Understanding and Inductive Inference

Abstract

This talk will be about different kinds of understanding, including especially that provided by deductive and inductive inference. Examples will be drawn from Galileo, Kepler, and Fermat. Applications will be given to the physicist’s problem of inferring the laws of nature, and to the restricted case of inferring sequences in Sloane’s Encyclopedia of Integer Sequences.

While there is much theory and understanding of deductive inference, there is relatively little understanding of the process of inductive inference. Inductive inference is about hypothesizing, hopefully inferring, the laws of physics from observation of the data. It is what Kepler did in coming up with his three laws of planetary motion.

Once laws are in place, deductive inference can be used to derive their consequences, which then uncovers much of the understanding in physics.

This talk will define inductive inference, state some of its open problems, and give applications to a relatively simpler but still largely unexplored task, namely, inferring a large natural class of algorithmically generated integer sequences that includes (as of this writing) 20in Sloane’s Encyclopedia of integer sequences.