Piphilology

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Piphilology comprises the creation and use of mnemonic techniques to remember a span of digits of the mathematical constant π. The word is a play on Pi itself and the linguistic field of philology. Even before computers calculated π, 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.[citation needed] The Guinness-recognized record for remembered digits of π is 67,890 digits, held by Lu Chao, a 24-year-old graduate student from China.[38] It took him 24 hours and 4 minutes to recite to the 67,890th decimal place of π without an error.[39]

There are many ways to memorise π, including the use of poems, which are poems that represent π in a way such that the length of each word (in letters) represents a digit. Here is an example of a poem: How I need a drink, alcoholic of course [or, in nature] 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 in this manner. However, poems 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).

Contents

[edit] 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 to 2000 places, presenting one of 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. An institution from Germany organizing “Pi World Ranking”. The details can be found at http://www.pi-world-ranking-list.com

[edit] 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. 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 as these, of course, do not take one very far down π'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 as 3.141592653, while the first only brings it to the second five. Indeed, many published piems use truncation instead of one of the several roundings, thereby producing a less accurate result when the first omitted digit is greater than or equal to 5. 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.

Yet another example is:

How I wish I could recollect, of circle round, the exact relation Arkimedes learned

In this the spelling of Archimedes is altered so that it represents 9.

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.

Some mnemonics, such as this poem which gives the first 20 digits, use the separation of the poem's title and main body to represent the decimal point:

Pie
I wish I could determine pi
Eureka, cried the great inventor
Christmas pudding, Christmas pie
Is the problem's very center.

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.

The following sonnet is a mnemonic for pi to 75 d.p. in iambic pentameter:

Now I defy a tenet gallantly
Of circle canon law: these integers
Importing circles' quotients are, we see,
Unwieldy long series of cockle burs
Put all together, get no clarity;
Mnemonics shan't describeth so reformed
Creating, with a grammercy plainly,
A sonnet liberated yet conformed.
Strangely, the queer'st rules I manipulate
Being followéd, do facilitate
Whimsical musings from geometric bard.
This poesy, unabashed as it's distressed,
Evolvéd coherent - a simple test,
Discov'ring poetry no numerals jarred.

Note that in this example ten-letter words are used to represent the digit zero.

There are piphilologists who have written poems encoding hundreds of digits. This is an example of constrained writing. See Poe, E.: Near a Raven[4] for an extreme example, and Cadaeic Cadenza for an even more extreme one.

It is also possible to use the rhythm and sound of the spoken digits themselves as a memorization device. The mathematician John Horton Conway composed the following arrangement for the first 100 digits,

                        _     _   _
            3 point  1415  9265  35
                     ^ ^
             _ _  _ _    _ _   __ 
            8979  3238  4626  4338   3279
              **  **^^          ^^   ****
             .   _    _   __   _    _      _ . _ .  
       502 884  197 169  399 375  105 820  974 944 
        ^  ^                       ^  ^
                59230 78164
                 _     _    _    _
              0628  6208  998  6280
               ^^   ^^         ^^
             .. _  .._
             34825 34211 70679,
                         ^  ^

where the accents indicate various kinds of repetition. [5]

[edit] Examples in other languages

[edit] German

This statement yields π to nine decimal places:

Wie, o dies π macht ernstlich so vielen viele Müh

Translation:

How, oh this π seriously makes so many struggles to so many

[edit] French

The following statement and question consists of words each with a number of letters that yields π to 126 decimal places:

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.
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 like to teach this number useful to the wise.
Immortal Archimedes, artist, engineer,
in your opinion who could estimate its value?
For me, your problem had equal advantages.
Long ago, mysterious, a problem blocked
All the honorable process, the great work
That Pythagoras revealed to the Ancient Greeks.
Oh quadrature! Old philosopher's torment
Unsolvable roundness, for too long you have
Defied Pythagoras and his imitators.
How to integrate the plain circular space?
Form a triangle to which it is equivalent?
New invention: Archimedes will inscribe
Inside a hexagon; will appreciate its area
Function of a ray. Not too much to hold onto there:
Will split each previous element;
Always the calculated orb will approach
Will define the limit; finally, the arc, the limiter
Of this disturbing circle, an enemy too rebellious
Teacher, teach its problem with zeal
...

