# BGCT

**URL:** <http://discourse.iapct.org/t/bgct/1497>\
**Category:** CSG2003\
**Created:** [December 22, 2003, 7:22pm UTC](http://discourse.iapct.org/t/bgct/1497 "2003-12-22T19:22:27Z")\
**Posts on this page:** 19\
**Page:** 1

<div class="post-metadata">

**Author:** ![Bruce\_Gregory4](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/7feea3/32.png) [@Bruce\_Gregory4](http://discourse.iapct.org/u/Bruce_Gregory4)\
**Post date:** [December 22, 2003, 7:22pm UTC](http://discourse.iapct.org/t/bgct/1497/1 "2003-12-22T19:22:27Z")

</div>

[From Bruce Gregory (2003.12.22.1421)]

While Marc is hard at work on MACT I thought I would introduce my own  
ideas for a heterodox version of control theory (BGCT).

Let me start by quoting Bill's recent post:

"Remember that in PCT all action is driven by error signals. No  
exceptions.  
The amount of action indicates the size of the error signal, with the  
most  
energetic actions being the result of the largest error signals."

When I apply this theory to my bicycle riding (I try to get in an hour  
every day) I arrive at the conclusion that I must be constantly  
experiencing error while I ride and the faster I pedal, the larger the  
error I must be experiencing.

In BGCT there is no direct coupling between action and error signals. I  
pedal faster because I set the reference level for pedaling higher. I  
normally experience very little error, no matter how fast I am  
pedaling. This helps explain why I enjoy cycling rather than making  
great efforts to avoid doing it. because of the constant error I  
experience.

I anxiously await your slings and arrows!

Bruce Gregory

"Everything that needs to be said has already been said. But since no  
one was listening, everything must be said again."

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Andre Gide

---

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**Author:** ![bnhpct](http://discourse.iapct.org/user_avatar/discourse.iapct.org/bnhpct/32/34_2.png) [@bnhpct](http://discourse.iapct.org/u/bnhpct)\
**Post date:** [December 22, 2003, 7:47pm UTC](http://discourse.iapct.org/t/bgct/1497/2 "2003-12-22T19:47:24Z")

</div>

[From Bruce Nevin 2003.12.22 14:47 EST]

Bruce Gregory (2003.12.22.1421)--

> Let me start by quoting Bill's recent post:
> 
> "Remember that in PCT all action is driven by error signals. No  
> exceptions. The amount of action indicates the size of the error  
> signal, with the most energetic actions being the result of the  
> largest error signals."
> 
> When I apply this theory to my bicycle riding (I try to get in an hour  
> every day) I arrive at the conclusion that I must be constantly  
> experiencing error while I ride and the faster I pedal, the larger the  
> error I must be experiencing.
> 
> In BGCT there is no direct coupling between action and error signals. I  
> pedal faster because I set the reference level for pedaling higher.

What system sets the reference level for rate of pedalling to a higher value? Is there no error behind that change of value? What happens to the system controlling rate of pedaling when "I" set its reference level higher? Is there no error when the reference rate is 10 and the perceived rate is 5? What do you call the difference between a reference rate of 10 and a perceived rate of 5, if not the error output of the comparator for rate of pedaling?

> I normally experience very little error, no matter how fast I am  
> pedaling.

It seems that perhaps Bill's locution "the amount of action" is imprecise. Would it further the discussion if you were to criticize this imprecision and suggest an alternative, perhaps having to do with effort?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;/Bruce Nevin

> **···**
>
> At 02:22 PM 12/22/2003 -0500, Bruce Gregory wrote:

---

<div class="post-metadata">

**Author:** ![Martin\_Taylor2](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/b4bc9f/32.png) [@Martin\_Taylor2](http://discourse.iapct.org/u/Martin_Taylor2)\
**Post date:** [December 22, 2003, 7:48pm UTC](http://discourse.iapct.org/t/bgct/1497/3 "2003-12-22T19:48:22Z")

</div>

> [From Bruce Gregory (2003.12.22.1421)]
> 
> While Marc is hard at work on MACT I thought I would introduce my own  
> ideas for a heterodox version of control theory (BGCT).
> 
> Let me start by quoting Bill's recent post:
> 
> "Remember that in PCT all action is driven by error signals. No  
> exceptions.  
> The amount of action indicates the size of the error signal, with the  
> most  
> energetic actions being the result of the largest error signals."
> 
> When I apply this theory to my bicycle riding (I try to get in an hour  
> every day) I arrive at the conclusion that I must be constantly  
> experiencing error while I ride and the faster I pedal, the larger the  
> error I must be experiencing.
> 
> In BGCT there is no direct coupling between action and error signals. I  
> pedal faster because I set the reference level for pedaling higher. I  
> normally experience very little error, no matter how fast I am  
> pedaling. This helps explain why I enjoy cycling rather than making  
> great efforts to avoid doing it. because of the constant error I  
> experience.
> 
> I anxiously await your slings and arrows!

