On Sep 1, 3:20 am, Brent Meeker <meeke....domain.name.hidden> wrote:
> marc.ged....domain.name.hidden wrote:
>
> > The description itself is an algorithm written in symbols.
>
> Peano's axioms aren't an algorithm.
Er..you're right here of course. I'm getting myself a bit confused
again. Careful when thinking about these profound topics - it's easy
to get oneself tied in knots. So lets try to get this right. What I
should have said is that there are different levels of abstraction in
one's descriptions....Peano's axioms are a mathematical description at
a higher level of abstraction than a description of a computational
procedure.
>Algorithms are computational procedures and aren't necessarily written in symbols. Writing the symbols might be an *instance* of an algorithmic process. As I type >my computer is executing algorithms that are embodied in electronic processes.
Well, there's the 'algorithm' itself (considered as a *static* data
structure), and there's the algorithm considered in the sense you are
talking about, as an implemented computational system or process.
Again, more than one sense of mathematical terms. But again, you're
right that in neither sense does the algorithm need to be written in
symbols. Writing the symbols would a *physical* instance of a static
description.
>
> > So three senses of math here:
>
> > (1) The platonic forms (which are timeless and not in space and
> > time)
>
> > (2) An actual implemenation of these forms in space-time (a
> > *process* or computation)
>
> > and
>
> > (3) The symbolic representation of (2) - an algorithm as written on
> > a peice of paper, described , drawn as diagram etc.
>
> > You can see that the *process of counting* (2) is not the same as the
> > description of counting (3). When you (Brent) engage in counting
> > your brain runs the algorithm. But a description of this process is
> > simply symbols written on a piece of paper.
>
> No, a description is Peano's axioms or some other axioms that describe the numbers and their relations.
Yes, you're right, see above, I was a little confused at time of
writing that. There's more than one level of description for math
terms is what I meant to say. Of course all math has a descriptive
component, but consider the possibility that platonic math forms do
exist. Then of the sake of argument one needs to distinguish between
*descriptions* of a thing and the thing itself. Peano's axioms are
one kind of description...the kind that I thing do correspond to
objectively existing platonic math forms. The second level of
description would be a description of a computational procedure....
this level of description corresponds to well. computional procedures
of course. Finally you have the third level of description which is
of an algorithm considered as a static data structure.... and I don't
think that this third level of description is objective, but would
agree that it's simply a human DP Modelling concept. The symbols
written on paper would be a *physical* instance of this third level of
description.
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Received on Sat Sep 01 2007 - 02:29:14 PDT