[From Oded Maler 920810]
{Since I received no feed-back (from the list-server..) on this
post from yesterday, I re-send it. I apologize if eventually it
will be posted twice}
(Concerning the recent exchange on simplifying assumtion, disturbance-free
worlds, modeling etc.)
[In this short unfocused essay I use often the term "Blocks world"
which is a common metaphor characterizing symbolic AI toy worlds,
where the world consists of objects,(block-a, block-b), properties (
green(block-a) ), relations ( on(block-a,block-b) ) and operators that
transforms the state of the systems (e.g., remove one block from
another). This gives the flavor of the world on which classical AI
problem-solving took place.]
···
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Suppose for the moment that the object of study of AI, AL, etc. is
not defined with any reference to any reality of living systems. It
is the study of mathematical platonic entities obeying some rules,
interacting with some environment which is also an abstract object
with its own formal dynamics. I'm sure that at this level no one will
object the validity of various results obtained there (only their
relevance to something interesting). I'll give two concrete
examples one in AI flavor and one in AL:
1) An algorithm, that given a "goal" (in this setting, a representation
of some configuration of the "environment") produces a sequence of
"actions" that leads from any state to this state.
2) A set of simple local dynamical rules, that when employed by many
similar abstract entities leads to an interesting emergent global
"behavior" (=trajectories in the state-space).
Now, we try to see whether there is any relevance to the "real" thing.
Considering the first example, we all know (by now) that the world
does not come with labels "a" and "b", and making sense of the sensory
input is a big mess. We also know that any abstract action that we want
to perform should be realized in a smaller scale with disturbances etc.
In other words, the real world is not the Blocks-world. On the other hand,
we feel from introspection that *some* of our mental activity is done in
this (graph-searching, if-then-else) mode, and *if* the lower-level
systems take responsibility for all the messy details, uncertainties,
and disturbance, it can transduce the real-world into a Blocks-world,
and then a higher-level system can operate at this abstract level, and
thus the achievements of systems of type (1) above can become relevant.
This was (and probably is) the tacit assumption of symbolic AI,
cognitive psychology, etc. and without it all this research is rather
irrelevant to human mentality and of little relevance to engineering
(except for some non-robotics AI such as [non-video] game playing).
There might be two objections to this view:
I) It is impossible to construct such a real-to-abstract transducer
without solving the unsolvable categorization problem (and certainly
not in real-time).
II) - And this is the most intriguing fact for me - *EVEN* if such a
translation exists, except for some small toy problems, the planning
problem in such a world is computationally intractable.
All this means that the blocks world is uncomparable in its complexity
to the real world (as perceived by our problem-solving level): in one
sense it is simpler because its availiability to us subsumes a
non-existent unrealistic transducer, and on the other hand it is more
complex because many problems that we can solve with our slow brains,
can not (provably) be solved in the blocks world using the fastest
computers.
The second observation might suggest that concerning negative results,
simplifying assumption are useful bacause it demonstrates that *even*
in a disturbance-free environment, something cannot work - so it
certainly won't work when ideal transducers are replaced by noisy ones.
I've been attracted to the bottom-up approach (e.g., Powers, Brooks) hoping
that some principles discovered while going up in the levels will explain
how, after all, it is possible to plan and solve problems in the real-world
in the higher level. In what way does the fact that the symbols on which
the higher-level systems work, are "grounded" (to use a popular term) in
lower-level interaction with our particular concrete world, make
problem-solving easier than is some arbitrary abstract world (and this
is also, I think, related to some of the ecological ideas of Gibson).
Ok, I see I'll not touch the AL example this time. Feed-back (of any
polarity) is wellcome.
--Oded