Sentences Are Commutative, Words Are Not

February 27, 2012 at 12:34 pm 4 comments

While playing Scrabble® on my phone today, I had a rack with following letters:


Near the top of the board was TAVERNA, and it was possible to hook above the first six letters or below the first two letters. There were other spaces on the board to place words, but this was clearly the most fertile. The full board looked like this:


On my rack, the letters weren’t in alphabetical order (as above), so I missed a seven-letter word that would have garnered 78 points. Instead, I played ABLE for a paltry 13 points.

After my turn, the Teacher feature showed me the word I should have played:


Kickin’ myself. I’ll get over not seeing BANAL, LANAI, or even LEV. But how does a math guy miss ABELIAN? I would not put up a fight if someone wanted to rescind my Math Dorkdom membership card.

What loves letters and commutes?
An abelian Scrabble player.

(That’s a joke. Please don’t play Scrabble while driving.)

Entry filed under: Uncategorized. Tags: , , , , .

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4 Comments Add your own

  • 1. xander  |  February 27, 2012 at 2:17 pm

    Are commutative English in not sentences. That is to say,
    sentences are not commutative in English. 😛

    However, in most flexive languages (such as Russian), many sentences are commutative. For instance, “я тебя люблю” and “Тебя я люблю,” mean the same thing (minus any spelling errors).


    • 2. venneblock  |  February 27, 2012 at 9:23 pm

      I used to work with Amish carpenters who would say things like, “The deer over the fence jumped,” a carry-over from German where the verb usually goes at the end (“Das Reh über den Zaun gesprungen”). If stated so that the verb is not at the end, it would be “Das Reh sprang über den Zaum.” But in that case, the form of the verb is different (sprang versus gesprungen), so it’s not commutative.

      I’m not a linguist. I wonder how many languages are commutative?

  • 3. xander  |  February 29, 2012 at 12:39 pm

    Way back in the day, when I was studying anthropology, I had to take a few linguistics classes. So, while I can’t claim to be an expert by any stretch of the imagination, I believe that the answer is something like this:

    Human languages basically fall into two categories: flexive languages, and syntactic languages. In flexive languages, grammatical meaning is carried by pre- or suffixes attached to words, and the ordering of words is entirely irrelevant. In syntactic languages, meaning is carried entirely by the order of words in a sentence.

    At least, that is the broad strokes theory. In reality, most languages carry elements of both. English, for instance, is basically a syntactic language. The order in which words appear in a sentence determines their role in that sentence (i.e. the subject comes first, then a verb, then an object which is acted upon by the verb). However, there are some flexive elements left over from some ancient root language. For instance, plurals are generally produced by suffixing a noun with an s, and verbs still carry some information about tense.

    Russian has basically the opposite thing going on. The language is basically flexive, in that grammatical meaning is carried by altering the word: verbs are conjugated in order to denote tense and the actor, nouns and adjectives are declined in order to indicate whether they are part of the subject or object, and so on. However, there is a somewhat standard order, and changes in that order can subtly change the meaning of a sentence by shifting the emphasis from, for instance, the object to the subject. Poets like Pushkin had a lot of fun with this.

    So, to attempt an answer to the question: there probably aren’t any languages that are truly commutative, but there are almost certainly a very large number of languages in which many sentences will commute.


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The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

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