I'm going to explore the society-level implications of normalization and its opposite, schizophrenia [1]. Because these are big, complicated topics, I will be developing a mathematical model [2] to accompany them. Each section will use the model to demonstrate the phenomenon being discussed.
[1]Don't let the language about 'normal' and 'schizophrenic' confuse you! This article is talking about these phenomena on the level of societies, not individuals.
[2]These definitions exist in binary opposition to each other, but are neither exclusive nor absolute. Any group of individuals will display some degree of agreement and disagreement with each other. There is also no perfect line between the two.
Definition Normal (adj.):
When a group of beliefs all have a high alignment with each other.
Definition Schizophrenic (adj.):
When a group of beliefs are all disparate, or have little agreement or alignment with each other.
Let P_i be a vector of enums representing a person i's beliefs, where each index in the vector corresponds to a given question, and the value corresponds to that person's belief about the answer. For the sake of simplicity, we'll consider only binary questions, where 1 signifies an affirmative belief and 0 signifies a negative belief.
Consider the following sequence of belief questions:
Is freedom is more important than equality?
Does a monotheistic God exist?
Do you have free will?
Have you found the one?
Is your honor important?
Is there life after death?
Is life generally getting better?
Are you competent?
Are you smarter than average?
Is intention more important than consequence?
Do good things tend to happen to good people?
Let's suppose we have a set of individuals with the following belief matrix [3].
[3]Our belief matrices can be manipulated by re-arranging their rows or columns. This is possible because there's no requirement that the individuals or questions come in any particular order. Additionally, because we are limiting ourselves to binary questions, we can flip the values in a column with impunity.
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q11
P_1
1
0
1
0
1
0
1
0
1
1
0
P_2
1
0
1
1
0
0
1
1
1
0
0
P_3
1
0
1
1
0
0
0
0
1
1
1
P_4
0
0
1
0
1
0
1
1
1
1
0
P_5
0
0
1
0
0
1
0
1
1
1
1
On the questions of the existence of God (Q2), free will (Q3), and being smarter than average (Q9), we have complete agreement between the individuals. These beliefs can be therefore considered normal [4]. Beliefs with much disagreement (e.g. 2 vs 3) can be considered schizophrenic.
[4]Being normal isn't enough to make a belief true. Consider the rather obvious case of the belief `Are you smarter than average?` We have unanimous agreement across our opinion-universe, but it's simultaneously impossible for everyone to be above average [4-1].
[4-1]Unless you live in Lake Wobegon.
Normal at Scale
Whether or not a group of beliefs is normal depends on the scale at which the beliefs are considered. Consider the following matrix:
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q11
Q12
Q13
Q14
Q15
Q16
Q17
Q18
P_1 [5]
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
P_2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
P_3
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
P_4
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
P_5
1
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
0
1
P_6
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
P_7
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
P_8
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
P_9
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
P_10
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
[5]The matrix above has been put into P_0's canonical form. In the canonical form, one individual is selected and the matrix is transformed s.t. they appear in the first row, and all of their beliefs are affirmative. The other individuals have been loosely ordered by how much they agree with P_0.
At the scale of the entire population, we see that Q1 and Q2 have unanimous agreement, and are therefore normal at this scale. Simultaneously, we see that Q3 through Q6 (the next four columns) are split into two separate blocks. Dividing the matrix between those two blocks yields two competing belief groups. Each group is normal with respect to itself, however at the scale of the entire population, it appears schizophrenic between the two alternatives.
In general, a scale is a submatrix [6]. The more all of the beliefs within the submatrix all agree with each other, the more normal that scale is.
[6]Our base case is a single cell in the given matrix, or a single individual's belief on a single question. At this basic scale, everything is normal. Only as their scope increases does de-normalization take hold.
Schizophrenic at Scale
Schizophrenia occurs when multiple interrelated scales disagree with each other. Two scales are interrelated if they have the same columns [7].
[7]Having the same rows does not make two scales interrelated. This is because we can trivially flip the values of columns, but not of rows. Flipping a column is negating a question. Flipping a row is negating an individual, which is absurd.
Because we are limiting ourselves to binary questions, schizophrenia here presents itself as being two-headed. There are two ways this can be expanded: independent dimensions and dependent dimensions. In both cases, a dimension is just a set of competing scales.