Piphilology

Piphilology comprises the creation and use of mnemonic techniques to remember a span of digits of the mathematical constant πぱい. The word is a play on Pi itself and the linguistic field of philology. Even before computers calculated πぱい, memorizing a record number of digits became an obsession for some people. The current world record is 100,000 decimal places, set on October 3 2006 by Akira Haraguchi.

There are many ways to memorise πぱい, including the use of piems, which are poems that represent πぱい in a way such that the length of each word (in letters) represents a digit. Here is an example of a piem: How I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics. Notice how the first word has 3 letters, the second word has 1, the third has 4, the fourth has 1, the fifth has 5, and so on. The Cadaeic Cadenza contains the first 3834 digits of πぱい in this manner. However, piems prove inefficient for large memorizations of pi. Other methods include remembering "patterns" in the numbers (for instance, the "year" 1971 appears in the first fifty digits of pi).

History

Recent decades have seen a surge in the record number of digits memorized.

Until the 20th century, the number of digits of pi which mathematicians had had the stamina to calculate by hand remained in the hundreds, so that memorization of all known digits at the time was possible. [1] In 1949 a computer was used to calculate πぱい to 2000 places, presenting one the earliest opportunities for a difficult challenge.

Subsequent computers calculated pi to extraordinary numbers of digits (more than a trillion as of 2006), and people began memorizing more and more of the output. The world record for the number of digits memorized has exploded since mid-century, and stands at 100,000 as of October 2006. [2] The previous record (83,431) was set by the same person (Akira Haraguchi) on July 2, 2005[3], and the record previous to that (42,195) was held by Hiroyuki Goto.

Examples in English

The most common mnemonic technique is to memorize a sentence in which the number of letters in each word is equal to the corresponding digit of πぱい. The most famous example has several variations, including:

(1) How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics!

(2) How I need a drink, alcoholic in nature, after the tough chapters involving quantum mechanics!

Short mnemonics such at these, of course, do not take one very far down πぱい's infinite road. Rather, they are intended more as amusing doggerel. If even less accuracy suffices, the following examples can be used:

(1) How I wish I could recollect pi easily today!

(2) Can I have a large container of coffee? Thank you.

This second one gives the value of πぱい as 3.141592653, although 3.141592654 is a more correct figure. Indeed, many published piems use truncation instead of true rounding, thereby producing a less accurate result when the first omitted digit is greater than or equal to 5. It should however be noted that it is advantageous to use truncation in memorising if the individual intends to study more places later on.

Another mnemonic is:

The point I said a blind Bulgarian in France would know

In this mnemonic the word "point" represents the decimal point itself.

Longer mnemonics employ the same concept. This example created by Peter M. Brigham, can be used for 21 or fewer digits:

How I wish I could enumerate pi easily, since all these bullshit mnemonics prevent recalling any of pi's sequence more simply.

Another, more poetic 30 digit version is:

Sir, I send a rhyme excelling,

In sacred truth and rigid spelling,

Numerical sprites elucidate,

For me the lexicon's dull weight,

If nature gain, not you complain

Tho' Dr Johnson fulminate.

There are minor variations on the above rhyme, which still allow pi to be worked out correctly. However, one variation replaces the word "lexicon's" with "lesson's" and in doing so, incorrectly indicates that the 18th digit is 7.

There are piphilologists who have written poems encoding hundreds of digits. This is an example of constrained writing.

Examples in other languages

French

The following statement and question consists of words each with a number of letters that yields πぱい to 126 decimal places (3.141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 105 820 974 944 592 307 816 406 286 208 998 628 034 825 342 117 067 982 148 086 513 282 306 647 093 844):

Que j'aime à faire apprendre ce nombre utile aux sages !

Immortel Archimède, artiste ingénieur,

Qui de ton jugement peut priser la valeur ?

Pour moi, ton problème eut de pareils avantages.

Jadis, mystérieux, un problème bloquait

Tout l'admirable procédé, l'œuvre grandiose

Que Pythagore découvrit aux anciens Grecs.

Ô quadrature ! Vieux tourment du philosophe

Insoluble rondeur, trop longtemps vous avez

Défié Pythagore et ses imitateurs.

Comment intégrer l'espace plan circulaire ?

Former un triangle auquel il équivaudra ?

Nouvelle invention : Archimède inscrira

Dedans un hexagone ; appréciera son aire

Fonction du rayon. Pas trop ne s'y tiendra :

Dédoublera chaque élément antérieur ;

Toujours de l'orbe calculée approchera ;

Définira limite ; enfin, l'arc, le limiteur

De cet inquiétant cercle, ennemi trop rebelle

Professeur, enseignez son problème avec zèle

Translation:

How I would like to learn this number useful to the wise.

Immortal Archimedes, artist, engineer,

in your opinion who could estimate its value?

...

Alternative:

Que j'aime à faire apprendre un nombre utile aux sages !

Glorieux Archimède, artiste, ingénieur,

Toi de qui Syracuse aime encore la gloire,

Soit ton nom conservé par de savants grimoires !

...

Ancient Greek

Yielding πぱい to 22 decimal places (3,1415926535897932384626):

Αεί οおみくろん Θεός οおみくろん Μέγας γεωμετρεί,

τたうοおみくろん κύκλου μήκος ίνα ορίση διαμέτρω,

παρήγαγεν αριθμόν απέραντον,

καί όν, φεύ, ουδέποτε όλον θνητοί θしーたαあるふぁ εύρωσι

If the reader's computer does not have the fonts necessary to render the above, here is a graphic version:

File:Pipoem.gif

Translation:

The great God always uses Geometry;

So that he could define the perimeter of the circle using its diameter,

He produced a never ending number which mortals,

Unfortunately, will never define in its entirety.

Russian

In Russian language, there is a well-known phrase in the pre-1917-reform orthography of old tradition: "Кто и шутя, и скоро пожелаетъ "Пи" узнать число - ужъ знаетъ." (The one who would wish to know the number Pi easily and quickly, already knows it.)

A more modern rhyme is:

Это я знаю и помню прекрасно,	I know the following and remember it perfectly
Пи многие знаки мне лишни, напрасны.	Multitudes of the digits of Pi are unnecessary and idle for me.

A short approximation is: "Что я знаю о кругах?" (What do I know about circles?)

In addition, there are several non-folklore verses that simply rhyme the digits of Pi "as is", see the Russian wikipedia article ru:Пи.

See also

• Feynman point
• Cadaeic Cadenza

External links

• Piphilology at Wikiquote
• Andreas P. Hatzipolakis: PiPhilology. A site with hundreds of examples of πぱい mnemonics
• Mike Keith's World of Words & Numbers; Poe, E.: Near a Raven
• Memorize 1000 digits of pi
• Memorise 300 digits of pi