|
David,
Sorry for the
delay. You wrote:
How many ways do you (or whoever feels compelled to
respond) think that f:A--->B "metabolism" can be interpreted? Surely a
great many and not all of them need be mathematical interpretations,
right? My intuition is generally not mathematical. Also the arrow
gives the impression of time but why could it not be merely an
association? I would imagine
there are an infinite number of ways that the formal statement "f:A -> B"
could be interpreted; that is, I would imagine that there are an infinite number
of formal systems of which that statement could be a model, as well as a large,
if not infinite, number of natural systems of which that statement could be a
model.
'Metabolism' in
the general (M,R)-system model is a network, which could be very complicated
indeed. Abstracting that to "f:A -> B" does no harm for the purpose for which
the more abstract description serves. Unfortunately, the ability for this to be
an abstraction of so many different things can lead to confusion. The main
criticism in the Landauer-Bellman paper relied on an assumption that this kind
of abstract mapping must be an abstraction of an analytic equation (what
they called the "equational distinction"), rather than an algebraic relation.
As
you suggest, the statement does describe an algebraic
relation. And while any analytic equation can be abstracted into an algebraic
description, not all algebraic relations can be converted into analytic ones. In
this form of algebraic relation, I consider that time is abstracted out as an
explicit quality, and the arrow indicates a type of relation, just as the colon
indicates a type of relation.
Regards,
Tim
|