# Insights into level 5 (?)

**URL:** <http://discourse.iapct.org/t/insights-into-level-5/5710>\
**Category:** CSG1998\
**Created:** [October 28, 1998, 4:24pm UTC](http://discourse.iapct.org/t/insights-into-level-5/5710 "1998-10-28T16:24:58Z")\
**Posts on this page:** 8\
**Page:** 1

<div class="post-metadata">

**Author:** ![Richard\_Kennaway2](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/r/a87d85/32.png) [@Richard\_Kennaway2](http://discourse.iapct.org/u/Richard_Kennaway2)\
**Post date:** [October 28, 1998, 4:24pm UTC](http://discourse.iapct.org/t/insights-into-level-5/5710/1 "1998-10-28T16:24:58Z")

</div>

[From Richard Kennaway (981028.1540)]

Bill Powers (981028.0631 MDT):

> Repetitive cycles. We need to control them to sing or play music, recite  
> poetry (doggerel, anyway), walk or run, push someone on a swing, pound  
> nails, saw wood, jack up a car, paint a wall, or write a list like this.  
> Many of them are tied to natural physical rhythms like gaits, but many are  
> not -- they're rhythmical because at this level speed of repetition is the  
> main controlled variable.
> 
> So, does this level go between events and relationships, or does it replace  
> events? Try it on, let me know what you think.

I just read this and haven't had time to do any thinking, but just before I  
dash off on travels until Monday, I thought I'd mention that I've just  
added some walking behaviour to my simulated insect, which I haven't posted  
anything about for a long time. It consists of a rhythmic cycle of actions  
with the legs. Pick up front legs, move them forwards, put them down. Pick  
up middle legs, move them forwards, put them down. Pick up rear legs, move  
them forwards, put them down. Repeat. "Walking" arises from the fact that  
the bug tries to control its body position so as to remain vertically above  
the centre of its footprint, and parallel to the best-fit plane through its  
feet. Turning around is done similarly, by swinging pairs of legs  
clockwise or anticlockwise.

As yet, this behaviour is not part of the control of any perception, but  
just a blind cyclic program. However, if pointed in the direction of a  
staircase it can successfully walk up and down without losing its balance.  
Oh yes, for those who have seen earlier versions of the Bug, I've added a  
variety of different terrains for it to walk over.

Running on a 400 MHz Pentium II, this has a big Wow! factor. You can  
actually see it walking and struggling to keep its balance on the stairs,  
with the animation running at upwards of 150 frames per second.

Coming next will be control systems which will use the walking and turning  
routines to make the bug steer towards a visual landmark.

The latest version is at  
[http://www.sys.uea.ac.uk/~jrk/JRKBug-1.1/BugApplet.html](http://www.sys.uea.ac.uk/~jrk/JRKBug-1.1/BugApplet.html). It's a Java applet  
which in principle should run in any Java-equipped web browser (running  
Java 1.1 or later). It works with Internet Explorer, but Netscape has  
problems, I don't know why. It also needs a powerful computer with a  
fairly big screen. If you want to download files to run it locally (which  
will make no difference to the speed, but means you can use an applet  
runner instead of a web browser), the only ones you need are BugApplet.html  
and AppletClasses.jar. If your applet runner doesn't understand jar files,  
you need to get all the \*.class files instead.

No time to document all the zillions of controls, but for those who may  
have a suitable machine, here is what you need to do after loading the  
applet to make it walk up and down stairs:

1. Click on the "Parameters" button, and set the following values in the  
scroll bars:

Anim. step: 0.001 (this is the time interval of the simulation, in  
seconds -- 0.001 is the minimum possible. Larger values may cause  
instability due to bad approximation.)

Walk step: 0.1 (this is the time between successive actions in the  
walking cycle)

2. Click on the "Terrain" button, then click on the "Staircase" button.

3. Click on the "Walk" button, then click on the "Walk fwd." button (or  
"Walk back", "Turn right", or "Turn left").

4. Click on the "Run" button to set it going.

5. For added fun, click on the "Switches" button, then click on any of the  
resulting left-hand column of buttons to shoot legs off. If it walks fast  
enough and the parameters are tuned right, it can walk with just its front  
and rear legs.

