Heart of the Art

There's  a common maths problem that comes in various guises. The problem illustrates the concept of geometric series, sometimes called deterministic chaos, or more commonly the  power of exponential growth. I prefer a term coined by Yale.edu 'The unbearable quickness of doubling', or even better I like to think it of as 'how quickly things can get out of control'.

This is how it goes:

Apparently the ruler of India many years ago was delighted with the newly created game of chess. So pleased in fact that he wanted to reward its creator, who as it just so happens was somewhat of a wise man and full on mathematician. (Well what else would you expect from the creator of chess)?

The wise man appeared humble when he asked for simply 1 grain of rice to be placed on the first square of the chessboard on the first day, then double that number of grains of rice on the second square on the next day, and so on until all 64 squares had been filled.

It all sounded very simple and cheap and the ruler readily agreed. And sure enough it set off simple enough.

Square 1,  1 grain

Square 2,   2 grains

Square 3,   4 grains

By square 10, 512 grains. still not all that much.

This wise man's a fool thought the ruler. 

Square 20, 524,288 grains

Still within the bounds of reality and easy grasp of human thought.

Square 24, things are slipping a little out of bounds- it's up to over 8 million been added.

Then along comes day 32  and it's an amazing 2,147,483,648

And then something quite dreadful happens, it's at this half way point of doubling that things take a  shocking turn.

On day 36,  34,359,738,368 grains of rice are added.

by square 64 it's a whopping 9,223,372,036,854,775,808

It's an awful lot, in fact I'm told thats if all that rice was piled up it would reach the top of Everest. I haven't checked but feel free if you're inclined.

That wise man was no fool.

In fact the phrase the second half of the chessboard is often used to explain how quickly growth comes to have a significant impact on a businesses strategy and performance. In other words it's at the point of square 32, where things start to boom at extraordinary levels that businesses are really hit hard by the process of exponential growth.  At best its beyond chaos, at worst it's entirely unsustainable.