The Evolution of Co-operation, by Robert Axelrod

Just finished reading this wonderful book by Robert Axelrod. I was first introduced to this book by a scientist from Microsoft Research, who gave a talk at IISc, almost entirely focussing on this book.

The crux of the book is what is known as the Iterated Prisoners’ Dilemma, which simulates the way in which fundamentally selfish agents behave. The heart of IPD is a pay-off matrix, which details the pay-offs for mutual co-operation, as well as defection. This presents a long-term incentive for co-operation as well as a short-term incentive for defection. It fits (casts) several real-world problems as an IPD and discusses very interesting scenarios. One of the scenarios that is indeed striking is when during the World War II, there existed a co-operative tie between warring factions, when the two camps used to fire at each other, but deliberately off-target, both indicating the potential for defection as well as the incentive to co-operate. Several interesting scenarios in biology and trade are also highlighted.

Tit for tat
Of all the computer programs that participated in Axelrod’s contest, Tit for Tat (which works by co-operating to begin with and reciprocating the opponent’s previous move in the rest of the moves) was the winner. There was also a second edition of the contest, with all information about the first one being made public, and (not so?) surprisingly, Tit for Tat finished first again! There is a lot of discussion about Tit for Tat in the book.

The Importance of being Nice(st)
Another observation in the results of the contests was that the nicer rules, i.e. the more forgiving rules, mostly performed better. Coincidentally, there was also a paper in Nature, yesterday that discusses the importance of being nice and ‘non-punishing’.

There is a small summary of interesting findings in the book, which I shall try and update soon…

Overall, it’s an amazing book that you would not want to miss out!

Also see http://en.wikipedia.org/wiki/The_Evolution_of_Cooperation

The Man Who Knew Infinity, by Robert Kanigel

No wonder, this book is on on the great Donald Knuth’s reading list!

What a wonderful book this is… full of Ramanjuan’s exploits, told with an exquisite touch of admiration for Ramanujan and in wonderful detail. I’ve been wanting to review this book, but found a wonderful review elsewhere, which more than states what I would have.

Let me just put forth a few excerpts from the review first:

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When it comes to biographies, I personally find it a delight when the author is overwhelmed by the person he is writing about, because it is then that you get to see hidden visages of the person. Robert Kanigel’s book is replete with such engaging depictions..“When he thought hard, his face scrunched up, his eyes narrowed into a squint. when he figured something out, he sometimes seemed to talk to himself, smile, shake his head with pleasure. When he made a mistake, too impatient to lay down his slate-pencil, he twisted his forearm towards his body in a single fluid motion and used his elbow, now aimed at the slate, as an eraser…”Ramanujan used a slate for working out his mind-boggling results and began entering the concise results themselves in notebooks. These notebooks have nothing short of a cult status in mathematical circles. They have helped pure mathematics branch off into stunning new fields, inspired thousands of research papers and are still being plumbed for their depth after a hundred years.

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Hardy paid the ultimate tribute to Ramanujan during one of his lectures. He summarized, “Suppose that we rate mathematicians on the basis of pure talent on a scale from 0 to 100, I give myself a modest 25, Littlewood 30, the great Hilbert 80 and Ramanujan 100.“

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Apart from Ramanujan, this book also adequately addresses the Hardy, with a whole chapter devoted to him. It’s quite funny to read about Hardy’s love of cricket, his atheism, and above all his passion for math.In a postcard to his friend, Hardy (during the 1920s) listed six New Year wishes:
(1) prove the Riemann hypothesis;
(2) make 211 not out in the fourth innings of the last Test Match at Oval;
(3) find an argument for the non-existence of God which shall convince the general public;
(4) be the first man at the top of Mount Everest;
(5) be proclaimed the first president of the USSR or of Great Britain and Germany;
(6) murder Mussolini.

I’ll try and add some more snippets from the book, but be assured that it is a book that must adorn the library of any math enthusiast!