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.



Suresh S said...

Science and Maths have become very involved subjects late in the 20th century. Atleast Physics and Maths are not very easily understandable in the current age. This has to do a lot with the depth of the subject matter as well as the nature of reality. The quantum two slit experiment still doesn't have an answer inspite of many people, including string theorist, trying to solve it.

Some of the science like String Theory are still neither here nor there. Penrose says that the math in String Theory is quite beautiful and that people get attracted due to it. But he doesn't believe that String Theory gives the required answers. There are lot of scientists who are not enamored with string theory and think that the latest experiments with particle accelerator prove the string theory wrong.

In the coming years the challenge is going to be on how to communicate what physics and math say to the common public in simple terms. The problem is that there may be no simple term anymore!!

Mukund Srinivasan said...

We live in an era where "arts" is considered to be devoid of math. The best of practitioners, though, differed in their perspectives and considered Math or Science to be a form of Art. Just like the management paradigm which refers to the concept that people rise to levels, until they face a challenge (positive term, to incompetence, for the management parlance puritans!), the deepest principles of science and math are not understood because most find their purpose with just the basics. It is the core-practitioners and their sheer passion that keeps it from a "been there, done that" to a "relevant, art form".

P.Varadarajan (Varad) said...

Even without reading the book, I know for sure that a lot of the contents would fly way overhead, as far as I am concerned. But I beg to differ with you, Madhu, re the analogy offered regarding the authors' attempts to explain complicated things. While the greased pole is okay, I dont think they, the authors climb that; readers like me are the ones led up to the greased pole and make that condemend-to-begin-with climb!


பகலவன் கிருஷ்ணமூர்த்தி said...

Looks like another interesting book to read. Nugget # 1 seems typical of Russel's Paradox ?? Thanks for sharing info on this. Certainly, it will not be an easy, on the go reading but will be a little intensive, is what I understand from your comments. Thanks Madhu..!

MV said...

We are living in incredible times where our understanding of the nature of our existence is challenged from several fronts- particle physics, astronomy, life science, ecology, morality, economic system, political systems. All are under tremendous pressure to accept new ideas. By the time a kid finishes high school they should prepared to unlearn what was taught.
Only Math has remained relatively unchallenged. Leaving the representation of math (number systems, geometry, transforms) out, the concept of prime number, value of pi,e etc and their relationship has been untouched for centuries. Mathematical proofs have remained verifiable for ever. Perhaps the language of logic/reason will not change with new discoveries.
From a talk titled "this is water" by david foster Wallace
"There are these two young fish swimming along and they happen to meet an older fish swimming the other way, who nods at them and says 'morning, boys. How's the water?' And the two young fish swim on for a bit,and then eventually one of them looks over at the other and goes 'what the hell is water?' "
Pretty much sums up where we are in the grand scheme of things.
Mohan V.