Re: Gedanken Graphs
Calvin B. DeWitt (cbdewitt@facstaff.wisc.edu)
Sat, 29 Jun 1996 09:06:42 -0500>[This is a repeat transmission due to some transmissions having been
>trunkated.]
>
>Date: Fri, 28 Jun 1996 09:51:36 -0500
>To: asa@calvin.edu
>From: "Calvin B. DeWitt" <cbdewitt@facstaff.wisc.edu>
>Subject: Gedanken Graphs
>
>
>Dean Ohlman uses the example of a bent walking stick in his recent
communication.
>
>I present below another way of getting at what he has written:
>
>Here is a curve showing the response of a critically-damped system to a
disturbance-- there is no "over-shoot" and thus it takes a long time for the
system to come into line with the horizontal line.>
>
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time------>
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>Here is a curve showing the same for a system with approximately 64% of
"critical amping"-- there is "over-shoot" with the result that the system
comes into allignment much mre quickly than it would for the case of
critical damping.
>
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time------>
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>Here, for reference, are Dean's thoughts:
>
>>One final analogy. As I hobby I make hiking staffs (staves?). When a young
>>sapling dries it often bows. I have learned now how to heat a bowed staff and
>>with foot pressure make it straight. What is required is when the staff is
>>hot you must press it back well beyond the center line in the opposite direc-
>>tion almost as far as it was out of alignment the other way. When it springs
>>back and is then cooled down, it stays straight. The analogy almost says it
>>without explanation in reference to our behavior and rhetoric concerning
>>environmental degradation. I am willing to allow some exaggeration beyond the
>>center line in the opposite direction so that when things cool down, you have
>>them straight. For instance, I think it may be wise to declare a complete
>>moratorium on harvesting timber on public lands, not because I think we should
>>not cut trees, but in order to stop all abuse instantly and force the forest
>>products industry to prove they can do things right on their own land before
>>they are ever allowed back into the public forest. This is what I think is
>>bowing the staff beyond the center line in order for it to come back to
>>center. We don't have to resort to lying or misrepresentation, but we can be
>>bold and decisive and require some tough discipline in order to set things
>>right again. After all we usually learn more from our economic setbacks than
>>we do from our days of extravagance.
>>
>>Dean Ohlman
>>Cornerstone College