Vladimir,
I'm not trying to be difficult or critical but I literally can't understand
what you're saying, because you haven't given any example of a problem,
where "knowledge of concepts' relations and implications" somehow supersedes
or is independent of physical casting/ recasting.
Your analogy though of what I might be saying about maths (or other symbols)
is wrong. Numbers and arithmetic are based on and derive from physical
objects and our ability to add and subtract objects etc . Geometry is
obviously based on an analysis of physical objects and shapes. They are
totally physically object-based and can only be understood as such. To point
this out is not at all the same as suggesting that their figures are
composed of ink. I am talking about what their figures (and other symbols
like language) refer to, not what they are composed of. (Even a
mathematical concept BTW like "infinity" only became acceptable in maths
about the time of the printing press - when it became possible physically/
realistically for the first time to imagine objects being produced ad
infinitum).
And I would suggest that our ability to perceive the kinds of concept
relations you may be thinking of is very much physically based and
"digital" - IOW based on pointing with our digits to different objects in a
scene (even if only in our mind's eye) - to explain, for example, by
pointing to how "this moves that" and classify by pointing out that "he is
the parent of her" etc.
Your ink analogy BTW is also, very much I suggest, a physically based and
technically fascinating operation. How do you think you arrived at it -
other than physically and spatially? Do you think you could arrive at such
an analogy simply by comparing sets of symbolic properties of scientific
problems and their physical recasting , on the one hand, and symbolic
properties of numbers and ink on the other?
(Such an analogy is where the Fauconnier-style analysis of "conceptual
blending" of "mental spaces" comes into its own. How the brain achieves an
analogy as complex as your ink one is still something quite awesome and
problematic, even with Fauconnier's help - and still way beyond computers, I
suggest).
Vladimirwrote:
Vladimir,
No I'm sure the problem-solving isn't all down to recasting in terms of
physical models. But can you think of a scientific problem area, where
such
recasting isn't involved?
I just tried to provide my reason for considering it a mirage: even if
problem-solving doesn't involve physical reasoning, it can be
introspectively recast as sequence of spatial representations.
Domain-specific concepts involved in problem-solving can easily be
placed on spatially arranged schemata, but reasoning is correctly
carried out because of knowledge of these concepts' relations and
implications, not simply because of spatial setting in which they are
arranged. It's equivalent to calling mathematics ink-reasoning because
it's historically performed with help of remarks made by ink on paper
and any result can be written down by ink on paper.
(Very tangentially, what comes to my mind is chess. I'm confident that
human
problemsolving here - and the ability to search through only scores as
opposed to billions of chessboard scenarios to arrive at moves -
depends
on physical models, and is an ahem graphic illustration of the very
different ways in which current computers and a true general intelligence
think).
Vladimir: These 'recastings' of problems are essentially inference steps,
where
> each step is evident and is performed by trained expert's intuition.
> Sequence of such simple steps can constitute complex inference which
> leads to solution of complex problem. This recasting isn't necessarily
> related to physical common sense, even though each intermediate
> representation can be represented as spatially-temporal construction
> by virtue of being representable by frame graphs evolving over time,
> which does not reflect the rules of this evolution (which are the
> essence of inference which is being performed).
>
> On 10/11/07, Mike Tintner <[EMAIL PROTECTED]> wrote:
>> Just to underline my point about the common sense foundations of logic
>> and
>> general intelligence - I came across this from : Education & Learning
>> to
>> Think by Lauren B Resnick - (and a section entitled "General
>> Reasoning -
>> Improving Intelligence).
>>
>> "Recent research in science problem solving shows that experts do not
>> respond to problems as they are presented - writing equations for
>> every
>> relationship described and then using routine procedures for
>> manipulating
>> equations.Instead they reinterpret the problems, recasting them in
>> terms
>> of
>> general scientific principles until the solutions become almost
>> self-evident."
>>
>> He points out that the same principles apply to virtually all subjects
>> in
>> the curriculum. I would suggest that those experts are recasting
>> problems
>> principally in terms of physical common sense models. NARS, it seems
>> to
>> me,
>> "responds to problems as they are presented."
>>
>>
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>
>
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> Vladimir Nesov mailto:[EMAIL PROTECTED]
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