Alex's Adventures in Numberland - Alex Bellos [70]
In 1991 David and Gregory’s homemade contraption calculated pi to more than two billion places. Then they got distracted by other problems. By 1995 Kanada was ahead once again, and he reached 1.2 trillion digits in 2002, a record that lasted only until 2008, when compatriots at the University of Tsukuba revealed 2.6 trillion. In December 2009 the Frenchman Fabrice Bellard claimed a new record using the Chudnovsky formula: almost 2.7 trillion places. The calculation had taken 131 days on his desktop PC.
If you wrote a trillion digits in small type, the distance would cover from here to the sun. If you put 5000 digits on a page (which is very small type) and stacked the pages on top of each other, the pi in the sky would be 10km high. What is the point of calculating pi to such absurd lengths? One reason is very human: records exist to be broken.
But there is another, more important motivation. Finding new digits in pi is ideal for testing the processing capacity and reliability of computers. ‘I have no interest as a hobby for extending the known value of pi itself,’ Kanada once said. ‘I have a major interest for improving the performance of the computation.’ Pi calculation is now essential for quality-testing supercomputers because it is a ‘high-duty job which requires large main memory, operates huge number-crunching and gives [an] easy [way] to check [the] correct answer. Mathematical constants like the square root of two, e* [and] gamma are some of the candidates, but pi is most effective.’
The story of pi has wonderful circularity. It is the simplest and most ancient ratio in maths, which has been reinvented as a massively important tool on the frontline of computer technology.
In fact, the Chudnovskys’ interest in pi came primarily from their desire to build supercomputers, a passion that still burns brightly. The brothers are currently designing a chip that they claim will be the fastest in the world, only 2.7cm wide but containing 160,000 smaller chips and 1.75km of wire.
On discussion of their new chip, Gregory became very high-spirited: ‘Computers double their power every 18 months, not because they are faster but because they can pack more stuff in. But there is a catch,’ he said. The mathematical challenge was how to partition the smaller pieces so that they can talk to each other in the most efficient way. His laptop showed the chip’s circuitry. ‘I’d say the problem with this chip is that it is a capitalist chip!’ he exclaimed. ‘The problem is that most of the stuff here is not doing anything. There are not too much proles here.’ He pointed at one section. ‘This is just management of the stores inside the chip,’ he lamented. ‘The majority of these guys just do warehousing and accounting. This is awful! Where is the manufacturing sector?’
In Carl Sagan’s bestselling book Contact, an extraterrestrial informs a woman on Earth that after a certain amount of digits the randomness in pi stops and there is a message written in 0s and 1s. This message occurs after 1020 decimal places – which is the number described by 1 followed by 20 zeros. Since we currently know pi to ‘only’ 2.7 trillion places (27 followed by 11 zeros), we have a little way to goe s to check that he was making it up. Actually, we have further to go since the message is apparently written in base 11.
The idea that there is a pattern in pi is an exhilarating one. Mathematicians have been looking for signs of order in the decimal