Probability

[From Chris Cherpas (970109.1550 PT)]
  re:[Martin Taylor 970109 10:50] and [Bill Powers (970107.1500 MST)]

Powers -

To me, likelihood and frequency of occurrance are the same thing.

Taylor --

Whereas, to me, past frequency of occurrence is just one of the ways you have
developed your perceived likelihood of whatever it is occurring the _next_ time
the appropriate situation >arises.

cc:
Perceiving frequency is just perceiving frequency. Frequency is just another
observed "fact" or piece of information, having no special epistemological
status than the occurrence (I prefer Martin's spelling!-)) of the now-famous
"single event."

Sure, as your sample size gets bigger and bigger, you expect the [relative]
frequency to converge to some probability distribution that may serve as a
reference, but you can never collect enough evidence to be able to say that my
perception of the probability distribution is now "objective reality" (but,
then, I don't think the people on CSGNet need to be reminded of that).

PCT Questions:
1. Is "frequency" a crucial part of the PCT model of reorganization?
[rhetorical, I assume no.]

2. Could the reorganization model be said to resemble a probabilistic
conditionalization/revision process (Bayesian learning)? In other words, is
what's going on between relatively stable organizations characterizable
probabilistically or not?

3. Could rationalizing the ever-famous Test as a probabilistic revision process
help make administering the Test more efficient? Of course, you would still
want to show how the rationalization itself involves program- and other-level
perceptual control.

Powers -

I see no way to apply such measures to a single event, just as you can't apply
the concept of pressure to a single molecule of air.

Taylor --

Bad analogy.

Powers -

I guess I'm trying to persuade you that it is reasonable to perceive
probabilities as aggregate measures, but not as measures of single events.

Taylor -

I see it as reasonable that the perception of probability can be (but is not
necessarily) derived from observations of aggregate events, though it can apply
_only_ to single events.

cc:
Why can't I bet on a particular outcome being a given frequency being observed?
In that case, the "event" is simply an observed frequency.

Actually, contrasting different levels of scope or aggregation may reveal the
most important contribution of the discipline of probability (forget the
classical dice-throwing trivia for a moment): it's to stabilize some point of
view during the process of reconciling relatively well-established macro- and
micro-theories which are not coherent, to find coherence "in the meantime" while
you try to figure out some deterministic scheme/perception to control for that
is all-encompassing. I'm assuming that in general the references you want your
inputs to match are themselves deterministic/scalar (?) in most practical
matters (...for entertainment, you might want to be surprised more).

Taylor -

Only after the theorists got busy was it likely that people started to be
trained to look at >probability as you do--as some property of masses of
identical events (a ludicrous concept in itself, considering that no event is
ever repeated, and nor are the circumstances surrounding two events).

cc:
Identical, no. That is absurd. _Exchangeable_ with respect to some purpose,
yes. I think Martin's been saying this all along: it always comes down to what
you're willing to consider exchangeable from the point of view of perceived
value or degree to which some purpose is fulfilled, where it's the cost of a
penny or the time spent on a theory that seems to go nowhere. (Gertrude Stein
might have said a dollar is not a dollar is not a dollar, whereas Shakespeare's
rose smelling as sweet says something about exchangeability.)

Powers -

Most of experience, however, doesn't come packaged in events. Even if you look
at an event from >a different perspective, the world is continuous; few events
happen at a single instant of time, like a firecracker going off.

cc:
A speculation: I'd like to propose that the event level may be especially suited
for (category-level?) representations to be shared, verified, and/or challenged
socially and culturally. Perhaps enduring/public/external representations of
events are easily agreed-to or compared. I've noticed that people can even
agree to talk about the entire universe as an event (with lots of sub-events
going on between beginning and end) without feeling too uncomfortable, which
attests to events as being metaphorically rather yeasty. Again, it seems to
depend on your purposes. Perhaps cultural contingencies, cultural discourses,
social designations, and collectively controlled perceptions of social activity
(to use some categories discussed in McClelland, 1996), tend to get framed in
event language and tend to endure and grow relatively coherently by controlling
for event perceptions amongst those us the human tribe. It seems to
important in social/cultural contexts that we agree on such-an-such an event.
Maybe the Test can be performed more easily on event perceptions.

