# Toward More Efficient Number Mnemonics

By Keith, Mike | Word Ways, August 2009 | Go to article overview

# Toward More Efficient Number Mnemonics

Keith, Mike, Word Ways

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]. …

If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items
Notes

#### Cited article

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

#### Cited article

Toward More Efficient Number Mnemonics
Settings

#### Settings

Typeface
Text size Reset View mode
Search within

Look up

#### Look up a word

• Dictionary
• Thesaurus
Please submit a word or phrase above.

Why can't I print more than one page at a time?

Help
Full screen
• Highlights & Notes
• Citations
Some of your highlights are legacy items.

### How to highlight and cite specific passages

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

## Cited passage

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

## Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.