The Vertigo and the Lion - Intuition Can Be Hazardous to Your Health

Sometimes, when a pilot flies at night with no visual reference, he gets disoriented, and his senses and intuition can cause him to think the instruments aboard his plane are wrong. He can be on a straight and level flight, but feel like he’s turning or even flying upside down. This dangerous phenomenon is called Vertigo. Pilots train for this condition and know that when their intuition disagrees with the instruments – they should trust the instruments.

Now consider this scenario: You are in Africa trying to hide from a lion. There are 3 small bushes with just enough space for one person/animal. You know the lion is waiting for you in one of the bushes (you don’t know which one) and your only hope is to pick a bush to hide in, hoping it’s lion-free. You randomly select bush #1 and start crawling at its direction hoping the lion is not there. Suddenly you see your friend crawling towards the bushes from the other side. He sees you are aiming for bush #1, so he can’t choose that bush even if it’s lion-free (no place for two people). You know he can see the lion from his angle but he can’t show you where it is because he’s afraid of making big sudden moves (or maybe he just thinks a satiated lion will give him a better chance). He aims for bush #3 (he’s sure it’s lion-free because he can see the lion from his angle), reaches it and hides there safely. So you are left with bush #1 and bush #2, one of them hides the lion.

Now, should you:
a. Stay with your original choice of bush #1.
b. Change your choice to bush #2.
c. It doesn’t matter – both bushes got the same probability for containing a hungry lion.
Please make your choice before reading on.

This was an example of how our intuition sucks. If you chose c - you are wrong, but take comfort in knowing you belong to the majority. If you chose b - you deserve to be eaten by a lion, please close your browser and book a flight to Congo. If you chose a - you are correct (this scenario is my weird inverted version of the Monty Hall problem). As you might have guessed, this problem is counter-intuitive so most people get it wrong.

While I can understand how evolution didn’t bother to equip us with intuition capable of avoiding Vertigo while night flying a high altitude super sonic metal machine, it seems like nothing short of a miracle that Homo sapiens has managed to get out of Africa in one piece with our fucked-up lion spotting intuition.

~~~
p.s. If a tree falls in a forest and no one’s around, should you blame the Jews?

10 comments:

ian russell said...

that reminds me of the two friends out in the bush and they come across a lion. one of the friends puts down his pack and gets out his trainers. his friend says, ''don't be daft, you can't outrun a lion!'', to which his friend replies, ''I don't have to, I only have to ourun you!''

love that monty hall problem - it's a devil.

Uri Kalish said...

:-)

Stephen Feloney said...

Your monty hall problem is wrong. You should pick b) change your answer. Even if you read the link you provided. It shows that you should change. To begin with you had 1/3 of being right. So 2/3 chance being wrong. So assume you are most likely wrong. Your friend is choosing a bush which you now know has no lion. We are already assuming that you are wrong. So changing you bush gives you a higher probability of not getting eaten.

Uri Kalish said...

If this was the Monty Hall Problem you would have been right, but I’ve changed the problem to better suit my point. In the MHP you are looking for one car, in my case you are NOT looking for one lion. Therefore, in MHP you should switch, but in my scenario you should not.

fiona-h said...

this is cool - thanks for pointing it out!

PS - how did you find my blog? If I search for the "monty hall problem" I get 1.2 million hits and my blog is nowhere near the top!

turdblossom said...

This seems easy, if the friend could see where the lion was the whole time, and was initially crawling towards bush #1, then bush #1 should be lion-free. Am I missing something?

Uri Kalish said...

@turdblossom,
YOU aimed for #1.

Jayne said...

I would have to say I still disagree, and yes I'm disagreeing too with the monty hall popular solution.

Once one choice is removed, the 'second stage' is a whole new problem by itself and should be considered independently from the 'first stage', which means each bush has the same probability of having a lion.

To illustrate, let's have a third guy, who you don't see, coming in towards the other of the remaining two bushes from the other side. the both of you see that the third bush has been occupied and has no lion. Does this mean each of you have 1/3 chance of finding no lion or 2/3 chances of finding a lion at the same time, as the popular solution seem to suggest? That's impossible.

Also, trying the monty hall scripts, 'switching' all the time has a 40%-50% chance of winning the car, and 'not switching' all the time has a 40%-50% chance of winning. Screenshots can be provided.

Jayne said...

Oh hey, I realised there's imageshack useable. Silly me.

1: No switches through, picked the middle door and sticked with it for 10 tries: http://img29.imageshack.us/img29/5092/try1o.jpg

2: Switched throughout, picked the leftmost door and switched everytime: http://img132.imageshack.us/img132/7469/switchedtry1.jpg

Seems that switching doesn't give you a higher probability of finding the lion or car, depending on your scenario.

Uri Kalish said...

Hey Jayne,

You just have to play more. Here is what I've got after 100 games:
http://farm4.static.flickr.com/3439/3951389052_a7171e093f_o.jpg
The more games you play, the closer you get to the real 2/3 - 1/3 ratio.