Slide1: The Art of π
A PotpourrI
of Pandigital Pleasures
Mike Keith
Antan Productions
© 2003 Mike Keith
Outline: Outline Decimal digits of π: a quick tour
Literary uses of π
Short mnemonics
Long-form π pieces
Multiple constraints & the Oulipo
Musical π
Visual π
Miscellany
Finale: “Near A Raven”
What’s the Point?: What’s the Point? Axiom: π is cool
So of course we want to use it artistically
The limitation-liberation paradox
Restriction becomes the mother of invention
The computer as a tool
Creation assistant or accuracy tester
Can construct works otherwise difficult or impossible
The First 85 Digits: A whirlwind tour: The First 85 Digits: A whirlwind tour 3.14159 26 535 89 79 32 38 462643 38 32 79 5028 84 1971 6 93993 751 0 5820 97494 4592307816 40 628 620 8 998 628 palindromes The Grand Palindrome petr beckmann Orwell perms. of 5280
(feet in a mile) all odd 3’s and 9’s 4’s, 7’s, 9’s permutation
of 0123456789 permutations all Fibonaccis
(5, 3, 5, 89) The Grand Philindrome
(.620 + .998 = 1.618 = phi)
The word-length mnemonic: The word-length mnemonic The classics:
How I need a drink, alcoholic in nature, after the heavy lectures involving quantum mechanics!
Attributed to Sir James Jeans
May I have a large container of coffee?
How I wish I could recollect pi !
The “Piem”: The “Piem” Now I, even I, would celebrate
In rhymes inapt, the great
Immortal Syracusan, rivaled nevermore,
Who in his wondrous lore,
Passed on before,
Left men his guidance how to circles mensurate.
But a time I spent wandering in gloomy night;
Yon tower, tinkling chimewise, loftily opportune.
Out, up, and together came sudden to Sunday rite,
The one solemnly off to correct plenilune.
- Joseph Shipley, 1960
A few modern ones: A few modern ones “Dad, I need a Honda hatchback!” (So states every sly young teenager preceding college.)
For a time I liked Tennessee in summer, until the usual mosquito invasions started.
How I hate a movie overblown in visual style and, while artistic, perfectly lacking cinematic fun – as, for instance, Dune.
The English Pilish Transform: The English Pilish Transform The first sentence of the novel Paul Clifford,
by Edward Bulwer-Lytton (1830):
It was a dark and stormy night; the rain fell in torrents, except at occasional intervals, when it was checked by a violent gust of wind which swept up the streets (for it is in London that our scene lies), rattling along the housetops, and fiercely agitating the scanty flame of the lamps that struggled against the darkness.
Slide9: Was a dark, a windy nighttime, in Bulwer Style, the first novelish sentences tritely detailing all of the tiresome plot basics to London does our Sir Clifford now go, braving December’s windy snowstorms in resolute quietude (like a fireplace heating a drafty apartment) and forthwith, observing his friends among a Piccadilly crowd, scurries to administer heartfelt salutes, thus embracing them with “Hello”, “Greetings”, “Ho!”, etc. It was a dark and stormy night; the rain fell in torrents, except at occasional intervals, when it was checked by a violent gust of wind which swept up the streets (for it is in London that our scene lies), rattling along the housetops, and fiercely agitating the scanty flame of the lamps that struggled against the darkness.
Dealing with zeros: Dealing with zeros Was a dark, a windy nighttime, in Bulwer Style, the first
3 1 4 1 5 9 2 6 5 3 5
novelish sentences tritely detailing all of the tiresome
8 9 7 9 3 2 3 8
plot basics to London does our Sir Clifford now go,
4 6 2 6 4 3 3 8 3 2
braving December’s windy snowstorms in resolute
7 9 5 0 2 8
quietude, like a fireplace heating a drafty apartment, and
8 4 1 9 7 1 6 9 3
forthwith, observing his friends among a Piccadilly
9 9 3 7 5 1 0
crowd, scurries to administer heartfelt salutes, thus
5 8 2 0 9 7 4
embracing them with “Hello”, “Greetings”, “Ho!”, etc.
9 4 4 5 9 2 3 . . .
The rules of Standard Pilish: The rules of Standard Pilish An N-letter word represents
the digit N if N 10
e.g., a 12-letter word represents “1” then “2”
Punctuation = no digits, but is a separator
“male/female” is 4,6, “not-so-hot” is 3,2,3
One exception: the apostrophe (“Bill’s” = 5)
Note that 1,1 (or 1,2 etc.) can be represented in two ways
Gives the composer a little extra freedom
Short vs. Long Pilish: Short vs. Long Pilish Obviously long works in Pilish take more effort to construct than short ones
More words = more work
Two longest Pilish works (currently) are
Near A Raven, 740 digits
Cadaeic Cadenza, 3835 digits
But there are subtler reasons why short sentences are more easily constructed.
