Differentials / Integrals --> The map is not the territory

This forum contains all archives from the SD Mailing list (go to http://www.systemdynamics.org/forum/ for more information). This is here as a read-only resource, please post any SD related questions to the SD Discussion forum.
Locked
"Finn Jackson"
Junior Member
Posts: 9
Joined: Fri Mar 29, 2002 3:39 am

Differentials / Integrals --> The map is not the territory

Post by "Finn Jackson" »

Ed Gallaher asked:
Can anyone provide examples that contradict Jays assertion?

Jay Forrester wrote:
"No where in nature or human affairs is a
true derivative to be found. Nature only integrates or accumulates.
No instrument can instantaneously measure a rate; all such
instruments contain some form of integration."

####################

On the one hand, Jay is correct simply by definition of the words he uses.

When he says "derivative" he means "time derivative".
So when he says "rate" he means "rate per time".
So when he says "no instrument can instantaneously measure a rate [per
time]", the response is "of course not, because in order to measure a rate
per time you have to have allow at least a little bit of time to pass (if
you want to measure the feathers per chicken you have to measure at least a
little bit of one chicken) ... in which case the measurement is no longer
instantaneous."

####################

But on the other hand, what about the red-shift of light from distant stars?

The frequency of the red-shifted light instantaneously measures our
relative speed of recession, and speed is the time-derivative of
distance).

(This Doppler Effect also applies to police sirens, car horns, jet planes,
racing cars... so it is not a one-off.)


####################

Whether or not we can find an exception to Jays rule, his important message
is surely to retain a focus on the real world, and the simple (accumulative)
ways in which it works.

Differential equations can be a useful construct, but once we start
introducing them it is easy to become lost in the beauty of our models for
their own sake.
We can then (as he tells us) deduce "that water flows from the faucet
because the water in the glass is rising, instead of the water flowing
because the level of water in the glass is not yet to the target value."


Our models are often useful and interesting maps of the way the real world
works.

But the map is not the territory.


(And if we want to know whether differential equations or integrals are "a
more fundamentally correct way of representing dynamic systems" then we have
to agree with Jay that "Integrations and the feedback around them are the
fundamental
structure of the real world.")



Finn Jackson
Finn.Jackson@Tangley.Com
Locked