Critical Thought Experiments

cannabineer said:
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
Click to expand...

So I'm tryin to turn the light on? Hmmm.this is a tough one. I don't even have an initial gut feeling about any of them. For no reason at all, I wanna say the one closest to the door, which was not specified and probably dosent matter.
 
Eureka!!

At first I wanted to systematically eliminate switches by opening the door to check. But I figure we only get one shot or else the question is unnecessary. Stumped, I started looking at the wording. 'Ordinary'. This got me to thinking about different bulbs, which made me think of my grow tent. Why do I not use ordinary bulbs... spectrum, cost.. and heat. I sometimes feel the tent without opening it to see if it's too hot. If the lights are off, it's not even warm. So I was thinking we could turn on a switch, feel the door and see if it warms up, but I guess doors don't normally heat up from ordinary light bulbs. But the bulb itself gets hot, which lead to my eureka moment, scaring my cats in the process. We ignore the first switch and turn on the second long enough to warm up the bulb. We then turn off the second switch and turn on the third. When we open the door, if the light is on it's the third switch. If the light is dark but warm it is the second switch, and if the light is dark and cold, it's the first switch. Of course I can't actually tell you which switch is the one unless I am there in person.

How about it?
 
cannabineer said:
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
Click to expand...

You are correct. The problem seems to be that people instinctively think of it as if it were a car or bike where they remain stationary with respect to an outside observer. They have a cognitive block where they just can't get the concept of the thrust acting on the air mass above the treadmill with free spinning wheels in the gear. The speed of the treadmill is irrelevant, the plane can take off at belt speeds higher than take off speed, it will only make the wheels spin faster.
 
Here is another puzzle dealing with probable outcomes, easy one this time. Everyone should get this if they think about it. This requires only logic.

You are blindfolded and standing in front of a drawer which contains only the following: 10 red socks, 10 green socks, 10 blue socks, 10 black socks and 10 white socks. Since you can not see, what is the minimum number of socks you need to pull out of the drawer to guarantee you have a matching pair?
 
Heisenberg said:
Here is another puzzle dealing with probable outcomes, easy one this time. Everyone should get this if they think about it. This requires only logic.

You are blindfolded and standing in front of a drawer which contains only the following: 10 red socks, 10 green socks, 10 blue socks, 10 black socks and 10 white socks. Since you can not see, what is the minimum number of socks you need to pull out of the drawer to guarantee you have a matching pair?
Click to expand...

6.

you pull sock 1, of color a.

you pull sock 2, of color b.

you pull sock 3, of color c.

you pull sock 4, of color d.

you pull sock 5, of color e.

when you pull sock 6, it will be either color a, b, c, d, or e, thus giving you a matching pair.

learned that one in fifth grade. new jersey has great public schools.
 
UncleBuck said:
6.

you pull sock 1, of color a.

you pull sock 2, of color b.

you pull sock 3, of color c.

you pull sock 4, of color d.

you pull sock 5, of color e.

when you pull sock 6, it will be either color a, b, c, d, or e, thus giving you a matching pair.

learned that one in fifth grade. new jersey has great public schools.
Click to expand...

Correct, but you left out the obligatory insult I have come to expect from each of your posts.

No points for you.
 
Heisenberg said:
Eureka!!

At first I wanted to systematically eliminate switches by opening the door to check. But I figure we only get one shot or else the question is unnecessary. Stumped, I started looking at the wording. 'Ordinary'. This got me to thinking about different bulbs, which made me think of my grow tent. Why do I not use ordinary bulbs... spectrum, cost.. and heat. I sometimes feel the tent without opening it to see if it's too hot. If the lights are off, it's not even warm. So I was thinking we could turn on a switch, feel the door and see if it warms up, but I guess doors don't normally heat up from ordinary light bulbs. But the bulb itself gets hot, which lead to my eureka moment, scaring my cats in the process. We ignore the first switch and turn on the second long enough to warm up the bulb. We then turn off the second switch and turn on the third. When we open the door, if the light is on it's the third switch. If the light is dark but warm it is the second switch, and if the light is dark and cold, it's the first switch. Of course I can't actually tell you which switch is the one unless I am there in person.

How about it?
Click to expand...

