Today I was trying out a “Math Jeopardy” game that a colleague had created, and one of the categories was “7 Letter Words”. An example of the sort of answer/question pair for that category:
ANSWER: This often is seen when the sun shines following a rain storm.
Question: What is a “rainbow”?
As I was reading through the questions in this category, my brain started anticipating “A word meaning `seven letter word'”.
Offhand, I didn’t know of a word meaning “seven letter word”. For that matter, I couldn’t immediately think of any words that meant “a word with n letters”, for any particular value of n.
But if such words existed… clearly, a word meaning “one letter word” would have more than one letter in it, since we can easily enumerate all the one letter words in English, and check their meanings. And it seemed pretty likely that a word meaning “one hundred letter word” would have fewer than 100 letters.
AH HA! I thought, for a fleeting moment… if such names start off too long, and eventually are too short, then somewhere in between they must be just right…, until I realized that there was no expectation of continuity, that any putative function for which f(n) = “the number of letters in a word meaning ‘word with n letters'” would map the natural numbers into the natural numbers, and so the intermediate value theorem need not hold.
A bit of thought, a trip to a latin dictionary, and then a forehead slap later, we had a few such words in mind:
- monoliteral (having one letter)
- centiliteral (having 100 letters)
Now the root “literal” has seven letters, so we cannot slap a prefix in front of it and get a 7 letter word, much less a 7 letter word meaning “has seven letters”. But if we can find number prefixes whose length is 7 less than the number they signify, we’d at least be able to create words whose length matched the length they aimed to describe. And happily, I did manage to create a few examples:
- duodeliteral (having 12 letters)
- undeliteral (having 11 letters)
- decliteral (having 10 letters)
Playing around with this suggests some other fun avenues for exploration:
- In English, the word “four” has 4 letters. A bit of thought is perhaps enough to convince you that no other english word could use the same number of letters as the word it represents. What would a proof of that look like?
- What happens in other languages? Are there languages where more than one word uses “its” number of letters? Are there languages where there are no such coincidences?
A far more general linguistic/logic topic: adjectives that apply to themselves. “Short”, or “polysyllabic”, or “English”. Perhaps “ostentatious”, or “unabbreviated”. Does “mispelled” count?
But then what of “Nonselfapplicable”? Does it apply to itself? Is “nonselfapplicable’ a nonselfapplicable word?
(I see this last paradox is just over 100 years old. That’s me, always late to the party.)
From now on, I will always associate Goldilocks and the Three Bears with the intermediate value theorem.
360 
April 1, 2009 at 6:28 pm |
I wish that I could, indeed, tell you a one-letter word meaning “one-letter word.” If I knew such a word, it would be the very heart of my ONE-LETTER WORDS: A DICTIONARY.
April 1, 2009 at 7:26 pm |
I thought for sure you were going to mention “sesquipedalian”, toward the end there.
delightful post! thank you.
April 1, 2009 at 8:54 pm |
My version of the Goldilocks theorem: In a triangle, the smallest angle is opposite the shortest side, the mama angle is opposite the mama….
April 1, 2009 at 8:59 pm |
In French, there are no words that have a number of letters equal to the number they represent. However, let f(n) = the number of letters in the French word for n. For example f(1) = 2, since “un” has two letters.
Then f(3) = 5, f(5) = 4, f(4) = 6, and f(6) = 3 — there’s a cycle. (The French for 3, 4, 5, 6 are trois, quatre, cinq, and six respectively.) And if you iterate f in this manner you eventually always reach that cycle.
In English there’s similar behavior, except the analogous function (call it “e”) always reaches the fixed point 4. I won’t try to give a proof, but basically you evaluate the function for small n and then convince yourself that for sufficiently large n, e(n) < n. (Since e(n) should grow logarithmically with n this seems obvious.)
Spanish has both a cycle (4, 6) and a fixed point (5). I’d look at more languages but the three I named are the only three where I’m sure I know how to spell all the small numbers.
April 2, 2009 at 2:09 am |
Well, of the languages I can count in: Spanish, German, and Italian share the field with English, using cinco, vier, and tre, respectively. And French has none.
A little investigation shows that the Scandinavian languages match in “three” and “four”, and all but Swedish do “two” as well — Norwegian, for example, has “to”, “tre”, and “fire”. That seems to be the winner.
A google search on “numbers languages” gets this page, which then leads to this one, where you can find that in Finnish, the word for “eight” has nine letters, while the word for “nine” has eight letters — maybe that’s interesting too. There’s also a lot of African languages there (in Bemba, the word for “ten” has ten characters, if you count the space).
More than you ever wanted to know….
April 4, 2009 at 10:28 pm |
I’m not sure I understand the question, but just in case I do, in Japanese, if you use Roman letters, the number 2 is “ni” and the number 3 is “san”. ( And 4 is “shi”; and 5 is “go”.) And if you are counting objects, 6 things = “muttsu” and 7 things is”nanatsu” and 9 things is “kokonotsu”–the others don’t match.) (Ah, and 5 people is “gonin”.)
And, if you are looking at kanji, 1, 2, 3 each have 1, 2, 3 strokes, respectively. 4 has 5 strokes, and 5 has 4 strokes.
Whew!
April 5, 2009 at 11:43 am |
The kanji equivalent to this question might be: is there a single character for “12 stroked” or “comprising 12 strokes”? And if so, how many strokes does it have? And then from there, can we change the number 12 to some other number so that the number and the strokes used match up.
June 12, 2009 at 12:11 pm |
Some seven letter words are Awesome, Grandma, Hamster and Screams
April 4, 2010 at 9:03 am |
I’ve got your centiliteral right here…
April 7, 2010 at 6:04 pm |
[…] a song By Batman Maybe that should read “in a song”. In response to What’s a seven letter word for “seven letter word”?, Kurt gives us the following […]
May 17, 2011 at 1:24 pm |
In Turkish, the word for number 4, “dört”(read almost the same as “dirt”) is the only number-word that has the same number of letters as the number it represents. “dört” also has four phonemes in it, as every letter corresponds to a single phoneme in Turkish.