What are some of the reasons why a scientific question might be unanswerable? I'll limit myself to just three here. The first is that insufficient data has survived. That can be a problem in ur-linguistics, archaeology, and history. The second is that contingent events, sometimes called frozen accidents, may limit our ability to explain certain phenomena. (On the other hand, as Stephen Jay Gould eloquently argues, historical explanations in science can be as convincing as those arising from general theories.) Finally, resources, such as energy, may simply not be available in our part of the universe to discriminate among contesting theories about the universe.

Of course we must be very careful in stating that something is impossible or unknowable. We're all familiar with some of the notorious announcements concerning impossibility, such as, there cannot be a heavier-than-air flying machine.

The unknowable has long been the province of philosophy and epistemology, with questions raised by giants such as Immanuel Kant and Ludwig Wittgenstein. My goal is to move the distinction between the unknown and the unknowable from philosophy to science and thereby enrich science.

What is the basis for my belief that we might succeed? The Zeitgeist seems right for tackling such questions. We have had great success in establishing impossibility results in mathematics and theoretical computer science. Although these ideas cannot be directly applied to science, I'm hopeful that the modes of thought might be transferable. Recent workshops at the Santa Fe Institute have brought together leading physicists, economists, cognitive scientists, biologists, computer scientists, and mathematicians who have strong interests in defining the unknowable in their own fields.

JB: What kind of predictive models will you use?

TRAUB: A central issue is the relation between reality and models of reality. I like to talk about this in terms of four worlds. There are two real worlds: the world of natural phenomena and the computer world, where simulations and calculations are performed. There are two model worlds: a mathematical model of a natural phenomenon and a model of computation. The mathematical model is an abstraction of the natural world while the model of computation is an abstraction of a physical computer. Incidentally, although most people are only aware of the Turing machine as the abstract model of computation, the real-number model is probably more appropriate for the continuous models of science, but that's a story for another day.

I'll give you one concrete example concerning reality and models of reality. I wrote about this in "On Reality and Models" which is a chapter in the recent book, "Boundaries and Barriers" edited by John Casti and Anders Karlquist, and which is also a Santa Fe Institute report.

All living matter is built out of proteins, and these proteins fold effortlessly. It takes nature less than a second. But even with the most powerful supercomputers, we cannot simulate protein folding, and theory suggests that the problem is what is technically called NP-complete, meaning it's conjectured to be computationally intractable. Why is there this dissonance between our models and reality? I'll confine myself here to just one possible explanation. Nature doesn't fold arbitrary molecules; the molecules that exist in nature have been selected by evolution for ease in folding. But in our theory we don't know how to model this selection.

Trying to understand the relation between reality and our perception of reality is an old issue. Some 200 years ago Immanuel Kant believed that three space dimensions and one time dimension has more to do with our brains than with "reality". Niels Bohr and Albert Einstein argued about this. Bohr said all I want from a mathematical model is the ability to predict and I don't know or care about "reality". Einstein felt that there is a reality which our theories describe. The debate continues today between Stephen Hawking and Roger Penrose with Hawking taking Bohr's view and Penrose taking Einstein's.