Saturday, September 29, 2007

Happy Birthday Dave

By the way: HAPPY BIRTHDAY TO DAVID. This wish is only two days late, but heartfelt even so.

The "Buffalo" Sentence

10/28/07

GRY

Explanation of the “Buffalo” Sentence

The word “buffalo” can be used in three ways:

  1. Buffalo – the city in New York. Use the notation “B” to refer to this meaning.
  2. Buffalo – the animal (bison in America). Use the notation “b” for this meaning.
  3. Buffalo – the transitive verb, meaning to intimidate. Use “$” for this meaning.

The first two meanings can be used to form categories, or sets, of animals as follows (using the short form for brevity):

b – the set of all animals called buffalo.

Bb – the subset of those animals near the city of Buffalo, or Buffalo buffalo.

We can divide these two sets into further subsets of animals that are intimidated by either of the first two sets:

bb$; Bbb$; bBb$; and BbBb$ – bison intimidated by other bison; Buffalo bison intimidated by bison; bison intimidated by Buffalo bison; Buffalo bison intimidated by other Buffalo bison.

Each of these four sets will have two subsets, made of those bison, and Buffalo bison, intimidated by each of the above categories of bison:

b(bb$)$; Bb(bb$)$; b(Bbb$)$; Bb(Bbb$)$; b(bBb$)$; Bb(bBb$)$; b(BbBb$)$; Bb(BbBb$)$

I have added the parentheses to make the categories more clear.

Each of these sets will have two subsets, made of those bison, and Buffalo bison, intimidated by each of the categories of bison. Each new set is made by adding “b” or “Bb” to the front, and “$” to the end, as follows:

b(b(bb$)$)$; Bb(b(bb$)$)$; b(Bb(bb$)$)$; Bb(Bb(bb$)$)$; b(b(Bbb$)$)$; Bb(b(Bbb$)$)$; b(Bb(Bbb$)$)$; Bb(Bb(Bbb$)$)$; b(b(bBb$)$)$; Bb(b(bBb$)$)$; b(Bb(bBb$)$)$; Bb(Bb(bBb$)$)$; b(b(BbBb$)$)$; Bb(b(BbBb$)$)$; b(Bb(BbBb$)$)$; Bb(Bb(BbBb$)$)$

Each of these sets will have two subsets, made of those bison, and Buffalo bison, intimidated by each of the categories of bison, and so on. Each category must have at least one animal in it, so when you run out of buffalo, there is an end to the categories.

Sentences can be formed by having any category intimidate any other category, in the form:

C1 $ C2

Example: Let C1 = Bb and C2 = b. The sentence is represented by “Bb $ b”. Written out, it is “Buffalo buffalo buffalo buffalo”, or “Bison in the vicinity of Buffalo, N.Y. intimidate other buffalo.”

In addition, the city of Buffalo could be intimated by any category, as in “b $ B”, or “Buffalo buffalo Buffalo.”

A valid English sentence can be formed for any number, n, of “buffalo”. For n=1, the shortest sentence, it is the declaration, “Buffalo!”

As a verb, “buffalo” is transitive, requiring an object. But, if it were to be used (mis-used) as an intransitive verb, one could say “b$” or “Buffalo buffalo” meaning “Buffalo intimidate”, yielding a sentence for n=2. Although one could also say, “Buffalo buffalo!” (Bb) indicating a recognition that the buffalo in question were associated with the city, or “Buffalo, buffalo!” (bb) indicating continued amazement at the appearance of buffalo.

Buffalo, the city, is always capitalized, so within the sentence, all capitalized “Buffalo” refer to the city. The first word in the sentence is also capitalized, so it could refer to the animal or the city, but not the verb, because the verb requires that an object precede it.

Example: Take the two categories Bbb$ and bb$, and form the sentence:

(Bbb$) $ (bb$)

It translates as the perfectly valid English sentence:

Buffalo buffalo buffalo buffalo buffalo buffalo buffalo buffalo.

Or, to take a more extreme example:

(b(b(bb$)$)$) $ (b(Bb(BbBb$)$)$) translates as the sentence:

Buffalo buffalo buffalo buffalo buffalo buffalo buffalo buffalo buffalo Buffalo buffalo Buffalo buffalo Buffalo buffalo buffalo buffalo buffalo.

But, care must be taken to get the capitalization right.