Because aor shouldn't have *all* the fun.

[theweaselking]

Pop quiz:
An airplane is on a gargantuan, infinitely-long treadmill.

The airplane starts it's engines. As soon as it begins to move, the treadmill begins moving in the opposite direction, as fast as you feel like having it go to prevent the plane's takeoff

Will the plane take off anyway?

EDIT: With an infinitely long, arbitrarily fast treadmill, we can also assume that our wheels can handle this arbitrary speed. The tires will not blow and the struts won't melt, no matter how fast those wheels start rolling.

Bonus points:
A game show has three doors. Behind one of them is a new car. Behind the other two are goats.

You're asked to pick one door. WITHOUT OPENING THAT DOOR, the host opens ONE OF THE OTHER TWO DOORS to show you a goat. He then asks you whether you want to keep your original selection, or swap to the last unopened door. You keep whatever is behind the door that you finally decide on.

What should you do to maximise your odds of getting the car?

EDIT: This is a GAME SHOW, people. You don't get to open the doors yourself - Vanna White does that - and she only does it after you tell Regis that yes, that is your final answer and Jeff Foxworthy has mocked you for being dumber than a fifth grader. And you don't get do-overs. Also,the question doesn't care if you prefer goats or not. The question is how to maximise your odds of getting THE CAR, which you can probably sell to buy several goats if that's your thing, but you have to do that after the show.

EXTRA Bonus Points

There is a king who CANNOT LIE.
A man wishes to marry the king's daughter, and is told he may do so if he passes a test.
The test is this: He will be placed in a pit that has five doors, labelled 1 through 5. He will be armed with a spear and a shield.
He must open the doors, one after another, in order, starting from #1.
Behind one of these doors, the king promises there will be a TOTALLY UNEXPECTED LION.
If the man kills the lion, he will be allowed to marry the princess.

So, the man thinks. If he opens the first four doors and there's no lion, then the lion will have to be behind the fifth door. Since he will then know where the lion is, it will not be unexpected. Therefore, the lion cannot be behind the fifth door.

So, the man thinks. If he opens the first three doors and there's no lion, and the lion can't be behind the fifth door, that would mean the lion must be behind the fourth door. And that's not unexpected, so the lion cannot be behind the fourth door.

Similiarly, he realises the lion cannot be behind the third, second, or first door and still be unexpected. Therefore, in order for the king to not be a liar (and the king CANNOT lie), there can't be a lion behind any of the doors at all. And, from a certain point of view, isn't "no lion" a really unexpected kind, under these circumstances?

So:
He confidently strides up to the first door and throws it open. No lion.
He confidently strides up to the second door and throws it open. No lion.
He confidently strides up to the third door and throws it open. No lion.
He confidently strides up to the fourth door and throws it open. Completely unexpectedly, the lion eats him.

What was the flaw in his logic?

Comments

[jackoutofthebox.livejournal.com]

1) The plane needs air to rush under the wing, it's not about distance. Technically if an airplane was on top of Mt Washington and the windspeed gets high enough, the plane could take off vertically.

2) You never stated you couldn't open the door chosen/ open it and if it's a goat, you can choose the remaining door for the car.

3) The flaw in his logic was getting into this pit in the first place.

[theweaselking.livejournal.com]

Whatever door you open, you keep. So if you open your choice and it's a goat, you get a goat.

[corruptedjasper.livejournal.com]

No, Switch (unless you prefer the goat), and It Was Unexpected, Wasn't It?

[theweaselking.livejournal.com]

The question has nothing to do with preferring cars or goats, and everything to do with maximising your chances to get the car.

I specifically worded it that way, because I know there are furries and scandahoovians who read this.

[dolston.livejournal.com]

1 - no
2 - pick a door and don't change your pick
3 - I need to finish my coffee and eat before I think that hard.

[jaffa-tamarin.livejournal.com]

I think the treadmill only stops the plane taking off if it goes fast enough to destroy the landing gear when the wheels overheat. But to be on the safe side, I'm using a Harrier Jump Jet.

[kail-panille.livejournal.com]

The overheated landing gear was my caveat to the initial "of course, why wouldn't it?" answer, as well.

[flemco.livejournal.com]

1) GOD DAMMIT YOU MOTHERFUCKER
YES, YES, A THOUSAND TIMES YES THE PLANE WILL BOTH MOVE FORWARD AND TAKE OFF GOD DAMMIT REGARDLESS OF WHETHER IT'S ON A CONVEYOR BELT, A GIANT LAKEBED COVERED IN MAYO OR ROLLING DOWN THE STREET SMOKIN' INDO SIPPIN ON GIN AN JUICE LAID BACK WITH ITS MIND ON ITS MONEY AND ITS MONEY ON ITS MIND

[silmaril.livejournal.com]

You cannot hold the plane down!