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 !
...

[edit] Katharevousa (archaizing) Greek

Yielding π to 22 decimal places:

Ἀεὶ ὁ Θεὸς ὀ Μέγας γεωμετρεί,
τὸ κύκλου μῆκος ἵνα ὁρίσῃ διαμέτρῳ,
παρήγαγεν ἀριθμὸν ἀπέραντον,
καὶ ὅν, φεῦ, οὐδέποτε ὅλον θνητοὶ θὰ εὕρωσι

Translation:

Always the Great God uses Geometry;
So that he could define the perimeter of the circle using its diameter,
He produced an infinite number,
Which, alas, mortals will never find in its entirety.

[edit] Spanish

The following piem, giving π to 31 decimal places, is well known in Argentina:

Fue y cayó. Y queda solamente la inútil cifra con pocos destinos poderosos, tristes devenires sin el más sencillo bien. Idiota, re idiota, sabe que sus encantos son ya latosos decimales. Pobre...

Translation:

It went and it fell. And only the useless figure remains, with little powerful destinies, sad future without the simplest goodness. Idiotic, very idiotic, it knows that its charms are now boring decimals. Poor...

[edit] Irish

This poem gives pi to seven decimal places.

Níl i mata, a shaoi, eolaíocht nó feidhm. ("Wise one, mathematics has neither science nor use.")

[edit] Russian

In the 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 — ужѣ 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"; for examples, see the Russian version of this article.

[edit] Portuguese

In Portuguese, we can use this sentence (pi to 11 decimal places):

Cai a neve e novas ferrovias de marfim serão por casas trocadas. (The snow falls and new ivory railroads will be exchanged by houses).

Or in Brazilian Portuguese: Sim, é útil e fácil memorizar um número grato aos sábios. (Yes, its useful and easy memorize a number liked by the wisemen)

Nós e todo o mundo guardamos pi usando letra por número. (We and all the world memorize pi using letter for number)

[edit] Japanese

Japanese piphilology has countless mnemonics based on punning words with numbers. This is especially easy in Japanese because there are two or three ways to pronounce each digit, and the language has relatively few phonemes to begin with. For example, to 31 decimal places:[6]

身 一つ 世 一つ 生 く に 無 意 味 い わ く な く 身 ふ み や 読 む 似 ろ よ さん ざん 闇 に な く
3. 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9
mi hitotsu yo hitotsu iku ni mu-imi iwakunaku mi fumiya yomu niro yo san zan yami ni naku

This is close to being ungrammatical nonsense, but a loose translation prioritizing word order yields:

A person is one; the world is one:
to live this way, it's meaningless, one says, and cries,
"step on it, will ya!" then reads—be the same!
Crying uncontrollably in the dark.

Japanese children also use songs built on this principle to memorize the multiplication table.

[edit] Chinese

三 點 一 四 一 五 九， 二 六 五 三 五， 八 九 七， 九 三 二， 三 八 四， 六 二 六
3 . 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6
san dian yi si yi wu jiu er liu wu san wu ba jiu qi jiu san er san ba si liu er liu

| Note: This is not an actual "piphilogical" sentence. It is merely the digits of pi written in chinese characters.

[edit] See also

[edit] Notes and references

  1. ^ "A history of Pi". http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Pi_through_the_ages.html. Retrieved on 2007-02-02. 
  2. ^ (Japanese) "(broken link)". Yahoo! News. http://headlines.yahoo.co.jp/hl?a=20061004-00000402-yom-soci. Retrieved on 2007-02-02. 
  3. ^ "Japanese breaks pi memory record". BBC News. http://news.bbc.co.uk/1/hi/world/asia-pacific/4644103.stm. Retrieved on 2007-02-02. 
  4. ^ "Poe, E.: Near a Raven (Archived)", Mike Keith's World of Words & Numbers
  5. ^ "Math Forum » Discussions » History » math-history-list", Math Forum
  6. ^ (Japanese) 暗記法 Japanese mnemonics for π (and some other languages as well)

[edit] External links

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