John Searle asked whether the mechanism in the Chinese room which passes the Turing test really understands what it is doing.
One can define understanding very simply:
U = K / C
Understanding = Kolmogorov complexity / Code size
Consider two programs that generate the first 1,000 prime numbers. The first uses a lookup table in which is stored the first 1,000 prime numbers. The second computes the primes using a conventional nested loop in a short program. Which program understands primes better? The formula concretely indicates the second program.
If the rule book in the Chinese room is small then the room understands well. If the rule book is huge or nearly infinite then the room’s understanding is negligible or infinitesimal.
Instead of the classical binary decision, the Turing test can be evaluated in a continuum according to K / C.
Similarly one can define intelligence as:
I = K
Intelligence (with respect to a problem domain) = Kolmogorov complexity (of the intelligence)
The second prime number program above has the same intelligence as the first, with respect to the problem of generating the first 1,000 prime numbers. However the second has a greater Understanding. The Chinese Room would be about as intelligent as an elegant artificial general intelligence if both pass the Turing test; but the understanding of the Chinese Room would be low or high according to the size of the rule book.
One can say then that understanding is intelligence density.