Bad math (repost)

[From Bruce Abbott (960117.0845)]

I sent the following out yesterday at 2 pm but it seems to have gotten lost
in cyberspace, so here is the repost.

[From Bruce Abbott (960116.1410 EST)]

Rick Marken (960116.0800) --

Bill Powers (960116.0500 MST)

No matter how you think about it, o + k.2i - o is just k2.i.

You've left out the slowing factor,

Oops. So my simulation is a proportional rather than an integral system. As I
said in the part of the post that you didn't scan because of your compiler
policy, I think in way over my head (obviously, since I didn't notice that
o + k.2i - o = k2.i).

It's worse that that, Rick. Without the slowing factor it isn't even a
simulation of a closed loop. All you've done is iterate the same pair of
equations I presented and, as you pointed out, this does not give a
closed-loop solution. In effect, you've made the same mistake I did.

Gotcha back. Obviously, you are just trying to control for the perception
that PCT and conventional psychology are compatible, by failing to grasp the
essential difference between an open and closed loop. (;->

I think the relevant points in this discussion are:

1. X(n) = g X(n-k) does not describe a closed loop system and

2. When loop gain in a positive feedback system is >= 1.0 the system becomes

Do these statements make it through the first pass?

Yes, but I don't think they are currently being disputed, either.

(1) X(n) = g*X(n-k) by itself is a spiral, not a closed loop. It can be made
     to behave like a closed loop by adding an integrating output with a
     factor s such that 0 < s < 1.0:

     X(n) = X(n-1) + s*[(g*X(n-1) - X(n-1)]

(2) No one here has disagreed with statement #2.