Critical Thought Experiments
- Thread starter Heisenberg
- Start date
cannabineer
Ursus marijanus
I think we can assume that the island is "on a human scale", not much less or much more than two miles long. (The datum that the fire would consume the island militates against it being as big as, say, Jamaica.) That leaves enough room for maneuver and not too much to cover. I assumed something like this.
To me the problem is that I found it under "logic puzzles" but i see it as a riddle, relying on the peculiar properties of small, managed fires to give an "out" from a topological impossibility. cn
cannabineer
Ursus marijanus
Imo the "daughters" riddle hinges on the lingual sophistication of the respondent. To me "any daughters" automatically means "one or more", so the construction doesn't have a biasing effect. So I say the chances of him having at least one daughter are unity, and two daughters, nonzero. But I don't know how to assign odds without dabbling in semantic sophistry, which has no value imo. cn
Heisenberg
Well-Known Member
The question plays on ambiguity, not a trick of semantics. The man doesn't have a son named 'daughter' or an effeminate son he refers to as daughter. The point is it asks for a statistical answer and most will give one of intuition.
cannabineer
Ursus marijanus
So is "definitely has one, could have two" a sufficient answer?
It reminds me of an anecdote my momma brought back from India. She asked a fellow if he had a family. "Yes", the man said proudly, "two sons and three children." Momma could have strangled him. cn
Heisenberg
Well-Known Member
Semantic riddles stress creative thinking, so I wont be including those here. Let me ask a different way. If you know a man has tossed a coin twice (two births) and you know one of those events resulted in tails (female), what are the odds that the other event resulted in tails as well?
cannabineer
Ursus marijanus
Since non-correlation is a golden principle of the statistics of randomness, I'd say 50%. cn
tyler.durden
Well-Known Member
I think 50/50. In flipping a coin I think the odds always reset to 50/50. For daughters, there are more women born than men in the world, so maybe in that case the odds may be slightly bent toward girls...
cannabineer
Ursus marijanus
... as am I. cn
PeyoteReligion
Well-Known Member
The second coin toss is no affect by the result of the first toss. So again it's 50/50.
cannabineer
Ursus marijanus
I'd be surprised if Heis tells us otherwise.
I'd like to offer one of my favorite logic puzzles.
In a room whose door is closed is an electric light of ordinary sort.
Outside the room is a switch plate with three switches.
One of the switches operates the light.
You are allowed to set the switches any way you want until just before you open the door; then it's hands off.
Figure out which switch operates the light.
cn
mindphuk
Well-Known Member
Here's a problem that completely crushed the post limit of a forum I was on when it was first introduced. The answer was already demonstrated by Mythbusters but if you have never heard of it, try to figure it out.
A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"
cannabineer
Ursus marijanus
No takers at all for mine? Do I smell bad?? cn
cannabineer
Ursus marijanus
A request for disambiguation. Is the plane moving relative to a stationary observer, or only relative to the conveyor apparatus? cn
Heisenberg
Well-Known Member
This is true. One event does not influence the other, yet that is not the issue. We want to know the likelihood that the events match.
Odds are the domain of numbers. The information we are seeking comes from that domain. The odds that any man who has sired two children will have two girls is 25%. If we look at each birth as an event, and each event as having two equally possible outcomes, we have four possible results, one of which gives us double female. It looks like this.
[TABLE="width: 250"]
[TR]
[TD][/TD]
[TD]Birth 1[/TD]
[TD]Birth 2[/TD]
[TD][/TD]
[/TR]
[TR]
[TD]1[/TD]
[TD]Y[/TD]
[TD]Y[/TD]
[TD]YY[/TD]
[/TR]
[TR]
[TD]2[/TD]
[TD]Y[/TD]
[TD]X[/TD]
[TD]YX[/TD]
[/TR]
[TR]
[TD]3[/TD]
[TD]X[/TD]
[TD]Y[/TD]
[TD]XY[/TD]
[/TR]
[TR]
[TD]4[/TD]
[TD]X[/TD]
[TD]X[/TD]
[TD]XX[/TD]
[/TR]
[/TABLE]
The chance of each birth resulting in female is 1/2. .... 1/2 x 1/2 = 1/4
If we account for the information the man supplied, that at least one child is a female, we can elminate the double male result. That leaves 3 possible outcomes, only one of which gives him two daughters. The chance of this man having two daughters is 1/3.
Intuition inclines people to view the two similar outcomes, male/female, female/male, as the same, since they both give a negative answer which leads to the same assumption. The brain doesn't want to have to take the time to distinguish as it sees no meaningful difference between the two results. This leads people to view the outcome as being 50/50. He either has two or he doesn't. There are many situations in life where making intuitive assumptions can be an advantage, but when we are seeking answers which dwell in the domain of numbers, we must use thier logic, which is sometimes counter-intuitive.
http://gwydir.demon.co.uk/jo/probability/info.htm
mindphuk
Well-Known Member
Will the plane move?
Heisenberg
Well-Known Member
I am pondering it. As I refuse to look it up, I may need a while to think.
cannabineer
Ursus marijanus
I'll have to commit my guess: "the plane moves in one direction" means it is in motion with velocity V relative to a stationary observer. If the conveyor moves at -V, the gear is spinning as if the plane were moving at 2V net. So I would say the plane has no difficulty taking off (assuming a long enough motorized runway for the plane to achieve V sub R!), since the wings and engines are moving air and not ground. Wonder if the tires are rated for the centrifugal force of 2V sub R, though ... cn
cannabineer
Ursus marijanus
Thank you. I was insufferable for days when I figured it out without peeking. cn