Slide13: 0% 5% 10% 15% 20% 25% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 English
(Emma, Jane Austen)
Pilish
(Cadaeic Cadenza,
3835 digits) Number of Letters in Word (n) % of words
with n letters The bad news - In the long run, Pilish is more awkward than English
because of the unnatural distribution of word lengths
- The scarcity of short words is especially painful
- Avg. word length for English is about 4.2,
for Pilish about 5.6 (average of 1 through 10 plus a bit)
Slide14: Benford’s Law
e Number of digits n Average of
first n digits The good news “Benford’s Law”: Random reals of the form bx (x unif. distributed) have non-uniformly distributed early digits (especially the 1st)
Small digits dominate: e.g., “1” as first digit has probability ~0.3 (not 0.111)
“Nature counts exponentially”
Numbers in many settings are exponential in nature, & so obey Benford’s Law.
π and e do even better than Benford predicts!
This is just luck, but it makes short Pilish statistically even closer to English.
The Oulipean aspect: The Oulipean aspect Oulipo
A group of mostly French modernist writers
Specialize in “constrained writing”
Forbidden or obligatory objects (letters, words, ...)
Palindromes, anagrams, other forms of word play
Mathematically determined structures
Examples:
G. Perec, “La Disparition” (and G. Adair, “A Void”)
G. Perec, “Les Revenentes” (and I. Monk, “The Exeter Text”)
Long Pilish texts fit the Oulipean mold well
Constrained enough, but with sufficient freedom
Cadaeic Cadenza: Cadaeic Cadenza Following the Oulipo custom, the story mirrors its lexical constraint
A powerful magician causes all books in the world to turn into Pilish
And Cadenza itself is a book written in Pilish
Written summer 1996
Average writing speed was ~5 minutes per word
5 x 3835 = the whole summer
How it was made or, Low-Tech in Ibiza: How it was made or, Low-Tech in Ibiza After typing in, checked by a computer program
And rechecked, and rechecked...
Multiple Constraints: Multiple Constraints The piku Bud, a stem, a bloom
sheltered by Basho’s great oak.
Large protects smallness.
Man (I know, I sense)
struggles to deduce life’s end.
Silly endeavor!
See a ring, a wheel.
Calculate my digits whole?
Not quite possible
Egg, a beer, a steak
decorates my shower floor.
I’ve drunk overmuch.
Slide20: Rot, a gill, a Shah’s alligator The pilindrome “Ted - a call, a cadet!”
(Theodore hears from his friend at West Point.)
“Not a ball - a baton!”
(The juggler yells at his incompetent assistant)
The translated piem: The translated piem Que j’aime à faire apprendre un nombre utile aux sages!
Immortel Archimède, artiste, ingénieur,
Qui de ton jugement peut priser la valeur?
Pour moi, ton problème eut de pareils avantages.
How I love π! Teach beginners my digits, handy for genii.
Immortal ‘Aρχημήδης, cunning number-guy,
Who in thy judgement will assess π’s extent?
This nut - its cracking - got me immense enjoyment.
(translation: Douglas Hofstadter)
A newsPIper: A newsPIper
music: music “π Symphony” by Lars Erickson
Digits map to notes in the diatonic scale for melody
Harmony and orchestration added by composer
“Pichelbel Canon” by M. Keith/J. Pachelbel
Pachelbel’s canon with time signature of each measure = successive digits of π.
Mr./Ms. pi: Mr./Ms. pi - Put digits of binary pi (11.001001000011111101...) in a hexagonal spiral
- Make 0’s light, 1’s dark
- Optional: paint a few of the contiguous light areas different colors Richard Lawrence, NY, 1998 Extended by M. Keith, 1999
One reason for the solidity: One reason for the solidity
A rug: A rug Plot points on a rectangular spiral
Brightness of point n is proportional to cumulative % of 0’s in binary π up to binary digit n
Misc. weirdness: Misc. weirdness Accidental Pilish Truly, said Bors, that may not be at this time,
for I have a great adventure to
do in this country.
Thomas Malory, Le Morte D’Arthur
It was our war-ship Clampherdown,
Fell in with a cruiser light
That carried the dainty Hotchkiss gun
And a pair o’ heels wherewith to run
From the grip of a close-fought fight.
Rudyard Kipling, The Ballad of the Clampherdown
“Ve a la plaza y merca
pan y vino y carne: quebremos el
ojo al diablo!”
Vida de Lazarillo, anonymous 16th c. romance And even: A man, a plan, a canal: Panama!
π: 3 1 4 1 5 (or 6 if you round)
Numbers & Letters: Numbers & Letters 123456789
ABCDEFGHI
JKLMNOPQR
STUVWXYZ Assign numbers as: QUARTER POUNDERS
8319259 76354591
Rearrange:
3.14159265358979 CARADEC
3191453
Rearrange:
3.141593
Poe, E: Near A Raven: Poe, E: Near A Raven
The illustrations are by
Gustave Doré, 1883
James Carling, 1882
A contemporary artist, 1989