Spheres of Competition

Last week I spoke of looking at a business taxonomy in new way. Generally, people think of taxonomies as a vocabulary with perhaps a hierarchical structure of categories and sub-categories. However when you build a multi-dimensional taxonomy as our team has, you can now start to think of it as a spatial topology. There are four trees and each one defines a dimension in our business taxonomy space. This thought is analogous to the special theory of relativity from physics where you have the x, y, z dimensions plus the time dimension. An "event" is a point in the space time continuum is defined by those four dimensions. In our business taxonomy space, a "company" is a point in the spatial topology defined by our four dimensions. If you draw a small sphere around a given company's point in our taxonomy, you will get all the competitors of that company. We have seen as you widen the sphere the outlying companies are less likely to be competitors. The key to making this work is to define the distances between points in a given dimension's tree. We generally realize that the distance between parent and child is shorter the deeper you get into the tree, and the distance between siblings is slightly more than that between parent and child. We also realize that you may define siblings where some siblings are closer in meaning than others. Our distance algorithm has to take all these things into consideration. Our work has been experimental, but has returned interesting results. We have use this in our drill-down feature on mandasoft.com.  The space defined has to be tweaked, and I may leverage algorithms similar to Einstein's general relativity where actual data defining company revenue at a point in our topology could warp the spatial distances, just like physical mass warps physical space. Any thoughts?