I'm wondering what you think an error signal is???

In orthodox PCT or HPCT, error is the difference between a reference  
value and its corresponding perceptual value. If you say that in  
cycling you normally set the reference level for speed higher, that  
means (in orthodox PCT) that if you did not pedal faster, you would  
experience bigger error, so you have to pedal faster to keep the  
error small. If you didn't pedal at all, you would have a huge error,  
and so you need "energetic action" to reduce it to a minimal level.  
That seems straightforwardly to illustrate what Bill says, as well as  
what you say you experience.

I'm puzzled. How does BGCT handle this--or rather, how does it handle  
the situation differently?

Martin

---

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**Author:** ![Bruce\_Gregory4](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/7feea3/32.png) [@Bruce\_Gregory4](http://discourse.iapct.org/u/Bruce_Gregory4)\
**Post date:** [December 22, 2003, 8:01pm UTC](http://discourse.iapct.org/t/bgct/1497/4 "2003-12-22T20:01:40Z")

</div>

[From Bruce Gregory (2003.12.22.1501)]

> Bruce Nevin 2003.12.22 14:47

> What system sets the reference level for rate of pedalling to a higher  
> value?

The aerobic exercise system. It determines that I should ride my bike  
whenever I can.

> Is there no error behind that change of value?

It would experience error were I \_not\_ to ride my bicycle.

> What happens to the  
> system controlling rate of pedaling when "I" set its reference level  
> higher?

It pedals faster. Otherwise it would experience error.

> Is there no error when the reference rate is 10 and the perceived  
> rate is 5?

Yes. But it does not lead to a violent effort to pedal faster, simply  
to a gradual increase in pedaling rate.

> What do you call the difference between a reference rate of 10  
> and a perceived rate of 5, if not the error output of the comparator  
> for  
> rate of pedaling?

It doesn't jump from 5 to 10, it slowly moves from 5 to 10 and the  
pedaling rate follows it with a minimum of error.

> > I normally experience very little error, no matter how fast I am  
> > pedaling.
> 
> It seems that perhaps Bill's locution "the amount of action" is  
> imprecise.  
> Would it further the discussion if you were to criticize this  
> imprecision  
> and suggest an alternative, perhaps having to do with effort?

I have no reason to believe that Bill was imprecise. We was quite  
emphatic and I assume he meant what he said. Do you have reason to  
believe otherwise?

Bruce Gregory

"Everything that needs to be said has already been said. But since no  
one was listening, everything must be said again."

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Andre Gide

---

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**Author:** ![Bruce\_Gregory4](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/7feea3/32.png) [@Bruce\_Gregory4](http://discourse.iapct.org/u/Bruce_Gregory4)\
**Post date:** [December 22, 2003, 8:09pm UTC](http://discourse.iapct.org/t/bgct/1497/5 "2003-12-22T20:09:05Z")

</div>

[From Bruce Gregory 92003.12.22.1508)]

> > [From Bruce Gregory (2003.12.22.1421)]
> 
> In orthodox PCT or HPCT, error is the difference between a reference  
> value and its corresponding perceptual value.

This is also true in BGCT.

> If you say that in  
> cycling you normally set the reference level for speed higher, that  
> means (in orthodox PCT) that if you did not pedal faster, you would  
> experience bigger error, so you have to pedal faster to keep the  
> error small.

Quite so.

> If you didn't pedal at all, you would have a huge error,

Yes.

> and so you need "energetic action" to reduce it to a minimal level.

Really? I thought I would just stop pedaling. Does this count as  
"energetic action" in your view?

> That seems straightforwardly to illustrate what Bill says, as well as  
> what you say you experience.
> 
> I'm puzzled. How does BGCT handle this--or rather, how does it handle  
> the situation differently?

You and I seem to be in agreement except that I do not see the  
cessation of pedaling as an "energetic action." Perhaps the problem is  
that I don't understand what an energetic action is. To me, pedaling  
fast is an energetic action. Apparently this is not true for you and  
Bill. So I'm puzzled, too.

