Hi Stevan, Thanks for your interesting ruminations. I have interdigitated
some reactions. Phil
> I'm right now teaching mental models to our 1st year's
> and I have a question:
>
> In what respect are mental models mental?
>
> If in doing a logical or spatial problem I generate mental tokens of
> exactly the sort you and Jane describe, how is that different from
> writing out the tokens in full on paper?
One is in your head, and the other is external. It makes a difference
in terms of integration, i.e. in order to form one external model
from two, you're going to have to get both the external models into
working memory.
> I mean we would not (I think) want to call counting in one's head
> "mental arithmetic" -- or would we? And if I carry the 1's in
> my head when I'm doing an addition, how is this more (or less)
> mental than if I write them out?
Same answer as above. Writing helps working memory, but ultimately
processes of integration (or of forming the successor to a natural
number) call for an internal representation.
> If we do in our heads what we could do with our hands I suppose it's
> covert, in some way, but doesn't mental (or perhaps cognitive)
> explanation begin where we start to explain what generates this
> kind of activity (whether it is overt of covert).
Agreed!
> Another way to put it: What would become of mental-models theory if
> everyone everywhere always did these things overtly on a scratch-pad,
> and it always transpired precisely as you predict: There would
> not even be a contest between your theory and its rivals
> (Lance's, say) because by direct observation of the scratch pad you
> could confirm that it is what you say that they are doing, and not what
> Lance says, that is correct.
Fabien Savary have results v close to those of your thought-experiment:
we video-taped people as they used pencil and paper to reason and
"thought aloud". Some of them produced various incremental diagrams
that are isomorphic to mental models. Victoria Bell then taught
this method to average reasoners, and it improved their performance
about 30%. She then showed that people could do it in their heads too.
What's the difference between what people do spontaneously and
what they did in the latter expt? Probably, that in the latter
experiment people adopted a cs strategy.
> In doing it on paper, would they make it into a paper-model,
> rather than a mental model?
We call them 'external models'.
> (I don't think, by the way, that this problem, if it is a problem, is a
> problem only for mental-models theory: It is a problem for any
> quasi-homuncular theory, in which, the explanation consists of
> positing that we do overtly what we could have done overtly.
Yes, the computer program implementing the theory shows how to get
rid of the humunculus, at least in principle.
> It seems that an explanation must discharge the homunculus after all --
> as Shepard's "mental rotation" does: For though we could of course
> do a slow rotation-match overtly, the mental task is accomplished
> so quickly that we had no time to rotate -- or even notice that we had
> "done" a rotation: It is then that the homunculus is dispensed with,
> because I confess that I was fed the outcome on a platter by my brain: I
> did not do the rotation; I just saw its outcome.)
>
> Ruminations, as old, perhaps, as introspection...
Phil Johnson-Laird
Department of Psychology
Princeton University
Green Hall
Princeton, NJ 08544, USA
Tel: (609) 258 4432
Fax: (609) 258 1113
http://www.cogsci.princeton.edu/~phil
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