Of course, this event-focus in the social and cultural spheres may reflect old-
time views of cause and effect which we will eventually outgrow, so to speak.
Enlighten me.

Best regards,
cc

*from Tracy Harms 1997;01,09.19:00 MST

Bill Powers (970107.1500 MST)

To me, likelihood and frequency of occurrance are the same thing.

Not so to me -- not at all. However, I really like your analogy with air
pressure.

Chris Cherpas (970109.1550 PT)

...
Sure, as your sample size gets bigger and bigger, you expect the [relative]
frequency to converge to some probability distribution that may serve as a
reference, but you can never collect enough evidence to be able to say that my
perception of the probability distribution is now "objective reality" (but,
then, I don't think the people on CSGNet need to be reminded of that).

While it is pointless attempting to justify such claims by collection of
evidence, once we abandon that goal we may indeed say that a claim
communicates an objective fact of reality. In saying this we might be
wrong, but we might perhaps be right.

Tracy

[From Bill Powers (970109.2010 MST)]

Chris Cherpas (970109.1550 PT)--

Powers -

To me, likelihood and frequency of occurrance are the same thing.

Taylor --

Whereas, to me, past frequency of occurrence is just one of the ways you
have developed your perceived likelihood of whatever it is occurring the
_next_ time the appropriate situation >arises.

cc:
Perceiving frequency is just perceiving frequency. Frequency is just
another observed "fact" or piece of information, having no special
epistemological status than the occurrence (I prefer Martin's spelling!-))
of the now-famous "single event."

Now that I've looked in the dictionary I prefer it, too. A natural mistake,
harumph. The e is only a knight's move from the a, efter ell. Not going to
let me get away with that? Ah, well.

Sure, as your sample size gets bigger and bigger, you expect the
[relative] frequency to converge to some probability distribution that
may serve as a reference, but you can never collect enough evidence to be
able to say that my perception of the probability distribution is now
"objective reality" (but, then, I don't think the people on CSGNet need to
be reminded of that).

Right, I think that question's settled. It seems to me, though, that
probability is entering in two different roles in this conversation. In one
role, it's the basis for identifying a perception or making a prediction.
It's taken as given, as part of the nature of an experience, so we can ask
"what is the probability that the blur I'm seeing is a cat?" Martin wants to
treat all perceptions in terms of probabilities. If we stop there, we have
to control on the basis of this uncertain perception, making a bet as it
were and acting according to the bet. In the other role, the probability
itself is a perception to be controlled in its own right. Instead of making
the bet, we act to change the odds. We put on our glasses, turn on the
lights, and move closer to the thing, changing it from a blur to a clear
image of either a cat or something else. Then, when we act, a bet is no
longer necessary (that is, nobody would bet against us). We pick up the
galosh lying by the sofa and put it with the other galosh instead of asking
the butler to put it outside for the night.

I think that this difference is largely a matter of how we have learned to
deal with uncertainty, once we have developed systems of a high enough level
to name such a thing. My recurring complaint about psyschology is that
having found the predictions of accepted theories to entail a rather large
margin of uncertainty, psychologists have simply accepted this uncertainty
as a fact of life and have adapted their thinking and their methods to its
apparently unavoidable existence. My view has always been that a science
that tries to operate in the presence of that much uncertainty can't really
be a science; that what is required is to adjust the theories to eliminate,
as far as possible, the uncertainties. When you've put on the right glasses,
turned on the appropriate light, and looked more closely at the subject
matter, it may prove to appear considerably less uncertain than before.