Bruce Gregory

"Everything that needs to be said has already been said. But since no  
one was listening, everything must be said again."

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Andre Gide

> **···**
>
> On Dec 22, 2003, at 2:48 PM, Martin Taylor wrote:

---

<div class="post-metadata">

**Author:** ![Marc\_Abrams1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/da6949/32.png) [@Marc\_Abrams1](http://discourse.iapct.org/u/Marc_Abrams1)\
**Post date:** [December 22, 2003, 8:14pm UTC](http://discourse.iapct.org/t/bgct/1497/6 "2003-12-22T20:14:45Z")

</div>

from [Marc Abrams (2003.12.22.1447)]

> [From Bruce Gregory (2003.12.22.1421)]

You are absolutely precious. MACT? I don't think so. Unless Bill set me up  
\_big time\_ (which I don't think) than I think that I am, and have been  
working on two aspects of HPCT that have not been fully extended. Memory and  
Emotion. The split hierarchy, which I like, and would like to explore more  
was, and is, Bill's idea. So please tell me where a MACT enters into the  
picture here?

> Let me start by quoting Bill's recent post:
> 
> "Remember that in PCT all action is driven by error signals. No  
> exceptions.  
> The amount of action indicates the size of the error signal, with the  
> most  
> energetic actions being the result of the largest error signals."
> 
> When I apply this theory to my bicycle riding (I try to get in an hour  
> every day) I arrive at the conclusion that I must be constantly  
> experiencing error while I ride and the faster I pedal, the larger the  
> error I must be experiencing.
> 
> In BGCT there is no direct coupling between action and error signals. I  
> pedal faster because I set the reference level for pedaling higher. I  
> normally experience very little error, no matter how fast I am  
> pedaling. This helps explain why I enjoy cycling rather than making  
> great efforts to avoid doing it. because of the constant error I  
> experience.

Pedaling slower or faster is only \_one\_ of the variables you are controlling  
for. Keeping and adjusting for balance \_while\_ you pedal slower or faster  
is another. You would realize this the moment you hit an unexpected pothole.  
Your 'speed' would become totally irrelevant.

You and I have had this discussion many times in the past taking on many  
guises and it all boils down to the same set of questions. A 'goal' you have  
has \_many\_ perceptions that need to be controlled. In your example you will  
pedal faster or slower until, or if, you encounter an error (pothole) that  
disturbs your effort. You don't realize it because it's all so automatic  
now, but you are \_continuously\_ adjusting your balance as you ride, so in  
effect you are experiencing 'constant' error, even though you are not aware  
of it. There are many things you are controlling for when you ride, but as  
Bill has said, when you experience error in \_any\_ of the variables, that  
variable will step to the head of the line, with the largest error getting  
the most action. That doesn't mean you are not correcting for other  
variables as well, or fully controlling for others too. We are capable of,  
and do deal with many control processes at the same time.

At least this is my take. Btw, what type of slings and arrows were you  
anticipating?

Marc

---

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**Author:** ![Bruce\_Gregory4](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/7feea3/32.png) [@Bruce\_Gregory4](http://discourse.iapct.org/u/Bruce_Gregory4)\
**Post date:** [December 22, 2003, 8:38pm UTC](http://discourse.iapct.org/t/bgct/1497/7 "2003-12-22T20:38:36Z")

</div>

[From Bruce Gregory (2003.12.22.1537)]

> Marc Abrams (2003.12.22.1447)
> 
> > [From Bruce Gregory (2003.12.22.1421)]
> 
> You are absolutely precious. MACT? I don't think so. Unless Bill set  
> me up  
> \_big time\_ (which I don't think) than I think that I am, and have been  
> working on two aspects of HPCT that have not been fully extended.  
> Memory and  
> Emotion. The split hierarchy, which I like, and would like to explore  
> more  
> was, and is, Bill's idea. So please tell me where a MACT enters into  
> the  
> picture here?

Apparently you are not as fool hearty as I am.

> Pedaling slower or faster is only \_one\_ of the variables you are  
> controlling  
> for. Keeping and adjusting for balance \_while\_ you pedal slower or  
> faster  
> is another. You would realize this the moment you hit an unexpected  
> pothole.  
> Your 'speed' would become totally irrelevant.
> 
> You and I have had this discussion many times in the past taking on  
> many  
> guises and it all boils down to the same set of questions. A 'goal'  
> you have  
> has \_many\_ perceptions that need to be controlled. In your example you  
> will  
> pedal faster or slower until, or if, you encounter an error (pothole)  
> that  
> disturbs your effort. You don't realize it because it's all so  
> automatic  
> now, but you are \_continuously\_ adjusting your balance as you ride, so  
> in  
> effect you are experiencing 'constant' error, even though you are not  
> aware  
> of it. There are many things you are controlling for when you ride,  
> but as  
> Bill has said, when you experience error in \_any\_ of the variables,  
> that  
> variable will step to the head of the line, with the largest error  
> getting  
> the most action.