Colleagues here get excited when they see it. It's only 5000 lines of  
Java. Half of that is the user interface, half of the remainder is the  
physical simulation. The most difficult thing to get across to people is  
that the bug knows nothing about how to walk over uneven terrain or up and  
down stairs. The only thing it is doing is executing that cycle of leg  
actions and attempting to keep its body centered over its footprint. It  
doesn't even know implicitly in any meaningful sense, because when I added  
the new terrain types, I hardly had to change the bug at all to make it  
walk over them. It didn't work at first (it fell over), but I eventually  
found that all I had to do was give it longer legs and reduce the  
simulation time step (and it may be that reducing the simulation time step  
would have been enough on its own).

-- Richard Kennaway, jrk@sys.uea.ac.uk, [http://www.sys.uea.ac.uk/~jrk/](http://www.sys.uea.ac.uk/~jrk/)  
&nbsp;&nbsp;&nbsp;School of Information Systems, Univ. of East Anglia, Norwich, U.K.

---

<div class="post-metadata">

**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [October 28, 1998, 3:23pm UTC](http://discourse.iapct.org/t/insights-into-level-5/5710/2 "1998-10-28T15:23:43Z")

</div>

[From Bill Powers (981028.0631 MDT)]

I've never been happy with the 5th level, "events." This morning my request  
for a better definition was granted, sort of.

It started when Bill Williams was here (last week) and I showed him a video  
of Bruce Abbott's rats "pressing a bar." This was the 25th day of  
experimentation on a Fixed Ratio 1 schedule, so the rats were settling down  
to a routine. The rats began each session hanging onto the bar and (just to  
the right of it) the food cup, with their noses swinging toward the bar and  
then toward the food cup as they leaned on the bar and (most of the time)  
it went down and caused a pellet delivery. That image stuck in my mind, and  
this morning I awoke with the results.

In conventional analyses, the pressing of the bar is conceptually separated  
from the delivery of a food pellet, and that is conceptually separated from  
consumption of the food pellet. This is how the human observer-experimenter  
chooses to perceive what is going on. Thus the theory: the probability of  
pressing the bar is increased when it results in delivery of a food pellet;  
after the delivery there is a "post-reinforcement pause" during which the  
pellet is consumed. As I watched the rats perform, this perceptual set  
gradually faded and I began to see what was happening without this  
interpretation.

The pause begins, during each experimental session, as a very brief  
cramming of the pellet into the mouth in parallel with pressing the bar for  
the next pellet, and half an hour to 45 minutes later, becomes a press, a  
pellet delivery, and a fairly elaborate and leisurely ritual of sitting  
back, holding the pellet in the paws, and turning it while nibbling on it  
and chewing each bit thoroughly.

When we analyze the data in terms of presses per minute and pellets per  
minute, what we appear to see is a declining pressing rate and pellet  
delivery rate during each experimental session, with each press preceding a  
pellet delivery. But if we forget those rates, we can also see this as a  
declining rate of executing a cyclical process consisting of postures and  
movements. Each time around, the cycle yields one consumed pellet, one  
press, (or n presses on other schedules) and one new pellet (sometimes more  
than one, but not often). At first, the rat goes through this cycle very  
rapidly, skipping many details because of starting the next element before  
the previous one is finished. The main thing limiting the speed of the  
cycle is that the rat must swallow some of the food in its mouth before it  
can get another pellet in. The rat often presses the bar and produces  
another food pellet, then pauses while it chews before picking up the  
pellet in the cup.

As the total amount of food consumed during the experimental session  
increases, the speed of the production-consumption cycle decreases, and  
each element, particularly the consumption process, expands to include all  
its details. Eventually, as the total intake approaches a limit, the speed  
of repetition approaches zero and other behaviors begin to appear such as  
nosing around in the cage or taking a nap. The fast-slow pattern may repeat  
once or twice, more briefly, before the end of the hour.

