> The following is from Hans-Cees:
>
>
> Dear Jeff, if you could forward this to the list, that would be
> great.
>
> I am not sure if I would consider the example beneath path dependence and
> independence. My thoughts are still a bit blurred, on this example,
> and also on the example of Don, about enzymatical systems with
> inhibitors, etc.
> In the example of a population of organisms the population was
> a system that was relatively inert with regard to internal changes,
> that would benefit the population, since the changes could be towards
> a selection criterium. For instance if there would be a shortage of
> water, the population would benefit from drought-resistence. It might
> not get it because the mutation mechanisms can't just pop up the
> solution needed, the solution must not disturb the functioning of other
> parts of organisms, etc. Dependent on the specific genetic make-up of a
> population at one time [the path] it will, or won't be able to get
> that benificial adaption in a certain time.
Ypur example is mathematically isomrophic with the one I gave which you
say you are not sure about. I don't understand?
If you look upon water shortage as an inhibitory factory and
so on, the problem can be expressed in the same way. All the
genetic factors do is to provide an explanation for where the activation/
inhibition patterns come from. In our private communication
I mentioned that ecosystems and population dynamics were in the
set of examples I was talking about as well as the biochemical
example you selectively mention here.
> So the essential part of path-dependence is that a system would
> benifit if it got somewhere, but its makeup at a certain point
> along with its limites ability to change inhibits that.
> The second example I coined was the example of laws. It was more easy
> in the sence that everybody knows how laws work and change, and not everybody
> knows how populations do that. But the example is a bit more tricky
> in the sense that the identification of what is the system that is
> path indepenent or not is not emediately clear.
> I think it is like this:
> there is a body of law at any one time, that we can call a system of
> rules for human interaction. This body contains rules for
> everyday interaction [you may not steal, or..], but also rules that
> state how the body of rules can be changed. In comparison, a
> population of organisms has also 'rules' for change. They would be
> rules for interbreeding, eggs and sperm must have certain
> charateristics to be able to merge, and if changes [mutations]
> interfere with these rules the change results in death for the genes
> that had the change in them. Other rules are the rules that exist for
> the kinds of mutations that can take place, etc.
> So the change in the body of laws is constrained by the laws that
> describe how this change can and cannot take place. Other constraints
> on change can be the make-up of the senate that must judge new laws.
> Thus the body of laws is path dependent because the change-laws, and
> the senate's particular 'path' form particular constraints at one
> time to change.
>
> I would like to know from Jeff in what respect his example is
> describable in these same terms.
>
As we have been saying, this is one of many examples of a fairly common
feature of systems. They have a rather similar nature to them.
What is unusual is the notion of path independence. If that unusual
notion did not exist, we would not be having this discussion!
> cheers,
> Hans-Cees
>
I think you need to study the mathematical model for this. You
keep trying to think of ways of saying it which make it different, but you
miss the similarity that way. The simple idea from the math is that
path independent systems arrive at the same end point from the same
starting point no matter which path they follow to get there.
The CONDITIONS for this happening are very restrictive. Real
systems (as Jeff's example as well as yours as well as mine all
demonstrate) would have to be VERY peculiar to meet these restrictions.
Thus, I assert once more, we are basically dealing with a straw man here.
This is a common result when we refuse to recognize the value of
mathematical models as tools for getting to the crux of an issue.
True the mathematical model is an idealization, but in THIS context that
strengthens the arguement. Even within that idealisation path
independence is a rarity!
Best Regards,
Don Mikulecky