Conundrum: The Digits of Pi
How do they calculate the digits of pi?
I mean, they’ve calculated the number out to billions of places. When they get a billion digits out, how do they know they’re right? Just think about how incredibly precise that is. A quark’s diameter can be described in 18 decimal places, so surely a billion places is far beyond the realm of any practical scientific purpose or authentic human experience.
From a purely mathematical standpoint, pi is defined as the ratio between a circle’s circumference and its diameter. But the only way we have of measuring such things mathematically is by using pi.
Wikipedia has this article on the subject, but I doubt you’ll be surprised when I tell you it is not helpful to me. We could ask Daniel Tammet but he’d probably just tell us what the algorithm tastes like.
Anyway, if all this math stuff is boring to you, check out this discussion thread putting a more philosophical spin on the digits of pi:
“Somewhere inside the digits of pi is a representation for all of us — the atomic coordinates of all our atoms, our genetic code, all our thoughts, all our memories. Given this fact, all of us are alive, and hopefully happy, in pi. Pi makes us live forever. We all lead virtual lives in pi. We are immortal.” – Cliff Pickover
This means that we exist in pi, as if in a Matrix. This means that romance is never dead. Somewhere you are running through fields of wheat, holding hands with someone you love, as the sun sets — all in the digits of pi. You are happy. You will live forever.
Silly, perhaps, but technically true. And somewhere in the digits of pi, there’s a version of the Shakespeare Teacher who understands how they calculate the digits of pi.
May 24th, 2007 at 11:33 am
Pi is one of my favorite movies of all time. Part of me thinks that Arronofsky made that film just for me. I enjoy all the ta-do about pi, I do. But really, honestly, what’s so special about pi? It’s just one number. Can you help me with that? Why is it the meaning of life all of a sudden?
May 24th, 2007 at 1:56 pm
You can find a string of digits (Shakespeare’s b-day perhaps?) at this site:
http://www.angio.net/pi/piquery
type in 4261564 and it starts at around the 28,000,000th place or so of PI…
May 24th, 2007 at 6:25 pm
That’s a pretty cool website. Thanks for sharing it. (Though Shakespeare’s birthday is usually considered to be April 23, 1564. He was baptized on the 26th, though.)
As for whether Pi is such a big deal, I would say that it is.
You can define a circle as being the set of all points that are distance r from point (x,y). That’s the simplest shape you can have in geometry. You can define it with just three numbers. Even a line needs two sets of coordinates.
And pi is the ratio between the circumference and the diameter of a circle. It’s exactly the same for any perfect circle in the universe. If that number were three, we’d memorize the formula and think nothing of it. But it’s not three. It’s this irrational neverending number that we can compute to billions of digits but will never be able to define precisely.
The thing is, though, that it’s not a number we made up. It’s a number that exists – not in nature – but in the very fabric of mathematics itself.
So if space aliens in a distant galaxy plot the points that are a given distance from a central point, and they take the ratio of the circumference to the diameter, their answer will be the same as our answer.
Also, I think the fact that it is infinite has captured our imaginations over the centuries. It never ends and it doesn’t repeat, so all possible finite combinations of numbers are in there somewhere (see the quote in the original post). It’s also a puzzle that mathematicians can continuously solve. They’ll never reach the end, so they can eternally challenge themselves to go farther. This can be seen as a marker of intellectual (including now technological) progress.
But how do they compute it? How do they know they’re right? That part still eludes me.
February 15th, 2010 at 12:11 am
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