cFlat's World

Memorizing Pi

Memorizing the digits of pi may seem like a useless activity and you may be saying to yourself something like, "cFlat, get a life!" But memorizing in general is an exercise of the brain and has similarities to exercising your body, like jogging, mountain climbing, and aerobic workouts. With memorizing pi there is an historical precedent that goes along with a long-standing fascination with this mysterious and "infinite" number.

There are many reasons why people memorize pi... Simon Plouffe was the world pi-memorizing record holder in the 1970's. It is quoted of him in The Joy of PI: "...memorizing the digits of pi was close to a mystical experience... To preserve the numbers in long-term memory, he periodically isolated himself in a room -- no lights, no noise, no coffee, no cigarettes. 'Like a monk',' Plouffe says. As he recited the digits to himself, they would gradually seep into his mind.".

For me, there is the challenge of it but there is also something unique and familiar in those digits. The following is a summary of my adventures in memorizing pi and a table of the first 200 digits with notes and associated commentary (I plan to do this for the first 600 digits and beyond as time permits).

A number of years ago I read an article in the Readers Digest about a Japanese man who had memorized pi to something like 10,000 decimal places (I understand he now has broken the world record with over 40,000 decimal places). This reminded me of my high school days when I had memorized the first 14 digits quite easily as it had a rather poetic ring to it:

I had no intention of memorizing pi to 10,000 digits, but for fun I wanted to see how hard it would be to memorize a hundred or so. Eventually I went to the library and found a book that listed PI to over 500 decimal places. By the time I got home that day I had memorized the first 100 digits. It seemed easy as the digits somehow grouped together into meaningful chunks that "told a story" in numbers. It helped that I found many groups of four-digits that had a sort of ryhming poetry to them (6535, 8979, 3238, 4626, 3832, 6939, 4944). In other cases I found sequences (14-15, 92...93, 58...59), internal repitition (2884, 4944, and 0899) and numbers that had personal meaning (1971). I later created cards that highlighted these features into 100-block sets that I used to memorize pi to over 500 digits.

Looking back, I avoided using mnemonic devices as I wanted to internalize the actual digits themselves. Using a mnemonic device would also involve learning how the device worked and then making up a story to go along with the digits of pi. If I forgot how the device worked or how the story went I would have lost the digits of pi. Also, with a mnemonic device you don't really memorize pi, you memorize a story that you later translate back into the digits of pi. I prefer to memorize the raw numerical story even if it seems harder. Besides, I have discovered that the numbers themselves have a beauty all their own that I like to explore close up... this could never be properly done with an artificial mnemonic device. I had previously used such devices and for me, at least, you can only make up so many stories about "red lamps eating giant green shoes" before you got sick of it (my apologies to those who successfully use such devices to memorize thousands of digits of pi).

The following are the tables of digits with corresponding comments. For the most part I felt it natural to group the digits into 4-digit words. For me, I find it easy to memorize such a words as a whole due to the poetry that seems to be present. There are occasional 5-digit words and in some cases there are 3-digit words (e.g. 111 and 555). Early on I discovered two-digit sequences that seemed to function as punctuation marks. Each block of 100 digits is divided into six or seven lines, each line ending in a two-digit comma. Within some lines I found two-digit sequences that served as brackets (e.g. 58-59). In other cases a two-digit punctuation mark is repeated and serves as quotation marks (e.g. 84-67481-84). In many cases the commas at the ends of lines form sequences or reveal interesting patterns. For example in the 201-300 block the first two lines end in 33, the next two end in 45, the fifth line again ends in 33 and the last line ends in 73 (the 73 forming the closing bracket of a 72-73 sequence). Some of these notes and observations may seem a bit teadious and contrived but they have helped me in the memorization process. If it helps someone else in their quest for the pi "summit" then I will consider that a bonus.

Here are some other definitions:

• A mini-poem is where the two halves of a word "rhyme". In some cases it rhymes on the last digit (e.g. 6535) and in other cases it rhymes on the first digit (e.g. 3832).
• An outer-shell is where the first and last digits of a word are the same (e.g. 6406).
• An inner-shell is where the second and third digits of a word are the same (e.g. 2884).
• A cluster is a group of digits that are the same somewhere in the word (e.g. 4460, or 111).
• A flip is where the first part of a word is reversed with the second (e.g. 3238 & 3832).
• An echo is where a word appears in one line and appears again later.
• A simile is where a word appears in one line and apears in a slightly altered form later (e.g. 7950 in line 3 and 7510 in line 4).

The following table is a summary of the digits of pi divided into 100-digit blocks. Click on a block for a commentary on the block including detailed notes on each line in the block.