Monday, January 27, 2014


When I moved to US from India, I had no idea who Yogi Berra was. Soon, I started noticing that journalists sometimes insert his quotes in their stories on many diverse topics. In India, the term "Yogi" has some specific meanings. With that kind of name, and those uniquely styled quotes made me really curious about him. He seemed like some modern day Confucius!

Wikipedia didn't exist then. (Really!) So I found out about him the old fashioned way - by asking around. Turned out that he was one of the greatest Baseball players, Lawrence Berra, and a celebrated Yankees coach, and the name "Yogi" was given to him jokingly for his sitting style.

He stopped playing even before I was born. Although I enjoy Baseball, and watch the play-offs, specially when SF Giants are playing, I am not a fan enough to learn history, or dig up old videos to see him in action. But I did try to read up about his quotes. Were these intentional? Turns out, these brilliant quotes were just accidental.

I just decided to note my favorites, "Yogisms". Why and why today? Why not? :-)

The following are used so often, that we have stopped noticing the tautology and the paradox. I really find it amazing that we have actually adjusted our minds to use these appropriately.
It ain't over, till it's over.
It's Deja'vu all over again.
Nobody goes there anymore. It's too crowded.
Some can be very thought provoking. It's remarkable that someone can say these without actually meaning to be intellectual.
The future ain't what it used to be.
If the world were perfect, it wouldn't be
Some are just funny, but still require a bit of attention to notice the humor.
I usually take a two hour nap from one to four.
Always go to other people's funerals, otherwise they won't go to yours.
The real Yogism's to me are the ones that make you go, "What? Come again ...".
When someone asked him what's the time, he replied, "You mean, now?"
It gets late early out here.
90% of the game is half mental.

While giving directions to his home, "When you come to a fork in the road, take it."
You can observe a lot by watching.
If the people don't want to come out to the ballpark, nobody's going to stop them.
Never answer an anonymous letter.
We made too many wrong mistakes.
A nickel ain't worth a dime anymore.
Naturally, the question is, how much of this is falsely attributed to him. I don't know. He has published a book called the "The Yogi Book" that explains the stories behind his quote. I haven't read it. May be I should. But he himself answered that question best, by saying,
I didn't really say everything I said.

Monday, January 20, 2014

Euclid's Window

Book Review : Euclid’s Window
Author : Leonard Mlodinow
My Rating : 4 out of 5

The complete title of the book is “Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace”.

Geometry is a very special subject. It’s one of the oldest branches of knowledge - we started studying it to solve real life problems related to land and measurements. There is an even more important reason for calling it a special subject. That reason is Euclid, one of the most revered figures in Mathematics. He created an edifice for Geometry, whose schematic has been used to organize all mathematical knowledge.

His approach is irresistibly beautiful. At the core are the axioms, the self evident truths about the topic. Using these, and basic laws of logical reasoning, we prove simple theorems. Then we use these simple theorems to prove more complex theorems, and so on. This approach is at the foundation of modern mathematics.

Naturally, the book starts with Euclid and the Greek mathematicians. We proceed to Descartes who gave us the first main enhancement, what we now call Cartesian Geometry. If you have read many books on popular science/math, then some of the material so far will be a repetition for you. It’s still well written.

Then the author moves on to non-Euclidean geometry and the book becomes very interesting. Let me take a detour and give an idea as to what is non-Euclidean geometry.

Note that, in Euclid’s scheme, everything is built on a few trivial self-evident truths, called axioms. There is no way to prove them, but everything else is proven using them. If you change an axiom, you get a very different theory. This is not a random act. The only reason to change an axiom would be if it doesn’t feel as a self-evident truth.

Euclid’s 5th and last axiom roughly (very roughly) states that in a plane, 2 parallel lines do not meet if extended forever. It is not trivial as first 4 axioms. Compare it with the absolute simplicity of the 4th axiom which states that “all right angles are equal to one another”. The 5th axiom, often called as “The Parallel Postulate” has never appeared to be self-evident to mathematicians. Its history and surrounding controversy is a big topic in itself.

The Parallel Postulate reflects our intuitive idea about space. We mentally extend two parallel lines on a plain paper to infinity, and feel that they will never meet each other. But how do we know that space will indeed behave this way at astronomical distances? This is an important and interesting topic that ties mathematics with physics at a fundamental level. Author Leonard Mlodinow does a great job at explaining this in a very accessible and entertaining way. What he is telling is more a story of our understanding of space than a story of Geometry, but that’s a minor complaint against the title of the book.

The author explains how it was not easy challenging Euclid. Gauss did not publish any of his ideas because of the fear of backlash. Others were bolder, and persisted. Eventually these ideas were accepted as valid for Mathematics. But is their any real value in these competing geometries? Or is this just a mathematical curiosity? After all, given a line and a point outside that line, we really cannot draw 2 distinct lines that are in the same plane and are parallel to the original line. So why care about non-Euclidean geometry?

The answer, as we know now, came via Einstein. His work on the General Theory of Relativity proved that space is not Euclidean. You can really construct a triangle in space whose angles total to more than 180 degrees. This is one of the many seemingly bizarre, counter-intuitive ideas that have been brought to us by the 20th century. Here, the author focuses more on how our understanding of space changed with the theory of relativity, and less on other paradoxical aspects of the theory and justifiably so.

The last segment in the book is about how String Theory is changing that understanding even more radically, with its 10+ spatial dimensions. That’s another challenging task, and again I think the author did a great job.

I have to add a note on the style. Leonard Mlodinow has a peculiar sense of humor. I enjoyed his witty remarks throughout the book. He also tries to illustrate some points by creating scenes involving two brothers, most likely his sons, if I remember correctly. I was mildly annoyed by these examples. These two aspects of the book might irritate some readers.With these caveats I definitely recommend this book. This is not a mathematical textbook, it’s more a history. The reader is not expected to be a math graduate, but just a curious individual. So go for it.

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