PCT Questions:

1. Is "frequency" a crucial part of the PCT model of reorganization?

[rhetorical, I assume no.]

2. Could the reorganization model be said to resemble a probabilistic
conditionalization/revision process (Bayesian learning)? In other words,
is what's going on between relatively stable organizations characterizable
probabilistically or not?

Well, you've just demonstrated that it can be said to be whatever you said,
not that I know what that is. If you're suggesting that the _mechanism_ of
reorganization includes repetitive calculations of conditional probabilities
with revisions based on interim outcomes, I would say unequivocally, no. How
we _characterize_ things doesn't need to have anything to do with how they
actually work. Characterizations are generally attempts to force-fit ideas
that don't really belong together. You could characterize an automobile as a
means of minimizing the space-time incongruities between the existential and
the conceivable, but that would be your problem to figure out, not that of
anyone driving somewhere in a car.

3. Could rationalizing the ever-famous Test as a probabilistic revision
process help make administering the Test more efficient?

I don't think so. On the other hand, it might. And on the third hand,
rationalizing it that way might change how we view it, but not how we do it.

Powers -

I see no way to apply such measures to a single event, just as you can't
apply the concept of pressure to a single molecule of air.

Taylor --

Bad analogy.

Powers -

I guess I'm trying to persuade you that it is reasonable to perceive
probabilities as aggregate measures, but not as measures of single events.

Taylor -

I see it as reasonable that the perception of probability can be (but is
not necessarily) derived from observations of aggregate events, though it
can apply _only_ to single events.

cc:
Why can't I bet on a particular outcome being a given frequency being
observed? In that case, the "event" is simply an observed frequency.

A steady continuous frequency is not an event, is it?

Actually, contrasting different levels of scope or aggregation may reveal
the most important contribution of the discipline of probability (forget
the classical dice-throwing trivia for a moment): it's to stabilize some
point of view during the process of reconciling relatively
well-established macro- and micro-theories which are not coherent, to find
coherence "in the meantime" while you try to figure out some deterministic
scheme/perception to control for that is all-encompassing.

Chris, there's just GOT to be a simpler way to say that. I'll wait until you
find it.

Powers -

Most of experience, however, doesn't come packaged in events. Even if you
look at an event from >a different perspective, the world is continuous;
few events happen at a single instant of time, like a firecracker going >>off.

cc:
A speculation: I'd like to propose that the event level may be especially
suited for (category-level?) representations to be shared, verified,
and/or challenged socially and culturally.

I think you have some narrow range of categories in mind. What about the
category we call "above?" What about "green?" What about "moving?" What
about "bright?" When we speak we speak in categories, no matter what level
of experience we're talking about. What's so special about the "event" level?

Perhaps enduring/public/external representations of
events are easily agreed-to or compared.

In the sound that a clock makes, what events can you perceive? Do you
perceive tic-toc, or toc-tic? Isn't it hard to understand a spoken foreign
language because we haven't learned to split the continuous flow of sound
into the word-events that correspond to what we would read? I don't see that
events are any easier to agree about than colors or meter readings.

I've noticed that people can even
agree to talk about the entire universe as an event (with lots of
sub-events going on between beginning and end) without feeling too
uncomfortable, which
attests to events as being metaphorically rather yeasty.

Yes. It's typical of a hierarchy of perception that when you select one
level through which to be aware of the world, everything takes on the
appearance of that level. If you're perceiving consciously at the level of
relationships, the world is made of relationships. If you're focused on the
configuration level, everything is an object. And if you're operating from
the symbol-handling level, everything consists of descriptions in words that
are defined only in terms of other words.

Of course, this event-focus in the social and cultural spheres may reflect
old-time views of cause and effect which we will eventually outgrow, so to
speak.

I'm sure that perception in terms of events has some useful part to play in
the functioning of the whole system. But no one level of perception is
useful by itself.

Enlighten me.

Too much to do. Seek out your own salvation with diligence.

