When in doubt, trust a computer algorithm (aka The Myth of Intuition)

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Call it karmic interference. I have been reading this book and a myriad of articles in the last few days that gave examples on debunking the myth of intuition. Yes, intuition is not universally applicable.

Consider this example I read in today's New Yorker article by Jonah Lehrer on why smart people are stupid:

In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake

?

Your immediate response is 24 days. Now if you were like me, you would think that was too quick an answer. Then slowly Geometric Series strikes you. And if you were still like me, you would think that writing a formal equation to solve this is simply too complex. There must be an easier way of reasoning this out. 

So you just take a smaller example. Say it takes 2 days to cover the lake, what would your answer be then? 1 day. Similarly for 48 days, it must just be the day before. So the answer is actually 47 days.

Whew. That took some thinking. But wonder why your brain seeks out a shorter route each time?

Daniel Kahneman in his book Thinking fast and slow discusses such an innate weakness of the human brain that is wrongly dubbed as "intuition". Slow deliberating thinking is hard work whereas quick impulsive thinking is lazy. In fact, there is sufficient evidence that procedural way of thinking can be superior to human reasoning when it comes to predictions. And so in his book, he says: When in doubt it is better to trust a computer algorithm. Atleast they can't perform worser than intuitive judgements made by humans in such cases.

Also makes me wonder aloud about the power of Geometric Series in general. An amusing story I came across in this book on micro lending is just the perfect example to demonstrate the power of Geometric Series and our lack of misgivings while making a judgement in such cases:

The story goes like this: a prisoner who was condemned to death was brought before the king and was asked to make a last wish. The prisoner pointed to the chessboard which was to the right of the king’s throne, and he said, ‘I wish only for a single grain of rice on one square of the chess-board, and that you double it for each succeeding square.

‘Granted,’ said the king, not realizing the power of geometrical progression. For soon the prisoner had the entire kingdom. 

So if you really get down to solving the geometric series the prisoner gains 2^64 -1 which is 1.8 x 10^19 grains. And this is (to give you a scale of comparison) more than the total number of grains of sand on Earth! (which is 7.5 x 10^18)

That brings me to the lily pads example above as well. After 48 days, you have about 2^48 lily pads (even if each pad is about 10 cm in diameter, so about 75 sq. cm in area) that covers about 75 * 2 ^ 48 sq cm area which is about 2 million sq. km.  That is one big ass lake! (largest lake is about 371 sq km only, the Caspian Sea)

Moral of the story: Obvious is too obvious. Think stupid to break out of the bias :-)