Vector: The Monty Hall Problem
- The Monty Hall Problem:
From Wikipedia: A thought experiment, sometimes called by the German name gedankenexperiment, is a proposal for an experiment that would test or illuminate a hypothesis, theory, or principle.
Given the structure of the proposed experiment, it may or may not be possible to actually perform the experiment and, in the case that it is possible for the experiment to be performed, no intention of any kind to actually perform the experiment in question may exist. The common goal of a thought experiment is to explore the potential consequences of the principle in question.
Famous examples of thought experiments include Schrödinger's cat, illustrating quantum indeterminacy through the manipulation of a perfectly sealed environment and a tiny bit of radioactive substance, and Maxwell's demon, in which a supernatural being is instructed to attempt to violate the second law of thermodynamics.
To Wikipedia: The Lady or the Tiger: The semi-barbaric King of an ancient land utilized an unusual form of administering justice for offenders in his kingdom. The offender would be placed in an arena where his only way out would be to go through one of two doors. Behind one door was a beautiful woman hand-picked by the king and behind the other was a fierce tiger. The offender was then asked to pick one of the doors, without knowing what was behind it. If he picked the door with the woman behind it, then he was declared innocent but was also required to marry the woman, regardless of previous marital status. If he picked the door with the tiger behind it, though, then he was deemed guilty and the tiger would rip him to pieces.
One day the king found that his daughter, the princess, had taken a lover far beneath her station. The king could not allow this and so he threw the offender in prison and set a date for his trial in the arena. On the day of his trial the suitor looked to the princess for some indication of which door to pick. The princess did, in fact, know which door concealed the woman and which one the tiger, but was faced with a conundrum - if she indicated the door with the tiger, then the man she loved would be killed on the spot; however, if she indicated the door with the lady, her lover would be forced to marry another woman, a woman that the princess deeply hated and believed her lover has flirted with. Finally she did indicate a door, which the suitor then opened.
At this point the question is posed to the reader, "Did the tiger come out of that door, or did the lady?" The question is not answered, and is left as a thought experiment regarding human nature.
To Wikipedia: The Monty Hall Problem: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
- The Curious Incident of the Dog in the Night-Time
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And this shows the intuition can sometimes get things wrong. And intuition is what people use in life to make decisions. But logic can help you work out the right answer.
It also shows that Mr. Jeavons was wrong and numbers are sometimes very complicated and not very straightforward at all. And that is why I like The Monty Hall Problem.
- Google Reader: Pigeons Outperform Humans at Monty Hall Dilemma:
Each pigeon was faced with three lit keys, one of which could be pecked for food. At the first peck, all three keys switched off and after a second, two came back on including the bird’s first choice. The computer, playing the part of Monty Hall, had selected one of the unpecked keys to deactivate. If the pigeon pecked the right key of the remaining two, it earned some grain. On the first day of testing, the pigeons switched on just a third of the trials. But after a month, all six birds switched almost every time, earning virtually the maximum grainy reward.