[argaive.livejournal.com]

Pop Quiz:
Unlike a person walking or an automobile driven by its wheels, an airplane's engines don't act against the surface it rests on when not in flight, so the treadmill will have no effect once the airplane is moving under its own power.

Bonus points:
At that point the odds are fifty/fifty, so you can't really do anything to change your odds; that's as good as they'll get.

Extra bonus points:
He was right about the fifth door, but he carried that logic too far. Besides which, if the King said there was a lion and he couldn't lie, then there had to be a lion.

How'd I do?

A.

[scifantasy.livejournal.com]

You got the first one right.

The second one, wrong...Wikipedia actually has a pretty good article on the Monty Hall problem (as this one is called), take a look.

The third is right.

[leighdb.livejournal.com]

1. Not Going There Again. 116 comments and I still don't really get it.

2. Ask the host to open one of the other two doors before choosing. (Hey, you didn't specify that you have to make the choice without opening either of the other doors.)

3. I suck at logic as well as physics! But, I think the flaw here is that the only door the lion could not have been behind and still been unexpected was the fifth door, for exactly the reasons the man says.

However, after the man had made the logical deduction that followed (that therefore the lion also couldn't be behind the fourth door, or third, etc.), that's where it falls down, because to find that there was a lion behind one of the doors after all would of course have been totally unexpected.

[publius1.livejournal.com]

In fact, once he determines that it's totally expected that it'd be behind the fifth door, and since the lion is supposed to be unexpected, if he opens the fifth door and a lion is there, then that'll be pretty fucking unexpected. So even the fifth door is a possibility!

[lonebear.livejournal.com]

1 - proven. IF the wheels were powered then the treadmill would matter. However, since the power for an airplane has nothing to do with what the wheels are doing it does take off.

[psyco-path.livejournal.com]

The treadmill needs to be on a merry go round

I would rather the goat.

Completely unexpected would be a hippogriff eating him.

[flemco.livejournal.com]

[ceramufary.livejournal.com]

1) Plane needs air speed! If the treadmill keeps the plane in place, plane can't take off. What a waste!

2) Always switch! First choice was a 1/3 chance, but after the choices are whittled down to two doors, switching means changing to a 1/2 chance. But I /know/ that one previously, and still can't get my head around it. Once the goat-door is opened, isn't your first choice now a 1/2 chance too? It is madness.

[theweaselking.livejournal.com]

Once the goat-door is opened, isn't your first choice now a 1/2 chance too?

No.

Think of it this way: You're getting either the original door you picked, or the best of ALL OTHER DOORS YOU DIDN'T PICK.

Does that help to explain why you're getting better odds switch?

What if the host told you "Okay, you've picked door #1. Now, you need either stick with door #1, or open all the other doors one at a time until you find the car">

[ben-raccoon.livejournal.com]

1) Yes, because the wheels roll freely; airplanes are powered by the jet engines when taking off. This just means the wheels will spin twice as fast when rolling downt he runway.

[ceramufary.livejournal.com]

Ohhhhhhhh. *blush!*

[neobitch.livejournal.com]

1. The treadmill has nothing to do with the plane taking off. A plane's wheels are not powered. The Straight Dope explains this one nicely, for those who have a hard time wrapping their brain around it.

2. There is nothing you can do to improve your odds at this point. It's 50-50.

3. I got nothin'. I'm looking forward to seeing the answer.

[theweaselking.livejournal.com]

1: Mostly Right! The wheels *do* provide the treadmill with a way of moving the plane since they're not frictionless, but they can't stop it unless it goes so fast that the wheels explode.
2: Wrong!
3: Answer coming later, or maybe tomorrow.

[ursulav.livejournal.com]

1. The plane takes off anyway, as Mythbusters has proved, because a plane isn't a car, goddamnit.

2. You should always switch, because the game show host knows which door is which, and would open the one that definitely didn't have the car.

3. The flaw in the man's logic was assuming that the king had a perfect grasp of logic.

[theweaselking.livejournal.com]

1. Not everyone watches Mythbusters, and Mythbusters gets it wrong a fair amount of the time. But yes, they're right this time.

2. True, Monty does know where the car is, and so he definitely opens a goat and not the car.

3. That's an excellent way of putting things, but not quite correct.

Re: Airplane

[theweaselking.livejournal.com]

It tricks people who are used to wheel-powered vehicles, where pushing against the ground is the source of motion.

Just like the second question tricks the human brain, too.

[chaosrah.livejournal.com]

when do we get the answers? there are too many comments here for me to sort through, lol.

[torrain.livejournal.com]

For number 2, always switch. I know this, because he has explained this to me. I think three times now. And it makes sense, intellectually, even though it still (and I suspect will always) seem counter-intuitive.

I believe that for number 3, there is no flaw in his logic.

