Friday, October 08, 2010

The Probability of Probability

The probability of probability is 0 or 1.

Recently I read the book 'The Black Swan' by Nassim Nicholas Taleb. The book is highly philosophical and often shows the dumbness of probability. Here is my take:

We may say there is 80% chance of rain today. Truth is either it "rains" or it 'doesn't rain'. The probability is either 0% or 100%.

A coin may have 50% chance to fall on its head or tail. That suggests if you take 100 sample examples, 50 times it will fall on its head, other 50 times it will fall on its tail.

Suppose you experimented with a coin only twice. Both the times head came on top. So based on your two experiments, the probability of getting head is 100% which you surely know (from your practical experiences) is not true.

Well, NN Taleb used some similar examples in his book. Many people criticized this book as he (almost) insulted financial economists (directly). His logics are infallible and he has proved how many times they have been proven wrong (even Nobel laureates). When I read the book I didn't have any particular issue in my mind, I simply wanted to enjoy the book. And of course I had some expectations.

But the book has surpassed most of my expectations. It has taught me to be a skeptic, to be empirical rather than optimistic or pessimistic.

Lets look at another theoretical example (this one from his book).

In 1994 the price of oil per gallon was 27$. Some financial farms (based on probability) predicted in 2024 the price of oil for the same quantity will be 54$. Alas, in 1994 itself, within 7 months from the date of announcement, the price became 54$. So this is how wrong probability can be.

(note: my memory surely has betrayed me while writing the above paragraph. But please don't focus on the accuracy of the numbers, the concept is main and that is accurate).

NN Taleb pointed out one of the prime reasons this probability game fails because we always expect people will behave rationally in the given time which surely people don't do.

You don't know whether you GF is gonna dump you tomorrow. Based on the probability which is based on the statistics gathered from all your previous dates, you are gonna have a wonderful dinner with her tomorrow. But this probability appears to be right till the moment she dumps you. At that moment the value of probability is 0. If you have had 100 dates with her including the day she has dumped you, based on the statistics the chance of having another date with her is 100% (because she has shown up all the previous 100 times). But in reality it is 0. Human beings don't behave rationally and that's why we are human beings.

Forget all this probability game. If you meet an astrologer who is going to tell you your future, listen to him till he finishes and  the next moment give him a tight slap. Tell him he is a con man and liar. If he knew his own future, he would not take you as his customer. He would act smartly and avoid the slap!


Anshul said...

Just one correction....if probability is 0.5 it does not mean out of 100 times the coin will show heads 50 times and tails 50 means that if this experiment of tossing a coin is repeated infinite number of times,in ideal conditions.....then the number of heads obtained will tend to be equal to number of tails obtained, making their probabilities tend to 0.5 but only when it is done infinite times which simply means a very very large number of times not 100 times :-) rest of what you wrote...I enjoyed ;-)

Torumoy said...

@Angshul: What you are saying is 100% right ideologically. But if we try to use this data in practical life, then we must doubt several times before using it as reference. The whole idea behind this blog post is "We must do what we think is right and empirical". Probability often falsifies things and we must be very aware of that.

Faysal said...

لا يعمل

Anshul said...

Agreed.And you know , I am making the same point which you are.By posting the real actual mathematical meaning of probability , I just wanted to tell you that the concept of probability is not at all a wrong notion or concept....what is wrong, is people/things using it practically.It can not be used in practical life/situations precisely just because it is defined like that. :-))