sensing complexity in systems? This is related to questions about entropy maximization algorithms.
There are many definitions of duality in mathematics so I am not entirely clear on 6. For example the notion of duals from category theory has already been very helpful in understanding or developing many algorithms. In fact a generous viewing will allow for even enterprise software in the form of LINQ and Observables to have made use of duals in their development.
I am neither clear on 7. I wish I knew what he meant about MaxEnt in particular, there's a lot of neat explorations from the connections between entropy and learning.
But specific to what I interpret as a better Occam's Razor, my vote will have to go to Marcus Hutter as the person who is currently doing the most interesting work in that area. Specifically his work on approximating universal priors. Schmidhuber also has interesting stuff on complexity, search for his talks - they're great.
"Develop a mathematical theory to end, once and for all, humanity's fatal attraction to War; to the glorification of State power, and to the ideology that ends always justifies the means; and in particular, to the perceived need to dominate and control other human beings at scale and through nearly limitless violence and coercion, generally."
Huh? As far as I'm concerned that's the wrong way to think about neuroscience. Although perhaps the goal here is to replicate parts of the brain's function without regard to the underlying structure, in which case I suppose this is a fair way to go about it.
And "The Geometry of Genome Space: What notion of distance is needed to incorporate biological utility?" is a question I work on every day!
I find many of the rest to be quite vague though. "What are the Fundamental Laws of Biology?" huh? The same fundamental laws as the rest of the universe . . .