What line? I'm sure you meant to say with the largest error generating  
the most action.

> That doesn't mean you are not correcting for other  
> variables as well, or fully controlling for others too. We are capable  
> of,  
> and do deal with many control processes at the same time.

I don't take exception with what you say, but it seems not to be  
relevant to my major claim to fame, namely that the speed at which I  
pedal is not related to any error in the system.

> At least this is my take. Btw, what type of slings and arrows were you  
> anticipating?

You don't propose a new control theory without expecting to draw fire.

Bruce Gregory

"Everything that needs to be said has already been said. But since no  
one was listening, everything must be said again."

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Andre Gide

---

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**Author:** ![Bill\_Powers](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/a183cd/32.png) [@Bill\_Powers](http://discourse.iapct.org/u/Bill_Powers)\
**Post date:** [December 22, 2003, 8:45pm UTC](http://discourse.iapct.org/t/bgct/1497/8 "2003-12-22T20:45:23Z")

</div>

[From Bill Powers (2003.12.22.1311 MST)]

Bruce Gregory (2003.12.22.1421) --

Let me start by quoting Bill's recent post:

> "Remember that in PCT all action is driven by error signals. No  
> exceptions.  
> The amount of action indicates the size of the error signal, with the  
> most  
> energetic actions being the result of the largest error signals."
> 
> When I apply this theory to my bicycle riding (I try to get in an hour  
> every day) I arrive at the conclusion that I must be constantly  
> experiencing error while I ride and the faster I pedal, the larger the  
> error I must be experiencing.

Yes, this is correct. I might guess that the controlled variable is your  
speed, in this case. If you set the reference speed low, only a small error  
is required to produce a leisurely pedaling action. As you raise the  
reference level, the pedaling action increases and the speed increases, but  
for this to happen, the error must also increase. Thus the perceived speed  
doesn't increase quite as fast as the reference signal does.

Suppose that when you intend to ride at 10 mph, the error is 0.1 mph so you  
actually ride at 9.9 mph. The output gain appears to be 9.9 mph/0.1 mph or  
99 mph per unit error. Assuming a linear system, what will the error be  
when you want to be riding at 20 mph? How fast will you actually be riding?

> In BGCT there is no direct coupling between action and error signals. I  
> pedal faster because I set the reference level for pedaling higher. I  
> normally experience very little error, no matter how fast I am  
> pedaling. This helps explain why I enjoy cycling rather than making  
> great efforts to avoid doing it. because of the constant error I  
> experience.
> 
> I anxiously await your slings and arrows!

No slings and arrows. I agree that you may normally experience very little  
speed error when pedaling. When you double your speed, you still experience  
very little speed error, because although the error is twice as large,  
twice as much as very little is still very little.

My theory requires that physiological preparedness for action is generated  
as a result of outputs to lower-level systems. A very small error, in a  
system with high output gain, can produce a very large output. Under the  
conditions of our example, an error of only 0.2 mph can generate a  
physiological state producing energy at the rate needed to sustain riding  
at 19.8 mph, which is probably a considerable amount. If you were cruising  
along at 5 mph, you would not want to have your heart rate so high, or your  
breathing so rapid and deep, or your circulating glucose at such a high  
concentration as when you're sustaining a speed of 20 mph. So it's a good  
thing your brain is able to adjust the reference levels for activity of  
your biochemical systems at the same time it adjusts the reference levels  
for motor activities.

Perhaps you were imagining that strenuous or rapid action would require  
large errors as a percentage of the reference signal. As you can see, a  
high-gain output function makes large error signals unnecessary. When you  
notice the pedestrian, I assume there is an error in your system for  
avoiding collisions, and the error results in your turning the steering  
wheel or slowing down. If the pedestrian is far away, the error remains  
almost, but not quite, at zero and the action is slow and moderate. If the  
pedestrian appears only 50 feet ahead, the error becomes far larger --  
perhaps as much as 10% of the reference signal -- and a very rapid action  
takes place with enough force to make sure the car turns or stops in time  
to avoid the collision. The reference degree of physical preparedness in  
the two cases would roughly correspond to the speed and strength of the  
output action, and therefore the intensity of the feeling state would also  
vary in the same way. So you might be a little annoyed at seeing the  
pedestrian in your path two blocks away, but scared out of your wits at  
seeing the pedestrian about to be hit by your car, 50 feet away.

