|
December 2005 Newer Math?Continued from page 1 By Rodney Brooks
These are just a few examples of what are sometimes referred to as complex adaptive systems. They have many interacting parts that change in response to local inputs and as a result change the global behavior of the complete system. The relatively smooth operation of biological systems -- and even our human-constructed Internet -- is in some ways mysterious. Individual parts clearly do not have an understanding of how other individual parts are going to change their behavior. Nevertheless, the ensemble ends up working. We need a new mathematics to help us explain and predict the behavior of these sorts of systems. In my own field, we want to understand the brain so we can build more intelligent robots. We have primitive models of what individual neurons do, but we get stuck using the tools of information theory in trying to understand the "information content" that is passed between neurons in the timing of voltage spikes. We try to impose a computer metaphor on a system that was not intelligently designed in that way but evolved from simpler systems. My guess is that a new mathematics for complex adaptive systems will emerge, one that is perhaps no more difficult to understand than topology or group theory or differential calculus and that will let us answer essential questions about living cells, brains, and computer networks. We haven't had any new household names in mathematics for a while, but whoever figures out the structure of this new mathematics will become an intellectual darling -- and may actually succeed in designing a computer that comes close to mimicking the brain. Rodney Brooks directs MIT's Computer Science and Artificial Intelligence Laboratory. |
Share »
Digg this
Add to del.icio.us
Add to Reddit
Add to Facebook
Slashdot It!
Stumble It!
Add to Newsvine
Add to Connotea
Add to CiteUlike
Add to Furl
Googlize this
Add to Rojo
Add to MyWeb
Favorite
Print
E-mail
A Quantum Leap in Cryptography
06/27/2005
Massachusetts Institute of Technology
Comments
Guest (Thomas Jewitt) on 12/30/2005 at 5:48 PM
1
I have used this type of mathematical system to uncover patterns of variation that result from relationships between data sources and that are transparent to mathematical models using the algebraic system that we use to balance our checkbooks (real numbers).
Guest (R. Narayanan) on 01/12/2006 at 12:00 AM
1
Guest (Fred Meinberg) on 01/20/2006 at 12:00 AM
1
Guest (T Heywood) on 01/31/2006 at 12:00 AM
1
Guest (Edward Lau) on 03/24/2006 at 12:00 AM
1
Mr Meinberg, this is not a place for corporate boosterism. If your ideas were only profound enough
Guest (K Brown) on 02/23/2006 at 12:00 AM
1
Guest (Thomas Jewitt) on 12/30/2005 at 5:48 PM
1
I have used this type of mathematical system to uncover patterns of variation that result from relationships between data sources and that are transparent to mathematical models using the algebraic system that we use to balance our checkbooks (real numbers).
Guest (Lee Smith) on 03/08/2006 at 12:00 AM
1