Talk:Principle of indifference
From an email:
I had to handle the Principle of Indifference a bit... I like your article but wonder how a novice would like it? May be a simpler introduction would help. At he end of the article, I suggest to introduce Dempster-Shafer Theory.
- Hrm, yeah, not too novice-friendly. A nice example would go a long way. I'll do that eventually, if someone doesn't beat me to it.
- Cyan 18:25, 11 Aug 2003 (UTC)
- I've got a book by Martin Gardner on paradoxes (the name eludes me at this time) that presents a user-friendly discussion on the Principle. If I remember, I'll paraphrase an example or two from it.
- CHz 20:12, 2 Jan 2004 (UTC)
- The book is "aha! Gotcha" by Martin Gardner. Here's the full citation:
- Gardner, Martin (1982). aha! Gotcha. New York: W. H. Freeman and Company. ISBN 0-71-671361-6.
- The following example occurs on pages 107-108:
- "Let's see how contradictions arise if the principle is carelessly applied to our questions about Titan and atomic war. What is the probability there is some form of life on Titan? We apply the principle of indifference and answer 1/2. What is the probability of no simple plant life on Titan? Again, we answer 1/2. Of no one-celled animal life? Again, 1/2. What is the probability there is neither simple plant life nor simple animal life on Titan? By the laws of probability we must multiply 1/2 by 1/2 and answer 1/4. This means that the probability of some form of life on Titan has now risen to 1 - 1/4 = 3/4, contradicting our former estimate of 1/2.
- "What is the probability of an atomic war before the year 2000? By the principle of indifference we reply 1/2. What is the probability of no atom bomb dropped on the United States? Answer: 1/2. Of no atom bomb on Russia? Answer: 1/2. Of no atom bomb on France? Answer: 1/2. If we apply this reasoning to ten different countries, the probability of no atom bomb falling on any of them is the tenth power of 1/2, or 1/1024. Subtracting this from 1 gives us the probability that an atom bomb will fall on one of the ten countries--a probability of 1023/1024.
- "In both of the above examples the principle of indifference is aided by an additional assumption in yielding such absurd results. We have tacitly assumed the independence of events that clearly are not independent. In light of the theory of evolution, the probability of intelligent life on Titan is dependent on the existence there of lower forms of life. Given the world situation as it is, the probability of an atom bomb falling on, say, the United States is not independent of the probability of such a bomb falling on Russia."
- (forgive any typographical errors: I'm tired)
- This is a great example that explains both how the Principle is applied and how it can be incorrectly used. I don't think I can rephrase in any better way, so does anyone have an objection to me slapping this into the article?
- I was also thinking about adding a simplified definition, maybe something like "In layman's terms, the Principle of indifference states that, if we have a list of several independent events and have no reason to believe that any are more or less likely to occur than others, then we should assume that each has an equal chance of occurring." Any thoughts? CHz 05:31, 5 Jan 2004 (UTC)