Does this seem reasonable?

Best,

Bill P.

---

<div class="post-metadata">

**Author:** ![Martin\_Taylor2](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/b4bc9f/32.png) [@Martin\_Taylor2](http://discourse.iapct.org/u/Martin_Taylor2)\
**Post date:** [December 22, 2003, 8:46pm UTC](http://discourse.iapct.org/t/bgct/1497/9 "2003-12-22T20:46:25Z")

</div>

[Martin Taylor 2003.12.22.1546]

> [From Bruce Gregory 92003.12.22.1508)]
> 
> > > [From Bruce Gregory (2003.12.22.1421)]
> > 
> > In orthodox PCT or HPCT, error is the difference between a reference  
> > value and its corresponding perceptual value.
> 
> This is also true in BGCT.
> 
> > If you say that in  
> > cycling you normally set the reference level for speed higher, that  
> > means (in orthodox PCT) that if you did not pedal faster, you would  
> > experience bigger error, so you have to pedal faster to keep the  
> > error small.
> 
> Quite so.
> 
> > If you didn't pedal at all, you would have a huge error,
> 
> Yes.
> 
> > and so you need "energetic action" to reduce it to a minimal level.
> 
> Really? I thought I would just stop pedaling. Does this count as  
> "energetic action" in your view?

If you just stopped pedalling, you'd have a huge error, not a minimal  
error. PCT says you wouldn't do that with a controlled perception.  
You would act so as to minimize the error, which is to say, you would  
pedal hard.

You yourself said that you agreed that if you didn't pedal at all  
you'd have a huge error. I don't think you can have it both ways.  
Stopping pedalling can't reduce the error to a minimal level and also  
make the error be huge.

Actually, I think Bill did slightly mis-speak. He should have talked  
about a major change in action, rather than a major action. If you  
were pedalling hard with no error, and your reference speed dropped  
to zero, you'd also have a big error, and a big change in your action  
would be necessary (i.e. going from hard pedalling to no pedalling).

Martin

> **···**
>
> > On Dec 22, 2003, at 2:48 PM, Martin Taylor wrote:

---

<div class="post-metadata">

**Author:** ![Marc\_Abrams1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/da6949/32.png) [@Marc\_Abrams1](http://discourse.iapct.org/u/Marc_Abrams1)\
**Post date:** [December 22, 2003, 9:06pm UTC](http://discourse.iapct.org/t/bgct/1497/10 "2003-12-22T21:06:30Z")

</div>

from [Marc Abrams (2003.12.22.1602]

> [From Bruce Gregory (2003.12.22.1537)]
> 
> What line? I'm sure you meant to say with the largest error generating  
> the most action.

Yes.

> I don't take exception with what you say, but it seems not to be  
> relevant to my major claim to fame, namely that the speed at which I  
> pedal is not related to any error in the system.

Yes, it's the 'error' you percieve of either not going fast enough or  
generating enough rpm's for your exercise.

> You don't propose a new control theory without expecting to draw fire.

I think your being a bit dramatic here.

Marc

---

<div class="post-metadata">

**Author:** ![Bruce\_Gregory4](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/7feea3/32.png) [@Bruce\_Gregory4](http://discourse.iapct.org/u/Bruce_Gregory4)\
**Post date:** [December 22, 2003, 10:41pm UTC](http://discourse.iapct.org/t/bgct/1497/11 "2003-12-22T22:41:42Z")

</div>

[From Bruce Gregory (2003.12.22.1741)]

> [Martin Taylor 2003.12.22.1546]
> 
> You yourself said that you agreed that if you didn't pedal at all  
> you'd have a huge error. I don't think you can have it both ways.

Killjoy!

> Stopping pedalling can't reduce the error to a minimal level and also  
> make the error be huge.

I agree. I said that it did not take a great deal of effort to stop  
pedaling.

> Actually, I think Bill did slightly mis-speak. He should have talked  
> about a major change in action, rather than a major action. If you  
> were pedalling hard with no error, and your reference speed dropped  
> to zero, you'd also have a big error, and a big change in your action  
> would be necessary (i.e. going from hard pedalling to no pedalling).

Agreed.