It's a good moment when you get it, no?
My protocol would have been a little different but equivalent.
I'd label the switches 1,2 and 3.
I'd leave 1 and 2 on and 3 off.
Just before entering the room, I'd turn off switch 2. So, if the lightbulb was (it was controlled by):

on: switch 1
off, warm: switch 2
off, cold: switch 3
cn

images
 
tyler.durden said:
Thank you, gentlemen, my mind is blown! This is the graph from your link, Neer, that finally simplified it enough for me to comprehend:

[TABLE="class: wikitable"]
[TR]
[TH]behind Door 1[/TH]
[TH]behind Door 2[/TH]
[TH]behind Door 3[/TH]
[TH]result if staying at door #1[/TH]
[TH]result if switching to the door offered[/TH]
[/TR]
[TR]
[TD]Car[/TD]
[TD]Goat[/TD]
[TD]Goat[/TD]
[TD]Car[/TD]
[TD]Goat[/TD]
[/TR]
[TR]
[TD]Goat[/TD]
[TD]Car[/TD]
[TD]Goat[/TD]
[TD]Goat[/TD]
[TD]Car[/TD]
[/TR]
[TR]
[TD]Goat[/TD]
[TD]Goat[/TD]
[TD]Car[/TD]
[TD]Goat[/TD]
[TD]Car
[/TD]
[/TR]
[/TABLE]
It's amazing that thousand of Ph.Ds could not see this. I guess I was in somewhat good company. Good, stupid company ;)
Click to expand...

My friend actually got up and walked out this morning over this question. Even after showing him the chart and demonstrating the only possible outcomes, which he accepted, he still couldn't reconcile it in his head, and so refused to believe it. He wanted to take the 'agree to disagree' route, but of course there is no arguing with math. This is a person who is passionately for evidence when it comes to creationism, ESP, and the like, yet when presented with something that countered his intuition, he wanted to let his intuition trump real world data. He is always asking me how people can be positive about God with all the doubt there is, and now he has experienced that himself. It's very hard to overcome what seems right in our heads.

Later, what finally convinced him was raising the original choice to one in a billion. With those odds, it's very unlikely the person picks the car first. He was able to agree on that. After we go through the process of eliminating all other boxes but one, I told him he couldn't switch. He had to stay with his original odds. This way, he was able to retain his doubt that the first pick overcame 1/billion odds, and recognized that to take advantage of the 50/50 he needs to switch.

I then asked him the 'daughters' question, and he got it wrong and wanted to argue, even after showing him the outcomes. So even though he learned to overcome his intuition in one case, he didn't learn the value of questioning it. If it is this hard to get a person with a skeptical disposition to accept something as certain as math, imagine the challenge we face in getting people to question their intuition on matters like god, health, or consciousness.
 
Two Gangsters are driving directly at each other each going 100mph. They enter a bridge 200 miles long from opposite ends. Immediately upon entering the bridge, one gangster fires a bullet at the other car. The bullet is magic, and travels at a constant speed of 1000mph. It travels to the other car and bounces off, travels back to the first car and bounces off, and so on until the cars, never slowing, meet in the middle in a fiery crash.

What is the total distance the bullet traveled?


No lesson to this one, just a brain teaser.
 
Heisenberg said:
Two Gangsters are driving directly at each other each going 100mph. They enter a bridge 200 miles long from opposite ends. Immediately upon entering the bridge, one gangster fires a bullet at the other car. The bullet is magic, and travels at a constant speed of 1000mph. It travels to the other car and bounces off, travels back to the first car and bounces off, and so on until the cars, never slowing, meet in the middle in a fiery crash.

What is the total distance the bullet traveled?


No lesson to this one, just a brain teaser.
Click to expand...

Ooo! Took me a moment, but I think I found the handle. (I am not giving it away.)

As for the daughters question, it really is instructive as to the resistance of our common sense against a certain sort of probability argument. A coupla nights ago, I "solved" the daughters one for myself by imagining a large population of dads with two children. Assuming a 1:1 probability of the children being boys and girls, 25% will have had two boys, 25% will have had two girls and 50% will have had boy girl or girl boy (25% for either of those).
What the question does is exactly equivalent to the leprechaun or goat problem : it removes a category, perturbing previously unremarkable odds. In the daughters case, it disqualified the 2M dads, leaving ponly MF and 2F dads in their 2:1 ratios.
So if faced with situations like these, spotting the category-removal situations becomes a difficultly-acquired skill ... cn

<add> I cannot PM you ... :?
 