During this \_repetitive cycle\_ we see a number of controlled processes  
going on. The posture transitions from the pressing posture, with the nose  
toward the bar and one forepaw on it, to the collection posture, with the  
nose toward the cup and a tendency to transfer weight to the cup-side paw,  
which releases the press by the other forepaw. Early in the session,  
loading the pellet into the mouth is followed immediately by a transition  
back to the pressing configuration, so there is essentially no manipulation  
of the food before it's stuffed into the mouth. The food is actually being  
consumed at the same time that the next press is occurring. Later in the  
session, the pellet is retrieved in the paws and nibbled on with the body  
in a sitting posture, neither paw on the bar or food cup.

What is it that is being controlled here? The new idea is that it is a  
\_repetitive cycle\_, with the \_speed of repetition\_ being the controlled  
variable. Possibly we should consider each element of the cycle as being a  
controlled \_event\_ as before, so we are now about to insert another level  
of control above the event level, a new level at which the speed of a  
cyclical event is the type of variable. Or perhaps we're replacing the  
event level.

During the World Series, I heard the crowd clapping this way at a fairly  
brisk pace, with each element taking the same amount of time:

clap (pause) clap (pause) clap clap clap (pause)  
clap (pause) clap (pause) (pause) clap clap (pause)

That pause at the end isn't obvious unless this whole cycle is repeated.

What sort of controlled perception is this? It's basically a temporal  
pattern (Bob Clark wanted to introduce a level of this kind many years ago,  
but I couldn't connect with it. Now it seems he could have been right).

But it's not just a temporal sequence or a pattern of variation. It's  
rhythmical. If you watch the rats go through their repetitive cycle, it's  
easy to miss the steady rhythm that slowly decreases. Once in a while  
there's what seems to be a reorganization -- a momentary break in the  
rhythm, which stands out precisely because the rhythm is so regular the  
rest of the time. Is this just a matter of each element having a controlled  
duration? I don't know. But there is plenty of evidence that organisms,  
particularly human beings, do all kinds of rhythical things.

The boy stood on the bur ning deck  
^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

These rhythmical things are patterns on a steady underlying rate of  
repetition. They can be seen as related harmonic rhythms: if the pattern of  
emphasis is written out, we have

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\* \* \* \*  
The boy stood on the bur ning deck  
^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

Which is a pattern at half the speed of the underlying beat of the words.  
If we take the initial "the" to be the last beat of a measure, we have the  
musical notation with a beat at the start of each measure:

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\> \> \> \>  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\>\* |\* |\* |\*  
The |boy stood|on the |bur ning |deck  
^ |^ ^ ^ |^ ^ ^ |^ ^ ^ |^  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\> \> \> \>

The slowest rhythm is the rate at which the whole cycle is repeated:

(1) | | | |  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\>\* |\* |\* |\*  
&nbsp;&nbsp;^ |^ ^ ^ |^ ^ ^ |^ ^ ^ |^ ^  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\> \> \> \>

(2) | | | |  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\>\* |\* |\* |\*  
&nbsp;&nbsp;^ |^ ^ ^ |^ ^ ^ |^ ^ ^ |^ ^  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\> \> \> \>

(3) | | | |  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\>\* |\* |\* |\*  
&nbsp;&nbsp;^ |^ ^ ^ |^ ^ ^ |^ ^ ^ |^ ^  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\> \> \> \>

etc.

Note that we can leave the words out, so that different lower-level  
variables can be substituted: drum beats, flashes of light, bass drum  
versus cymbal (^ = bass, \* = cymbal, or vice versa), or musical pitch  
(OOM-pah-pah OOM-pah-pah on a tuba).

Certain repetitive cycles and subycles are so strongly associated with a  
specific physical process that we can recognize them easily:

ga-da-da-dump ga-da-da-dump ga-da-da-dump ...

