Friday, March 14, 2008

Geek alert #1: Pi in the sky

You may not be aware of the significance of the date, but March 14th is Pi Day: the celebration (?) of the mathematical constant Pi, which represents the ratio of a circle's circumference to its diameter. The date, of course, is derived from the value of the constant. Pi to two decimal places is 3.14, hence the third month and the fourteenth day.

This endless number has been the source of endless fascination to mathematicians ever since Euclid first worked out his system of geometry. Archimedes was the first to give an approximate value to the constant, remarkably accurate considering that mathematics was still in its infancy at the time. (When Roman soldiers invaded his home in Syracuse, threatening damage to the circles he used for his calculations, he rushed towards them crying "Do not touch my circles!" They promptly killed him . . . a Pi-teous end if ever I heard of one.)

As the BBC points out:

Pi, more commonly known by the 16th letter of the Greek alphabet, is the most widely-known mathematical constant in the world. Even long after people forget their school lessons, they still recognise the symbol.

Pi conjures a sense of mystery, so the symbol makes regular appearances in popular culture - it's the secret code in both Alfred Hitchcock's Torn Curtain and the Sandra Bullock vehicle The Net.

And while pi is a number, its importance goes far beyond simple geometry. Pi represents a deep universal mystery - how is it that something this basic, this fundamental to maths and science, could turn out to be so incredibly difficult to pin down?

In fact, it's literally impossible to know what pi is, because its digits rattle off into infinity.

While there are many infinitely long numbers in maths, pi is the only one in which an infinitely simple idea - the circle - unfolds into an infinitely complex value. This paradox drives many people to distraction.

The value of Pi has been calculated again and again over the years. The most recent attempt by Japanese scientists in 2002 (using supercomputers, of course) calculated it to 1.24 trillion decimal places . . . and, of course, since it's an infinite number, we'll never know its full length. Many have memorized it to 50 or 100 decimal places. However, this is unnecessary. It's been calculated that Pi to 29 decimal places is detailed enough to measure anything in the known universe to a scientifically acceptable level of accuracy.

(Of course, there are those who object to such complexity. Famously, in 1897 Rep. Taylor I. Record introduced House Bill 246 in the Indiana House of Representatives to redefine the value of Pi and the area of a circle. The House passed it, but wiser heads prevailed in the State Senate, where it died. If it had been implemented, every building subsequently erected in the state of Indiana would have collapsed due to faulty calculations in its design. Read the article at the link for a good insight into legislative ignorance and stupidity.)

What really amazes me is the effort some people put into memorizing the value of Pi in incredible detail. There's an art known as Piphilology which consists of developing mnemonic techniques to help remember the constant to ridiculous levels of detail. Some devotee thought up "Pi-ems", which are poems where every word represents one of the digits of Pi in terms of the number of letters in the word. The famous Cadaeic Cadenza is a well-known example.

Akira Haraguchi is said to be the world record holder, reciting (from memory) Pi to 100,000 decimal places in 2006. It's said that he "views the memorisation of Pi as 'the religion of the universe' . . . and as an expression of his lifelong quest for eternal truth".

OK. If you say so. "Pi in the sky" sounds more like it to me . . .

There's even a remarkable musical rendition of Pi. Click here if you're in the mood to listen. It's actually quite fascinating . . . although one does want to know "Why?"!



Justin Buist said...

I'm one of those nerd type folks that like to memorize the number. On my 18th birthday (April 12, 1998) I stuck the last bit into my head for a total of 100 digits.

10 years later I can still do the first fifty from memory, even on a bad day.
3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510

After that I get sketchy. The trick, for me, has always been to find patterns that add up to common numbers.

1*4+1*5 = 9.

2*6 = 12 and 5+3+5 = 13.

89793.. well that's just easy.

2+3+8 = 11 and 4+6 = 10.

I've always focused around patterns that surround the number 10. It seems to have worked. You find a pattern that makes sense and you relate the numbers to that pattern until you can recall it without any thought. Once you've got that 5-10 digit block down you move onto the next one.

I'm a number nerd. I admit it.

I remember a problem presented in a biology class one day. At hour 0 there was 1 cell. Every hour after that they doubled. How many were there at hour 24?

The answer was 2^24th power. When I blurted out 16,777,216 before half the students even had their calculators out I got some odd looks.

Yeah, I'm a nerd.

Peripatetic Engineer said...

Engineer's Cheer

e to the x
e to the x
e to the x, dx
cosine, secant, tangent, sine

phlegmfatale said...

Kate Bush did a musical rendering of Pi on her last cd, Aerial. It was kind of pretty. However, I think in the editing of the music, a few numbers were left out. Still, it's a nice idea.