Best,

Bill P.

[From Bill Powers (970109.2110 MST)]

Tracy Harms 1997;01,09.19:00 MST --

... we may indeed say that a claim
communicates an objective fact of reality. In saying this we might be
wrong, but we might perhaps be right.

Ah, that's the basic problem of epistemology, isn't it? The problem is not
whether our statements about reality are right or wrong, but that we DON'T
KNOW WHICH. If they're right, but we can't prove it, we're no better off
than if they were wrong, knowledge-wise (survival-wise might be a different
matter).

Best,

Bill P.

[Martin Taylor 970113 13:40]
Bill Powers and Chris Cherpas, various messages Jan 9-...

Bill has queried what is special about the probabiity of an "event", which
is a one-shot occurrence. I had not intended to refer only to "event-level"
perceptions, but had meant it as a state or state change of any kind that
could be identified. It was a (to me) ill-defined concept, and a weak
point in my association of a probability (uncertainty) value with a
perception.

Chris mentioned "categories", and it occurred to me that the concept of a
discrete probability value can apply only to a category perception. Will
the light be (of category) "red" when I get there? Not: Will the light
have a hue near the spectral hue of 640 nm when I get there? For the
latter, one may describe a probability density function, but never a
probability.

If "probability" applies only to categories, and category-type perceptions
can be associated with _every_ level in the hierarchy, from sensation to
(presumably) system level, then it makes the whole notion of probability
easier to treat. A category is or is not perceived. Events may never be
repeated, but as Chris said, they can be interchanged, and if two events
or states can be interchanged, then they belong to the same category. So
the issue of probability becomes "If category X is perceived then how sure
am I that category Y will be (or was) perceived?" (Probability is always
conditional on something, even though the conditional context is often
ignored in talking about probability).

In my conception of the category "level" I know I differ from the orthodox
view. We have discussed it a few times over the years. My thought is that
category perceptions _and associations_ exist because of cross-links in
which the output of one Perceptual Input Function forms part of the input
to another _and reciprocally_. One cannot talk about either being at a higher
level than the other when each feeds directly or indirectly from the output
of the other.

In a mesh of such connections, some reciprocal loops will (1) have each output
trying to suppress the other output because of the configuration of positive
and negative input weights, some will have (2) one suppressing the other and
the other enhancing the first, and some will have (3) each enhancing the other.

Cases (1) and (3) represent positive feedback loops, while (2) represents
a negative feedback loop. (1) and (3) therefore tend to run away to saturation,
and do so if the gain is greater than unity. Case (1) produces mutually
incompatible category perceptions--either "A" is perceived or "B", depending
on the other inputs. Case (3) produces "association"--if "A" is perceived
then "B" is more likely than otherwise to be perceived (again depending on
the other data inputs). Case (2) tends to stabilize the perceptions of both,
whether they are both perceived or both not, or one of each.

The existence of the positive feedback connections tends to stabilize the
state of the mesh, such that some (associated) groups of perceptions tend
to occur together while other groups or perceptions don't occur when the
first ones do. (Such meshes often have chaotic behaviour, but I'll not
follow that up here, preferring to assert that reorganization has developed
a mesh that seldom goes chaotic--though it may well be on the edge of chaos,
as, for speed of response to data changes, it should be).

The strength of the associative or mutually inhibitory connections between
categorical perceptions has to be derived from experience. In a Hebbian
approach, the more often one perception occurs along with another, the
stronger the positive link will be--necessarily so, if we use the simple
Hebbian learning algorithm of increasing the positive synaptic weight when
the node (neuron?) output is high at the same time the input is high, and
reducing it if the input is low when the output is high.

Perceptions can include remembered perceptions, and in the category flip-flop
they ordinarily do so if the loop gain is high enough.

Looking at things in this way, the synaptic weight of a cross-link between
perceptual input functions seems very closely related to the (frequentist)
probability that the one accepting the input will occur when the one providing
the output has occurred. But it does not provide an obvious source for the
feeling of assuredness that I have been calling the perception of probability.