There's probably a physical reason why there are two beats between  
ga-da-da-dumps as the horse flies through the air. Three beats would leave  
you on the wrong foot, four beats would mean jumping too far, and one beat  
wouldn't give enough time to reset the first leg. So a four-legged creature  
gallops in waltz time, or 6/8 time. Is that true?

Repetitive cycles. We need to control them to sing or play music, recite  
poetry (doggerel, anyway), walk or run, push someone on a swing, pound  
nails, saw wood, jack up a car, paint a wall, or write a list like this.  
Many of them are tied to natural physical rhythms like gaits, but many are  
not -- they're rhythmical because at this level speed of repetition is the  
main controlled variable.

So, does this level go between events and relationships, or does it replace  
events? Try it on, let me know what you think.

Best,

Bill P.

---

<div class="post-metadata">

**Author:** ![Bruce\_Gregory](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/4bbf92/32.png) [@Bruce\_Gregory](http://discourse.iapct.org/u/Bruce_Gregory)\
**Post date:** [October 30, 1998, 8:37pm UTC](http://discourse.iapct.org/t/insights-into-level-5/5710/3 "1998-10-30T20:37:30Z")

</div>

Please forward to CSG

i.kurtzer (981029.1515)

Cycles? as a distinct kind? mmmmmm? They are most certainly a distinct  
perception, type-distinct from doggies and liberty; meaning that two  
dogs are different but that is a difference WITHIN the kind of  
"configurations" unlike Shelties and metallic-blue which are not  
interchangeable AT ALL. Cycles are also robust so that we can see the  
cycle of Spring-Summer-Fall-Winter and well as Shakespeare's seven stages  
of man. In fact, it a very powerful perception recognizes by EVERY  
society--that is also good evidence. However, as a separate kind I am  
hesitant but will think about this neat idea.

First: How is this distinguished  
from the subclass of sequences that eat their tails?

i.

---

<div class="post-metadata">

**Author:** ![R\_Marken](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/r/8797f3/32.png) [@R\_Marken](http://discourse.iapct.org/u/R_Marken)\
**Post date:** [October 30, 1998, 8:55pm UTC](http://discourse.iapct.org/t/insights-into-level-5/5710/4 "1998-10-30T20:55:29Z")

</div>

[From Rick Marken (981030.1400)]

i.kurtzer (981029.1515) --

> Cycles?

No. I think it was more like abstract rhythms. You can control  
for the rhythm of the words

Dum ... Dum ... Da Dada Tum

or for the first six notes of the Mozart C major piano quartet;  
same level 5 (or whatever) perceptions; different lower level  
components.

Best

Rick

> **···**
>
> --  
> Richard S. Marken Phone or Fax: 310 474-0313  
> Life Learning Associates e-mail: rmarken@earthlink.net  
> [http://home.earthlink.net/~rmarken](http://home.earthlink.net/~rmarken)

---

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**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [October 30, 1998, 10:00pm UTC](http://discourse.iapct.org/t/insights-into-level-5/5710/5 "1998-10-30T22:00:19Z")

</div>

[From Bill Powers (981030.1453 MST)]

> Cycles? as a distinct kind? mmmmmm? They are most certainly a distinct  
> perception, type-distinct from doggies and liberty; meaning that two  
> dogs are different but that is a difference WITHIN the kind of  
> "configurations" unlike Shelties and metallic-blue which are not  
> interchangeable AT ALL. Cycles are also robust so that we can see the  
> cycle of Spring-Summer-Fall-Winter and well as Shakespeare's seven stages  
> of man. In fact, it a very powerful perception recognizes by EVERY  
> society--that is also good evidence. However, as a separate kind I am  
> hesitant but will think about this neat idea.

Specifically, \_repetitive\_ cycles with dimensions like amplitude and rate  
of repetition.

> First: How is this distinguished  
> from the subclass of sequences that eat their tails?

Sequences are concerned with temporal ordering: A then B rather than B then A.

