Thursday, August 1, 2013

Euclid’s Window by Leonard Mlodinow

From causes which appear similar we expect similar effects. This is the sum of all our experimental conclusions”. Thus spoke Scottish philosopher David Hume. Profound stuff or a prosaic observation depending on your view, but in the domain of Math is it tenable? Where is the cause and where is effect to be observed in Math? It is abstracted as equations and concepts all over - Math is one domain (or discipline) rest of sciences use all the time as a base and in some cases engulfed by it.

This book is very narrowly but well positioned – not a coffee table book but also not meant for an expert in Math either. Surprisingly, it cannot fit into the popular science category since the topics covered are way too deep and one can only simplify so much without losing the main theme.  For example, 5th dimension or ten dimensions is very difficult to articulate in words and even with figures: explaining such concepts is more like climbing a very greasy pole. For sure, author has worked with some of the finest minds and has done a comprehensive job of going through old records to cite stories or episodes to make them more authentic.

Author takes us on a nice tour all the way from Plato to Euclid to Gauss, Newton, Descartes, Einstein, to the latest string theory experts like Witten.

Let me cite some nuggets.

1: The theorem of logic states that, if any false theorem is allowed into logical system, irrespective of what it pertains to, you will be able to prove 1 equals 2. He quotes a legend, where one skeptic asked Bertrand Russell, “If I allow one is equal to two, then prove that you are the pope”. Russell gave a quick response thus: “The Pope and I are two; therefore Pope and I are one”.

2:  Science in the past was a deadly mix of ancient knowledge, religion, and superstition and hence belief in miracles and astrology are common. Funding of science was based on the ruler’s whim. Frederick II founded University of Naples way back 1224 and for his love science he indulged in some weird experiments – for example, he fed two prisoners the same huge lavish meal. He sent one happy man to bed and another to a grueling hunt. Afterwards, he cut them both open to see who has digested the meal better (couch potatoes will be pleased to learn that it was the man who slept).

3: Story of Rene Descartes was really fascinating. Circa 1618, in the small town of Breda in Holland he a saw a crowd trying to figure out a public notice that had a math challenge - in those days it was common. Descartes considered the problem and remarked offhand that is was easy. His translator, one of the greatest Dutch Mathematician of his time, Isaac Beckman, was irked and called stranger’s bluff challenging him to solve it. Descartes did solve it and they became very good friends. Later, Beckman became his mentor and helped him a lot.

Towards the end the book it deals with string theory that obviously flirts with extra dimensions.  As if it is not complicated enough, it introduces an idea that, at a fundamental level, space and time may not even exist.

What really grabs your attention is the extent to which chance events result in major breakthroughs eventually.

In the end, this book is all about mankind’s quest for truth and concomitant attempts to understand the world – it is through the eyes of some selected set geniuses (surely, far from exhaustive) who experienced the joy of discovery and for the rest of us it is the joy of partial (or for a rare few, full) understanding!

Thanks for reading this far.