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.
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.
cheers,
Hans-Cees
> Consider that you are the United States president and that you
> have a very specific social-political agenda. Consider that (due
> to some tragedy) that you have the opportunity to appoint all
> nine members of the US supreme court. Consider that (at the
> moment) there are enough like-minded people in the US senate
> so that your appointments will be ratified. Now, since you
> have a specific social-political agenda, what you want is for the
> new supreme court to always make the decisions that you want
> them to make. That is, at this particular moment in time, you
> have a procedure to make decisions (that satisfies your agenda)
> and you want the supreme court justicies to always follow that
> same decision procedure. Consider that this is what you want.
>
> Now, if you could pull this off (somehow get the new justices
> to make decisions in this way), the new justices would be
> making decisions in a path-independent way. (Although the
> appointment of the new justicies was VERY path dependent).
> The new judges would not be thinking for themselves. They
> would just be mindlessly following a pre-written formula. It
> would be completely arbitrary what order the cases were
> brought to the court. Any particular decision would provide
> no new information (as for how other cases would later be
> decided). Everything is already entailed by the decision
> formula that you provided at the time of the initial
> appointments.
>
> Now, consider a different situation. Consider that the justices
> are free to think for themselves. Consider that they aren't just
> implementing a pre-written decision procedure. Consider that
> it isn't guaranteed that they will come to the same decisions
> that you want. In such a case, each decision provides new
> information and can affect future decisions. In this situation, it
> would be impossible (over time) to guarantee that your
> particular social-political agenda would always be followed.
> The order of the cases brought to the court matters. There is
> now path dependence.
>
> Path independence (in this example) is associated with the
> mindless following of rules or formulas. No new information
> emerges along the way. Everything is entailed from the
> beginning. The end-point is certain. It doesn't matter what
> order the cases come in.
>
> Path dependence (in this example) is associated with the
> justicies being free to make real decisions. New information is
> being produced (emerging) along the way as a result of these
> decisions. This new information then partly influences future
> decisions. It becomes impossible to predict (from the start)
> how the justicies will decide in future cases. Everything is not
> entailed from the beginning. It does matter what order the
> cases come in.
>
>
> _______________________________________________________
>
>
> I hope this helps. Please comment if anybody thinks that
> aspects of the above explanation misses the point of the
> distinction between path-dependence and path-independence.
>
> Jeff Prideaux
>
> P.S. I kind of patterned my explanation after the types of things
> Kampis said in his book "Self-modifying systems in biology and cognitive
> science".
>
Theories come and go, the frog stays [F. Jacob]
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