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Connections between models and reality
Posted by John Gunkler on 3/10/2004
In Reply To:Connections between models and reality Posted by Steve Kipp on 3/9/2004
Steve Kipp writes: "I’m not sure I agree that you can’t directly measure flows (what about wind speed, electrical or liquid currents, births or deaths per year, kilometers per hour in a car, and so on?)"
This is a point I struggled with, too. But Jay Forrester is adamant about it. You cannot directly measure any flow. The reason, which has to do with the definition we use for "flow" in SD models, is a bit subtle but compelling. By definition, a flow is an amount of something that changes over time. You must have at least two measures of the amount (at two different times) in order to compute the change -- so, by definition, you cannot measure a flow instantaneously -- that is, with one measurement at one instant of time.
Now, we certainly can (and certainly do) measure flows over very short periods of time; and the way we measure some flows can make it seem as if we were measuring instantaneously (we look at the read-out from a wind gauge at one instant and we get a number) -- but if you look into how that reading came about, you'll always discover that there was a process that took some time (however small) to create the reading.
Part of what confused me, I think, was that we can (and do) provide a measure of flow at an instant of time. We can say, for example, that at a particular instant the wind speed was precisely Y (although doing so is a little more difficult than it may seem and may require evidence of the shape of the rate equation at that instant so we can interpolate a number between two measurements.) But that doesn't mean that we arrived at that number by taking one instantaneous measurement.
So, another way I came to look at this was to see that a rate is expressed as "amount per time unit." Now, take a look at the "time unit." Say it's a year (or an hour, or a month, or a second.) What is the rate per half "time unit?" How would you find out? Sure, it seems as if we look at the total number of births for the previous year and say that's the "annual birth rate." And it seems we looked at one instant of time. But did we? What was the "annual birth rate" figured from the number of births after exactly six months? Is it necessarily the same as the one calculated at the end of 12 months? No. So what, really, is the rate calculated at the end of 12 months? Isn't it an average of all the birth rates we saw during the year? That is, isn't it the average of the Jan. 1, 2, 3, ...,Dec. 30, 31 birth rates? And aren't each of those birth rates the average of the Midnight to 1 a.m., 1 - 2 a.m., etc., birth rates?
Forrester explicitly says that any rate is in reality the calculation of an average, over some period of time. So no rate can be instantaneously calculated
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