DARPA Mathematical Challenges

I'm blatantly copying this from a solicitation from DARPA. See here for my original source of the material.

Mathematical Challenge One: The Mathematics of the Brain
Develop a mathematical theory to build a functional model of the brain that is mathematically consistent and predictive rather than merely biologically inspired.

Mathematical Challenge Two: The Dynamics of Networks
Develop the high-dimensional mathematics needed to accurately model and predict behavior in large-scale distributed networks that evolve over time occurring in communication, biology and the social sciences.

Mathematical Challenge Three: Capture and Harness Stochasticity in Nature
Address Mumford’s call for new mathematics for the 21st century. Develop methods that capture persistence in stochastic environments.

Mathematical Challenge Four: 21st Century Fluids
Classical fluid dynamics and the Navier-Stokes Equation were extraordinarily successful in obtaining quantitative understanding of shock waves, turbulence and solitons, but new methods are needed to tackle complex fluids such as foams, suspensions, gels and liquid crystals.

Mathematical Challenge Five: Biological Quantum Field Theory
Quantum and statistical methods have had great success modeling virus evolution. Can such techniques be used to model more complex systems such as bacteria? Can these techniques be used to control pathogen evolution?

Mathematical Challenge Six: 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 Seven: 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.

Mathematical Challenge Eight: Beyond Convex Optimization
Can linear algebra be replaced by algebraic geometry in a systematic way?

Mathematical Challenge Nine: What are the Physical Consequences of Perelman’s Proof of Thurston’s Geometrization Theorem?
Can profound theoretical advances in understanding three dimensions be applied to construct and manipulate structures across scales to fabricate novel materials?

Mathematical Challenge Ten: Algorithmic Origami and Biology
Build a stronger mathematical theory for isometric and rigid embedding that can give insight into protein folding.

Mathematical Challenge Eleven: Optimal Nanostructures
Develop new mathematics for constructing optimal globally symmetric structures by following simple local rules via the process of nanoscale self-assembly.

Mathematical Challenge Twelve: The Mathematics of Quantum Computing, Algorithms, and Entanglement
In the last century we learned how quantum phenomena shape our world. In the coming century we need to develop the mathematics required to control the quantum world.

Mathematical Challenge Thirteen: Creating a Game Theory that Scales
What new scalable mathematics is needed to replace the traditional Partial Differential Equations (PDE) approach to differential games?

Mathematical Challenge Fourteen: An Information Theory for Virus Evolution
Can Shannon’s theory shed light on this fundamental area of biology?

Mathematical Challenge Fifteen: The Geometry of Genome Space
What notion of distance is needed to incorporate biological utility?

Mathematical Challenge Sixteen: What are the Symmetries and Action Principles for Biology?
Extend our understanding of symmetries and action principles in biology along the lines of classical thermodynamics, to include important biological concepts such as robustness, modularity, evolvability and variability.

Mathematical Challenge Seventeen: Geometric Langlands and Quantum Physics
How does the Langlands program, which originated in number theory and representation theory, explain the fundamental symmetries of physics? And vice versa?

Mathematical Challenge Eighteen: Arithmetic Langlands, Topology, and Geometry
What is the role of homotopy theory in the classical, geometric, and quantum Langlands programs?

Mathematical Challenge Nineteen: Settle the Riemann Hypothesis
The Holy Grail of number theory.

Mathematical Challenge Twenty: Computation at Scale
How can we develop asymptotics for a world with massively many degrees of freedom?

Mathematical Challenge Twenty-one: Settle the Hodge Conjecture
This conjecture in algebraic geometry is a metaphor for transforming transcendental computations into algebraic ones.

Mathematical Challenge Twenty-two: Settle the Smooth Poincare Conjecture in Dimension 4
What are the implications for space-time and cosmology? And might the answer unlock the secret of “dark energy”?

Mathematical Challenge Twenty-three: What are the Fundamental Laws of Biology?
This question will remain front and center for the next 100 years. DARPA places this challenge last as finding these laws will undoubtedly require the mathematics developed in answering several of the questions listed above.

Fair Projects

Actually, the site is "FairSoftware.net" but the idea is to enable a project leader to seek out partners to implement their business visions. Superficially, it's a business site that's trying to connect business-people who need help getting their ideas off the ground. Though, it pretends to also be a business site and the services they have available include registering and administering an LLC (without filling out the state paperwork for you).

From my brief searches through the site, most of the listings appear to come from predatory businesses who are trying to establish their own mini blog advertising business. For this reason, I fully expect the site to fail or stagnate because only lowlifes want to be involved in stuff like that. There was one bright spot, though. I found a guy trying to make a movie. That sounds like an interesting way to get people trying to break into the business to work with each other. Perhaps one day I'll add Life's Experiences as a project to FairSoftware.net... but for now I am holding off. It seems too young and too immature at the moment.

Longball

For those of you who have read my book you'll know I invented a sport called Longball.

The primary goal at the time had been to develop a game that's more of a war than anything that exists today. I don't mean this in a sense of killing and violence, but rather in a sense of strategy that's leaps and bounds more complex than baseball's "double switch" or the decision in football to execute an "onside kick". I wanted a game that was rich with content to the point where broadcasting all of it within a 90-inch by 50-inch screen wouldn't even begin to do it justice. I wanted a game where you could reasonably flank your opponent. A game where manager's couldn't simply manage from the sidelines by announcing what plays they wanted their teams to run, but rather a game where leaders on the field would direct traffic so their team could surge towards the goal.

The secondary goal was to create a game that could be played by literally hundreds of players. In the novel, when played at the "Professional" level it's written that each team is comprised of 2k players on the field with another 8k waiting on the bench. The playing area a "Professional" game was a field with a radius of about a mile. For lesser "Amateur" games the idea is to have far fewer players and saner field sizes. I imagine a standard Football field or soccer court would be large enough to support two teams with 3 dozen players each.

But I digress, because the size and scope are details that can be ironed out later. The meat of the game is a far more interesting topic of discussion. How is it possible to create a game as rich and complex as I talked about that could be accessible to so many different types of athletes? Well... let's reason out what makes baseball, soccer, volleyball, football, tennis, and anything else you can imagine so incredibly simple. Mind numbingly simple. Simple to the point where playing the sport take immense specialization. Where wins are measured by individual heroics and championships are attributed to the heroes. And the reason for this simplicity is that all these games have a single focus. Heck... all these games are named after the object which is that focus. It's this singularity that prevents games from reaching out beyond their extremely limited scopes of play.

So how does Longball eliminate the singularity? Well, it borrows elements from several other simple, but well known games and meshes them. With the pre-established rules associated with each of several different sports it would be easy to build complexity. As they same, the sum of the whole is greater than the value of the individual components. In a candid view, Longball (on the "Professional" level) blends 36 games of soccer, 36 games of rugby, and 36 games of Ultimate Frisbee and sets them up on the same field. Again, for "Amateur" play these numbers get scaled down to 3 or 4 of each game, but the inherent complexity that's intertwined within them will remain as an emergent property of the sport.

And it's this "Amateur" version that I'd be very, very interested in playing on a real field with 6 dozen of my closest friends. Who else would be interested?