by Bill Graham

It’s not magic. In any paragraph of reasonable length without too many unusually long words, if you start on two different words in the first sentence, you will usually come to some common word along the way. From then on you are destined to end up on the same word. The only way this is not likely to happen is with a short paragraph with lots of long words.

If all of the words had an even number of letters, then beginning on a odd-numbered word would result in always staying on odd-numbered words. Similarly with even-numbered words. A single odd-length word in the sequence would guarantee that one of the sequences would switch.

Some more analysis shows that a sequence of two words with the first word having one more letter than the second will result in paths through those two words merging. Similarly, if words are two apart, then having the first with two more letters than the second will result in paths through those two words merging. Long enough paragraphs with enough fairly short words will result in many such patterns.

In the actual paragraph, here are some such path-merging patterns.

Position of first word	Words
4	that you
6	should start
9	choosing - - - this the
17	Count - - in
19	letters - - word
25	ahead that

In the absence of any such patterns, you would not merge paths. The likelihood of no such patterns is small unless it's deliberate.

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Contents copyright 2004 by Bill Graham and ParaComp, Inc. All rights reserved.
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