I believe I have an unfair edge over most of my colleagues right now – my mind works better than my mouth does.
Psychometric theories use what Sternberg has called a geometric analogy for intelligence; people are seen as varying along dimensions of intelligence in much the same way that they vary along the dimensions of height and weight. Different theories identify different dimensions, but the geometric analogy is maintained. This is a useful way of summarizing variations in intelligence across populations, but it has a serious shortcoming. The geometric analogy does not explain the processes that make up thinking.
To see what this means, imagine two individuals, Ignatz and Horatio. We first determine their psychometric intelligence, in terms of the g-VPR model, and then ask them to attack the following two problems. The first problem makes use of the English rules that permit center embedding, putting one relative clause inside another. Ignatz and Horatio are presented with sentences of the form
The rat ate the cheese
The rat the cat chased ate the cheese
The rat the cat the dog scared chased ate the cheese
The rat the cat the dog the man owned scared chased ate the cheese.
And so on
and we determine at what point each person finds the sentence incomprehensible.