The following belief-matrix demonstrates independent dimensions. The groups of columns 3 to 7, 8 to 12, and 13 to 17 each separately represent two competing normals. In each group, half of the individuals are in each block. The blocks themselves however are perfectly uncoordinated and are independent (hence the name) of each other. This population therefore has three separate binary schizophrenias. Each one represents a way of dividing the population in two.
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q11
Q12
Q13
Q14
Q15
Q16
Q17
Q18
Q19
P_1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
P_2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
P_3
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
0
P_4
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
P_5
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
0
P_6
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
P_7
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
P_8
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
P_9
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
P_10
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
P_11
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
P_12
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
P_13
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
P_14
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
P_15
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
P_16
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
Dependent Dimensions
Some belief questions may be predicated on each other. For example, the belief "Have you found the one?" depends on the belief "The one exists". Allowing dependent questions means that our belief matrix may become sparse, where some cells are undefined. Consider the following:
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q11
Q12
Q13
Q14
Q15
Q16
Q17
Q18
Q19
P_1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
P_2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
P_3
1
1
1
1
1
1
1
1
1
1
1
1
1
0
P_4
1
1
1
1
1
1
1
0
0
0
0
0
0
1
P_5
1
1
1
1
1
1
1
0
0
0
0
0
0
0
P_6
1
1
1
1
1
1
1
0
0
0
0
0
0
1
P_7
1
1
0
0
0
0
0
1
1
1
1
1
0
1
P_8
1
1
0
0
0
0
0
1
1
1
1
1
1
0
P_9
1
1
0
0
0
0
0
1
1
1
1
1
1
0
P_10
1
1
0
0
0
0
0
0
0
0
0
0
0
1
P_11
1
1
0
0
0
0
0
0
0
0
0
0
0
1
P_12
1
1
0
0
0
0
0
0
0
0
0
0
1
0
Observe the same three blocks of columns as in the independent example above. The middle block has a dependency on some belief in the first block being negated, and similarly the third block has a dependency on some belief in the first block being affirmative. The result is that each of the two normals present in the first block are further subdivided. If we take our submatrix to have the columns from all three groups, and three individuals in each one, our population appears to be schizophrenic with four heads.