Turing's Cathedral: The Origins of the Digital Universe (Penguin Press Science)

by George Dyson

It is no coincidence that the most destructive and the most constructive of human inventions appeared at exactly the same time.

Turing proved that within any formal (or mechanical) system, not only are there functions that can be given a finite description yet cannot be computed by any finite machine in a finite amount of time, but there is no definite method to distinguish computable from noncomputable functions in advance. That’s the bad news. The good news is that, as Leibniz suggested, we appear to live in the best of all possible worlds, where the computable functions make life predictable enough to be survivable, while the noncomputable functions make life (and mathematical truth) unpredictable enough to remain interesting, no matter how far computers continue to advance.

“Von Neumann was one of the greatest of all mathematical artists,” says Goldstine. “It was never enough for him merely to establish a result; he had to do it with elegance and grace.

Vladimir Kosma Zworykin was a pioneer of television (and the last entry in many encyclopedias) who would live to regret that his invention’s capacity for transmission of intelligence had become a channel for so much noise.

The Computron and the Selectron, antediluvian ancestors of solid-state integrated circuits, were vacuum-tube versions of the microprocessor and memory chip. “The idea was to make a single tube which could multiply two numbers and add a third number to the product, the numbers being expressed in digital binary code,” Rajchman explains. “A number of electron beams emanating from a single central cathode were deflected each by three electrodes, corresponding respectively to a digit of the multiplier, a digit of the multiplicand, and a ‘carry-over’ digit…. In effect, the tube was made by ‘integrated vacuum technology,’ as we would describe it today.”