QnA

Q. If they make a 3D version of Snakes on a plane, what would it be called?
A. Snakes in a Space [According to Wikipedia].

OK. I am bored.

Longitude

Just finished reading Longitude by Dava Sobel. We've met her in planets, and Longitude delivered on the high expectations set by the earlier book. The story revolves around the solution of the 'Longitude Problem', namely, determining your longitude in the sea (lattitude could be determined from the elevation of the pole star, which is overhead at the north pole and at the horizon at the equator). This was a pressing issue, a single accident in 1707 due to the miscalculation of longitude turned into loss of four ships and two thousand lives. This led to the Longitude Act of 1714 in UK, where a prize of 20000 pounds was declared for the correct resolution of the problem. The problem could be solved if a clock reliable enough to work accurately in the unsteady sea could be constructed. Then you can set the clock to some known meridian time, take it with you on the ship and compare its reading with the local time. The time difference can be converted to a longitude reading. But constructing such a clock was an undertaking of no small magnitude. Pendulums could not be kept steady in the turbulent sea, temperature differences meant different parts might expand and contract by different amounts, and there was the general problem of reliability (it's a bit hard to appreciate these difficulties in our age of Rs20 digital watches, sold by kilos, and more accurate by orders of magnitude than the best of that era). A self taught clockmaker named John Harrison, using novel techniques invented by himself succeeded (his still surviving masterpieces are named H-1 through H-4), but had to struggle long to claim the prize money because the evaluation committee, composed of Astronomer Royal and other learned men was predisposed towards astronomical solutions and against what 'mechanics' wrought. Especially, Nevil Maskelyne, the fifth A.R. did everything to make Harrison's life miserable [As a side note, Maskelyne was instrumental in establishing Greenwich as the de facto prime meridian which had earlier resided in Rome, Pisa and Paris among other places. And as a side note to this side note, the de facto standard became de jure in the 1884 International Meridian Conference]. But Harrison and his clocks triumphed in the end, and launched into a new era of marine clockmaking and it has been suggested that the source of naval power that made the British empire was this advance in navigation.

Sobel's writing is as is to be expected, wonderful. The Longitude Problem occupied all the great minds of the time including Galileo, Halley, Newton, Hooke and Cassini, but interestingly, we do not hear much about their contributions in this area. I am just glad that I picked this book.

Enjoy!

The Equation that couldn't be solved

Talent does what it can, Genius does what it must.

-Owen Meredith

The Theory of Groups is the branch of mathematics in which you do something to something and then compare the result with the result obtained by doing the same thing to something else or something else to the same thing.

-James Newman

The book I recently read, The Equation that couldn't be solved is about these two things chiefly, Genius and Group Theory. I say chiefly because it really does cover a very wide range of topics, but aforementioned themes stand out. The equation in title is the general quintic (which is a just a fancy name for an equation of degree 5, like the quadratic is an equation of degree 2). If nothing else, all our schools taught us the formula to solve the quadratic. Solutions to ax² + bx + c = 0 are

[Image from Wikipedia]
This formula is effectively known since the time of Babylonians. But what about equation of higher degree? Mathematicians over the years discovered similar (but more complex) formulas for third and fourth degree equations (known as cubic and quartic respectively). It was thought that the trend will continue for equations of higher degrees until two nineteenth century genius, Abel and Galois proved that no such formula (expressed in terms of coefficients, and using only the four arithmetic operations plus extraction of roots) can exist above quartic. But both these genius' led tragic lives and died in their twenties. Consider this
1. Abel proves the insolubility of quintic and sends it to Gauss, the best mathematician of his day. After Gauss' death, Abel's letter is found in his papers, unopened.
2. Mathematical establishment fails to consider even his later work.
3. Abel dies at twenty seven, in his own words 'as poor as a church mouse'.
Irony: Abel prize, which is given in his memory, is worth $992,000 today.

Or about Galois
1. Galois loses his father in political intrigue at a young age.
2. Galois submits his landmark work on the insolubility of quintic (the progenitor of Group Theory) for a prize contest. One of the judges, Fourier takes the work home, but dies after a few days and the work is lost.
3. Galois dies in a duel at twenty, after spending time in prison in the politically turbulent climate.

But despite this not-too-promising start Group Theory survived and has become a keystone of modern science, and the book covers the basics well. The chapter on Galois is a short and very readable mini biography. The history of the solutions of cubic and quartic is worth a separate book in itself. As Group Theory is the official language for describing symmetries of a system (e.g. an equilateral triangle under rotation by 120, 240 or 360 degrees, there is even a bingo ad about this ;-), the book also touches on fields ranging from visual perception to anthropology and music to evolutionary psychology where symmetry pops up. All in all, this book is a masterpiece. Don't miss!!

Enjoy!

The Loom of God

Mathematics is the loom upon which God weaves the fabric of the Universe.

-Clifford Pickover

Mysticism fascinates all. Math fascinates (remarkably) few. So it might come as a surprise that a lot of mysticism has its roots in math (admittedly ancient though). Take for exaple the tetrektys of pythagoreans, who lived about 2500 years ago

It was a symbol they worshipped. It shows important musical intervals (3:2-fifth, 4:3-fourth, 2:1-octave), and pythagoreans beleived that just as simple numerical ratios create harmony in music, so is true for the Universe. The total number of dots is 10, which a triangular number. Or consider the sacred pentacle,

the digonal of which is in golden proportion with its side, which is considered to be the most irrational number of all (if you want to know why, go here). And if you want more of this stuff (and chances are you do if you've read 'Da vinci'), be sure to pick a copy of The Loom of God by Clifford Pickover.

Pickover takes us through many places and times, we visit ancient monuments like stonehenge, see ancient computing devices like quipu, and even hear many predictions of apocalypse (many of which have passed their expiry date). There are programs in the end to compute many of the number sequences discussed (beware that many of these are in BASIC though). Overall the mathematical material is not significantly different from what is found in other popular science books, but the blend with mysticism is worth a try!

Enjoy!

[All images taken from Wikipedia].

More books..

The last long long weekend (as the long weekend was appended by 2 days leave) allowed me some much needed time to read, in quiet. Here I am always surrounded by some kind of noise, but my hometown gives me a nice break. I managed to finish one-and-a-half books actually, with the remaining half taking last two days.

The first one was Carl Sagan's Pale Blue Dot, sequel to the legendary Cosmos. I liked it even better than its predecessor. The book present Sagan's vision about the human future in space. He ranges over our planetary system and the places where life may be found (Titan for example), the social issues surrounding spaceflight (who needs it when thousands are dying of hunger), the achievements of past missions and what we can expect in the future. Sagan's acclaimed writing style means you won't want to leave this book once you start. Read this book even if you are not a fan of space, just to see how the master wrote (and as a bonus, you might in fact become a fan in the end).

The second one was Gurcharan Das' India Unbound, which is a fundoo look at our journey as a nation from the independence to the 21st century. The book can be divided in two parts, with the first part talking about the polito-economic history from independence to the reforms of 91, which is a tour de force. The second part talks about the post reform India and the rise of the information economy, but it has a kind of the-world-is-flat feel about it and it rather bored me. But there is a lot to learn in this book, and the writing style will keep you glued. And as an added bonus, after reading it, you might be better able to appreciate 80's bollywood movies :).

Enjoy!