<Bill Cunningham 940530.1530>
<Tom Bourbon 940527.1225>
Their lack of knowledge cannot be quantified as so many bits,
can it? To do those calculations, who would have the requisite
knowledge of all the things the authorities do not know, and the
number of bits of uncertainty each authority "has" for those
items. Or am I missing something _very_ basic in the points you
are trying to make?
I think you are missing something very basic, but most likely
because I have not made the point clearly. You are quite correct
to note that the uncertainty resides with the recipient, and that
formal calculation of the uncertainty requires knowledge of the
decision space of each recipient. The point I failed to make is
that if uncertainty has changed for any of the authorities I
mentioned, then information has flowed and it remains up to us to
describe a process by which that might have occurred. I propose
to introduce 2.5 examples that are simple enough to deal with for
much of the discussion that is likely to follow. First, the easy
one.
One if by land and two if by sea
And I on the opposite shore will be
Ready to ride and spread the alarm.
Through every Middlesex village and farm.
Paul Revere's problem is simple enough. By other means he knows
that the Brits are about to conduct a raid on Concord, which the
upstart Yanks will oppose. There are two known routes to Concord
and it is deemed necessary to delay the Brits to provide time to
gather enough Minutemen to properly defend Concord. There are
not enough Minutemen to delay on both routes and still defend
Concord, a classic resource allocation problem. It is also
deemed necessary not to reveal the intended opposition until the
Brits can't do anything about it. Thus Revere's uncertainty
reduces to two bits: Have the Brits committed to action Y/N? By
land or by sea? That is why two lights were required, not one.
Controlling for reduction of uncertainty, Revere positions
himself to observe whether 0 or 1 or 2 lights are displayed. So
long as he perceives 0 lights, he remains uncertain and in the
dark. Once he perceives 1 or 2 lights, he controls for riding
and spreading the alarm.
:
Now consider a Middlesex villager or farmer, who doubles as
Minuteman. Normally, he controls for villaging or farming or
whatever. At that hour (depending when Revere rides by), he
controls for rythmic breathing & snoring, making love, or maybe
lighting fires for early baking. He certainly isn't controlling
for hightailing it for Lexington or Concord or "site X", the
other delay point. "To arms! To arms! The British are coming."
This is alerting information, (per Martin Taylor 940530.1700). It
does two things. First, requires the recipient to control for
something that was previously unimportant. In so doing, it
reduces the recipient's degrees of freedom with respect to many
things that could be controlled for. The ability to put
"controlling for dressing and arming oneself" on the back burner
permits the recipient to go on about his normal life, but to
convert control from say farming to militiaing on a minute's
notice is what makes him a Minuteman. Unlike Revere, he was not
seeking this information. How much information has been
received? Well, if you construct the decision space as "control
for A/control for NOT A, then the answer is 1 bit. And that's
the whole point about alerting. It overrides a bunch of other
things one might be controlling for and demands attention for
something that has become most important.
Our Minuteman still needs to know his assembly point, which will
be Lexington, Concord or "site x". Given his known location and
the potential British march routes, this can be reduced to
assembling at delay point near him because he is on/near the
reported route, else boogie to Concord. The last part is quite
deterministic, given knowledge of the route chosen.
And so again, we have a two bit problem.
ยทยทยท
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Now to introduce a slightly more complex example, much closer to
the fire captain's.
Consider the triage process during any emergency overloading of
medical resources. The protocol calls for deferring surgery on
patients who will not die unless treated immediately AND for
withholding surgery for those expected to die whether or not they
receive surgery. This is also a two bit problem in terms of the
ultimate decisions, but that is more clearly seen from the
results than from what led to them. Decisions are highly
judgemental and based on medical resources available with respect
to demand (which effects estimate of delay getting to surgery)
and results of very cursory examination of patient. Both
decisions are subject to Type I and Type II errors. Committing
to surgery for one patient denies surgery for another. If
patient death is viewed as a scalar cost, we clearly have an
optimal decision problem. Whether this is an optimal control
problem depends on whether the process is made adaptive to the
ongoing situation and the longterm feedback on success. So how
might this work?:
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
<Bill Powers 940527.1400>
The enumeration creates a blank form, specifying the kind of
perception required but the specific value of it.
.......
This process is like a clerk scanning over a form, not to read
it, but just to see there are no blank places left.
I think this is a very good start. I prefer to call the forms
"situation templates" where the patterns represented by the
templates represent potential models for that aspect of the
world, based on experience, study, conjecture. The pattern
represents one hypothesis of many. For now, let's consider them
mutually exclusive. If the value of a particular entry is
important, additional templates can be created to resolve that
ambiguity.
What I envision is an finite array of situation templates for any
particular general situation, eg the triage problem. Each of
these templates is fed to its own comparator. The comparators
are fed in parallel from the bottom with perceptions from the
lower level(s?) What we've got is a situation pattern
recognition scheme, which needs refining. First, there must be a
means for recognizing that no match occurs. This could take
several forms: a "no-match" template fed to a comparator might
pick up gross mismatches; a NOR gate fed by all the comparators
would achieve the same result; a more sophisticated scheme would
identify specific match points missing as Bill P suggests,
reducing greatly what must be sought.
