[Martin Taylor 970428 10:30]
Bill Powers (970428.0645 MST)]
My only hangup is the idea that there is _mutual_ information in a
unidirectional relationship. I can see that while A is influencing B, you
can say that the state of A constitutes information about B (if the moon is
up there will be a tide in 6 hours), and that the state of B constitutes
information about _what A must have been_ (i.e., the high tide indicates
that the moon must have been up 6 hours earlier) -- if nothing else can
influence the water level. Both of these "informations" are really about the
influence of the moon on the tide. They imply nothing about the influence of
the tide on the moon, even though it is said that the tide contains
information about the moon.
Right. Actually, it's your own model that is bringing in the idea about
the moon influencing tide. My specification of the measures only allows
you to measure the midnight brightness of the moon in Arizona and the
6am level of water in a harbour somewhere. There's no statement that the
person doing the measuring has even heard of "tide" or the influence of
the moon on the ocean. There's only two sets of measurements linked one-to-one
by the day on which each measurement was made.
When you say the "informations" are "really about the influence of the
moon on the tide" you are taking the same position as the analyst of a
control loop who has the wiring diagram in hand while looking at the
waveform sample measurements. The analyst _knows_ which way the influences
work, and can say "it's really about ...".
I guess I am still wondering how the water level can give information about
the moon if it was raised by pumping.
It can't, and that was the whole point of the example. I used an extreme--
ridiculously extreme--example to show that forcing X to take on a value
would destroy the correlation when X in fact does not influence Y. The
correlation measure would hold if X were the only coherent influence on
Y and you manipulated X.
By judicious manipulation of the
pumping rate and direction, you could give the impression that the moon was
anywhere in its orbit, couldn't you?
Yes, and if you were trying to confuse an enemy who was relying on the water
height to determine the brightness of the moon, that might be what you
would do. But you'd have to be sure the enemy didn't know you were pumping,
interfering with the correlation that he had measured earlier. It's a
standard tactic of disinformation, to put some false data into a normally
reliable source. But it doesn't work if the enemy realizes that a novel
influence is being brought to bear.
ยทยทยท
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Dammit, Martin, go solve your puzzle for yourself. I'm just a distraction to
you.
In one sense, you are. But more importantly for me, I've learned more about
psychology from you in five years than I learned in the previous 35. (At
least _I_ think so, even if Rick doesn't 
I think I understand enough
control theory and PCT to make some theoretical contributions, and I think
that the informational approach is one fruitful direction among several. If
you came to understand it--or rather, to understand the way I look at it--
to the degree that you can rock me rather than puzzle me when you have a
complaint or a problem, any contribution from the informational approach
would be _much_ more secure than if I just try to develop it on my own.
At present, most of the "distraction" comes from my spending time trying to
deal with the basics. That's only a problem if there's no progress. And I
do see signs of progress. I hope you will continue to be a distraction. And
a critical collaborator.
Martin