This didn't seem to get distributed. Here we go again (slightly

edited); I apologize if it repeats. (I also apologize for using

1/f() to denote the inverse of f();-))

## ···

----------------

From Rick Marken (970128.0900)]

Me:

The nervous system controls perceptual inputs; it doesn't

calculate actions.

Scott Stirling (970127)--

So no mathematical calculations are involved, right?

Excellent questions in your post, Scott. Avery.Andrews (970128, Eastern

Australia), one of our other resident linguists, gave an excellent

answer. But I think this topic is so important that I will try to give

one myself.

Control theory is about how people produce intended results (such as

a caught ball). PCT says this is done by control of a hierarchy of

perceptual variables. Blom et al (the "Modern Control Theory" -- MCT

--crowd) say it is done by calculation of outputs based on a "model" of

the environment.

Here is a way to look at the MCT approach to the production of

intended results. MCT recognizes that intended results are produced

by the outputs of the system and that there is a functional

relationship between outputs and results. This functional relationship

is called "the environment function" or the "feedback function". Here

is an example of an environment function that relates a human output

(neural current) to a result of that output (distance of a ball from

the hand):

Result + |<---------------------------------*

(Hand/Ball | * |

Distance) | * |

> * |

(caught) 0|<----------------------- * |

> * | |

> f(o) * | |

> * | |

> * | |

- | * v v

-----------------------------------------

Output (neural current, spikes/sec)

The stars map out the "environment function", f(o), that relates

what your nervous system does (generates neural currents) to a result

of that neural activity (movement of your hand to a position relative

to the ball). Note that the function is VERY non-linear, though it

is monotonic.

According to MCT, if you intend to produce a particular result (such

as the result "ball zero distance from hand" which I call "caught" on

the graph) then you have to _compute_ the neural currents that you

have to generate to produce this result. In order to do this, you

have to have a model of f(o) in your brain (this is the "model" in

"model based control"). If you have a model of f(o), then you compute

the output required generate that result by "working back" from the

intended result (the value of f(o)) to the output (o) that produces

that value of f(o). That is, you find the inverse of f(o); this is the

value of output that produces the intended result f(o).

Computing the inverse of f(o) is like moving from the intended result

on the y axis above, along the horizontal line until you hit f(o). At

that point you move verticaly to the point on the output axis to find

that value of output that produces that value of f(o) (the intended

result).

If you intend to produce a different result (such as having the ball go

over your hand by a certain amount) then you start from this new result

(which is the value of f(o) at the + sign), move horizontally to the

f(o) curve and then move down to find the output value that produces

this result.

So MCT says that, in order to produce intended results, we have to

have a good "model" of f(o), the environmental function that relates

neural activity (the only output that is completely determined by the

control system itself) to the intended result. PCT questions this

model on two grounds: 1) it seems VERY unlikely that the brain can

do the computations required to estimate f(o) OR to compute it's

inverse and 2) this model fails to explain how we produce intended

results in the context of _unpredictable_ and _undetectable_

disturbances. The result on the y axis is not just a function of our

outputs; it also a function of forces that are independent of our

outputs -- such as gusts of wind -- that are completely unpredictable.

Despite such disturbances, we are able to reliably produce the results

we intend; we can, for example, catch a ball rather reliably on a windy

day.

The MCT approach to the production of intended results is based on

open-loop concepts of behavior that were (unfortunately) borrowed by

control theorists (who had been moving in the correct direction until

then) from psychologists.

A real closed loop control system doesn't doesn't compute outputs;

the outputs of a closed loop control system are always proportional

to r-p, the difference between the intended, r, and actual, p, results

of output. PCT explains the behavior that MCT says is computed output

in terms of controlled INPUT. A control system produces intended

results because it can PERCEIVE the state of those results (for

example, it can perceive the distance of the ball from the hand) and

it can vary its outputs appropriately (meaning, with the appropriate

SIGN and GAIN) to keep "pushing the perception of the result toward the

intended state, r.

The significant "computation" that goes on in a control system occurs

onn the INPUT (perceptual) side of the system and in the ORGANIZATION

of the relationship between control systems. In order to catch a ball

you have to design a control system that can _perceive_ the state of

the intended result; that can _continuously_ percieve the distance of

the ball from the hand, for example. You also have to design other

control systems that can control perceptions of acceleration and

velocity of the hand (to move the hand relative to the ball),

perceptions of convergence of the eyes (to keep the ball and hand

"centered" in vision), etc.

All of these aspects of the design of a hierarchical perceptual

control system, one that can produce intended results in a disturbance

pronce environment (and in an environment where even the environment

function, f(o) can change!), are embodied in Bill Powers' Little Man

demo that Avery mentioned. When you understand how the Little Man

works you will have gone a LONG way toward understanding how HPCT

works and (I believe) how humans work, too.

Best

Rick