[From Bill Powers (2004.12.15.0450 MST)]
Note to Fred Nickols:
In your interchange with Martin Taylor, you understood the word "integrate"
differently from the way it was intended. The sense you used was that of
organizing into a whole, bringing together, which is the way neurologists
use the term. Martin meant the mathematical sense, which is "accumulation."
The output function integrates the error signal to produce the output
quantity, so if a constant error signal exists, the output quantity keeps
getting larger as time passes -- faster if the error signal increases,
slower if it decreases, and in the opposite direction if it reverses. Think
of the error signal as a stream of water from a spigot, and the output
quantity as the level of water in a bucket under the spigot (positive
values of error only in this case). The rate of rise of the water level is
proportional to the magnitude of the water flow, and the amount of water in
the bucket is the accumulated flow since the time the flow started (or the
bucket was last emptied). That is "integration" in the mathematical sense:
PS. A friend sent this bit of wisdom:
From: "Randy and Kathy Fischer" <firstname.lastname@example.org>
>Date: Tue, 14 Dec 2004 14:59:22 -0700
> U.S. Election Analysis
>In Two Sentences
>The Democrats' mistake was thinking that a disastrous war and national
>bankruptcy would be of concern to the electorate.
>The Republicans saw, correctly, that the chief concern of the electorate
>was to keep gay couples from having abortions.