Bruce Gregory

"Everything that needs to be said has already been said. But since no  
one was listening, everything must be said again."

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Andre Gide

---

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**Author:** ![Bruce\_Gregory4](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/7feea3/32.png) [@Bruce\_Gregory4](http://discourse.iapct.org/u/Bruce_Gregory4)\
**Post date:** [December 22, 2003, 11:59pm UTC](http://discourse.iapct.org/t/bgct/1497/12 "2003-12-22T23:59:59Z")

</div>

[From Bruce Gregory (2003.12.22.1900)]

> Bill Powers (2003.12.22.1311 MST)
> 
> Does this seem reasonable?

Sigh. Yes, it does. Back to the drawing board....

Bruce Gregory

"Everything that needs to be said has already been said. But since no  
one was listening, everything must be said again."

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Andre Gide

---

<div class="post-metadata">

**Author:** ![Bruce\_Gregory4](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/7feea3/32.png) [@Bruce\_Gregory4](http://discourse.iapct.org/u/Bruce_Gregory4)\
**Post date:** [December 23, 2003, 3:44pm UTC](http://discourse.iapct.org/t/bgct/1497/13 "2003-12-23T15:44:47Z")

</div>

[From Bruce Gregory (2003.12.23.1043)]

> Bill Powers (2003.12.22.1311 MST)
> 
> Yes, this is correct. I might guess that the controlled variable is  
> your  
> speed, in this case.

Just for the record, the controlled variable is more likely to be  
cadence. You shift gears to maintain your cadence, speed is rarely a  
consideration (except when it gets too great going downhill).

Bruce Gregory

> "Everything that needs to be said has already been said. But since no  
> one was listening, everything must be said again."

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Andre Gide

---

<div class="post-metadata">

**Author:** ![Bill\_Powers](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/a183cd/32.png) [@Bill\_Powers](http://discourse.iapct.org/u/Bill_Powers)\
**Post date:** [December 23, 2003, 4:30pm UTC](http://discourse.iapct.org/t/bgct/1497/14 "2003-12-23T16:30:01Z")

</div>

[From Bill Powers (2003.12.23.0909 MST)]

> Bruce Gregory (2003.12.23.1043)--

> > Yes, this is correct. I might guess that the controlled variable is  
> > your speed, in this case.
> 
> Just for the record, the controlled variable is more likely to be  
> cadence. You shift gears to maintain your cadence, speed is rarely a  
> consideration (except when it gets too great going downhill).

I am guessing that cadence is cycling jargon for the repetition rate of the  
pedaling cycle. The gear shifting is an interesting means of control,  
because it alters the environmental feedback function -- the conversion of  
pedaling pressure to propulsive force. So you can control cadence in two  
ways -- by varying how hard you push on the pedals, and by varying the gear  
ratio.

What is it that you're controlling, then -- is it the pedaling speed or the  
amount of force your feet (legs) exert on the pedals? Or is it that you  
maintain a constant amount of pedaling force, and use the gearshift to keep  
the pedal rotation speed constant? And what about the rate at which you  
expend energy?

Hmm. I can see that this is more complicated than it seems at first. Have  
you had any technical thoughts about just what all the controlled variables  
might be? I'm sure there must be tons of information in the ergonomics  
literature.  
Or is this like asking the old man if he sleeps with his beard under or  
outside the covers? I don't mean to spoil the enjoyment.

Best,

Bill P.

---

<div class="post-metadata">

**Author:** ![Marken\_Richard](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/e19b73/32.png) [@Marken\_Richard](http://discourse.iapct.org/u/Marken_Richard)\
**Post date:** [December 23, 2003, 5:59pm UTC](http://discourse.iapct.org/t/bgct/1497/15 "2003-12-23T17:59:01Z")

</div>

[From Rick Marken (2003.12.23.1000)]

Bill Powers (2003.12.22.1311 MST)--

> My theory requires that physiological preparedness for action is generated  
> as a result of outputs to lower-level systems. A very small error, in a  
> system with high output gain, can produce a very large output. Under the  
> conditions of our example, an error of only 0.2 mph can generate a  
> physiological state producing energy at the rate needed to sustain riding  
> at 19.8 mph, which is probably a considerable amount. If you were cruising  
> along at 5 mph, you would not want to have your heart rate so high, or your  
> breathing so rapid and deep, or your circulating glucose at such a high  
> concentration as when you're sustaining a speed of 20 mph. So it's a good  
> thing your brain is able to adjust the reference levels for activity of  
> your biochemical systems at the same time it adjusts the reference levels  
> for motor activities.

