July 1, 2008
What example(s) from your work (or the work of others) best illustrates the fruitful use of a computational and/or informational approach for foundational researches and/or applications?
I’ve now spent about 25 years applying computational ideas to questions in basic science. The single most fruitful concept has been exploring the computational universe of possible programs.
The exact sciences have always tended to use a fairly small set of models, mostly based on traditional mathematics. A key new concept from computation is to enumerate all possible programs—and potentially use them as models.
Studying the universe of possible simple programs defines a new kind of basic science. And what I’ve found is that that new kind of basic science is not only rich and fascinating in its own right—but is also immediately applicable. For what I’ve discovered is that in the universe of simple programs there are ones immediately relevant for understanding the natural world, for creating technology and for creating all sorts of new forms and artifacts.
Learning about the computational universe also informs many old foundational questions in science and elsewhere. It shows us at a basic level why complexity is so easy for nature to produce, and so widespread. It shows us that there are fundamental computational limitations to traditional mathematical science. It gives us insight into how similar phenomena like intelligence are to natural processes. It shows us how special—and in many ways arbitrary—the formal systems like mathematics that we have built are.