>My experience with the notion of path dependence (lock-in is an example)
>is through thermodynamics, but the idea is quite general. There would
>be no need for the term if someone had not concieved of "path independence".
>What THAT implies is that certain processes can be counted on to end at
>the same end point given the same starting point, regardless HOW they
>get there. In thermodynamics and in biology that is closely linked to the
>idea
> that EVERY system has a unique description called its "state" ( tell me
>the temperature , pressure, etc. and you have automatically said
>EVERYTHING to be said about the system). This is true for those models
>of systems which are idealized so much as to ignore interactions, etc.
>We might call them "simple" systems. Such systems do not really
>exist except as constructs in physics, economics, biology and other texts.
>Real systems (or COMPLEX systems) are not this way and ALL are influenced
>by how you get there (often profoundly influenced by how you start out...as
>in
>lock in).
In a message dated 96-05-03 11:48:11 EDT, Jeff P. gave the example of the
area under a given graph-path as a path-independent property:
>
>For this population of curves, the property of area is path-independe=
>nt. =20
>But notice that (for this set of curves) the property of curve length=
> is
>path dependent. Also, the amount of information needed to
>describe how to draw any particular curve is path dependent.=20
>
>For this population of curves, if you tabulate all the properties
>you can think of, you will find that most are path-dependent.=20
>As Don points out, path-independent properties are fairly rare
>among all possible properties. =20
>
>What is remarkable is that traditionally, science has focused on
>path-independent features of systems (when in fact, most
>features are path-dependent).=20
>
>
It seems that the thermodynamic properties of phase-space apply here- for a
given end-state there are many 'paths' that can lead to the state
(path-independence). Cumulative/aggregate properties are desirable for
experimentalists to the extent they *are* path independent, else we would be
stuck with an impossible search for the exact 'path' that led to the state.
>>P.S. I agree that genetic "lock-in" is an example of path dependence.=<<
Biology and other complex systems would then be path-dependent evolved
systems.
Yet it appears that some genetic 'solutions' arrive from multiple pathways,
inasmuch as the same solution seems to pop up in different organisms in
different environments and eras.
Also, I am uncomfortable with 'path-dependence' as a universal feature of
complex systems. It hearkens back to classical linear determinism (one fixed
state inevitably leads to another future state), which seems contrary to the
contemporary notion of emergent properties from complex systems. Of course,
this may be the perfect time to dispell my naivete about the matter :) !
-Mike Lash-