641 karma · joined October 21, 2009
It is the most counter-intuitive statistic problem I know (worse than Monty Hall), it trips everyone up at first.
No problem about the stubborness ;)
In the problem I pose, the person does not randomly come forward and tell me "I have a boy born on a tuesday". In my problem I ask random people who I know have two children if they have "at least on boy born on a tuesday" until someone says yes.
Try something easier, for example two dice. The probability to roll 1 1 is less than to roll 1 2, because 1 2 can be rolled either by first rolling a 1 or a 2, while 1 1 can be rolled only by first rolling a 1. That information is used often in dice games like backgammon.
Same with children: BT BT can only be "rolled" if your first child is BT, whil BT BW can be "rolled" if your first child is either BT or BW.
Do you see?
It is the nature of technology that bitcoins will someday become MySpace.
I am open to be convinced otherwise by someone knowledgeable.
I think switching the usual meaning of = and == will be confusing. O'Caml uses = and == for deep and shallow comparison respectively and <- for assignment. That is a possibility.
Not exactly dependent types, but practical, I think.
I promise not to make the Haskell struct mistake.
Likewise there is obviously a great number of programs in Turing complete languages that you can prove properties about. Thus, there is a class of pleasant programs (or [program, property] pairs).
We do not know for certain how many of the programs that we want to write that is in each class. I would venture a guess that >99% of all programs ever written are in the "nice" class. If it is really impossible to reason about some property of a program, why would you think it works?