[dgillmore.livejournal.com]

1) CAVEMAN WANT FLY PLANE

2) Always switch to maximize your odds (with 3 doors) from 1:3 to 2:3

3) The flaw in his logic was attempting to deduce when to expect the lion. The king said it would be unexpected, and the king cannot lie.

[publius1.livejournal.com]

Even if he's not got what you're thinking, weasel man, he's got #3 100% correct.

[elffin.livejournal.com]

#3: His flaw was in thinking that bald is a hair colour, and that atheism is a religion. Zero is NOT the same as the NULL set.

I love this one because it totally fucks up careless superrational players by meta-gaming the fact that they're superrationals. "Yes, Australia. And you must have suspected I would have known the powder's origin, so I can clearly not choose the wine in front of me."

The flaw in his logic was in trying to deduce what would be unexpected, rather than stab-stab-stabbitying behind every door because there's no penalty for expecting a lion behind every door.
Also/Related: the King made the truth value of his statement entirely dependent upon (descriptively) the attitude of the suitor, who then made his attitude entirely dependent on the prescription that the king's statement had an inherent truth value.

[elffin.livejournal.com]

Which is to say, that had he simply expected the lion behind every door, he would have made the king into a liar upon opening the fourth door.

Who would have promptly vanished in a puff of logic. "Dear me. *poof*"

And then he would have opened the fifth door and out would have come a second lion, who then completely unexpectedly eats him.

And the king re-appears in a puff of logic and says "Works every time."

---

the Princess wept that night in her chambers, and drew to her a slender box. Opening it, she picked up an ornately decorated stilletto, and held it to her bosom, and prepared to plunge it into her heart.

"There is a shortage of perfect quotes in this world. 'Twould be a pity to damage yours."

"Oh, WESTLEY! Oh! But you died! I saw it!"

"Never happened."

"what do you mean?"

"did you say 'I Do' - ?"

The case of the unexpected lion

[jaffa-tamarin.livejournal.com]

There is a lion behind (at least) two of the doors. The second one is the unexpected lion.

I know One but the others not to sure.

[wraith-mistress.livejournal.com]

Ok

1. Plane takes off. :) The Engie is powering the propeller not the wheels.

2. I don't know.

3. The flaw in the logic is that the King *knows* where the lion is. He doesn't know so he isn't lying. Which is why he said behind one of the doors in an Unexpected lion.

Please let me know about question 2 and 3. I'm not sure about those.

M.

[jackoutofthebox.livejournal.com]

So the Lion jumps out of door #2 and mauls the contestant who doesn't get the plane that can't fly.

now that's unexpected.

[anuptaphobic.livejournal.com]

If I were the king, I would have put a lion behind all the doors... Now if he happens to kill the lion behind Door #1, opening door #2 to another lion would be totally unexpected... after that, unless he's a complete idiot, he'd kinda half expect lions when opening the other doors... now technically he only has to kill the unexpected one behind door #2, but he has to open all 5 doors... and he can't really open a door to a lion and not kill it or it would kill him... so in reality he would have to survive fighting 5 lions...

man, if I were a king, I'd really be an asshole...

[ironphoenix.livejournal.com]

Pop quiz: Yes, the plane will take off. flemco expressed the reason with maximal vitriol.

Bonus question: Switch doors. ursulav expressed the reason with optimal succinctness.

EXTRA bonus question: Er, because the king knows that having said that, nobody can expect the lion behind any door.

[cmseward.livejournal.com]

#3 - the flaw in his logic is that once he "deduces" there cannot be a lion, *any* lion is unexpected again.

[faeriemuriel.livejournal.com]

The bonus question was addressed in "The Mysterious Incident of the Dog in the Nighttime" which is a very good book. But you always switch, and there is math to prove it. It's not, for some reason, a 50/50. I read the paragraph a hundred times and still don't understand it,but you always switch.

[falconwarrior.livejournal.com]

The explanation that got me the first time was when Marilyn vos Savant put it on a larger scale. It is difficult to see the difference with only three doors, but imagine there were instead 1,000,000 doors, and when you had chosen, all but two remained: your choice, and one other, one of which has the car. It's all a matter of perspective; not 1 door being removed, but all except 2 doors being removed.

[peristaltor.livejournal.com]

Starting in the OPEC crunch some jetliner manufacturers installed electric motors in the landing gear of their planes. This way they only had to rev the gen sets to power a taxi-ing, rather than blow a shit-load of fuel out the nozzle. After the price of fuel stabilized, most were removed (they proved more expensive to maintain than they saved in fuel).

But if some were still around. . . . Your little test didn't specify which engines are driving the plane on the treadmill, after all, the ones driving the props/jets or the ones powering the electric motors.

So #1? Not enough info. Hah. I win at arcane vagueness! Another empty victory!

[corruptedjasper.livejournal.com]

Also, maybe that was before the come-alongs became standard? These days they have special trucks that tow the planes for most of the taxi.