Where that comes from is a matter for more thought. And experiment, if it
can be associated with thought:-)

Bill P. has said that his view of probability has come from the intellectual-
analytic tradition in which he was schooled. I'm inclined to think that
the notion of "probability density function" that applies to a continuous
variable such as the "redness" of a light comes from intellectual analysis,
and that it originally derives from the "naturalistic" perception of
the discrete probability that a category perception will occur, given that
another one has or had occurred. The "naturalistic" perception of
probability is what leads us to choose one course of action rather than
another ("That patch of purple is most probably a plum, since I perceive
the tree to be shaped like a plum tree, so I'll go over there and ensure
myself that it is--and if so, eat the plum"). "Probability density" does
not apply to these situations. Category perception and "probability" do.

Quite apart from the speculative and partial proposal for a mechanism, does
the association of a perception of probability with category perceptions
ring true?

Martin

PS. My Mail software kindly deleted most of the Jan 8 messages before I saw
them (I saw that they existed, but they vanished non-recoverably after I'd
seen perhaps five of twenty messages). If anyone sent a message on that date
that they would have liked me to see, please send me a private copy of
it if you have it still handy.

[From: Chris Cherpas (970113.1326)]
  [re: >Martin Taylor 970113 13:40]

Will the light be (of category) "red" when I get there? Not: Will the light
have a hue near the spectral hue of 640 nm when I get there? For the
latter, one may describe a probability density function, but never a
probability.

I'm glad you brought up the density function here to keep us from thinking
too simplistically about this, but the sense of "nearness" is what I think I
subjectively experience most in situations considered probabilistic.

(Probability is always conditional on something, even though the conditional
context is often ignored in talking about probability).

Again, thanks for making this explicit here too.

I'm inclined to think that the notion of "probability density function" that
applies to a continuous variable such as the "redness" of a light comes from
intellectual analysis, and that it originally derives from the "naturalistic"
perception of the discrete probability that a category perception will occur,
given that another one has or had occurred.

I tend to think of just the opposite: the discrete derives from the continuous.
However, this is based on intuition, not a model I have developed. On the other
hand, couldn't both be operating concurrently and interdependently, rather
than the dependency going in just one direction? Sorry this is so vague.

The "naturalistic" perception of probability is what leads us to choose one
course of action rather than another... "Probability density" does
not apply to these situations. Category perception and "probability" do.

I realize one cannot change one's commitment from stepping with the left
foot after having just done so without possibly splitting one's pants, but
I wonder if at the moment of choosing one course rather than another, one
stops perceiving probabilities at all and at that point only "perceives
deterministically." The moment of perceiving probabilities is over with.

Quite apart from the speculative and partial proposal for a mechanism, does
the association of a perception of probability with category perceptions
ring true?

It certainly rings, but I can't tell if it's one of those "truth rings" yet.
At the moment, I certainly find your proposal intriguing and thought-provoking.

Best regards,
cc

[From Bill Powers (970114.0400 MST
)]

Martin Taylor 970113 13:40]--

Bill has queried what is special about the probabiity of an "event", which
is a one-shot occurrence. I had not intended to refer only to >"event-level"
perceptions, but had meant it as a state or state change of any kind that
could be identified. It was a (to me) ill-defined concept, and a weak
point in my association of a probability (uncertainty) value with a
perception.

Chris mentioned "categories", and it occurred to me that the concept of a
discrete probability value can apply only to a category perception. Will
the light be (of category) "red" when I get there? Not: Will the light
have a hue near the spectral hue of 640 nm when I get there? For the
latter, one may describe a probability density function, but never a
probability.

