Posted by
glen ep ropella on
URL: http://friam.383.s1.nabble.com/Mathematics-and-Music-tp473042p475471.html
Günther Greindl wrote:
> Hmm - in the background he will have hypotheses; knowledge which is
> implicit in the neural weigthing in his brain (representing the evidence
> he has seen and categorized). So the physician has a mathematical
> (probabilistic) model of the situation, albeit maybe not
> verbalized/symbolized. He is probably not even aware of the mathamtics
> his brain embodies.
Excellent point! But, I'm not sure it's right to call that wet-ware
"mathematics". It is certainly correct to call it a model, though.
More specifically, the physician's brain (in that mode) is an analog of
the patient. (By "analog", I mean one extant object that mimics or is
largely similar -- by some similarity measure -- some other extant object.)
It would be closer to say that the physician's wet-ware brain is an
implementation of a (implicit) mathematical model. Or, perhaps it would
be better to say that the wet-ware _could_ be mathematically described
but isn't.
So, I agree with you that it's a model; but I disagree that it's a
mathematical model except in the pathological limit-case where all of
reality is somehow defined as "mathematics". A strong Platonist might
well say that all reality is mathematics. And if that's your point,
then it's well taken!
I find such an extreme limit case degenerate, though, because it
obviates the need for one of the two words. If all reality is math and
all math is reality, then we don't need both terms and we shouldn't use
both terms. We could just say stuff like:
"Bobby, go and do your reality homework!" [grin]
> When you go mathematical, you make it explicit. Knowledge can be
> transferred exactly. You can even mechanize it, meaning that you do not
> rely on neural weighting of the brain to which you communicate (drawing
> on the other person's experience of living in the same world as you
> actually).
I can't argue with that! I'd like to; but I can't. Since I'm
obstinate, however, if I were able to argue against it, I'd have to go
back to the distinction between a real object versus a
representation/description of an object. a.k.a. an implementation vs. a
specification.
A construct in math, being a story/description/specification would then
be _less_ particular than an implementation that was described by that
story. If the story were so very explicit as to permit only 1
implementation, _then_ we might be able to claim what you claim ... that
knowledge can be transferred exactly with math.
But if the mapping from the set of constructs to the set of real things
is not injective, then that leaves open the chance that any one story
defines an equivalence class of implementations. And that means that
the implementations are _more_ exact than the story.
--
glen e. p. ropella, 971-219-3846,
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