The Cultural Calculus: An Example of Polymathic Methodological Transfer

Psychologist Charles Spearman hypothesized that for every intellectual task the performance of an individual is determined by traits specific to the task (s) and traits general to all or most intellectual tasks (g). Suppose we chose 100 people at random and gave them a test on number progressions. A performance rank order would result. Now suppose we gave the same 100 people an analogy test. There are three distinct relationships the two results could have to one another.

The first is that they are inversely correlated. In other words, a person who scored in the top 50 on one test would have a greater than random chance of scoring in the lower 50 on the second test. This is the constant intelligence theory that says that everyone has about the same amount of intelligence and if a person is better than average in one task it is because they are applying more of their intelligence to it. Consequently, they have less to apply to other tasks and they can be expected to score below average on those tests.

The next theory is the random theory. In other words, g=0 and all the proficiency a person has in a specific intellectual task is related to traits that only affect that intellectual task. If Spearman is correct, the rank order of a person on one test will have predictive value on the other test. The greater the predictive value the more g dominates the explanation of intellectual performance.

The problem of determining the predictive value between many tests was a difficult one and Spearman developed Factor Analysis to deal with it. It turned out that Spearman was correct. In fact, it turned out that g explained most of the difference in intellectual performance between people. Thus, a new and more rigorous definition of IQ was born. IQ is a measure of g, which is extracted from the results of questions diagnostic of many types of intellectual tasks.

Factor Analysis has been utilized polymathically in geochemistry, ecology, hydrochemistry and economics. Marketing analysis has used a simpler form by creating correlation matrices. Here we are going to give an example of an intentional rather than accidental use of polymathy to develop a Cultural Calculus. In doing so, we will provide a theoretical basis for a new way to evaluate history, understand the present and contemplate the future.

Suppose we gave a number of people a questionnaire that explored their attitude toward abortion. We could then assign values to each person with 1 representing someone who believes that abortion should be illegal in all circumstances and that anyone involved in an abortion should be considered to have committed or been accessory to murder and 100 representing someone who believes that abortion should be legal at all points in a pregnancy and, nobody, including the father or the courts, my abridge that right. We would expect that this questionnaire would result in a bimodal population if plotted on a graph where the x axis is the value between 1 and 100 and the y axis is the number of people with the specific rating. We would expect the left mode to be represented by people who believe that abortion should be illegal except in the cases of incest or rape or to save the life of the mother. The right mode, we expect would be centered on people who believe that abortion should be legal in the first trimester of a pregnancy.

Now suppose we gave the same people a questionnaire that explored their attitude about welfare. We, again, would expect a bimodal population with one group centering around a view that welfare should be limited, locally administered and with significant assistance from the philanthropic and religious communities and the other group centering around a federally mandated suite of government entitlement programs.

Let us expand our graph to three axes, with x being the rating on the abortion scale, y being the rating on the welfare scale and z being the number of people at each particular (x,y). We believe that now we will find a conical mound centering around those who take a low numbered position with regard to both abortion and welfare and another centering around those who take a high numbered position to both. We are not sure whether those not among the two major nodes will be evenly distributed or if there would be one or more smaller nodes. Some people might argue that the graph would have more than two modes. Others may argue that concentrations would be small and the majority of people would reside on a 100 X 100 plane of relatively little topography. We are unaware of any studies of this nature and, consequently, the disagreement cannot be definitively resolved.

Since very few people can visualize hyperdimensional objects, we are going to add one more questionnaire and then stop. Now we will include a questionnaire on the degree to which government should abridge the freedom of action of citizens and enterprises for the sake of preserving the ecological status quo. At the low end will be people who believe that the government has no right to abridge such actions at all and on the other extreme are people who believe that the government has an absolute obligation to proscribe and assess fines for any act that may disturb the current environmental conditions. Now, since we need the z axis for our third questionnaire, we will need to do this a little differently. We will make a volume comprised of 100 X 100 X 100 = 1,000,000 cubes each of which represents one unique (x,y,z) and capable of holding many dots. We believe that this exercise would render two very dense centers surrounded by a halo of loci of decreasing density as the radius from the center increases. For those familiar with astronomy, it would look like two globular clusters, one centered around moderate positions in favor of abortion, welfare and environmental restrictions and one that centered around moderate positions against abortion, welfare and environmental restrictions. Again, we are unsure whether there would be smaller clusters at different locations.

We can imagine that the same questionnaires are given to a statistically valid and consistent group of people over time. We now can see our concept space evolving. Perhaps clusters will become more dense or less dense. Perhaps a piece of a cluster will break off and travel to a different locus, picking up members as it goes. Perhaps portions of our concept space will develop a new attractor and start growing and increasing in density spontaneously. Perhaps we can see the distance between the two major clusters become closer or farther apart. In other words, we will be watching a movie of cultural fragmentation, coalescence and evolution.

Of course, Cultural Analysts, well versed in the more complex mathematical methods required to extract meaning from a larger number questionnaires will take this several steps further than we will here. They will create hyperdimensional models that will move, transform and evolve in ways that can only be approximately represented in three dimensional models. Using factor analysis, they can create a kind of central definition of culture, perhaps extracting central or core factors that define each culture. Even though not easily visualized, characteristic statements, then, can be made about the conformation of the concept space and how it has changed over time.

Not only is this an example of methodology transfer being utilized in the Polymathic Method, it also allows us to provide a more complete explanation of the meaning of Polymathica. If questionnaires were given to people to assess their sense of refinement and erudition, we consider it obvious that few people would find themselves in the 90’s on a scale of 1 to 100. Most of civilization has become rather crass, crude, hedonistic, vulgar and anti-intellectual. Consequently, Polymathica is creating an attractor at one end of the refinement and erudition dimensions of concept space that, we hope will begin to grow through accretion and become more defined through shared cultural literacy.

This post also gives us a common pattern language with which to discuss issues of culture.