something much more significant than speculating at the time: He was laying the foundations for the digital revolution. As a graduate student at MIT, he worked for Vannevar Bush on the Differential Analyzer. This was one of the last great analog computers, a room full of gears and shafts. Shannon’s frustration with the difficulty of solving problems this way led him in 1937 to write what might be the best master’s thesis ever. In it, he showed how electrical circuits could be designed to evaluate arbitrary logical expressions, introducing the basis for universal digital logic. After MIT, Shannon studied communications at Bell Labs. Analog telephone calls degraded with distance; the farther they traveled, the worse they sounded. Rather than continue to improve them incrementally, Shannon showed in 1948 that by communicating with symbols rather than continuous quantities, the behavior is very different. Converting speech waveforms to the binary values of 1 and 0 is an example, but many other sets of symbols can be (and are) used in digital communications. What matters is not the particular symbols but rather the ability to detect and correct errors. Shannon found that if the noise is above a threshold (which depends on the system design), then there are certain to be errors. But if the noise is below a threshold, then a linear increase in the physical resources representing the symbol results in an exponential decrease in the likelihood of making an error in correctly receiving the symbol. This relationship was the first of what we’d now call a threshold theorem. Such scaling falls off so quickly that the probability of an error can be so small as to effectively never happen. Each symbol sent multiplies rather than adds to the certainty, so that the probability of a mistake can go from 0.1 to 0.01 to 0.001, and so forth. This exponential decrease in communication errors made possible an exponential increase in the capacity of communication networks. And that eventua