By Alfred Renyi
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Additional info for A diary on information theory
This, as he told me later, did not prove to be a very fruitful exercise. First, he had looked through the Marxist classics, and then turned to Hegel but to no avail at all. He felt a httle offened when I remarked that, to solve new problems, one should not so much look up old quotations, as employ new thinking. In the meantime, I had realized that, wherever energy has a role, information transmission gets into the picture, too, and from that point on, the analogies become self-evident. Let's consider the seemingly unrelated area of history.
Let ^= 1 or ^ = 2 if we choose the first or the second urn, respectively. Let tj—l if the ball is red and t]=2 if it is white. , determine the amount of information supplied by the color of the chosen ball about which urn it came from. Let Ai denote the event when ^=1 and Az that when ^ = 2 ; similarly, let 5i denote the event when ti=l and ^g that when i]=2. Then: P(A,) = P(A,) = P(B,) = P(B^ = - i , P(A^B,)-=P(AM = a 2(a + 6) ' P(AM = b 2ia + b) = PiAM and so. r/K N ^ 1 '^ a+b 2a ^^a + b b . 4564.
By the way, if we substitute for the total, word by word memorization of a book with a memorization more appropriate to the human brain — that is, relating to its content, or message — then every teacher is a walking book, but one which hasn't been printed. That should be the main goal of education at a university, namely, that the professors should teach only what is missing from the textbooks and exists only in their minds. There are some of our professors who do exactly that, but there are others who read aloud or recite by heart what is in the books and then are surprised that most of the students do not attend the second lecture and that whoever does, does so only to sleep at the back.
A diary on information theory by Alfred Renyi