[From Rick Marken (930406.2100)]
OK. I couldn't resist. Here is some more data for those
who savor detailed PCT. This is data from one run of
the "logic renunciator" which is a control system
simulation with a non-linear environment function between
o (the output of the control system) and p (the input).
Here's the data from a 5 second period of a simulation
(50 samples with dt = .1 sec). The first column is the
perceptual variable, the second column is the disturbance
and the third column is the output of the control system
(actually, -o so that the correlation between o and d will
be positive). The correlation between o and d is .27. The
rms deviation of p from the reference (zero) during this
period was .68 (less than 1 pixal).
p d o
-0.05115 72 55.372811
0.246705 75 55.619516
-0.311127 77 55.308389
0.462088 79 55.770477
-1.424896 80 54.345581
1.025085 82 55.370665
0.390295 84 55.760961
0.128121 86 55.889081
-0.186967 87 55.702114
1.54768 89 57.249795
-0.454676 90 56.795119
0.695761 91 57.49088
0.589501 92 58.080381
1.652194 94 59.732575
0.025205 95 59.757781
1.582707 96 61.340487
-0.304565 96 61.035922
1.783961 97 62.819884
1.257379 98 64.077263
1.243333 98 65.320596
1.672312 99 66.992908
1.190354 99 68.183262
2.179768 99 70.36303
1.195389 99 71.558418
2.396135 99 73.954554
2.85908 99 76.813634
2.214821 99 79.028455
3.375569 99 82.404024
3.411332 99 85.815356
3.603108 98 89.418464
4.110612 98 93.529077
4.406214 97 97.935291
4.92018 96 102.85547
6.515741 96 109.371211
6.409319 95 115.78053
7.164602 94 122.945133
7.167859 92 130.112991
9.028816 91 139.141807
2.340662 90 141.482468
-8.622903 89 132.859565
-12.644674 87 120.214891
-11.374062 86 108.840829
-10.691522 84 98.149308
-9.278856 82 88.870452
-7.981747 80 80.888705
-5.93314 79 74.955565
-5.451121 77 69.504444
-5.625154 75 63.879289
-5.29394 72 58.585349
-3.81754 70 54.767809
The outputs, o, are the actual outputs generated by the
control system during closed loop operation. These are
outputs based on the perceptual inputs, ie. o = o + ko (r-p)*dt.
Nevertheless, there outputs have a VERY weak relationship
to the disturbance (correlation between d and o = .27). If
these outputs are added to the disturebance values the level
of control (in terms of rms error) becomes MUCH worse -- by
orders of magnitude. Yet these are the outputs that should
be determined by the information about the disturbance that
somehow manifests itself in perception -- the information that
should make it possible to generate the outputs that counteract
the disturbance. Clearly, no such information has manifested
itself in this case -- yet there is nearly perfect control.
Magic? No. Just closed loop control of perception.
Now, on to sociology.
Best
Rick