[From Rick Marken (920508 8:30)]
Thanks to all who have commented on the paper so far.
Special thanks to Bruce Nevin (Fri 92048 08:04:11):
I agree with all your suggestions -- they are excellent
and I will incorporate them all (or, at least, those that
I am not to lazy to do, but you already did most of the
work for me -- thank you).
In a personal note, Gary Cziko asked:
Could you please take me by the hand and show how you got from equation (2)
to (3)? I know what it means to solve simultaneous equations, but I'm
having trouble getting the anwer in the form that you have which simplifies
so nicely when K.o >> K.f and K.o >>1.
I also suggest that you post this to the net.
OK.
(1) r = k.o(s*-s) and (2) s=k.f(r) + k.e(d)
substituting (2) into (1) for s we get
r = k.o (s* - [k.f(r) + k.e(d)])
multiply through by k.o giving
r = k.o (s*) - k.o k.f(r) - k.o k.e (d)
Now put the terms with r together on the left so:
r + k.o k.f (r) = k.o (s*) - k.o k.e (d)
Now the tricky part. Cancel r out of the separate terms on the left so
r (1 + k.o k.f) = k.o (s*) - k.o k.e (d)
Finally, divide both sides by (1 + k.o k.f) giving equation (3)
in the paper
r = k.o/(1+k.o k.f) s* - (k.o k.e)/ ( 1 + k.o k.f) d
Now, if k.o is VERY large (say, 100,000) and k.f is relatively small
(say, 100) then the ratio
k.o/(1 + k.o k.f) is approximately 1. (100000/100101)
and the ratio
(k.o k.e)/ (1 + k.o k.f) is approximately k.e/k.f since
(100000*k.e)/(100001*k.f) = approx. k.e/k.f
soooo:
r = s* - (k.e/k.f) d
A quick note on "social control";
I think I have been making the mistake of sounding like I believe
that people CAN control other people -- and shouldn't. What I mean
is that people TRY to get other people to act as they (the would-be
controller) wants. Of course, the controller is not REALLY controlling;
but the controller is acting as though he/she can control (and it looks
enough like control so that people imagine that it can be done). The
fact is, of course, that if you REALLY try to control someone (make
them do behavior X, no matter what) than you are simply placing yourself
in conflict with that other control system. Most of what passes for social
control is just social "influence" (manipulating a side effect of control,
for example, by disturbing a controlled variable). When the controller
becomes implacable (because the controllee fails to continue being
influenced) then you get problems.
To Tom Bourbon (if he is around) -- What a wonderful forward to LCS II.
The only thing wrong with it is that it's MUCH better than my forward
to LCS I.
Oh, and Bill, the book's pretty good too (like, INCREDIBLE!).
Best regards
Rick
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Richard S. Marken USMail: 10459 Holman Ave
The Aerospace Corporation Los Angeles, CA 90024
Internet:marken@aerospace.aero.org
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