Obviously, repetitive cycles and sequences have something in common, so we  
need to think more about how to eliminate the common aspect of temporal  
ordering.

Bill

---

<div class="post-metadata">

**Author:** ![Bruce\_Gregory8](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/5f8ce5/32.png) [@Bruce\_Gregory8](http://discourse.iapct.org/u/Bruce_Gregory8)\
**Post date:** [October 31, 1998, 12:18pm UTC](http://discourse.iapct.org/t/insights-into-level-5/5710/6 "1998-10-31T12:18:37Z")

</div>

i.kurtzer (981029.1901)

[From Bill Powers (981030.1453 MST)]

isaac:

> \>Cycles? as a distinct kind? mmmmmm? They are most certainly a distinct  
> \>perception, type-distinct from doggies and liberty; meaning that two  
> \>dogs are different but that is a difference WITHIN the kind of  
> \>"configurations" unlike Shelties and metallic-blue which are not  
> \>interchangeable AT ALL. Cycles are also robust so that we can see the  
> \>cycle of Spring-Summer-Fall-Winter and well as Shakespeare's seven stages  
> \>of man. In fact, it a very powerful perception recognizes by EVERY  
> \>society--that is also good evidence. However, as a separate kind I am  
> \>hesitant but will think about this neat idea.
> 
> Specifically, \_repetitive\_ cycles with dimensions like amplitude and rate  
> of repetition.

Amplitude should already be handled by any continuous scalar signal about  
one quality. We don't need two perceptual functions for detecting light  
and detecting how much. How much is given by the scalar value and "that  
its a light detector" is given by its relationship to the world--as seen  
by us. Further, since there should be a continous scalar of Transitions,  
rate should also be non-problematic. So it seems to me the dimensions are  
already there in the model. For example, to have any real piroette--which  
is an event--we must have some speed at which she is turning and some  
degree of tightness of the ankle cross and "hoopness" of the two arms. So  
we have a piroette, an event, with a particular tempo and amplitude as  
given by the configuration, transition, and relationship levels. Now we  
could arrange piroettes with others kicks and jumps each different  
and malleable in duration, extent, and inter-duration. And there could be  
in a specific order where it went a long way and then  
repeated itself. But that potent quality of repetition might not be  
different level just a different dimension at an already enumerated level.  
So that round things ARE different then square things but not as  
configurations--they are both configurations--and there no need  
for an extra "square" level because the make crummy tires. 😉

> \>First: How is this distinguished  
> \>from the subclass of sequences that eat their tails?
> 
> Sequences are concerned with temporal ordering: A then B rather than B

then

> A.
> 
> Obviously, repetitive cycles and sequences have something in common, so we  
> need to think more about how to eliminate the common aspect of temporal  
> ordering.

I'm game to shifting around the kinds if its needed. What is it do you  
feel that is not handled by the levels as they are?

i.

---

<div class="post-metadata">

**Author:** ![Bruce\_Gregory8](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/5f8ce5/32.png) [@Bruce\_Gregory8](http://discourse.iapct.org/u/Bruce_Gregory8)\
**Post date:** [October 31, 1998, 12:18pm UTC](http://discourse.iapct.org/t/insights-into-level-5/5710/7 "1998-10-31T12:18:40Z")

</div>

i.kurtzer (981030.1900)

[From Rick Marken (981030.1400)]

i.kurtzer (981029.1515) --

> \> Cycles?
> 
> No. I think it was more like abstract rhythms. You can control  
> for the rhythm of the words
> 
> Dum ... Dum ... Da Dada Tum
> 
> or for the first six notes of the Mozart C major piano quartet;  
> same level 5 (or whatever) perceptions; different lower level  
> components.

