I couldn't sleep last night. All I was thinking about was:
The ultimate social science experiment [short of raising people from birth in 100% controlled environments]. Here's how it would go:
1. Find a set of N social variables that are, to the best degree possible, completely orthogonal, and span the set of all social properties [!].
2. Design a test--like a very carefully conducted interview--to measure position along the variable axes for a very large number of randomly selected people. Each person would need to answer, say, 10 weighted questions to resolve their position along a single axis.
3. Instruct a computer to create an N-dimensional cube [hypercube, n-cube, whatever] containing all the data. Each person would be represented by a single point within the volume of the cube.
4. Calculate the effective entropy of the configuration, and other interesting things
Question: what would it "look" like?
To simplify things, imagine a 3-dimensional cube [the normal kind]. Along one edge might be the variable "pacifism," measured between -1 [hawk] and +1 [dove]. Another edge would measure, say, "deference to authority" and another possibly "analyticity." If you scored (1,1,-1) then your position would be at one of the bottom corners of the cube, and indication that you are extreme in views. If lots of people end up there--if there is a clustering somewhere--then we can conclude that the variables either have [a] correlation in substance or [b] correlation in occurance. Since the axes are chose to avoid--as much as is possible--correlations in substance, grouping means correlation in occurance. Meaning, there's a "type" of person begging to be labelled there, typified by location near a particular corner of the box. Occurance correlations could be very profound, though there's no way of identifying cause [ie. nature or nurture] without plotting gene occurances along yet more axes [and that's still partially ambiguous]!
Expanded to N-dimensions, we can do all kids of neat statistical tricks to tease out interesting information. How about a polarization test on all axes combined? As in, are people generally one way or the other, or do they generally fall along a flat continuum? Correlation tests, looking for structure: filaments in N-space would indicate that some variables have give-and-take relationships with others. Projection on axis pairs will unobfuscate correlations that might be hidden by completely uncorrelated variables. Entropy is a good measure of how "organized" the resulting distribution is: do people really fall into categories?
The great thing about cubes is that every axis connects to each vertex. A 3-dimensional cube has 12 edges and 8 vertices, but each vertex touches one edge in the x direction, one in the y direction, and one in the z direction. So all the correlation information in the whole system is contained in an n-cube.
The overall key to this exercise is asking the right questions. Take the "pacifism" axis, for example. Questions like "suppose a terrorist struck a major US city, would you support retailiation" tap into conscious political biases. Stripping away contextual biases in the questions, to get at how people really ARE would be incredibly difficult but essential.
So I ask again: what do you see? Do you see a cloud of dots in the middle, with outliers near the edges? A hole in the middle? A gas [uniform density]? Structure? What about dynamics: do dots clump over time, disperse, oscillate, rotate, collapse, expand?
