Music of the primes

Music is the pleasure the human mind feels by counting, without being aware that it is counting.

-Gottfried Wilhelm Leibnitz

Riemann Hypothesis is one of the great unsolved problems in mathematics today. It was first proposed in 1859, and has withstood assault by some of the finest mathematicians so far (that is more than 150 years). Like Fermat's last theorem, the person to crack it will earn eternal glory. And if that is not enough, it is also one of the millennium problems, which means it carries a reward of $1,000,000 (P=NP? is also on that list by the way). And like Fermat's last theorem, there is a nice book for general audience on the topic ($DEITY be thanked).

Before going further, let me try to define what it is. It says that the zeroes (inputs for which the output is 0) of a particular function (the Riemann Zeta function, whose input and output is complex numbers) lie on a particular straight line (line parallel to y axis running through 0.5 on the x axis of the complex plane). Obvious question, why is this important? Answer to that is that a large body of mathematics has been built on it being true (an example, it would allow an exact prediction of number of primes less than a number); if it were to be false, this body will die. The problem attracted many brilliant minds (even before there were a million dollars. What mankind would do without such minds? $DEITY be thanked again). Advances have been made; it has been proved that around 40% of all zeroes lie on this 'critical line'. Computers have been used to check trillions of zeroes and they all obey the hypothesis, but numerical evidence is not enough for mathematicians. The problem lives. One of the great mathematicians of 20th century, David Hilbert was once asked if he were allowed to sleep for 500 years and then wake up, what would he do? He replied, "I'll ask if anyone has proved Riemann Hypothesis."

The major plus point of the book is that it successfully evades a general problem with popular science books, excessive dumbing down of subject matter. The treatment is logical, writing is lucid, and it is altogether hard to put down the book once you start it. The book tracks the historical development of the problem; from Gauss and Euler to today's leading mathematicians, and in the process conveys some of the appreciation for not only the problem but also for mathematics. A worthy read.
[And to my utmost delight, today I discovered this wonderful poem about RH written by Tom Apostol].

A humble question

There are popular science books for
Poincaré Conjecture
Riemann Hypothesis
Fermat's last theorem
maybe others too..

Why not P=NP?
[It's important, no doubt]
[Or is there one? let me know if you know of any]

book_reviews.tgz

Weekend was good. Was able to read to my heart's (and eyes') content. Without further ado, here is what.

Dracula: A good novel. Typically victorian, with hardly any grey shades (did I say I enjoy its kind?). But instead of writing more about how good it is, I'll mention a couple of other things I noticed along the way..
Bram Stoker (the author) graduated in pure mathematics from Trinity College, Dublin. How many good novelists you know fit that criteria?
Dracula was first published in 1897. Early in the book, a character mentions using his 'kodak' to take photos of the dreaded castle. I knew the dates, but snap clicking tourists are hard to reconcile with castles, counts and horse driven carriages, and it still came as a surprise.

Hothouse: It is a science fiction novel, published by Penguin (lest you be confused). The story of earth in the far future (talk billions of years), with sun on its way to extinction, and its energy output gone through the roof. Unlike most science fiction, humanity does not occupy centre stage in this future; plants reign, animals are few and far between with their niches occupied by still more plants, and humans have returned to their ancestral home, trees. You'll meet ever stranger things along the way; plants which grow crystals to focus sunlights on their enemies; plants which drop cages onto their victims, using their dung, and later when they die, their bones to make their own compost; and mysterious entities which transplant beings in this world to other realms of existence in an attempt to control overcrowding of the planet. And if this sounds too weird, just imagine how weird you reading these words (and me writing them) would have seemed to someone in the cambrian. Seriously. Boring at places, fascinating at others, but probably not for everyone.

Enjoy!

Preserve..

Light rains..
Magnificient clouds..
Fine wind..
Ample greens..

Preserver your sanity! :)

Strange true story

Dictionaries are a neat idea (and not only on your shelf; in your programming language too, Thank you Python). But that's where my thoughts pretty much ended about dictionaries. Dictionaries are hardly fascinating I mean. But there is this book I recently read that forced me to change my opinion, at least for one such learned tome. I am talking about The Surgeon of Crowthorne.

You are sure to be familiar with the central character of the book, the Oxford English Dictionary, known to affectionados as OED. One sight of the immense multi-volume tome is enough to convince anybody of its learned pedigree. OED was begun because people were not very happy with dictionaries available at the time, the mid 19th century that is. Just like many open source projects begin from a developer's etch. (At this point you would be right to question your truly's mental state. Open source? Where did that come from? But please bear with me). So back to the story, a system was set up, and a new approach was decided upon. OED guys wanted to illustrate the words through published quotations; what was the first documented use of a word, how its use changed over centuries, what different senses the word could be used in and so on. And OED guys also realized that commendable as the goal was, it was too much to ask for from a single team. So they sent out a call for volunteers (just like an open source project). Volunteers were to read books, dig out illustrative quotations, and report them back. The team would also publish a list of the words it was presently looking for (much like an open bug tracker). To send a quotation, the volunteer should write the word on top left of a half sheet of paper, write the citation (book name, author, published year and so on) below it, and then follow it with the actual quotation. In case you wanted to submit more than one slip, they were to be alphabetically sorted, packaged and sent (and doesn't it sound like the coding guidelines you must comply with before your patch gets accepted?). I guess you got my point.

And there is more drama here. A volunteer turned up, a certain Dr Minor, who impressed everyone back at the headquarters with his systematic and prodigious work, over a period of more than two decades. Sir James Murray, leader of the project, casually assumed that he was 'an established medical man with a good deal of leisure'. Murray wanted to thank him personally for his work. And here comes the punch, Dr. Minor turned out to be a convicted murderer, confined for the last two decades to a lunatic asylum. The crime was committed under the effect of the psychiatric disorder from which he was suffering. And born in an era when psychiatric treatment was just beginning, he essentially remained uncured, losing his mind bit by bit; his work on OED providing a much needed link to the real world. It is hard not to be moved by this tragic story.

The writing is good and I think certified bookworms (you know if you are one) will derive a not-easy-to-explain tingling, seeing this story of words unfold (I did). Highly recommended.

Timescape

I just loved Timescape. There is a dearth of good science fiction, what bookshelf volumes say notwithstanding (who had this bright idea of cataloging science fiction and fantasy together anyway?) and it's been quite a long time since I had read good sci-fi. Timescape was a welcome break. The science is plausible, there is no mumbo-jumbo whose allure is hard to ignore even to the greats. But the thing that sets Timescape apart is that it would qualify as a good novel in its own right too. Character development is good, and realistic. The narrative keeps you glued. And it leaves deep traces, especially the part towards the end, which reminded me of story of sissyphus. A very good read. And if you actually give a damn about a science fiction, you cannot miss this one.

ps a

The river of wisdom emrges from the mountain of pain. Life just flies away. That completes the picture.

If anything is true, it is this moment. Not past, not future. What meaning is there and what is the sum total we call life. Does it actually converge to a meaning, or the only way is to re-normalize, ignoring the infinites?

A lowerer resolution would have been better, each photon decoheres me.

It is raining.