Once, a normal unbiased die was rolled inside an box and so nobody could tell what number was rolled.
One person was told to give the probability that the number 6 was rolled. The person was intelligent. So he calculated correctly. He said the probability that 6 was rolled is 1/6. That is also the same probability that 1, 2, 3, 4, and 5, were rolled.
The die was not rolled again. Nothing about the experiment was changed.
Another person was asked the same question... "What is the probability that the number 6 was rolled?" However, this person was given some more information. He was told that an even number was rolled. Since this person was also intelligent, he concluded correctly that the probability of 6 being rolled was 1/3rd.
The die was not rolled again. Nothing about the experiment was changed.
A third person was asked the same question, but he was given more information. He was told, that the number rolled is even and is not less than or equal to 3. The third person also happened to be intelligent and so concluded, that the probability that 6 was rolled is 1/2.
The above simple story was written from an experiment that my advisor Carl Sturtivant told me to make his point about the importance of information.
Note that every intelligent man had faith that the information given to him was true. He trusted the source.
I want to respect the beauty in the simplicity of the experiment by not writing explicit conclusions from it except allude to one. I recently read a quote I found agonizingly painful. Here - "Actually faith and intelligence are alternatives. You can't have both of them at the same time." This experiment probably brings out why I find that statement so painful.
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