Whether a group of beliefs is normal or schizophrenic is directly a function of the scale at which they're being considered. It would be great if we had an algorithm for finding such insights into a matrix.
In order to do this, we need two things:
A metric for evaluating the normality of a given scale.
There's no right answer to this question. For my own uses, I've considered using the product of the fraction of agreement between beliefs, multiplied by the number of cells in the scale. Ex:"If we have 4 beliefs across 5 individuals and their agreements are 5/5, 4/5, 4/5, and 5/5, their score will be (5/5)^2 * (4/5)^2 * 4 * 5 = 12.8."
A process for finding scales with high normalities.
This suffers from combinatorial explosion. The number of submatrices of an N x M matrix is 2^N * 2^M = 2^(N+M). This is a very large number, and represents a huge search space.
We can limit the scope of the problem by fixing one of the dimensions (either the beliefs or individuals). I call this process sharding. Sharding can be done over beliefs → or over population →.