Mmm. I think I got what you're saying.  
You can control the rhythm of words, and that is because we can perceive  
rhythmicity; but at what level rhythmicity might lie would seem  
to be at the Sequence with the stops as background to the Dums and Da's  
and STARTING with the dum before the dum next to da.😉 So  
Dum...Da Dada Tum Dum... is a DIFFERENT RHYTHM because the sequence is  
different while the the rythmicity of:  
Rick ... Rick ... Mar Marken S  
is the SAME SEQUENCE:  
1! 3# 1$ 2$ 1% 1! 3#

I am marking the blanks as explicitly represented and I do not think that  
would be psychologically inaccurate. Here there is a representaion of  
absence.  
So the question is what is not captured in these rhythms by the current  
levels?

i.

---

<div class="post-metadata">

**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [October 31, 1998, 5:39pm UTC](http://discourse.iapct.org/t/insights-into-level-5/5710/8 "1998-10-31T17:39:43Z")

</div>

[From Bill Powers (981031.1005 MST)]

> i.kurtzer (981029.1901)

> Amplitude should already be handled by any continuous scalar signal about  
> one quality. We don't need two perceptual functions for detecting light  
> and detecting how much.

Yes, we do. Intensity says there is some amount of a perception. "Light"  
says it is a particular kind of sensation, as opposed to warmth or sweetness.

> How much is given by the scalar value and "that  
> its a light detector" is given by its relationship to the world--as seen  
> by us.

Perceptual systems don't perceive detectors, nor do they perceive the  
world. They perceive only signals. All neural signals are alike, so it's  
only the way a signal is handled in a perceptual input function that  
identifies it.

Are you abandoning the idea of a layered hierarchy with each level being a  
function of levels below it?

> Further, since there should be a continous scalar of Transitions,  
> rate should also be non-problematic.

Rate, at the transition level, is supposed to be an analog signal which,  
when constant, represents a continuous change occurring at a steady rate:  
the constant motion of the second-hand of a clock, or of a ceiling fan, or  
a waterfall, is an example. Repetition rate, at the next level (?) is a  
complex variation of configurations and transitions that recurs at specific  
intervals. The least possible number of repetitions is one, reducing the  
perception to our former definition of an event.

Creating a repetitive cycle requires some sort of pattern generator to  
serve as an output function, an oscillator or a more complex device, which  
has inputs that can vary its speed of operation, the amplitude of its  
output signal variations, and the phase of its output (advancing or  
retarding the starting point). The controlled perceptions at this level  
would correspond to the dimensions in which the operation of the pattern  
generator can be varied.

A good example of control at this level is one person using a finger to  
track another person's finger. The other person moves the target finger up  
and down in a regular sine-wave pattern, gradually increasing the speed  
until the motion is too fast for tracking random movements. Then the target  
person abruptly freezes the target finger in space. The tracking person  
continues to produce the sine-wave motion for several tenths of a second,  
showing that it is being independently produced by an internal sine-wave  
generator that is adjusted in amplitude, frequency, and phase to match the  
target movements.

This is different from tracking a randomly moving target. When a  
randomly-moving target is abruptly frozen in space, the tracker stops  
moving in a much shorter time. The delay is also shorter when a person is  
tracking a slow motion in which no independent generator is required.

> So it seems to me the dimensions are  
> already there in the model. For example, to have any real piroette--which  
> is an event--we must have some speed at which she is turning and some  
> degree of tightness of the ankle cross and "hoopness" of the two arms. So  
> we have a piroette, an event, with a particular tempo and amplitude as  
> given by the configuration, transition, and relationship levels.

Sorry, but they have to be \_given\_ reference signals changing in such a way  
that they produce changes at the right speed of repetition. You have to be  
very careful here not to superimpose your own higher-level perceptions on  
lower systems that lack the ability either to perceive or control what  
you're perceiving. After all, you can always claim that a spinal reflex  
controls a relationship between an applied force and a muscle force that  
opposes it. But that's your own relationship level talking.

> Now we  
> could arrange piroettes with others kicks and jumps each different  
> and malleable in duration, extent, and inter-duration.

\_WHO\_ could arrange that? A higher system. But there is no level in the  
existing hierarchy that can perceive and control durations.

We'd better let this idea age for a while longer.

Best,

Bill P.