Friday the 13th today, and Pi Day tomorrow. Horror is cold-shouldering me a little, so here‘s a piece of pi:
284811174502841027019385211055596446229489549303819644288109756659334461284 756482337867831652712019091456485669234603486104543266482133936072602491412 737245870066063155881748815209209628292540917153643678925903600113305305488 20466521384146951941511609… (If you’re still hungry, there’s some more here.)
Can I give a small anecdotal … life’s too short, but that’s a fragment of ‘Pilish’ apparently:
Many poems have been written in pilish – “piems”, of course – and there’s even a pilish novel 10,000 words long.
Since π was proven to be transcendental (by Ferdinand von Lindemann in 1882) we’ve known that squaring the circle is impossible. Everyone reveres Euler’s identity (e^iπ + 1 = 0), but there’s more: “Pi is also interesting to mathematicians because it crops up frequently in areas with no obvious connection to geometry or circles. For example, if you toss a coin 2n times, and n is very large, the probability of getting equal numbers of heads and tails is 1/√(nπ).”
… since pi is an irrational number … the digits in its decimal expansion will never repeat in a periodic pattern. It is also likely that pi is “normal”, meaning that each of the digits from 0 to 9 will appear in the expansion exactly one tenth of the time. Pi’s digits seem to mimic randomness exceptionally well, meaning that – theoretically, at least – it should be possible to find any number string somewhere in pi.
Since Gödel it has been understood that any possible statement can be coded as a number, which means that everything that could ever be said lurks somewhere in π. Conceive a library, of arbitrary vastness, and its entire contents — perfectly ordered — are virtually pre-existent within it. π implicitly anticipates every religious doctrine, philosophy, scientific theory, epic novel, and poem — to restrict ourselves to its loftier regions. There is nothing mathematics can ever discover that the single sign π does not already tacitly whisper to us, if only we could read it with absolute intelligence. To taste a speck of infinity tomorrow would be appropriate.
ADDED: Joseph Shipley’s 31 digit Pilish poem —
But a time I spent wandering in bloomy night;
Yon tower, tinkling chimewise, loftily opportune.
Out, up, and together came sudden to Sunday rite,
The one solemnly off to correct plenilune.
(31 is, of course, the qabalistic key of Thelema — as well as the first two digits of π — but that is no doubt a coincidence (or perhaps two)).
ADDED: Why Pi matters. (Tau gets an early mention.)