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How does this all fit together?

Most research areas at CYPHYNETS share some common themes. At a more fundamental level, there is a pivotal reliance on the power of abstraction to deal with similar problems in different settings using a single unified language – the language of mathematics. For example, by considering the pathways in a gene regulation circuit and coordination schemes in a team of robots as instances of the same abstract problem, one can not only provide insights into both of these problems but also solve the same problem for other physical instantiations of that abstraction.

This is the same process of unification, that led Newton to model revolving planets and falling apples using the same equations of motion, and the grand unification that scientists sought to this day [9]. Keeping in mind that the ignorance of experimental science becomes a hurdle in creating good theory, the real challenge in applied research amounts to recognizing the critical points where experimental data cannot be explained without unifications. But hundreds of years of research in the mathematical sciences have taught us how to find good unifications [10]. The abstract unified picture should provide a surprise – something that the disjoint perspectives cannot reveal independently. It must generate new insights and provide correct predictions that cannot be obtained without resorting to the abstraction. For problems in applied research, one should also add efficient computability. I believe that all three areas in my research program are excellent candidates for such unifications. Moreover, all three promise scientific revolutions in the sense of Kuhn [11]. They are banked on

  • dramatic shifts from existing methods and paradigms;
  • responding positively to the challenges unanswered by current science;
  • promising more elegant and simpler solutions to already solved problems.

At CYPHYNETS, the various research themes have strong connections to both the greatest engineering challenges that we face today [7] as well as the most important unresolved mathematical mysteries of our time [6]. The recent resolution of the Poincaré conjecture in mathematics [6], [12] and the breathtaking performance of autonomous robotic vehicles in the recently held DARPA grand challenges on robotics [13] are heartening assurances that a research program banking on the maturity of abstract techniques in topological & geometric methods; and the reliability of engineering design in robotics and embedded systems has a great chance of success.

[6]. Millennium Prize Problems in Mathematics, Clay Mathematics Institute / American Mathematical Society, 2000.

[9]. The Road to Reality: A Complete Guide to the Laws of the Universe, Roger Penrose, Knopf publishers, 2005.

[10]. “Unification becomes a science,” in The Trouble with Physics, Lee Smolin, Mariner Books, 2007.

[11]. The Structure of Scientific Revolutions, Thomas Kahn, University of Chicago Press, 1962.

[12]. “The Poincaré Conjecture Proved”, Dana Mackenzie, Science, Dec 2006.

[13]. The Grand Challenge in Robotics, DARPA. http://www.darpa.mil/grandchallenge/

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