> ERAY:
> May I interject here?

Of course. Was hoping you might.

> The computational power of an analog computer or
> a quantum computer is equivalent to the computational
> power of a discrete computer. That is *why* we can
> say discrete computer without any loss of generality.

Right. Of course. That's essentially what I'm saying, but I was hoping that a
different way of expressing the idea might get through to someone who doesn't
seem to understand "computational power". Looks like it did not work.

What the equivalence means is that they can do the same things, that anything
one can do the other can do.

It still remains that the description of (digital) computation as formal symbol
processing can be misleading, can lead to things such as Searles intuition that
computers cannot do various things that we take brains as doing. It also leads
GOFAI workers to attempt a misguided implementation of AI in which the elements
of mental experience are formal symbols instantiated in the program for direct
manipulation.

It is my contention that at least one level of indirectness is required for the
implementation of AI.

I say that we should not in general program algorithms that directly implement
semantics and understanding. Those must develop through observation of and
interaction with the world. So we program algorithms to implement that
development, not to implement directly the things that will develop.

If we program a computer with methods for doing intelligent things, then it is
difficult to imagine how it will come to do new intelligent things unlike any we
happened to program. In early GOFAI days this attracted considerable attention,
and was framed as "the frame problem".

The solution is to program the computer to learn for itself. Not just "learn"
in the limited sense of adapting an existing understanding to accommodate
specific conditions encountered, but learn entirely new concepts and
relationships having no representation at all in the original programming.

The structures that develop are implicit in a combination of both the formal
algorithms we provide and in the real-world processes which they come to model
and thus understand. Those structures themselves represent or model concepts
and relationships both static and dynamic and can be taken as doing some sort of
"computations" of their own, both explicitly when they reason through a problem
and implicitly when the experience the modeled impact of various observed or
projected changes in their elements.

However, the computations done at this level may not be best explained as
discrete formal symbol manipulation, even though they ultimately derive from
such computation at another level.

Is this making sense to you?

Bill