dashcues
Well-Known Member
I had to cheat.I should've paid more attention to your hint.Heh, I heard the question before, but being from a redneck state they were looking for a different answer.
Critical Thought Experiments
- Thread starter Heisenberg
- Start date
cannabineer
Ursus marijanus
I found one that bothered me ... imo there is a flaw in the answer, which I had to look up. cn
Alexander is stranded on an island covered in forest.
One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole island, killing the man in the process.
There are cliffs around the island, so he cannot jump off.
How can the Alexander survive the fire? (There are no buckets or any other means to put out the fire)
Alexander is stranded on an island covered in forest.
One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole island, killing the man in the process.
There are cliffs around the island, so he cannot jump off.
How can the Alexander survive the fire? (There are no buckets or any other means to put out the fire)
cannabineer
Ursus marijanus
Oh my. My mistake for not more carefully vetting a c&p. Oops.
However when "father&son" is mentioned, it conforms to a common phrase that remains in use for direct relatives. But I applaud "getting your lawyer on". cn
PeyoteReligion
Well-Known Member
I think he should set fire to the center of the island, and follow the burned area west. The original fire will be unable to follow as it has already been burned up.
Heisenberg
Well-Known Member
Would depend on how big the island is. At first I thought he could dig a hole, but he probably doesn't have time and he might suffocate. Then I thought maybe he dug a hole the day before complete with vent chamber. But what if the fire lingers over the hole... better to clear out brush and trees from around the hole. But if he is going to clear out flammable stuff from around the hole, he really doesn't need it anymore. If the clearing is big enough the fire wont touch him. In fact, he could create a clear space across half the island down the middle so the fire would burn out before it reached him, but the only way he could do that quickly is burn it. With the wind coming in from the west he would only accelerate his death if he attempted a burn line. He can not put out the fire he started any more than he can the original fire.
Hrmm
Heisenberg
Well-Known Member
I think this is right, start a new burn and follow it. It would be one way at least.
dashcues
Well-Known Member
might depend on where Alexander is on the island.He may be farther west than the lightning strike hit?If so he should stay where he's at.
dashcues
Well-Known Member
Scratch that..."the fire will burn the whole island" .
PeyoteReligion
Well-Known Member
This is a wildfire survival technique, so I'm for sure going with it.
cannabineer
Ursus marijanus
This was essentially the given answer. I approached this as a problem in topology and could find no way to cross the fireline. The given answer involves stealing a firebrand from the blaze's edge, retreating to the windward side of the island, and setting a counterfire.
In real life this would work since one can control a small fire and step into the burnt area. But as a topology puzzle it dissatisfied, since a fire would spread from a point, recognizing only the island's edges and the burnt areas as boundaries. There's no getting "behind" a closed circle of fire that was necessarily started from outside the circle.
One of the comments cracked me up: " ... only to die days later from exposure and starvation." cn
Heisenberg
Well-Known Member
One day you are running through a forest and meet a leprechaun. He says he will give you his pot of gold if you can find it. He presents three boxes and tells you the gold is under one of them, and the other two are empty. You point to a box, but rather than reveal what's under it, he picks up the box beside it and shows you that one was empty. He then says that you can change your pick if you want, or stay with your original. If you want to give yourself a statistical advanage which choice would you make, or does it not matter?
PeyoteReligion
Well-Known Member
I approached it like a real life situation, and the solution was pretty easy. This has come close to happening to me while hiking near Cle Elum in eastern Washington. Except the island part, but being in the woods just the same.
cannabineer
Ursus marijanus
Not sure if my analysis is valid, but I would change my pick every time. cn
PeyoteReligion
Well-Known Member
Statistically it shouldn't matter. Your choice does not affect which box the gold will be under. Stick with my first guess.
cannabineer
Ursus marijanus
Iirc it turns out that this is a case where a quirk of statistics turns up.
I would change every time.
If I stay with my first choice, I have a one in three chance of hitting. But if I always change, my chances improve to one out of two.
The trick is: the leprechaun engages in a maneuver that changes the odds; he always selects an empty box. If I stay, I'll have chosen before he discards a blank. If I always change, I'll have chosen after he discards the blank. I want to use that advantage. cn
PeyoteReligion
Well-Known Member
At this point we are assuming that we get to continually choose and get shown an empty box. Op never specified if the leprechaun would be so generous or if at that point we need to make a 50/50 shot between your original pick and the other box not yet revealed. I'm pretty high right now, but how do your odds get any better than that? I bet that fucking leprechaun has all sorts of tricky maneuvers to not give the answer away. Btw, is t he already supposed to fork over the gold once you cantch him anyways?
tyler.durden
Well-Known Member
I would say the statistics would be the same if there wasn't more to it, but it's best to stick with your first choice: I assume the lad wouldn't want me to take his gold, so if my original pick didn't have the gold under it, he likely would have picked up the box and I'd lose right then. Why give me another shot if my choice was wrong?
cannabineer
Ursus marijanus
No; we get to choose twice, but the leprechaun only gets to make the one maneuver. We make an initial choice; the leprechaun acts; we make a second choice (stay or switch).
Actually I believe I understated the benefit of switching.
Let's say you pick a door and hold. Your chances of winning are one in three, and the leprechaun's discard doesn't help or hurt those chances.
Let's say you pick a door and switch. The chances that your original pick was good is one in three. This means the chances of the gold being in the two other boxes are two out of three. The leprechaun will assuredly discard an empty box, leaving you with one choice that has a 2/3 chance of hitting.
Always switch. cn
mindphuk
Well-Known Member
Nope, 'neer is right. This is a rewording of the Monty Hall problem that fools a lot of mathematicians. It is always correct to change. It works out to 1/3 of the time you lose, 2/3 you win.
tyler.durden
Well-Known Member
I don't get this: when the leprechaun discards one, the probability of your original pick instantly changes to 2 out of 3, the same as if you switch, no? Am I missing something?
