Information carried by perception, part I

[From Rick Marken (960628.1330)]

Me:

The whole notion of "information in perception" assumes that perception
exists to "inform" or "tell" the system about the world beyond the senses.

Martin Taylor (960628 15:20) --

If you start by insisting on believing this, you will never come close
to understanding what "information carried by perception" is all about.

A much better place to start is by thinking of information as a kind of
analogue of correlation, or something like that.

Ok. Let me give it a try. Here's what I understand "information carried by
perception" to be all about. I'll use the little diagram below:

                                           Noise
                                          Source
x.1 |
x.2 v
x.3 ------>Sensory---C(x.i)-->Neural--->N[C(x.i)] --->Brain---->Perception
. Encoder Channel Decoder or
. Action
. x.i'
x.n

The x.i on the left is a set of possible environmental events such as a set
of differennt letters. The environmental event that actually occurs is
transformed into coded form, C(x.i), by a sensory encoder (like the retina).
The coded "message", which could be called a "perception", is carried along
a neuron (the neural channel) to its destination. Noise may be added to the
message as it travels along the channel so the message becomes a noisy code
of the environmental event, N[C(x.i)]. This noisy code is the "decoded" in
the brain (the reciever) where it becomes a percpetual experience (a
perception of a letter, say) or an action (saying what letter occurs). The
decoded version of the message, x.i', is the brain's idea of which event
occurred in the environment.

The information about x.i that is carried (transmitted) by the neural channel
is measured in terms of the conditional probabiliy (over many trials) that
x.i' equals x.i. Indeed, the measure of treansmitted information, T(x;x'),
is proportional to

SUM.i(log2[sum(p(x.i|y.i))/sum(p(x.i)])

according to Sheridan and Ferrell (1974). T(x;x') could also be measured in
terms of the correlation between x.i and x.i'. The higher the correlation,
the greater the amount of information transmitted by the channel about x.i by
x.i'. In a perfect, noiseless channel with proper encoding (with distinct
codes for all x.i) the correlation between x.i and x.i' will be 1.0.

So the term "information carried by perception" refers to the measured
correlation between the events that actually occur (x.i) and the events that
are experienced or reported (x.i') by the subject.

I suppose that the word "perception" in PCT corresponds to the coded neural
representation, C(x.i), of x.i in the information diagram above. This neural
signal carries a coded representation of the x.i that actually occurred in
the environment to some "receiver". I don't know what you think the
"reciever" is in a control system. But we can worry about this later. Let's
just see if this representation of "information carried by perception" seems
OK to you.

Best

Claude Marken