Top chess players, until recently, held their own against even the most powerful chess playing computers.  These machines could calculate far deeper than their human opponents and yet the humans claimed an advantage:  intuition.  A computer searches a huge number of positions and then finds the best.  For an experienced human chess player, the good moves “suggest themselves.”  How that is possible is presumably a very important mystery, but I wonder how one could demonstrate that qualitatively the thought process is different.

Having been somewhat obsessed recently with Scrabble, I thought of the following experiment.  Suppose we write a computer program that tries to create words from scrabble tiles using a simple brute-force method.  The computer has a database of words.  It randomly combines letters and checks whether the result is in its database and outputs the most valuable word it can identify in a fixed length of time.  Now consider a contest between to computers programmed in the same way which differ only in the size of their database, the first knowing a subset of the words known by the second.  The task is to come up with the best word from a fixed number of tiles.  Clearly the second would do better, but I am interested in how the advantage varies with the number of tiles. Presumably, the more tiles the greater the advantage.

I want to compare this with an analogous contest between a human and a computer to measure how much faster a superior human’s advantage increases in the number of tiles.  Take a human scrabble player with a large vocabulary and have him play the same game against a fast computer with a small vocuabulary.  My guess is that the human’s advantage (which could be negative for a small number of tiles) will increase in the number of tiles, and faster than the stronger computer’s advantage increased in the computer-vs-computer scenario.

Now there may be many reasons for this, but what I am trying to get at is this.  With many tiles, brute-force search quickly plateaus in terms of effectiveness because the additional tiles act as noise making it harder for the computer to find a word in its database.  But when humans construct words, the words “suggest themselves” and increasing the number of tiles facilitates this (or at least hinders it more slowly than it hinders brute-force.)

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