Algorithms: Exploration and Discovery

Much of the emphasis in teaching algorithms is placed on time complexity analysis with occasional mentioning of space complexity, accuracy, and parallelism, etc. This optimization view of algorithms is valuable, but a wider view is possible, that of algorithms as a means of exploration and discovery.

A classic example is the proof of the four color theorem. It shows how computers can extend the frontiers of human knowledge. Although in some cases, human understanding is limited, and the soundness of computer generated results is in doubt, computers still provide a great deal of value for research. We no longer just talk about how fast a algorithm operates, but also what new stuff it can find out.

In a certain technical sense, computer exploration is crucial, because there is no Turing machine that can predict how a arbitrary computer program will end. Exploration is a tool to find out what a algorithm actually performs.

Moreover, research often deals with uncertain postulates, rather than established knowledge, which is why a knowledge engine is inherently limited. The possibility to explore various postulates is critical for solving open problems. Deep neural networks are valuable not only because they can store knowledge, but also because they offer heuristics in the unknown region.

Here we hope Google's ambition doesn't stop with knowledge, for much more is possible.