There is another construct that needs consideration. Given the
triage problem, there isn't much time to seek information. What
is necessary is choosing the situation template closest to the
perceived pattern. This is where Kanerva's approach makes so
much sense--basically choosing the minimum Hamming distance from
the perceived coordinate to contending situation coordinates, in
the Kanerva n-space. This has other implications. First, the
Hamming distance could be taken as an error to be driven towards
zero. If it remains large, there is a bad mismatch between
available templates (hypotheses) and available perceptions. Note
that changing either the available perceptions or synthesizing a
new template could reduce that error. Second, except for the
unlikely event of an exact match, there will be what amounts to
quantizing error in decoding. Third is the phenomenon of jumping
to conclusions. If a partial match leads to a false match
indication, the non matched properties get dragged along for the
ride. But since the false match provides the basis for
subsequent control, subsequent perceptions are controlled to fit
the false match. Shannon's 10th theorem offers some insight on
how to deal with this, since the great problem with a false match
is that it, by definition, is not perceived.
:
Moving onward toward a diagram, I envision a set of "course of
action (COA) templates, which if selected will become the primary
reference on the effector side. Each COA would pass through the
equivalent of an analog gate, activated (or not) by the OR of
appropriate situation comparator outputs. In general, there are
m COA for n situational templates. At least one COA must be
"find out more (about ....?)" At the crudest level, it is just a
"find out more", but depending on other aspects of situation and
the effector reference could be quite specific. Regardless, the
selected reference would drive behavior to change the perception
fed to the comparators, ultimately reducing uncertainty--whether
measured in terms of reduced ambiguity between situation
templates or by the Hamming distance from the available choices.
And thus, a system that _can_ control for reduced uncertainty
along with all the other things it might control for. None of
this appears to violate anything about PCT, but may shed some
light on how switches might be thrown.
Now to try a diagram. I'm not good at ASCII diagrams and may
need some help.
Building blocks
_________________________
: ith Situation Template :......... abbreviated STi
-------------------------
____________________________
: ith Situation Comparatory :----> ith output....abbreviated
:___________________________: SCi-->o
___________________________
: upward distribution bus :
---------------------------
_____________________
: ith COA template : .......abbreviated COAi
---------------------
\ __________________
--OR*: ith analog gate : ....abbreviated Si, without showing
/ ------------------- multiple input to OR gate.
____________________________
: downward summing junction :
-----------------------------
:
One last thing. I will use a carat (shift 6) for up arrow. My
mailer may convert this to something weird. If a signal path
isn't downward, as indicated by V, then it is upward.
Arbitrarily, the nth Situation Template is the "Huh?" situation,
shown as STn? and the mth COA is "go fetch"
(fetch)
ST1 ST2......... SSTn? COA1 COA2 ......COAm
: : : : : :
: : : : : :
V V V V V V
SC1->o1 SC2->o2 SC3-o? S1 S2 Sm
^ ^ ^ : : :
: : : V V V
---------------------------- --------------------------
: upward distribution bus : : downward summing junct :
---------------------------- --------------------------
^ ^ ^ ^ ^ ^ ^ ^ :
: : : : : : : : :
available perceptions V
Reference for action
(fetch when selected)
:
A pair of remaining thoughts concerning the triage problem. We
have already discussed alerting and seeking information. I'll
leave the business of IT within controlling for Martin. There
are two other categories to address.
It is not unreasonable for either triage medic or the holding
medic to place deferred/waiting patients in some sort of
prioritized queue. Rather than control for specific information
about each patient, it is quite reasonable to monitor perceptions
about many, perhaps after controlling for setting up a mechanical
sensor for each. The point here is that whatever variables are
monitored need not be actively controlled. This provides
tremendous efficiency in the use of effector resources, whether
personal or organizational. So long as the monitored variables
stay within acceptable bounds, no action is required. So the
degree of uncertainty is with respect to the bounds, a far
simpler problem to deal with.
When a patient does reach a surgeon, the diagnosis is partial at
best. Even the surgeon's own preliminary diagnosis needs
confirming. Some data can be sought, eg existing medical
records. However, in many (hopefully most) cases, the surgeon
will have to explore to see his/her hypothesis is correct.
Exploring involves controlled action to see of the resulting
perceptions are in keeping with the hypothesis held. It implies
a willingness to change the hypothesis if there is no match or if
the Hamming distance to any extant hypothesis is above some
limit.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
That does it for today! While not perfect, this does show a way
to deal with uncertainty that does not appear to violate anything
truly fundemental to PCT. As I said up front, given evidence that
information has flowed, it remains to pose a means for having
done so. This is _a_ means, not necessarily the only means
Regards, Bill C.
Regards,
Bill C
PROFS: mon1(cunningb) Internet: cunningb@monroe-emh1.army.mil
Phone (804) 727-3472/DSN 680-3472. FAX ext 3694/2562
*Eschew Obfuscation*