On Shoulders of Giants

When I should have been doing something else, I spent last evening reading Keith Devlin's book and the exchange of letter between Blaise Pascal and Pierre De Fermat.
In a series of letters Pascal and Fermat developed the theory of probability, or more accurately a priori or objective probability.

The problem that concerns the letter is the Problem of Points which Fermat solved rather easily using his more elegant and shorter 'method of combinations', and which Pascal solved correctly, but without the intuition, using his more complicated recursive formula.

Two things were striking - people had been gambling for centuries before anyone took the challenge in the early 17th century to find a mathematical method to predict the odds.

Also, what took the greatest minds in Europe a better part of a century to solve, took me only about few minutes to solve the 'Problem of Points'. Upon reading Pascal's source of confusion, I realized how simple it is to apply a method, but how very subtle it is the really understand the problem. We truly stand on the shoulders of giants.

The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern


Adi said...

For an interesting perspective on why no one before the 17th century tried to predict the odds, read "Against the Gods: The remakrable story of risk" by Peter Bernstein.

In the middle ages, everyone was busy fighting. Before that, to the ancient greeks, the very idea of predicting odds was blasphemous. After all, god decided the outcome of random events.

Hirak said...

Will check that one out. This book also mentions that predicting the future was considered the work of gods and not something that human minds would ever be able to figure out. But, tacitly everyone who gambles is predicting the future, or at least believing that the gods are on their side.

nepali said...

gaints and timid do they watch? i doubt. but sometime timid may win. you can find in this clip. http://www.youtube.com/watch?v=NVBQikG3GoA
interesting, isnt it?

Ashutosh said...

Quite true! I had heard of Devlin's book and now should check it out. I would also second the Bernstein book quoted above (my father recommended it to me) and should also note that the "Cartoon Guide to Statistics" which has a chapter on Fermat, Pascal and conditional probability is marvelous.

Hirak said...

Yeah, I have read the Cartoon Guide. It's excellent!