# Allan Randall's proposed experiment

[From Bill Powers (930329.1930 MST)]

This day is never going to end.

Allan Randall (930329.1700 EST) --

We would first run the control system under normal closed-loop
conditions, recording disturbance and output, and noting that
the disturbance is almost perfectly countered at the output.
The control system's perceptual line would then be cut, and
superceded by a new experimental line. All possible perceptual
inputs would then be presented, one at a time, starting with
the shortest and working up. This would be repeated until the
disturbance recorded from the first experiment appears on the
output.

This is not very practical. The disturbances we use range in
value from about -350 to 350, or roughly a 10-bit number. The
outputs have, of course, about the same range. The range of
deviations of the controlled quantity, the input, is about 5% of
this range, with a moderately difficult disturbance (medium
bandwidth). So the record of inputs will be representable by a
string of 5-bit numbers.

During a one-minute run on a VGA screen, we record 1800
consecutive 5-bit numbers for the input deviations. In order to
single 5-bit number, cycling through all 32 possibilities, then
do the same for the next number, and so forth until you reached a
string of 1800 5-bit numbers. To reproduce an arbitrary
disturbance waveform in this way you would have to try, on the
average, half of the possible strings of 1800 numbers, which
amounts to something like (32^1800)/2 possibilities. To say the
least, the chances are small that you would ever run across the
input that matches the waveform seen with the loop closed. Even
if every proton in the universe were a Cray computer. If I
remember correctly, there are only an estimated 10^72 protons in
the universe.

The other problem is that if you cut the input line and start
feeding the subject aribtrary inputs, you will cease immediately
to get tracking behavior -- just as soon as the subject realizes
that the control handle is no longer affecting the input.

So I don't think your proposed experiment can be done, unless I
have misunderstood it.

Best,

Bill P.

[Allan Randall (930330.1330 EST)]

Bill Powers (930329.1930 MST) writes:

>...All possible perceptual
>inputs would then be presented, one at a time, starting with
>the shortest and working up...
...To reproduce an arbitrary
disturbance waveform in this way you would have to try, on the
average, half of the possible strings of 1800 numbers, which
amounts to something like (32^1800)/2 possibilities. ... If I
remember correctly, there are only an estimated 10^72 protons in
the universe.

Yes, to do this experiment for real would require either a very
small control experiment, or some very big simplifying assumptions.
I was hoping that we could agree on the outcome without the need to
actually do the experiment. The number of possible programs for
most languages you can think of grows exponentially with the
program size. This, however, is a legitimate problem in trying to
calculate the "true entropy" of something. If you want to be sure
you have the "minimal program" for something, you will have to
check all programs that are shorter and make sure none of them
produce the same output. Nonetheless, for a sufficiently restricted
control task, such an experiment could be done.

However, I do not see why we should need to do the experiment at
all (or at least not any of it requiring exponential search).
Showing that H(D|P) = 0 is trivial and involves no exponential growth.
One of the assumptions was that the original experiment produced
output with 100% of the information about D. Thus, computing H(D|P)
will *exactly* replicate the output of the first experiment on the
first try: P0. So we can conclude that H(D|P) = 0 without actually
doing the experiment. Rick claims that H(D) = H(D|P), so it follows
mathematically that H(D)=0, which is equivalent to blind control. If
we can all agree that blind control is not an interesting case of
control, there is no need to compute H(D). Rick's claim has been
disproved before the experiment got past the starting gate. We don't
actually get around to doing any exponential search of P-space. In
other words, actually doing the experiment is mostly redundant.
The main point of the experiment is that it shows Rick's claim to
be either logically unsound *or* a claim for blind control.

The other problem is that if you cut the input line and start
feeding the subject aribtrary inputs, you will cease immediately
to get tracking behavior -- just as soon as the subject realizes
that the control handle is no longer affecting the input.

I think you misunderstood on this point. I was talking about a simple
control system completely under our control - a small simulation
on a computer - not a real world experiment with human subjects. That
would be most impractical (although still possible as a thought
experiment).

ยทยทยท

-----------------------------------------
Allan Randall, randall@dciem.dciem.dnd.ca
NTT Systems, Inc.
Toronto, ON

[From Rick Marken (930330.1130)]

Allan Randall (930330.1330 EST)--

I was hoping that we could agree on the outcome without the need to
actually do the experiment.

A very common sentiment when the cause-effect crowd meets the PCT
loonies. Hang in there; you're in for some BIG surprises when you
start to run the experiments.

Showing that H(D|P) = 0 is trivial and involves no exponential
growth.

Well, I think you'll find showing this to be quite NON-trivial. Try
the experiment!

Rick's claim has been
disproved before the experiment got past the starting gate.

That would make things a lot easier for your horse, indeed. But
don't scratch me yet. Just fire up the ol' simulator and see
what she does. Ol' "Stewball" Marken might surprise you.

Best

Rick ("There's no information about disturbances in controlled
perceptions") Marken