However, if he is designing the structural components for the St. Louis Arch, he may need 7 digits of accuracy, otherwise the last piece in the Arch won't fit. I wanted 5 to 7 digits of accuracy so that an engineer could use my program with confidence. That would require 30 to 42 digit computations. It was a shattering lesson. Computers can't do everything, even when they have a good program.
Computers are finite.
Computers are machines. Computers not only fail but sometimes make mistakes. Computers must be programmed by man. Because computers are finite, no computer will ever find the exact square root of 2. This would require infinite time and infinite memory.