Besides the link above (to former UB Prof. John Case's
webpage on CoLT, see also
"What is COLT?" (when you click on this link, scroll
down to "What is COLT?").
Here are some examples of why this is difficult:
"… surely, at least the mathematical questions on IQ tests are
objective. This mistakes the issue. If asked to continue the sequence
‘1, 1, 2, 3, 5’, many people would
recognize the Fibonacci sequence and say ‘8’. But there
are infinitely many other sequences where the next number is 7 (for
example, ‘pick the largest prime number less than or equal to the
sum of the previous two numbers’), or even 11 (‘pick the
smallest prime number greater than or equal to the sum of the previous
two numbers’). What's tested by [such sequences] is not how well
you can find patterns, but how well you can find the patterns [that the
author of the question] liked." (p. 247.)
"Suppose that some natural process yields the sequence
1,2,3&hellip How does it continue? Of course, we have far too little
data to know. It might oscillate (1,2,3,2,1,2,3,2,1…), become
‘stuck’ (1,2,3,3,3,3&hellip), exhibit a Fibonacci structure
(1,2,3,5,8…), and any of an infinity of more or less plausible
alternatives. This indeterminacy makes the problem of
[…]induction of structure from the natural world difficult,
although not necessarily hopelessly so, in the light of recent
developments in statistics and machine learning […]. But consider
the parallel problem of [cultural] learning—we need not guess the
‘true’ continuation of the sequence. We only have to
coordinate our predictions with those of other people in the
community. This problem is very much easier. From a psychologocial
point of view, the overwhelmingly natural continuation of the sequence
is ‘…4,5,6….’"