Re: the use bifurcation

[Howard Pattee <***>]

Comment on ?bifurcation?:

Judith: When my father uses "bifurcation", he means; deviation between what a
model is predicting and the actual behavior of the real system the model is
representing. That's all. It doesn't specify a number of anything. You
could use the word "deviating" if you like it better.

Bob used the word bifurcation several ways. It has dictionary meanings and technical 
mathematical meanings in dynamics. In Anticipatory Systems, for example, on p. 20 he uses 
it as just a deviation, as Judith says, and on pp. 185-186 he explains its mathematical 
meaning that is much more serious than just a deviation. In dynamics a bifurcation is a 
kind of instability that occurs at some value of a parameter such that a set of 
trajectories (often attractors) switch to a totally different set of trajectories. 
Multiple bifurcations can lead to deterministic chaos. It is like switches in a Chicago 
rail yard where because your watch is wrong (the parameter) instead of going Boston you 
go to Denver.

Bifurcation is a now popular dynamicists model for differentiation in development, like 
when stem cells suddenly commit to being nerve cells. Bob emphasized that bifurcation is 
only a metaphor for development.

When is a metaphor a good model? (I have no answer in mind.)

Howard