"A system is called complex if it has a
nonsimulable model." [EL 306]
"The rest of the world" speaks, theorizes.
calculates about "complex systems" as the ominous complicated,
hard-to-decipher constructs, MOSTLY consisting only of the RR's "simple" ones.
No "nonsimulables" included.
Would it be reasonable to add to the quoted
text "According to the RR terminology" or something similar?
[TG]
Especially for
the purposes of usage outside of this group....yes, it
would.
[JM]
Now a question to your conclusion: is a "model
of a system" an abstraction of it, or an extension which includes the system?
In the first case it is reductionistically a part of a reductionist model, ie.
the system, while in the second sense it does not make sense (going
into the undefined natural connections). Model
up or down?
Could you give a SHORT
explanation?
[TG]
I'd say a
model of a system (call it S) is definitely an abstraction of S.
Especially in the etymological sense of abstracted as "drawn away from".
When S
is a natural system, and the qualities of S are encoded into a model, there is
an inevitable abstraction occurring in the encoding of some quality of
the material world to some fixed symbolic entity, like a number. A formal
model also has a finite number of degrees of freedom, which is almost
certainly not representative of the actual degrees of freedom in the material
world.
The only case where the
notion of "abstraction" becomes trivial or non-existent is when S is a formal
system. In that case, S has a largest model, which is S itself [LI 55], and so
there no loss of any qualities in the model with respect to the original
system as one would normally expect with an abstraction. But that is
a rather trivial kind of "model".
JohnM