Economics and similar, for the sleep-deprived
A subtle change has been made to the comments links, so they no longer pop up. Does this in any way help with the problem about comments not appearing on permalinked posts, readers?
Update: seemingly not
Update: Oh yeah!
Tuesday, April 20, 2010
More on the stopped clock theorem
You look at your watch and see the time is 10am. You then see a stopped clock, which shows that the time is X ≠ 10am. Using Bayes' Rule, to what do you now revise your opinion of what time it is?
It's still 10am, isn't it?
Lemma: All stopped clocks are independent of each other.
(1) Either: the conditional probability (T=X| [A stopped clock says that T=X]) = 0
(2) Or: there is some, possibly infinite, vector V of stopped clocks showing times [X1, X2 ...], such that if you saw V when your watch said 10am, then you would change your mind about the time.
The second can't be right, so the conditional probability that T=X given that a stopped clock says that T=X is zero; ie, "A stopped clock is never right" QED.
Whatcha think about that? Answer in comments.
Tangentially semi-related link
this item posted by the management 4/20/2010 05:17:00 PM