/sci/ - Science & Math

>I got even more disturbed when I told the problem to the late Paul Erdös, one of the most famous mathematicians of the century, when he visited my home in 1995.
>Erdös was considered by number theorists as one of the greatest experts in probability theory. In a conversation about the use of probability theory in decision making, I mentioned the goats and Cadillac problem and the answer to Erdös, fulling expecting us to move onto the next subject. But, to my surprise, Erdös said, “No, that is impossible, it should make no difference.”
>I mentioned Bayes, and showed Erdös the decision tree solution I used in my undergraduate course. I reminded him that probability is not a fixed, static thing; it changes as time goes by. To my amazement this didn’t convince him. He wanted a straightforward explanation with no decision trees. I gave up at this point, because I have no common sense explanation. I came to the conclusion
that unless your are educated in using decision trees, and know how to apply the real-world Bayes theorem, it is hopeless to understand the solution.
>So I told Erdös, “You don’t know about decision trees so you can’t understand the solution. Put on your earphones, listen to your music, and stop bothering me.” (When Erdös appeared in my house, the first thing he did was unpack his radio and start listening to classical music. The radio blasted from 5:00 am to midnight. He didn’t seem to be able to live without it.)
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> I ran the program, without the pictures, 100,000 times and found that if I do not switch, the host will smile about 2/3 of the cases. But if I do switch, he will be crying 2/3 of the cases.
>Erdös objected that he still did not understand the reason why, but was reluctantly convinced that I was right. A few days after he left, he telephoned to say that Ron Graham of AT&T explained to him the reasoning behind the answer and that now he understood. He proceeded to tell me the reasoning but I couldn’t fathom his explanation.