The Aaronson Oracle

The story Two machines in a corridor at Bell Labs This experiment is seventy years old, and it was built out of relays before it was ever written as software. c. 1951Bell Telephone LaboratoriesMurray Hill, New Jersey Some time in the early 1950s, at Bell Laboratories, an engineer named David Hagelbarger built a machine to play matching pennies against his colleagues. Two players each choose heads or tails in secret; one wins if the choices match, the other if they differ. Played against someone truly unpredictable, it is a coin flip and nothing more. Hagelbarger called his machine SEER, for SEquence Extrapolating Robot.2 SEER did not model you in any deep way. It tracked three facts about the last two rounds: whether it had won or lost the play before last, whether it had played the same or differently, and whether it had won or lost the last play. Three yes-or-no facts give eight possible situations, and for each of the eight the machine remembered whether playing the same had been working. It counted that on a small reversible counter that stopped at plus and minus three, which Hagelbarger described with a phrase worth keeping: the stops "in effect make the machine forget ancient history."2 WON BEFORE LAST PLAYED THE SAME WON THE LAST ITS COUNTER NNN NNY NYN NYY YNN YNY YYN YYY EIGHT SITUATIONS, EIGHT COUNTERS, EACH STOPPING AT ±3 PlateSEER's whole memory. Three yes-or-no facts about the last two rounds give eight situations, and each situation keeps one small counter of whether playing the same has been working. The stops at plus and minus three are what Hagelbarger meant by making the machine forget ancient history. Claude Shannon, who worked down the hall, took note and built his own. His memorandum of 18 March 1953 opens by giving Hagelbarger the credit plainly, and then makes a comparison that tells you exactly what kind of machine this is: That is the whole idea in one sentence. Game theory tells you the correct way to play matching pennies: flip a mental coin, be genuinely random, and no opponent can beat you over time. Poe's detective does something else entirely. He studies his opponent and guesses what sort of person would choose what. Shannon built the detective, because the detective wins. Not against an ideal player. Against an actual one. Shannon's machine looked for patterns and, in his words, "assumes that the player will follow the patterns the next time the same situation arises." When it had not seen a pattern repeat at least twice, it moved at random, and the randomness came from a commutator spinning about ten times a second, sampled at the moment you pressed the button. Its unpredictability was harvested from the jitter in your own timing.1 PlateNot the mind-reading machine, which is not photographed anywhere we could use, but one of Shannon's other game-playing boxes from the same years: Nimwit, c. 1953, which plays Nim. It is here because of its front panel. Two columns of lamps, player wins against machine wins, is the scoreboard this whole page inherited. MIT Museum, Cambridge MA. Photograph by Daderot, released under CC0 1.0. Source. He knew exactly how to beat it What makes Shannon's memo remarkable is that he did not oversell it. He worked out how beatable the machine was and published the method: The machine is not unbeatable. It is beatable three times out of four, on paper. You simply cannot run the method in your head while playing. That gap, between what is possible in principle and what a person can actually do in the moment, is the entire subject of this page, and Shannon named it in 1953. PlateTheseus, 1952. The mouse finds its way through the maze, and remembers the route. Shannon's habit of building the idea rather than only writing it down is the reason a memo about outguessing people came with a working machine attached. MIT Museum, Cambridge MA. Photograph by Daderot, released under CC0 1.0. Source. The two machines played each other Inevitably, someone wondered which machine was better. Hagelbarger recorded what happened: HAGELBARGER SEER THE LARGER ONE UMPIRE MACHINE SHANNON THE SMALLER ONE 44.2 55.8 SEVERAL THOUSAND GAMES, 1950s · RECHECKED IN SOFTWARE, 2020 PlateThe two machines were wired to a third that refereed between them. The scores shown are from the 2020 software replication, averaged over games of a hundred plays; Hagelbarger's own report of the original match put it at about 55 to 45.3 Shannon's simpler machine, built with about half as many relays, beat the more elaborate one. In 2020 a group at Sibiu reimplemented both in software and played them against each other ten times. Averaged over games of a hundred plays, Shannon's won 55.8 to 44.2. A sixty-year-old piece of laboratory folklore, checked and confirmed.3 Player 3507Machine 5010the lifetime score on the exhibit Shannon's machine still exists.