As you describe your example, it's clear that probability density (later in
your post) must be as far as you can go toward defining probability: "when I
get there," being a continuous measure, makes the probability of the
experience at any infinitesimal instant zero. Exactly when can you say that
you have "got there?" Probability clearly doesn't apply to a continuing
state of anything -- what is the probability that the light you see is red?
If you can see it, it is either red or not red; categorization coupled with
Aristotelean logic says it can't be both red and not red. It applies only to
a _change of state_, and that means events, things that can be counted after
they have occurred but can't be narrowed down to a single instant of analog
time.

There are two terms in your description of experienced probability: "the
light is red" and "when I get there" (the latter meaning, I presume, "when I
arrive at a position where its color matters"). The light may have been red
before you saw it or before you arrived at the point where you must either
brake or not brake, or you may have observed it turning red from a distance
but long before your car has approached it. The uncertainty is in _both_
terms, and at least one of the terms is inherently fuzzy. We can't perceive
in true geometric instants.

The result, I argue, is that there is always a span of time over which the
(conditional) probability (the time integral of probability density) of an
_observed_ change of state rises smoothly from zero to one. This makes
perceived probability into the equivalent of a smooth transition of a
perceptual signal from an initial to a final value.

If "probability" applies only to categories, and category-type perceptions
can be associated with _every_ level in the hierarchy, from sensation to
(presumably) system level, then it makes the whole notion of probability
easier to treat. A category is or is not perceived. Events may never be
repeated, but as Chris said, they can be interchanged, and if two events
or states can be interchanged, then they belong to the same category. So
the issue of probability becomes "If category X is perceived then how sure
am I that category Y will be (or was) perceived?" (Probability is always
conditional on something, even though the conditional context is often
ignored in talking about probability).

When you say that a category-type perception can be "associated with" every
level of the hierarchy, is this not functionally equivalent to saying that
there is a SINGLE category level which can receive inputs from any
lower-level system (as I claim) and represent them as categories? What I'm
concerned about is how to find a place for a category-type perception in,
say, the spinal cord and other places where the perceptual signal comes
directly from a sensory neuron. A category signal, as you describe its
nature, must either be continuously on or continuously off. Are there any
signals of that nature which could be construed as category-type perceotual
signals at or below, say, the thalamus? I have never heard of any. Maybe
someone else has.

In my conception of the category "level" I know I differ from the orthodox
view. We have discussed it a few times over the years. My thought is that
category perceptions _and associations_ exist because of cross-links in
which the output of one Perceptual Input Function forms part of the input
to another _and reciprocally_. One cannot talk about either being at a
higher level than the other when each feeds directly or indirectly from
the output of the other.

I think that reciprocal connections are a different subject; that's a matter
of the _means_ by which a categorical input function is constructed. My
objection to having such connections at lower levels is that they make
continuous control impossible if, indeed, they cause a flip-flop between two
stable states (reciprocal inhibition in the retina, for instance, does not
have that effect). Control at the lower levels requires continuously
variable perceptual signals, not signals that remain constant.

Bill P. has said that his view of probability has come from the >intellectual-
analytic tradition in which he was schooled. I'm inclined to think that
the notion of "probability density function" that applies to a continuous
variable such as the "redness" of a light comes from intellectual >analysis,
and that it originally derives from the "naturalistic" perception of
the discrete probability that a category perception will occur, given that
another one has or had occurred. The "naturalistic" perception of
probability is what leads us to choose one course of action rather than
another ("That patch of purple is most probably a plum, since I perceive
the tree to be shaped like a plum tree, so I'll go over there and ensure
myself that it is--and if so, eat the plum"). "Probability density" does
not apply to these situations. Category perception and "probability" do.

I claim that this way of decribing a perception is generated at the levels
where we manipulate symbols, where the symbols are already category signals.
The very way the decision is couched says so: "That patch of purple is most
probably a plum, since I perceive the tree to be shaped like a plum tree, so
I'll go over there and ensure myself that it is--and if so, eat the plum."

