The computer industry is known for its stunning and relentless rate of improvement: Computers have gotten faster, cheaper, smaller and better every year for many decades. Sometimes, however, the only way forward is to make a wrenching change, one that involves discarding legacy software and established ways of thinking. In the 1980s, the limits of the single-memory, single-processor approach forced the computer industry to change to parallel processing. That revolution was met with intense resistance, since it meant rewriting hundreds of billions of dollars worth of software. Some businesses that were unable or unwilling to adapt to this change did not survive. Today, every processor chip from cell phones to supercomputers contains multiple processors.

A new limit has been reached in recent years, and it stems from power consumption. Data centers use too many megawatts, and mobile device batteries do not last as long as we would like. A key part of this problem lies in the wasteful and outdated way that computers perform arithmetic, using numerical ideas that are over a century old. "Floating point arithmetic" is not merely inefficient; it is quite treacherous to use and has caused disasters that have destroyed billions of dollars and cost human lives. The revolution to change computer arithmetic itself is now underway, and it promises to be just as disruptive as was the transition to parallel computing. This talk will present some first-hand observations about both revolutions.