It seems like there is the possibility here for some really interesting  
studies of the relationship between biochemical activity and control. If  
preparedness for action (biochemical activity) is proportional to error then  
we should see the same level of preparedness for the same amount of error,  
regardless of the actual level of output. In the case of bike speed, the  
output gain (speed per unit error) can be varied using gears. Doubling the  
gear ratio (increasing wheel turns/pedal turns) doubles the output gain  
(with respect to speed) so that the same output (speed) is produced with  
half the error as before.

So doubling the gear ratio in this way while maintaining the cyclist  
maintains the same speed should cut error in half and, thus, reduce the  
level of activity of the biochemical systems, even though the cyclist is  
still using the same total amount of energy to produce that speed. Is my  
reasoning correct about this? If so, is there any evidence that there is a  
reduced level of activity of the biochemical systems (lower heart rate,  
breathing rate and concentration of circulating glucose) when you double the  
error output gain of the cyclist using gears?

Best

Rick

> **···**
>
> --  
> Richard S. Marken  
> MindReadings.com  
> Home: 310 474 0313  
> Cell: 310 729 1400

---

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**Author:** ![Bruce\_Gregory4](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/7feea3/32.png) [@Bruce\_Gregory4](http://discourse.iapct.org/u/Bruce_Gregory4)\
**Post date:** [December 23, 2003, 7:55pm UTC](http://discourse.iapct.org/t/bgct/1497/16 "2003-12-23T19:55:04Z")

</div>

[From Bruce Gregory (2003.12.23.1455)]

> Bill Powers (2003.12.23.0909 MST)
> 
> I am guessing that cadence is cycling jargon for the repetition rate  
> of the  
> pedaling cycle.

Indeed.

> The gear shifting is an interesting means of control,  
> because it alters the environmental feedback function -- the  
> conversion of  
> pedaling pressure to propulsive force. So you can control cadence in  
> two  
> ways -- by varying how hard you push on the pedals, and by varying the  
> gear  
> ratio.

Yes. And I have 27 gears to play with.

> What is it that you're controlling, then -- is it the pedaling speed  
> or the  
> amount of force your feet (legs) exert on the pedals? Or is it that you  
> maintain a constant amount of pedaling force, and use the gearshift to  
> keep  
> the pedal rotation speed constant? And what about the rate at which you  
> expend energy?

I try to maintain a constant "perceived effort." The most  
energy-efficient cadence is supposed to be between 60 and 90 rpm. My  
goal is closer to the lower limit. If I find myself having to exert too  
much force to maintain this cadence, I shift to the next lower gear.

> Hmm. I can see that this is more complicated than it seems at first.  
> Have  
> you had any technical thoughts about just what all the controlled  
> variables  
> might be? I'm sure there must be tons of information in the ergonomics  
> literature.  
> Or is this like asking the old man if he sleeps with his beard under or  
> outside the covers? I don't mean to spoil the enjoyment.

Fortunately, my beard is sufficiently short that this is not a problem.

Bruce Gregory

"Everything that needs to be said has already been said. But since no  
one was listening, everything must be said again."

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Andre Gide

---

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**Author:** ![Bill\_Powers](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/a183cd/32.png) [@Bill\_Powers](http://discourse.iapct.org/u/Bill_Powers)\
**Post date:** [December 23, 2003, 10:22pm UTC](http://discourse.iapct.org/t/bgct/1497/17 "2003-12-23T22:22:46Z")

</div>

From Bill Powers (2003.12.23.1504 MST%)]

Bruce Gregory (2003.12.23.1455)--

> I try to maintain a constant "perceived effort." The most  
> energy-efficient cadence is supposed to be between 60 and 90 rpm. My  
> goal is closer to the lower limit. If I find myself having to exert too  
> much force to maintain this cadence, I shift to the next lower gear.

So, how would we model perceived effort? Is this judged by the forces you  
exert (i.e., foot pressure), or by how your muscles feel? When you say "too  
much force," does this mean the limit is set in terms of amount of push, or  
is it set by the amount of muscle effort you can sustain without feeling tired?

