The Galois Lattice slides we are about to see represent the distribution of 19 Medieval industries and port cities across 299 circum-European cities for each 25 year period from 1175 to 1500. They are not statistical reductions but exact representations of the raw data recorded by Peter Spufford (2002). They show the growing combinatorial complexities of industrial complexes in those three centuries. (Next iteration: Add Capitals!)

Rather than a statistical synthesis of overall patterns and tendencies, however, the lattices show something that multivariate statistical analysis simply cannot show, because the lattice represents all the actual combinatorials of among 20 industries, possibilities which involve n-way interactions and millions of theoretical possibilities. The actual combinatorics, however, are vastly more limited.

Along with ports and the 19 industries are five population size variables (>10K, >20K, >50K, 100K and >200K).

Among the industries, some -- typically the most frequent -- occur independently of the others, and these “independent” industries recombine in various ways. Population levels FOR 1500 combinations of industries and ports. When a coding for Capitals is added as a predictor of consumption, one hypothesis is that multiple regression with industries, capitals and ports as independent variables predict 1500 population levels more closely as the industry data nears that date.

Lattices 1175 ... 1200 ... 1225 ... ... 1475 ... 1500

In the first diagram (1175) there are intersections between the population attributions in ten of the intersection nodes along the top with LINENS and PORTS. The node with all the incoming arrows at the bottom is the intersection at the null set, which indicates that sets intersection there are mutually exclusive of one another.

Node size is scaled according to number of cities with each combination of features. For the smallest nodes (1 or 2 cities) with several incoming features that define them, the names of the cities are given.