Thursday, October 05, 2006

Reciting pi



Can you say “rote learning”?



Kooiti MASUDA said...

I dislike rote learning (beyond that of the 9 by 9 table of multiplication or the first 3 digits of pi) as math or science education, but if it is done as a hobby I do not object.

A Japanese source (Mainichi news at; hat tip to mentioned a bit more about how Mr. Haraguchi memorized the digits. He tried to replace the string of digits with a sequence of Japanese words. (And I think that memorizing a sequence of meaningful words is not specifically Japanese tradition.)

How it was possible may be directly related to the point you mentioned. In Japanese Kanji has often many readings. And that is also the case for Kanjis signifying numerical digits. A number can be related to a native Japanese word as well as a Japanized Chinese word. This fact increases the chance to find a meaningful word corresponding to a string of digits. (Actually there are conflicts: There are cases where a native Japanese word meaning a number sounds like a Japanized Chinese word meaning another number. But perhaps each hobbyist makes his/her personal rule of preference.)

James Annan said...

Ah yes, I have noticed the mnemonics commonly used for telephone numbers in advertisements here. Unfortunately Pizza-La in Kamakura does not have one, but I just use "last number redial" for them anyway :-)

The English alternative is generally to use words with the appropriate number of letters in. Google reminds me of my uncle's mnemonic for a factor of the 8th Fermat number (F8 = 2^2^8 + 1) which he helped to factorise:

"I am now entirely persuaded to employ the method, a handy trick, on gigantic composite numbers”

ie 1238926361552897 (the other factor has 62 digits)

Kooiti Masuda said...

One of the mnemonics well known to secondary school students before pocket calculators became popular was that for sqrt(5), "Fuji sanroku, omu naku" (On the foothills of Mt. Fuji, parrots sing). It describes an unlikely but imaginable scene. But I remember it as grammatically more correct but numerically incorrect "Fuji sanroku ni ...". Perhaps many others do. Fortunately the fifth digit hardly matters in practical uses.

In 1990s, the phrase turned out to be an ominous prophecy. A dangerous sect called Aum (pronounced "omu" with long "o", not different from the word meaning a parrot if we do not care accents) built their base camps on the foothills of Mt. Fuji. Fortunately the camps were took down after they were arrested (though the sect still has their bases in Tokyo and elsewhere), and one interpretation of the phrase "On the foothills of Mt. Fuji, we do not find Aum" seems true now.

Kooiti MASUDA said...

I missed to mention probably the most widely known mnemonic for pi, beginning with "Mi hitotsu yo" (I have only one body), which sounds like a traditional 31-syllable poem (tanka). It is too "literate" for a just numerate pupil to understand the meaning. (Also I do not know whether its quality as a poem is high or low.) And I was never forced to memorize it. But I happen to remember the 31 syllables. Probably I remember it because I remember the first 22 digits of pi, not vice versa.

EliRabett said...

A much better reason to memorize pi which I had managed to lose in my bookmarks.

James Annan said...

Yes, it's clearly preferrable to make the effort to memorise it than have to listen to that song :-)