Shaw was raised in Los Angeles, California. His father was a theoretical physicist who specialised in plasma and fluid flows, and his mother is an artist and educator. They divorced when he was 12. His stepfather, Irving Pfeffer, was professor of finance at University of California, Los Angeles, and the author of papers supporting the efficient market hypothesis.
Shaw earned a bachelors degree summa cum laude' from the University of California, San Diego, a PhD from Stanford University in 1980, and then became an assistant professor of the department of computer science at Columbia University. While at Columbia, Shaw conducted research in massively parallel computing with the NON-VON supercomputer. This supercomputer was composed of processing elements in a tree structure meant to be used for fast relational database searches. Earlier in his career, he founded Stanford Systems Corporation.