Consider two points on the Cartesian plane. One at (0,0) and
another point at (1,1). Consider the exercise of drawing curves
connecting the two points so that the area under the curve (and
over the x-axis) equals =AB. =20
Note that one possible curve (fitting these criteria) is drawing a
straight line between the points. Another curve would be
pushing the lower part of the line in a bit (reducing the area)
and pushing the upper part of the line out a bit (restoring the
area back to =AB). This would result in some kind of sigmoid
shape. By following this kind of strategy, there would be any
number of curves or paths that could be drawn between the
points that had the same area underneath them. =20
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
Jeff Prideaux
P.S. I agree that genetic "lock-in" is an example of path dependence=
..