A triple anagram and word-length mnemonic

Mike Keith, Pi Day 2012


This poem was inspired by observing a nice coincidence involving word-length number mnemonics using the rules of Pilish, where each 0 digit is represented by a 10-letter word.  To wit:

The first 29 digits of π
the first 26 digits of e, and
the first 22 digits of the golden ratio, φ

all require the same number of letters, 134.

In the poem below, the first stanza is a word-length mnemonic for φ = 1.618033988749894848204..., the second stanza is a mnemonic for e = 2.7182818284590452353602874..., and the third stanza gives π = 3.1415926535897932384626433832.  In addition, all three stanzas are anagrams of each other, consisting of the same set of 134 letters arranged in different ways.

This is the shortest possible text of this kind involving π, e, and φ.  To go further into the digits with this idea we have to decide what to do when "1,1" and "1,2" occur in the digits, which hasn't happened yet.  (The rules of Pilish unambiguously specify how to convert from word lengths to digits, but in the reverse direction there are several options.)  I decided that "1,1" would always be represented by an 11-letter word (since two one-letter words in a row are almost always awkward), but all other pairs of digits (including "1,2") would be represented by two separate words.

Following these rules, the next longest text of this kind would have 416 letters in each part, which would represent the first 76 digits of π, the first 73 digits of e, and the first 72 digits of φ.  Amazingly, the first 72 digits of τ = 2π also require 416 letters, so in this case a four-way text would be possible.  The next occurrence of a four-way match is much farther out, at 6062 letters.


I marred a groaning silhouette,
Saw dim abhorrent freedoms cemented forever,
Till blackened paranoia bewitched this shadowed roof,
Smashing my despondent soul.

In meadows I remember my orations,
A forecast of degraded love:
Words cadential, proceeding from Hades
To the heart now shrunk,
Sublimated in helpless, binding hate.

You, a tree, a field overblown in summer,
Words and looks gathered, solicited, chanced,
Reminders now of the pleasing past
Bathed in bright heat and sad memories for me.