Magazine article Word Ways

# Toward More Efficient Number Mnemonics

Magazine article Word Ways

# Toward More Efficient Number Mnemonics

## Article excerpt

As pointed out by Ross Eckler in the Nov 2008 Word Ways ("Mnemonics for Number Sequences", p. 297), the well-known type of mnemonic which uses the length of successive words to represent a sequence of decimal digits (with a ten-letter word for each occurrence of zero) is not particularly efficient. If the sequence of digits being represented has a uniform probability distribution (as is the case for the digits of [pi] and e, for example) then in the long run this scheme will have an "inefficiency ratio", defined as (total number of letters used)/(number of digits represented), of 5.5. This is pretty far away from 1, which could be considered ideal in some sense.

Here is a poem that captures the first 134 digits of [pi] with somewhat better efficiency.

```   Darkness: heavy, dull, silky but somehow grotesque,
Interred within a frozen cell
Lined in macabre skin-framed pallets.

He wipes blood, old as an ache,
Pokes at a fly in disgust.
Chimes urge religious locals to vows of love,
Knees showing a form of loyalty he privately lacks.

Cramped, heavily bound, he heaves
A calm death-mocking word,
Pushing closer to tears.
Quiet scrapes over roads by shrill axles die,
Soundless as a scarecrow.

Voices of bygone folks flow swiftly
Over grave, granite, or greenwood,
Dying in a December sky.
```

To extract the digits of [pi] from this text, follow these simple rules:

(1) Take each word of three or more letters from the text, in order.

(2) Extract two digits from each word ("first digit" and "second digit") like this:

* Calculate the word's score in the game of Scrabble by adding up the score of the individual letters. The fight-most digit of the word score is the first digit.

* Add up the numerical values of the letters (using A=1, B=2, C=3, etc.). The right-most digit of this sum is the second digit.

Here is how this works out for the first few words of the poem:

```Word         Letter sum (= second digit)   Letter sum (= second digit)

DARKNESS     4+1+18+11+14+5+19+19 = 91     4+1+18+11+14+5+19+19 = 91
HEAVY        8+5+1+22+25 = 61              8+5+1+22+25 = 61
DULL         4+21+12+12 = 49               4+21+12+12 = 49
SILKY        19+9+12+11+25 = 76            19+9+12+11+25 = 76
```

with the underlined right-most digits making 3,1,4,1,5,9,2,6, the first eight digits of [pi]. …

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