The second paper on my Thinknet project is now available here. Below I reproduce the introduction.
In part 1 of this series I described the general idea of an association network as based on some of the ideas of Edward de Bono’s book The Mechanism of Mind. In this part I develop the theme a little further by giving it some mathematical backbone.
By August 91 I had written up an association network program on an Amiga 500. I had some vague notion about the tokens of the network being linked by some kind of probability weighting. Up until that time the Thinknet project was very software driven: I wanted to get out a system that did something regardless of whether or not I really understood what it was doing; much of it was an accumulation of several seat-of-the-pants decisions. I had guessed that the tokens of the network were linked by some probability but I didn’t really have any clear idea as to the theoretical underpinning of this probability. Initially all I did was to code in a universal linking probability factor that represented the fact that although token A would lead to or imply token B it wouldn’t do so with absolute certainty. But it was obvious that using a one size fits all probability was far from satisfactory. During one of our many family beach chalet holidays (10 August to 17 August 1991. Hemsby, Norfolk) I sat on the sand looking out to sea pondering what the underlying theoretical model should be and by early September I had the model up and running.
The model was based on a very simple idea; in fact the idea was essentially that of a literal interpretation of the Venn diagram. In this model the points on the Venn diagram are thought of as concrete items which can be collected together in various classes according to the properties those items have: In the Venn notation we draw a circle round a set of points on the diagram to represent a class of items, each of which have some selected property. If we draw two circles based on two classes each defined by their particular property then we can then represent the relationship between these two classes by the extent of the overlap, if any, between the two classes; an idea familiar to anyone who has seen a Venn diagram
This very literal interpretation of the Venn diagram using items and their respective properties to form classes of items gives us a very concrete model of set theory which immediately circumvents Russell’s paradox. It does this by distinguishing sharply between classes and the items of which they are composed in a similar way that Von Neumann’s version of axiomatic set theory makes a distinction between classes which are not elements and classes which are elements (where my items = elements).
The Thinknet project is really part of my Melencolia I series. The links relating to this series are below:
Also relevant are these links: