[gabriel to powers, but not in reply to new matl.]

Perhpas the following is an example that makes my point that inside

minimisers of functions where control theory can be used to hunt

for minima, is the following.

Suppose we have a box F that perceives x and generates a behaviour f,

both of which have representations by real scalars. F can be said to

compute f(x), and by computing f(x) and f(x+delta) can provide the

means to estimate df/dx.

Suppose we have another box M, that can stimulate F and observe its

behaviour. M can clearly, given x, measure f(x) and f(x+delta), and

estimate df/dx. Now add an ECS to M having reference 0, perception

of df/dx and x from M, and ouput x' such that either df/dx for x=x'

or f(x') < f(x). This ECS will need a layered protocol with M

if it is to find an x' that does as very good job - e.g. by

having the ECS estimate the second derivative of f(x) at x,

and then fit a quadratic function q(x) to f in the rgion of x,

and output the x' that minimises the value q(x'). Also to minimise

f() to within some acceptable delta will require more than one step.

Well, stick insects have to walk up twigs to find prey, so more than

one step is no problem. The function f() had better be continuous

and have well defined derivatives most places. This is the necessary

condition for successful use of a control system, as distinct from

some other means to drive perceptions towards desires. Not necessary

for minimisers in general though.

This seems very clumsy and expensive for x scalar if you just

want to make a composite system of M F and ECS to generate a

behaviour B that drives a perception P closer to a desired value

D.

But if x is vector of a few hundred components, it's actually a

very good way to drive P(x) closer to D(x) - x is a vector in

the external world that can be changed by the composite M,F,ECS

system.

These are the kind of complex problems where I am interested to apply

the central idea of BCP.

Now, if you look at the ways Governments or Corporations make bad

decisions, it's because the decision makers do not have Ashby's

"Necessary Variety" in their degrees of freedom, even though

there are likely to be unrecognised degrees of freedom that MIGHT

exert great leverage. And this is why being able to make new

percepts in Kanerva space is important to me. It's necessary

for strong inductive reasoning.

And many decision makers have very few important values - power, short

term profit, keeping up appearances, and acceptance by others of their

ilk. The rest of us suffer the consequences.

It is incidentally being able to recognise these degrees of freedom

that makes great fortunes in business, and wins wars if these are

regrettably unavoidable. My combat pistol instructor used to

emphasise that it was preferable to avoid need to use lethal force, but

if it DID happen to be unavoidable there was no medal for coming in

second.

It was this failure by the "Great Society" that set me off on a

path looking for a "better way".

Best

John