That sentence is the outcome of a verbal/logical reasoning process, and all
its major elements -- all the nouns and pronouns -- are categories. The
sentence could be recast as a syllogism. But to carry out its terms -- to
"go over there" -- requires control of continuous variables.

Quite apart from the speculative and partial proposal for a mechanism,
does the association of a perception of probability with category
perceptions ring true?

For me it does, because basically this is what I've been saying all along. I
have claimed that the whole genre of probabilistic notions depends on
converting the analog (lower-level) world of perception into discrete
symbols, and then reasoning logically or at least programatically about (and
with) those symbols.

When you adopt this mode of perception and control as the center from which
you analyze ALL perceptions, then naturally all perceptions, at any level,
seem to take on the characteristics of the discrete world of categories. You
can see categories even at the level of intensities, because you MAKE them
discrete by naming them: a _bright_ light versus a _dim_ light, and so on.
Since you can see categories in every level of perception, this leads you to
suppose that the categories must be _generated_ at those levels, rather than
seeing yourself, at the level from which you operate, as imposing the
categories once the signals reach your conscious perceptual levels.

I'm sure you're aware that I have repeatedly cautioned people on this list
to try to avoid the level-of-perception error -- attributing to ALL levels
the characteristics of the particular level from which you typically observe
the world. It's most obviously a valid criticism when you see it being
applied to someone else: when I point out that is projecting logical
functions or relationships or sequences or principles onto all experiences.
When a person is using a primary level of conscious perception that is
different from yours, particularly lower-level than yours, you can see that
the characteristics of that level are being inappropriately projected into
the wrong levels. A person who claimed that all perceptions at all levels
involve relationships, for example, would clearly be projecting relationship
perceptions into systems that know nothing of relationships.

The projection that's the most difficult to recognize is your own. This is
why it took me thirty years or so to discern (imperfectly) 11 levels of
perception _as levels of perception_. In every case, without exception, the
most difficult thing was to stop trying to _validate_ my perception by
attributing it to the objective world, to draw back long enough to see it as
a particular kind of _perceptual interpretation_ that I was actively
imposing on experiences.

The idea of definite levels of organization arose because I could see that
each type of perception, once identified, had a unifying concept in it, a
commonality that extended over all modalities and examples of perception. It
seemed to me that in order for such clearly delineated groupings of
perceptions to exist, there must be specialized types of perceptual
computation involved. From the evolutionary point of view, it seemed
reasonable that such types of computations would be added on in layers, as a
new kind of computing capability that doesn't already exist in the lower
layers, somewhat like (but not much like) the man riding the horse riding
the alligator. I spent a lot of time trying to imagine what I would be like
if I could perceive nothing higher than a certain level -- say,
configurations. Imagining the world WITHOUT a given level of perception is
part of the process of learning what that level of perception does.

How would the world look if you were unable to perceive categories or
probabilities? Between the amoeba and you, there must be _some_ creature
that can perceive at least to some degree all levels up to relationships,
but nothing higher than that. What would that creature be able to do, and
not be able to do?

Best,

Bill P.

[Martin Taylor 970114 11:40]

Chris Cherpas (970113.1326)]

I wonder if at the moment of choosing one course rather than another, one
stops perceiving probabilities at all and at that point only "perceives
deterministically." The moment of perceiving probabilities is over with.

Is there such a thing as "the moment of perceiving redness" or "the moment
of perceiving sequence-ABZXC-ness"? If so, you've introduced a new topic for
discussion that is worth following up. If not, why should there be a "moment
of perceiving probabilities?"

What I think you are saying is that when an action has started on one
discrete path that precludes acting on another path--one has passed by
one's bicycle and started one's car, for example--any probabilities that
may have contributed to the controlled perception, and that may themselves
have been controlled perceptions (as Bill P has several times reminded us),
are of no more relevance to that choice than are any of the other perceptions
that contributed to the choice.

And with that one sentence, I leave the question--for now.

Martin