The Aaronson Oracle: an interactive lesson in human predictability
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The story
Two machines in a corridor at Bell Labs
This experiment is seventy years old, and it was built out of relays<br>before it was ever written as software.
c. 1951<br>Bell Telephone<br>Laboratories<br>Murray Hill, New Jersey
Some time in the early 1950s, at Bell Laboratories, an engineer named<br>David Hagelbarger built a machine to play matching pennies<br>against his colleagues. Two players each choose heads or tails in<br>secret; one wins if the choices match, the other if they differ. Played<br>against someone truly unpredictable, it is a coin flip and nothing more.<br>Hagelbarger called his machine SEER, for SEquence Extrapolating<br>Robot.2
SEER did not model you in any deep way. It tracked three facts about<br>the last two rounds: whether it had won or lost the play before last,<br>whether it had played the same or differently, and whether it had won or<br>lost the last play. Three yes-or-no facts give eight possible<br>situations, and for each of the eight the machine remembered whether<br>playing the same had been working. It counted that on a small reversible<br>counter that stopped at plus and minus three, which Hagelbarger<br>described with a phrase worth keeping: the stops "in effect make the<br>machine forget ancient history."2
WON BEFORE LAST<br>PLAYED THE SAME<br>WON THE LAST<br>ITS COUNTER
NNN<br>NNY<br>NYN<br>NYY<br>YNN<br>YNY<br>YYN<br>YYY
EIGHT SITUATIONS, EIGHT COUNTERS, EACH STOPPING AT ±3
Plate SEER's whole memory. Three yes-or-no facts<br>about the last two rounds give eight situations, and each situation<br>keeps one small counter of whether playing the same has been working.<br>The stops at plus and minus three are what Hagelbarger meant by<br>making the machine forget ancient history.
Claude Shannon, who worked down the hall, took note and built his<br>own. His memorandum of 18 March 1953 opens by giving Hagelbarger the<br>credit plainly, and then makes a comparison that tells you exactly what<br>kind of machine this is:
This machine is a somewhat simplified model of a machine designed<br>by D. W. Hagelbarger. It plays what is essentially the old game of<br>matching pennies or "odds and evens." This game has been discussed<br>from the game theoretic angle by von Neumann and Morgenstern, and from<br>the psychological point of view by Edgar Allen Poe in the "The<br>Purloined Letter." Oddly enough, the machine is aimed more nearly at<br>Poe's method of play than von Neumann's.
Shannon, A Mind-Reading (?) Machine, 19531
That is the whole idea in one sentence. Game theory tells you the<br>correct way to play matching pennies: flip a mental coin, be genuinely<br>random, and no opponent can beat you over time. Poe's detective does<br>something else entirely. He studies his opponent and guesses what sort<br>of person would choose what. Shannon built the detective, because the<br>detective wins. Not against an ideal player. Against an actual one.
Shannon's machine looked for patterns and, in his words, "assumes<br>that the player will follow the patterns the next time the same<br>situation arises." When it had not seen a pattern repeat at least twice,<br>it moved at random, and the randomness came from a commutator spinning<br>about ten times a second, sampled at the moment you pressed the<br>button. Its unpredictability was harvested from the jitter in your own<br>timing.1
Plate Not the mind-reading machine, which is not<br>photographed anywhere we could use, but one of Shannon's other<br>game-playing boxes from the same years: Nimwit, c. 1953, which plays<br>Nim. It is here because of its front panel. Two columns of lamps,<br>player wins against machine wins, is the scoreboard<br>this whole page inherited.<br>MIT Museum, Cambridge MA. Photograph by Daderot,<br>released under CC0 1.0.<br>Source.
He knew exactly how to beat it
What makes Shannon's memo remarkable is that he did not oversell it.<br>He worked out how beatable the machine was and published the method:
A mathematical analysis of the strategy used in this machine shows<br>that it can be beaten by the best possible play in the ratio 3:1. To<br>do this it is necessary to keep track of the contents of all the<br>memory cells in the machine. […] It is extremely difficult to carry<br>out this program mentally because of the amount of memory and<br>calculation necessary.
Shannon, 19531
The machine is not unbeatable. It is beatable three times out of<br>four, on paper. You simply cannot run the method in your head<br>while playing. That gap, between what is possible in principle and what<br>a person can actually do in the moment, is the entire subject of this<br>page, and Shannon named it in 1953.
Plate Theseus, 1952. The mouse finds its way through<br>the maze, and remembers the route. Shannon's habit of building the<br>idea rather than only writing it down is the reason a memo about<br>outguessing people came with a working machine attached.<br>MIT Museum, Cambridge MA. Photograph by Daderot,<br>released under CC0 1.0.<br>Source.
The two machines...