ONT Re: Inquiry Driven Learning Environments (IDLE's)
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| Document History
|
| Subject: Extensions Of Mind
| Subhead: Essays And Reports On Intelligent Systems
| Contact: Jon Awbrey <jawbrey@oakland.edu>
| Version: Draft 3.03
| Created: 10 Sep 1993
| Revised: 08 Mar 1995
| Updated: 09 Feb 2002
| Advisor: C.C. Wagner
| Setting: Oakland University, Rochester, Michigan, USA
| Excerpt: Division 4 (An OAR For Odysseus: Offline Analytic Resource)
| Excerpt: Subdivision 4.2 (Prerequisite Orderings)
4.2 Prerequisite Orderings
A loose question about prerequisites: Is logic a prerequisite to arithmetic,
or arithmetic a prerequisite to logic? Consider the fact that real numbers
are a very special mathematical domain, satisfying a far greater number of
powerful and constraining axioms than the humble field of boolean values.
Remember that more axioms implies more specialized, not more general.
This has a bearing on the question of whether certain neural network
models, specifically, those that use real number arithmetic to explain
logical operations, are perhaps not using a more complex and specialized
capacity to construct and to explain a lesser, thus inverting the natural
order of prerequisites. To some people this affords all the esthetic and
technical satisfaction of using a nuclear reactor to drive a simulated
paddle-wheel boat. Others will argue that some dislocation of natural
orderings is a necessary precondition of any modeling enterprise, that
each personal choice of artificiality merely invokes the same technical
license required of all explanatory simulations. Besides, they might say,
in the real world intelligent systems are embodied in physical material and
embedded in spacetime. Consequently, for real systems it is supposed to be
the physical backdrop that carries out the analogue of infinite precision
arithmetic for us.
Not everyone thinks that nature has infinite information capacity, or that
intelligent systems could count on exploiting this ideal precision even if
they were constructed by means of it. In other words, even if nature has
its own brand of exact numerical co-processors, and has used them to build
intelligent creatures, it doesn't mean these critters have any constant or
current access to a channel of the same capacity. Or does it? Who knows?
We can dream, we can aspire -- but the antecedent If's are very big If's.
On the other hand, it's a rational counter to say that relying too much on
oracles, in effect, on transcendental sources, seems to ignore the reality
of information as a measurable dimension and to deny the aspect of finitude
that underlies effective computation. The actual universe may well fill the
role of an infinite source and store of information, and it may do so in each
of its smallest parts, but quantum mechanics and thermodynamics seem to place
strong bounds on the ability of isolated systems, intelligent or not, to access
and to control such overwhelming resources. It was indeed the due, and needless
to say, the long overdue appreciation of these bounds that first made the whole
computer revolution both possible and necessary. And wasn't that the door --
where we came in?
Jon Awbrey
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