When is reorganization?

[From Bill Powers (980416.0332 MDT)]

When I learned long division, I learned it as a program. First, set up the
problem in a standard configuration:

···

_____
      12 / 637

Then, starting with the leftmost digits of the dividend, find the number
that is greater than the divisor (in this case, 63). Guess how many times
the divisor will go into that number (here, 5), and write that number down
in the "appropriate" position:

          5
         _____
      12/637
         60
         ___
          37

... and so on. The "and so on" shows us that we're dealing with a program.

From here on, we can repeat the same operations and tests until the result

comes out even or we have as much accuracy as we want.

Obviously, I had to reorganize to learn this program. I was given endless
pairs of numbers and told to divide one by the other using long division,
so I had to go through the program again and again, gradually learning how
to estimate the trial divisors and how to "bring down" the numbers
correctly. I had to make mistakes, and get punished for making them (as if
the mistakes weren't embarrassing enough), and eventually install this
program in my brain so I could apply it to any pairs of numbers, including
those with decimal fractions.

A while later, I learned a similar procedure for taking square roots. It
involved "bringing down" pairs of digits, and a lot of other processes
similar to those in long division. But I don't remember those processes any
more, because I learned a simpler way, Newton's method, and more important,
I learned the _principle_ behind Newton's method, so I could recreate it if
I forgot it. The principle was successive approximation. Basically, I
wanted a number R such that R*R = N, N being the number I want the square
root of and R being the root. This involves another principle: if R1*R2 =
N, then a closer approximation to the trial root can be found from (R1 +
R2)/2. Given a "randomly" chosen trial root R1, R2 then can be found from
R2 = N/R1, so

R1(new) = (R1(old) + N/R1(old))/2,

... and there's the program. Just keep running it over and over until
R1(new) stops changing by a significant amount, and R1 will be the square
root of N.

Notice that I could simply teach you that program, and after you had
learned it you would "know how to take a square root using Newton's method"
just as you can "know how to do long division" without understanding the
principle. But if you forgot it, you would have to find me and ask me to
remind you of it, and you would have to relearn it. You would be dependent
on me and on re-memorizing the program, because of not knowing the
principle of successive approximation that's behind it. If you couldn't
find me, you'd just have to experiment and rediscover the program by trial
and error -- i.e., reorganization.

Learning that principle also required reorganization, but reorganization at
a higher level. The big advantage of learning at the higher level is that
you could then recreate the program _without reorganizing_. In fact, if you
forgot the program for long division, you could apply the same principle to
recreate that program, too, because the long division procedure is also a
method of successive approximation. Later on, you would find that the same
principle is part of the concept of a control system, so if you ever forgot
how a control system works, you could recreate that, too, with the help of
the same principle.

This longish example illustrates a number of principles of reorganization.

First, if you have a systematic way to achieve a result you don't need the
less efficient method of reorganization to achieve it. In fact, because the
systematic method is installed as an automatic control system, it will
correct errors as soon as they appear, leaving insufficient error to turn
on the reorganizing process.

Second, reorganizing at a higher level, if possible, is more useful than
reorganizing at a lower level. In some respects, the higher level system
can "work out" what is needed at the lower level without the need for rote
memorization or (random) trial-and-error. New situations can be dealt with
without the need for reorganization.

And third, you use reorganization only when there is NO systematic way to
get what you want. This is why reorganization has to be a random process --
random meaning "not according to any known systematic scheme." If you have
tried all existing systematic schemes and none of them corrects the error,
all that is left is a non-systematic -- random -- scheme. That is why, in
PCT, the output of the reorganizing system is a random process.

So -- when does reorganization occur? Apparently, whenever there is a
perception that we want to recreate, and we have no ready-made method of
recreating it.

All this is simply a description of what seems to happen. It's not a model.
The reorganizing system, with its intrinsic variables, reference signals,
comparators, and output functions is a model devised to explain what we see
happening.
---------------------------------------
Peter Burke has asked me to look at the paper with the following URL:

http://burkep.libarts.wsu.edu/Papers/Identity%20Levels%20and%20Agency.pdf

It is a study of the program and principle levels in 30 young mothers. It
shows how the interview technique can be used with profit in studying
higher-level organizations. I think it's a ground-breaking paper.

Best,

Bill P.

1 Like

[From Bruce Gregory (980416.1410 EDT)]

Bill Powers (980416.0332 MDT)

So -- when does reorganization occur? Apparently, whenever there is a
perception that we want to recreate, and we have no ready-made method of
recreating it.

All this is simply a description of what seems to happen. It's
not a model.
The reorganizing system, with its intrinsic variables, reference signals,
comparators, and output functions is a model devised to explain
what we see
happening.

Thanks, Bill. A very helpful post.

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[From Bruce Gregory (980417.1322 EDT)]

Bill Powers (980416.0332 MDT)

First, if you have a systematic way to achieve a result you don't need the
less efficient method of reorganization to achieve it. In fact,
because the
systematic method is installed as an automatic control system, it will
correct errors as soon as they appear, leaving insufficient error to turn
on the reorganizing process.

Second, reorganizing at a higher level, if possible, is more useful than
reorganizing at a lower level. In some respects, the higher level system
can "work out" what is needed at the lower level without the need for rote
memorization or (random) trial-and-error. New situations can be dealt with
without the need for reorganization.

I now see that much of what I have been trying to do in teaching has been to
get the students to restructure their perceptual hierarchy at the highest
levels--I want them to control based on a principle that I identify as "the
nature of science". The students can listen to what I say, but simply
repeating it, or even believing it, does not make it a principle in the HPCT
sense. (I note that the Test provides an elegant way to distinguish between
beliefs and principles!) Although this has been my agenda, it has been
hidden in an important sense. As a result, much of what happens in _my_
classroom never gets translated into any kind of practice in _their_
classrooms. Their high-order control structures remain unaltered. If I want
them to alter the way they practice, I will have to invite them to change
the way they perceive science at the level of principles. This is surely
asking a great deal of them. Probably asking too much for many of them.
Adopting a new principle has effects that propagate through much of the
hierarchy -- often with unexpected and not always pleasant results.

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