Re: grids and CT

Jim Legg (
Tue, 26 Nov 1996 11:56:41 +1300

G Douglas wrote:
> Dear colleagues,
> My interests in PCP relate to others in semiotics and the
> Semantic Differential of Osgood et al. I'd like to ask if anyone has tried
> to use Catastrophe Theory to model the semantic universes revealed by grids?
> I am thinking particularly of the situation where a string of implications
> leads eventually to the reverse correlation with the starting construct. It
> seems to me that a cusp surface could model this: if we imagine a line of
> constructs like pencils tied together at their centres then they could do
> any one of a number of things: be tightly together in a bundle;be laid out
> on a flat surface with anohter construct running orthogonally; be wrapped
> around a surface and end up in reverse orientation.
> Any ideas?
> Graham Douglas.

Dear Douglas,

I tried doing exactly what you propose and your cusp indications
were confirmed in two experiments.

The first experiment was done using currency exchange rates as published
in the newspaper. First, I manipulated the currencies in a spreadsheet
so that the constructs where the dates and the constraints were the
ratio between dates for each currency. The discontinuities did not
appear until each of the construct points as shown up in the final plot
were joined by a smoothed line in date order. Every time this line went
close to the center of the plot a discontinuity or directional change
was a probability. The opposite condition applied when the construct
loading was far from center in which case there was almost no
probability of change in directional swing. The odd thing was that the
discontinuities seemed to occur on the weekends. A trader confirmed to
me that this was only logical as the market tended to balance the
portfolios for the weekend break. The implication therefore is that
equilibrium was the condition needed for a discontinuity.

The second experiment was done using an essay as the grid material. Each
of the points in the essay were treated as both the elements and the
constructs in a distance grid. From the final plot the points were
joined in a smooth line in ascending point order. As in the first
experiment the discontinuity of this line came when it was close to the
center of the plot, the dramatic equivalent of an act-change.

In order to create the 3-D smoothed line I transfered the plot to Aldus
Freehand and used the curved line tool. This is easy to do by hand once
you've got the hang of it.

Does that help?