I'm gonna go with...1000 miles. It will take exactly an hour for the cars to crash so the bullet has a full hour to perform its journey.


You all should know by now how to uncover my spoiler.
 
Heisenberg said:
My friend actually got up and walked out this morning over this question. Even after showing him the chart and demonstrating the only possible outcomes, which he accepted, he still couldn't reconcile it in his head, and so refused to believe it. He wanted to take the 'agree to disagree' route, but of course there is no arguing with math. This is a person who is passionately for evidence when it comes to creationism, ESP, and the like, yet when presented with something that countered his intuition, he wanted to let his intuition trump real world data. He is always asking me how people can be positive about God with all the doubt there is, and now he has experienced that himself. It's very hard to overcome what seems right in our heads.

Later, what finally convinced him was raising the original choice to one in a billion. With those odds, it's very unlikely the person picks the car first. He was able to agree on that. After we go through the process of eliminating all other boxes but one, I told him he couldn't switch. He had to stay with his original odds. This way, he was able to retain his doubt that the first pick overcame 1/billion odds, and recognized that to take advantage of the 50/50 he needs to switch.

I then asked him the 'daughters' question, and he got it wrong and wanted to argue, even after showing him the outcomes. So even though he learned to overcome his intuition in one case, he didn't learn the value of questioning it. If it is this hard to get a person with a skeptical disposition to accept something as certain as math, imagine the challenge we face in getting people to question their intuition on matters like god, health, or consciousness.
Click to expand...

I was thinking about what you stated in this post, Heis. The majority of my friends are skeptical stoners, and the main reason I feel they are so willing to question their intuition,memory and perception in general is they are used to forgetting, misplacing, and perceiving things incorrectly because of heavy weed use. When it can take 20 minutes to find keys you left in your other jeans (or in the door from the night before), it's much easier to see how easy it is to be fooled by your own mind...
 
mindphuk said:
I'm gonna go with...1000 miles. It will take exactly an hour for the cars to crash so the bullet has a full hour to perform its journey.


You all should know by now how to uncover my spoiler.
Click to expand...

Correct, the bullet traveled for an hour at 1000 mph.
 
Heisenberg said:
Lets see if you learned anything. You meet an old high school friend on the bus. You ask if He has any children, and he says he has two. You ask if he has any daughters, and he says yes. You now know that he has two children and one is female. What are the chances that he has two daughters?

I expect not all will agree on this one.
Click to expand...

He either has mm, mf, fm, or ff. Those are the only 4 combinations of children he can have. You already know he has at least one daughter, so he doesn't have mm. So he has a 1/3 chance of having 2 daughters, and 2/3 chance having mf/fm.
 
Heisenberg said:
Exactly right. If I send out one letter this week, 2 next week, 4 the week after, ect, I am sending 67,108,864 letters on week 26. So I had to start by sending out this many.
Click to expand...

Wait a minute, you would only be sending 33,554,432 on week 26. You would be sending 67,108,864 on week 27.

2^(w-1) where w is the week number.

2^(1-1) = 1 for week 1,
2^(2-1) = 2 for week 2,
...
2^(26-1) = 33,554,432 for week 26.

So reverse that on week 1 you send 2^(26-1) = 33,554,432 letters, the next week you send 2^(25-1) and so on down to week 1 where you only send a single letter. So you end up with 2^25 + 2^24 + ... 2^0 which is (2^26)-1 = 67,108,863 total.

cannabineer said:
If we accept that the final accident is a unity-chance event, we have 2E25 binaries. So 2E25 letters were sent out as a first cut. Half each successive time, with only one recipient getting the final letter detailing the accident. he also received the final letter at the end of a convergent series, 2E25 plus 2E24 plus ... equals 2E26 minus one. Add the final letter, and I arrive at a (minimum) total of 2E26 letters sent, or 67,108,864. cn
Click to expand...

The final letter is already included in the series. it is 2E26-1, not 2E26
 
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