My status of today

Life is a collection of obsessions. I am but an iterator.

[Saving it for future reference. Currently *iter returns 'dark knight rises'].

Carl Sagan's Gifford lectures

Recently I finished reading Varieties of scientific experience by Carl Sagan. Carl Sagan, SETI pioneer, Pulitzer prize winning science communicator and a world class scientist, of course needs no introduction. The book introduced a new face of the dynamic man; his deep, rational interest in religion and how it fits in with the new world science has revealed. The book is actually the transcript of the Gifford lectures he gave in 1985 on the topic of natural theology (the theological knowledge achieved through reason alone). He talks about how our understanding of our place in the universe has broadened over time (Aristotle through Copernicus through Hubble and so on, to which probably we should now add the many worlds of quantum mechanics), possibilities of extraterrestrial life, the importance of search for it and its implications. He argues that the fruit of this search would not only be new knowledge, but would also help us see all our fellow humans as one. He discusses the traditional arguments proposed to 'prove' the existence of god and how they fare with our current knowledge (for example, the argument from design (as it is called) says a watch implies a watchmaker and the existence of the superbly well crafted organs (like our eye) implies an intelligent designer. But Darwin taught us that unintelligent natural selection is enough). And he stresses the need to be tolerant (cold war was a big issue at the time) to make progress, or just to ensure survival of the human species. A wonderful read, filled with interesting nuggets, and more importantly, a lot of wisdom.

Enjoy!

QOTD

To deny our own impulses is to deny the very thing that makes us human.

-Mouse, The Matrix

Surely..

I did not inherit the lecture gene from Dad.

[Had to present something to a bunch of freshers today. Too bad the thing was not technical. Hopefully they understood something. And to be honest, now that it is over, I feel a bit relieved].

One of the great days of science

Today. And not only due to the magnitude of the discovery, also because bitter priority disputes are the rule, and this one was a pleasant exception.

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]