Searle’s Chinese Room
Having said all that, I’m actually going to start with a thought experiment which is not really a puzzle or a paradox.? It was designed by a fellow named John Searle and published in a paper called: “Minds, Brains and Programs”.? The aim was to use the thought experiment to give us insight into the nature of human understanding.? He wanted to show that a particular explanation of human understanding was not correct.? His target was those who believed that human understanding was much like a computer – albeit a very complicated one.? The idea was that the human mind was just like a computer in that it ran a program which given certain inputs would produce certain outputs.
His thought experiment runs like this:
Say you are locked in a room.? You’re a native english speaker, and you don’t speak a word of chinese.? In fact you wouldn’t even recognise chinese characters from other character sets.? You could be looking at Japanese characters for all you know.? They’re are just marks on the page.
In this room in which you are locked is a giant book written in english.? It is titled: what to do if someone slides a piece of paper under the door.? Next to the book is a pile of blank paper and some pens.? You flip through the book and realise that it is just a set of instructions – if the paper has such and such characters on it, then write on the blank paper such and such characters.? At the end of the set of instructions it tells you to slide the piece of paper back under the door.
At some point a piece of paper is slid under the door, and it has all sorts of chinese characters written on it.? You don’t understand a word of it – but the book shows you step by step what to do.? ? If you see such and such a character, and it is next to such and such a set of characters, then write this set of characters – and so forth.? Being bored and having nothing better to do, you painstakingly work through the instructions contained in the book, and write a set of chinese characters down on the page.? You slide it back under the door.
Now in a sense you (the you that is locked in the room) really are a computer, and the book is the program that you are running.? Having nothing else to do you are just performing the instructions contained in the book.? The book is a very well written program, in that the responses you produce are completely intelligible and erudite replies to the inputs provided by the scientists.? The scientists claim that their computer can understand Chinese.? But you’re the computer – and it seems quite obvious that you don’t understand a word of Chinese.? You see a set of Chinese characters, and the book tells you to write another set of Chinese characters – but you don’t know what these characters mean at all.
And so, Searle concludes – the computer model of the mind cannot be correct.
Debate on this topic has been vigorous since Searle published his paper back in 1980.? I won’t go into detail about the ins and outs of that debate.? But it is a fascinating debate and it takes us right to the heart of issues such as the mind, understanding and language.? I encourage the reader to explore the subject further.
The Monty Hall Problem
This is a puzzle to which there is a correct answer.? However, it’s? still a confounding problem because the correct answer is not the one we? intuitively think should be correct.? It’s a puzzle concerning probability and runs like this:
Suppose you are on a gameshow and are asked to choose one of three closed doors.? Behind one of the doors is a car.? Behind the other two is some dud prize – a goat perhaps.? If you pick the door with the car, you win that car, if you pick one of the goat doors, you win a goat.? Having selected your door, the gameshow proceeds to open one of the doors you didn’t pick – and knowing which door has the car behind it, he always picks one that has a goat behind it.? So there are two doors remaining, one has a goat behind it and one has a car behind it, and you’ve chosen one of them.? You are now asked whether you would like to switch to the remaining door you didn’t pick or stay with your original choice.? The question is whether or not your odds of winning the car are improved by switching?
On a first thought, most people think that it makes no difference whether you switch or not because there are two doors left and therefore you have a fifty percent chance of being correct.? But the correct answer is that those who switch will win 2/3 times as opposed to those who don’t and win 1/3 times.
The reason for this is as follows:
There are 3 possible scenarios.? Either you picked the car or you picked goat 1 or you picked goat 2.? If you picked the car then switching will cause you to lose out.? ? Out of the three scenarios this is the only one where you lose out.? Because of the other two scenarios where you picked a goat, switching will cause you to win.? So 2 out of the 3 scenarios sees you the winner.? And it’s on this basis that we calculate the odds.
If this is still hard for you to see, then it’s advised that you increase the number of doors in the example.? Imagine there are one hundred doors – but other wise the example is the same.? You choose a door, and the host opens ninety eight of the other doors.? Those who switch will be right to do so 99 percent of the time.
? This puzzle was originally proposed and solved by? Marilyn Vos Savant in? her column for Parade magazine.? As an exercise one might try to come up with a good explanation as to why so many think the odds are 50 percent.
