“The Turk” was a mechanical chess playing device which toured the globe in the 19th century. It was remarkably successful, managing able to beat almost everyone, include Napoleon. It was later revealed that there was a human hiding inside the machine operating the robot.
Clever Hans was a horse which came to public attention in Germany in the early 1900s, because of his arithmetic skills. He was able to answer questions (by stamping his hooves) such as “if the eighth day of the month comes on a Tuesday, what is the date of the following Friday?” There was so much interest in the horse that the board of education ordered an official investigation (“The Hans Commission”, only in Germany...). They actually concluded that everything was above board. However psychologist Oskar Pfungst later demonstrated that the horse was in fact picking up unconscious cues (changes in posture and facial expression) from its trainer, which were apparently entirely involuntary. Hence the use of double blind studies in social science and medicine.
4 comments:
I suppose the difference between Paul and Hans is that Paul is answering a question that the humans could not easily know. Hans was just reputed to be able to count so human suggestion is an easy explanation. But Paul predicted 8 straight matches with odds that are extremely small if he is doing it unaided. I haven't calculated the exact odds (and its not as easy as it sounds as you have to factor in that Paul cannot pick a draw so depending on draw frequencies in first round world cup games the odds change) but they are something in the region of one in 400 (back of envelope).
The most likely suggestion is that the people behind Paul simply put food he likes in to the tank of the favourite team. Even then, the odds would be small but Paul has had runs before where he did not do so well so overall things become at least partially more explainable, basically this was a fairly predictable world-cup, particularly for the Germans. It still doesn't explain why they went for Serbia over Germany. I can only think this was a freak result that went in their favour. Perhaps Paul went for the wrong food that day and got a lucky bounce. All his predictions after that are simply going with the odds consistent with the idea that he is being guided in some way (e.g. by food placement). Germany winning against England and Argentina was not surprising nor was Spain beating Germany and Holland.
he predicted germany over uruguay also so that makes odds even smaller if he is not being helped but is consistent with the idea of him being guided toward the favourite
8 trials, 8 successes, and take 0.5 as the probability of success on each trial, then the probability of getting all 8 correct is 0.39% (0.5^8). Including the option of a draw would be interesting.
8 trials but 3 of them have three outcomes Keith. Though Paul was constrained to go for 2 of them. Assuming 0.5 gives about 1 in 250 as you have calculated. But 1 in 864 assuming three equally likely outcomes for the first round. It may even be the case that being forced to go for a win reduced his ex ante chances rather than increased them. Depends on the proportion of first round games that are drawn. I think there are a few tricks we are missing though.
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