Modeling this down to the last detail could end up being a major project.  
Is there some way we can approximate the controlled variable in terms of  
the rate at which your body can supply energy, and the energy losses due to  
internal friction in muscles? Suppose we said that your body can provide  
enough power to exert a total of 55 foot-pounds per second (0.1 horsepower)  
indefinitely. Also, we can say that the amount of energy lost in the  
muscles depends on how fast the pedals are rotating: the faster they go,  
the less energy is left to be applied to the pedals (with some adjustable  
constant to set the slope of the relationship). Then we might say that the  
preferred level of effort is that which uses 75% of the maximum sustainable  
power. When you're using energy faster than that, you start feeling that  
you're putting out too much "effort." Does this sound anything like the  
truth? I think that these relationships would end up with a solvable set of  
equations, but we'd just have to try them and see.

Best,

Bill P.

---

<div class="post-metadata">

**Author:** ![Bill\_Powers](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/a183cd/32.png) [@Bill\_Powers](http://discourse.iapct.org/u/Bill_Powers)\
**Post date:** [December 23, 2003, 10:31pm UTC](http://discourse.iapct.org/t/bgct/1497/18 "2003-12-23T22:31:15Z")

</div>

[Bill Powers (2003.12.23.1530 MST)]

Rick Marken (2003.12.23.1000)

> It seems like there is the possibility here for some really interesting  
> studies of the relationship between biochemical activity and control. If  
> preparedness for action (biochemical activity) is proportional to error then  
> we should see the same level of preparedness for the same amount of error,  
> regardless of the actual level of output. In the case of bike speed, the  
> output gain (speed per unit error) can be varied using gears. Doubling the  
> gear ratio (increasing wheel turns/pedal turns) doubles the output gain  
> (with respect to speed) so that the same output (speed) is produced with  
> half the error as before.

However, it would require twice the force, and error is more likely related  
to pedal force than rotational speed. Rotational speed will more likely be  
a controllable consequence of pedal force, wind resistance, grade, and  
internal losses due to muscle viscosity, rather than depending directly on  
error..

I think it will be necessary to set up some equations that represent the  
various relationships with reasonable -- that is, ball-park -- accuracy  
before trying to predict what all the interactions will be. It is an  
interesting problem. The only question is whether we want to commit the  
necessary time to it. Well, the other only question is whether somebody has  
already done this analysis and saved us the trouble.

Best,

Bill P.

---

<div class="post-metadata">

**Author:** ![Bruce\_Gregory4](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/7feea3/32.png) [@Bruce\_Gregory4](http://discourse.iapct.org/u/Bruce_Gregory4)\
**Post date:** [December 25, 2003, 12:20pm UTC](http://discourse.iapct.org/t/bgct/1497/19 "2003-12-25T12:20:34Z")

</div>

[From Bruce Gregory (2003.12.25.0719)]

> Bill Powers (2003.12.23.1504 MST
> 
> Bruce Gregory (2003.12.23.1455)--
> 
> > I try to maintain a constant "perceived effort." The most  
> > energy-efficient cadence is supposed to be between 60 and 90 rpm. My  
> > goal is closer to the lower limit. If I find myself having to exert  
> > too  
> > much force to maintain this cadence, I shift to the next lower gear.
> 
> So, how would we model perceived effort? Is this judged by the forces  
> you  
> exert (i.e., foot pressure), or by how your muscles feel? When you say  
> "too  
> much force," does this mean the limit is set in terms of amount of  
> push, or  
> is it set by the amount of muscle effort you can sustain without  
> feeling tired?
> 
> Modeling this down to the last detail could end up being a major  
> project.

It sure sounds like it!

> Is there some way we can approximate the controlled variable in terms  
> of  
> the rate at which your body can supply energy, and the energy losses  
> due to  
> internal friction in muscles? Suppose we said that your body can  
> provide  
> enough power to exert a total of 55 foot-pounds per second (0.1  
> horsepower)  
> indefinitely. Also, we can say that the amount of energy lost in the  
> muscles depends on how fast the pedals are rotating: the faster they  
> go,  
> the less energy is left to be applied to the pedals (with some  
> adjustable  
> constant to set the slope of the relationship). Then we might say that  
> the  
> preferred level of effort is that which uses 75% of the maximum  
> sustainable  
> power. When you're using energy faster than that, you start feeling  
> that  
> you're putting out too much "effort." Does this sound anything like the  
> truth? I think that these relationships would end up with a solvable  
> set of  
> equations, but we'd just have to try them and see.

I suspect it represents a model of a competitive cyclist. My own  
cycling is not that sustained except when I am going uphill and have to  
pedal at somewhere near my maximum output. Otherwise I have bursts of  
sustained output followed by recovery periods.

Merry Christmas to all!

Bruce Gregory

"Everything that needs to be said has already been said. But since no  
one was listening, everything must be said again."

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Andre Gide