The answers!
Feb. 2nd, 2008 09:24 amI posed three questions yesterday.
The answers are, in order:
1. Yes, the plane will take off. There is friction on the wheels, but the wheels spin freely and do not drive the plane, so as you accelerate the treadmill against the growing thrust of the jet engine, the wheels will simply start to spin faster.
The horizontal force that the treadmill applies to the plane through the wheels, while present, is trivial compared to the thrust from the jet engines. Even at ludicrous speed, the plane's wheels will spin much faster without allowing much more impact to the plane.
2. You should ALWAYS switch. This is the Monty Hall problem - and because you've got the initial choice before he removes a door, it does NOT reduce the problem to a coin flip between two doors. The entire setup is a deceitful way of asking the question "should you take the door you picked originally, or should you take the best of all other doors combined". And the answer to that, clearly, is "best of all other doors" - Monty just opens all the other doors EXCEPT the one he tells you is the best of all other doors.
3. Well, I fucked up the question. While "there could have been two lions" does technically meet the requirements, a more correct phrasing of the question would be "four of the five doors have nothing behind them. One door has a single totally unexpected lion, and nothing else."
And, given that:
A) There is only one lion.
and
B) The lion will be totally unexpected
... there's nothing wrong with his logic. He didn't make a mistake.
His logic is impeccable, and 100% correct. Since the lion has to be "unexpected", it can't be behind door #5, which means it can't be behind door #4, which means it can't be behind door #3, etc. His logic correctly deduces that there cannot be a lion who is unexpected - and because of his perfect logic, the lion *is* totally unexpected.
The answers are, in order:
1. Yes, the plane will take off. There is friction on the wheels, but the wheels spin freely and do not drive the plane, so as you accelerate the treadmill against the growing thrust of the jet engine, the wheels will simply start to spin faster.
The horizontal force that the treadmill applies to the plane through the wheels, while present, is trivial compared to the thrust from the jet engines. Even at ludicrous speed, the plane's wheels will spin much faster without allowing much more impact to the plane.
2. You should ALWAYS switch. This is the Monty Hall problem - and because you've got the initial choice before he removes a door, it does NOT reduce the problem to a coin flip between two doors. The entire setup is a deceitful way of asking the question "should you take the door you picked originally, or should you take the best of all other doors combined". And the answer to that, clearly, is "best of all other doors" - Monty just opens all the other doors EXCEPT the one he tells you is the best of all other doors.
3. Well, I fucked up the question. While "there could have been two lions" does technically meet the requirements, a more correct phrasing of the question would be "four of the five doors have nothing behind them. One door has a single totally unexpected lion, and nothing else."
And, given that:
A) There is only one lion.
and
B) The lion will be totally unexpected
... there's nothing wrong with his logic. He didn't make a mistake.
His logic is impeccable, and 100% correct. Since the lion has to be "unexpected", it can't be behind door #5, which means it can't be behind door #4, which means it can't be behind door #3, etc. His logic correctly deduces that there cannot be a lion who is unexpected - and because of his perfect logic, the lion *is* totally unexpected.