? So there you have two more puzzles to ponder over.
8 Comments
In your two posts about puzzles and paradoxes there is one big puzzle i missed. Its the prisioners dillema. How about a third post gathering more puzzles?
yes – that’s a very interesting one. I should do a post on the various decision theory problems actually – serve as a little intro to decision theory itself (which would be good for me as well).
This is Great!
-Steven Burda
About the last puzzle, the odds of winning haven’t changed. The odds obviously became much better because instead of having a 1 in 3 chance at winning, you now have a 1 in 2 chance at winning. But in the end, if you switched the door you still have the same chance, it still is 50/50. Her answer is wrong.
if you had a 1 in 3 chance of winning, and suddenly the odds get changed to a 1 in 2 chance of winning, switching will mean that you are working with 1 in 2 chances of winning, but choosing to switch or stay still makes it a 1 in 2 chance, the odds are already better but it is a 1 in 2 chance or 50% chance at winning not a 2/3 chance at winning.
The odds changed, and even if Marilyn vos Savant is a genius, this is one of those word play puzzles that confuses people but doesn’t prove anything.
So, from the standpoint of the beginning, the odds are 1 in 3. If one of the two possibilities you haven’t picked is removed, then you have a 1 in 2 chance of winning, therefore your odds of success have increased until you have a 1 in 2 or 50% chance of success.
“Just because the world agrees with false reasoning doesn’t make it right, it just makes the world wrong”.
As to Phillip’s answer, he is right, but wrong at the same time. Going over the logic from the original post, it is true that you have a 2/3rd’s better chance by switching. And here’s why. It’s all about “frame of reference”.
But in Philip’s example, he states that the odds change, which they don’t. You pick one door, and you have a 1/3rd chance of being right. Even if they open all three doors at the same time, you still have 1/3rd chance of being right. But they don’t. They open 1 door and remove a door. Now, You are given a second choice, which the other door you didn’t pick has 50:50 chance (because, the door you have still is only 1/3 of being right, it’s frame of reference is based on the original deal). So, using that logic, you still should switch, because the other door is 50:50 (new deal) and your door is 33:66 (old deal)
RxIntern.
Gentlemen Prefer Ferraris
The last puzzle I have seen posed with a Ferrari as the prize. In explaining the counter intuative result you must take into account that there are two types of probability; prior and posterior. The later refers to the fact that the probability of an outcome changes when you have more information on the system. In this case the outcome is choosing the door with the Ferrari/car behind it.
Initially faced with 3 doors and 1 Ferrari, the prior probability of making the correct choice is 1/3. However if the games show hosts provides more information e.g. he tells one of the doors has a goat behind it , the odds change and become posterior probabilities. In this case they would become 50/50 without any choice being made or if he decided to tell you which door had the Ferrari then the odds would become better still.
So you choose your door and the game show host reveals a goat. You are now faced with two doors one of which has a Ferrari behind it. What information do you have that changes the odds from 50/50?
The answer is you know which door you chose first up. If you forget this, or the game show host decides to shuffle the remaining goat and Ferrari around, then the odds are back to 50/50. This is the intuitive situation that people tend to base their decision upon.
So you know which door you chose and you know that it has a 1/3 chance of having a Ferrari behind it. The other door obviously has a 2/3 chance. So make the switch and enjoy the drive………………unless you prefer goats.
There’s a really easy way to get people’s intuitions going in the right direction on this puzzle. Imagine the following similar game.
You hare faced with 100 doors. Behind one of them is a car. You asked to pick one. After you pick one, the host open 98 doors without the car behind them leaving just the one you picked and one other.
You are now asked to stay with the one you originally chose or to switch. Clearly, if you played this game lots of times, you’d almost never do well by staying with your original choice. Only 1 in 100 times will that strategy pay off.
It’s exactly the same in the 3 door situation but since the numbers are less drastic, the intuition doesn’t work so well.
In one variation of the Monty Hall problem, Monty does not know which door hides the car. You make your first guess, then Monty opens one of the other doors, which happens to reveal a goat. Now it doesn’t matter whether you switch to the other door. It’s 50/50.
This variation tends to be counter-intuitive to those who understand the original problem. Many of them will insist it’s still 33/67.
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