Tuesday, June 7, 2011

The Rationality of Pi

Disclaimer: To all my regular readers, I have a feeling that this blog may not appeal to you so I offer you the link below which I found to be extremely funny and proof yet again that the internet is extremely effective at destroying all our childhood memories.

I would urge you to continue reading however because what follows is a remarkable story that has at its core the most least understood, yet universally known, irrationality that exists. Pi .

Pi is a mathematical constant whose value is the ratio of any circle's circumference to its diameter and is often expressed as 3.14. The truth is, as most of us are aware is that pi is an irrational number that continues into infinity in it's approximation. What is amazing about this number is that most serious mathematicians would tell you that they know nothing about Pi, yet the definition of Pi is really simple, It is just the ratio of the circumference to the diameter of a circle. Or, is it?

It is believed that Pi first entered our history in Ancient Egypt. It is there that the earliest know reference to pi occurs, written on a papyrus scroll in 1650 B.C by a scribe named Ahmes. Ahmes titled the scroll " The entrance into the knowledge of all existing things" ( I have to assume that Ahmes was not known for his modesty) and after some lengthy calculations he found the area of a circle using a cruder form of Pi. Thereafter, the great Greek philosopher Archimedes, who is now more commonly known in schools as 'that douche who has ruined my early childhood with all his damn theorems' found pi to be between 3 10/71 and 3 1/7. That is about 3.14 and you have to cut the Greeks some slack as they did not use decimals in 200 B.C. and this discovery was probably made using various circles and pieces of string. This approximation was more or less universally accepted until the German Mathematician Ludolph van Ceulen spent the greater part of his life approximating it to thirty five decimal places in the seventeenth century. This gave him such a sense of accomplishment that he had the digits engraved on his tombstone. The German's still call Pi 'the Ludophian number' but they are alone in this as they are with their obsession with David Hasselhoff music. The first person to use the greek letter Pi to represent this constant was the English mathematician William Jones and thus has it remained ever since.

There are many who believe that Pi holds within it a great mystery known to nature (and by inference God) similar to the uniqueness of Phi which Dan Brown explored to death in the 'Da Vinci Code'. With the advent of computers and mathematicians with nothing better to do, the race to determine the mystery of pi re-surfaced. Whilst we were watching the Olympic Games or Dallas, the nationalist battle to approximate Pi heated up. It began with George Reitweisner who derived Pi to 2037 decimal places. When the Japanese entered the battle things started getting silly quickly (Yasumasa Kanada and his team at Tokyo University used a NEC supercomputer to compute 2 million digits of pi, and found no signs of order). this continued in it's absurdity until the Chudnovsky Brothers announced to the world that they had obtained four hundred and eighty million digits of pi, a world record at the time. The record stood at one billion one hundred and thirty million one hundred and sixty thousand and sixty four decimal places in 1989 and was obtained by team Kanada. Surprisingly, to everyone but themselves, they still found no pattern!

Finally, this brings me to the main reason I wrote this blog ( I hope however you enjoyed the journey). It was the amazing story of the 'Chudnovsky brothers'. In short, these brothers were born in the Ukraine and eventually settled in America. They are brilliant mathematicians who one day concluded that it would be cheaper and more convenient to build a supercomputer in their apartment so that they could work with numbers to their hearts content. Gregory Chudnovsky suffers from a severe disease called myasthenia gravis which in his case has resulted in muscle weakness and difficulty in breathing. He is therefore confined to his apartment and used to do his research by dialing into a supercomputer and waiting many hours for a result. The result was often a message telling him that he had lost his connection! This therefore prompted these brothers to build their own supercomputer which they have  done using mail order parts with a combined cost of seventy thousand dollars. They thankfully have wives with conventional jobs and big hearts. This is in comparison to a Cray supercomputer which cost somewhere in the region of thirty million dollars.

I have recently read a significant amount regarding the lives and accomplishments of the Chudnovsky brothers but was most surprised (shocked) to learn that these great minds have no commercial backing or conventioanl academic jobs. Putting aside for the moment their genius mathematical ability, these guys built a working supercomputer in their apartment at a fraction of the cost! Nobody thinks that they warrant an investment? The thought of David Beckham being available for two months after the close of the US soccer season is unthinkable with European clubs trampling over each other to have the benefit of his services at remarkable costs. For some perspective, Beckham's deal with the LA Galaxy, those marauders of world club football, is \$ 32,5 Million over 5 years.

Contrast this to Gregory Chudnovsky who was described by Herbert Robbins (emeritus professor of mathematical statistics at Columbia University) as the greatest mathematician since David Hilbert (don't feel stupid, I never heard of him either) and that he is the last of his breed. For years, the brothers were supported by their wives and modest grants from the National Science Foundation of America until eventually, after campaigning by a select few academics they were appointed as Distinguished Industry Professors at the polytechnic institute of NYU.

This is part of what is wrong with the world. Our priorities are all messed up. We pay millions for people to play sport or act (don't get me started on that topic!) yet we don't reward academic brilliance forcing most of the brilliant minds into the corporate world where their passion to explore and break new ground is crushed. Of course, I (as both a bad football player and self confessed geek) will see it that way and who cares about how many digits you can approximate pi to anyways. I think it is safe to assume that if you did not find a pattern in a billion, you are probably not going to find a pattern in the next billion. But behind the search lies an algorithm that could one day solve a much more pressing problem like "What is the Ultimate Answer to the Ultimate Question of Life, The Universe, and Everything?" I assure you that David Beckham will not have a clue that the answer is 42!

P.S. I have added a reaction widget to the bottom of my blog posts and would love if you could give me feedback on what you thought. Comments would be great but if you don't have the time then perhaps just a tick in the appropriate box. Thanks.