[Martin Taylor 2017.08.28.13.48]
[From Erling Jorgensen (2017.08.28 1255 EDT)]
Martin Taylor 2017.08.27.08.55
Hi Martin,
EJ: I'm still confused about your assertion that the
“true” values of either references or perceptions can be
negative in the nervous system. You state it correctly in
this portion of this post:
>MT: Normal two-way control has the possibility that the
perception might be either greater or less than the reference
value. Since it is impossible for the number of firings of a
neuron to be negative, the only way for the comparator to send
a negative value to the output function is to send a positive
signal that terminates on inhibitory synapses.
EJ: However, you then go back to asserting that negative
values need to be represented as signals, apart from what is
happening via the inhibitory synapses:
The synapses are inhibitory BECAUSE the positive signals represent
negative values. There’s no “apart from”.
>MT: The added complexity of my newer diagram in the
thread “The hierarchy (was Re: Dealing with the limitation of
only positive neural signals)”, as opposed to the earlier
“top-left quadrant of Figure 4.6” is because of the need to
accommodate signal paths that represent negative possible
values for the perception and the reference.
EJ: I'm reproducing that portion of your improved diagram
for clarity’s sake, but I still take issue with it:
[Martin Taylor 2017.08.26.09.46]
EJ: I agree that the (-r+p) output needs to be routed
through an inhibitory synapse at the next step in the
equation, to preserve negative feedback control. But having
that represented as -r in a composite diagram like this ends
up misrepresenting the algebra, as if this “true” negative
signal can then be reversed by the inhibition (as in the upper
of these two units) into a net positive signal.
??? I have no idea what you are saying here. There's no "reversal by
inhibition" anywhere. Inhibition just is treated as though it
subtracts the positive value on the signal path from whatever other
input there may be to the unit to which it synapses
That's counting the negative signs twice. And it arises,
to my way of thinking, because of erroneously labeling a
signal path as negative.
How "erroneous"? What would you prefer the label to be? All it means
is “this is the path that is used when a lower-level process
produces a number that algebraically should be negative”, but I’m
not going to write all that on the figure. I think a simple “-” is
quite adequate. You don’t, so I presume you have a better
suggestion. What? I suppose I could write “p-” rather than “-p”, but
I prefer the latter, because it seems more clearly to suggest that
the value on the line is the negative of the negative value.
EJ: I still say we only need that initial upper left
quadrant of your diagram (without the need for the headings
about positive value, because all long-range neural signals
are positive), reproduced here:
EJ: You go on to discuss these signals in terms of
relationship perceptions, but I believe there are better ways
to model a function representing a relationship, than adding
minus signs to signal paths.
Let's just do a little analysis here. Suppose the perceptual
function of this control unit produces a relationship that the
external analyst would label “Above-Below”. When X is above Y, the
algebraic result of the perceptual function is positive, and that is
sent to the comparator as a positive value. This “upper-left
quadrant” diagram produces an inhibitory input (subtraction) for the
upper unit and an excitatory input (addition) for the lower unit.
When X is below Y the algebraic result of the perceptual function is
negative, but that can’t be sent as a negative value. It must be
sent as a positive value, the absolute value of the difference. If
it sent over the same path, it will produce the same result for both
locations of Y. So it must be sent over a different path in some
form. The simplest form in which to send it is its absolute value,
and that is what I have been assuming is sent.
Give these some numbers to make it more concrete. For the upper-left
quadrant as sufficient in itself: r=3, p=|±4|. The “r” value
indicates that X is supposed to be above Y by 3 units. If X is above
Y by 4 units (p=4), r-p = -1, yielding an output of 1 from the lower
half-comparator and zero from the higher, which is correct. Y is one
unit too low. If Y is higher than X by 4 units (p=-4, |p|=4), we get
the same result, whereas the external analyst who can see both X and
Y can see that Y is now seven units too high, being 4 units above X
when the reference is for it to be 3 units below X.
Now consider the "double-double" diagram above with separate paths
labelled “p”, “-p”, “r” and “-r”. This time, when X is above Y
there is a positive value on the path labelled “p”, and zero on the
path marked “-p”. When Y is above X, there is a positive value on
the path labelled “-p” and zero on the path marked “p”. Using the
same numbers as before, r = 3, “p” = 4, and “-p” = 0 when Y is low,
and r = 3, “p” = 0, and “-p” = 4 when Y is high. The outputs from
the two half-comparators are the same as before when “p” > 0, but
when “p”=0 and “-p” = 4, they are not. Now the upper half-comparator
gives a correct output of 7 and the lower gives zero.
You can do the same kind of analysis with the reference location for
Y being either above or below X (“-r” positive, “r” zero in the
latter case). You do need all four quadrants of my original Figure
4.6. All the connections from that figure are shown together in the
new “double-double” figure above.
···
However, you say you think there are better ways of representing a
relationship than by having a perceptual function that produces
positive values on just one of two signal paths that represent the
different directions in which the two related values might differ.
I’d be interested in how else it might be done. I can imagine
providing two different perceptual functions, one for each direction
of difference, but that would still result in a +p and a -p signal
path, both of which would have to be compared with the same
reference value, which might be of either effective sign (effective
means terminating on excitatory or inhibitory synapses).
[Not relevant for this discussion, but possibly relevant later, the
“double-double” figure can be generalized to provide an avoidance
comparator function. Possibly in a different thread, not here.]
Martin
Martin