The second paper on my Thinknet project is now available here. Below I reproduce the introduction.
1. 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).
***
Relevant Links.
The Thinknet project is really part of my Melencolia I series. The links relating to this series are below:
Also relevant are these links:
No comments:
Post a Comment