|The Third Culture|
| The Unknown and The Unknowable|
A Talk With Joseph Traub [3.11.97]
"Science is about understanding the universe and everything in it. Examples of scientific questions are: Will the universe expand forever, or will it collapse?; Will there be major global changes due to human activities, and what will be the effects on earth's ocean levels, and on agriculture and biodiversity? Note that there are, a priori, no mathematical models that accompany these questions. Science uses mathematics, but it is also very different from mathematics. Can we up the ante from mathematics and prove impossibility results in science?."
Starting in 1959, Joseph Traub pioneered research in what is now called "information-based complexity". Computational complexity theory studies the intrinsic difficulty of solving mathematically posed problems; it can be viewed as the thermodynamics of computation. "Information-based complexity" studies the computational complexity of problems with only partial or contaminated information. Such problems are common in the natural and social sciences and he is applying "information-based complexity" to a wide range of problems Other work ranges from new fast methods for pricing financial derivatives to investigating what is scientifically knowable.