SUO: Re: Discussion Period on Motion by Matthew West
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JA = Jon Awbrey
MW = Matthew West
JA: When I think about these things in systems theory terms,
it always starts with some state space X that contains
all of the logically possible states of the system you
want to think about. Your first stab at dealing with
process will then be in terms of a "path" p : R -> X,
where R is a real line that you think of as the time
domain. Physical laws and practical constraints are
then expressed as subsets of X and subsets of the
set {p : R -> X} of all possible paths through X.
MW: The states you [describe?] are essentially complex
properties of a system.
JA: This is where I begin to have trouble making translations
into a language that I understand. Let me think about a
state x in a state space X -- some people will be fussy
here and want to say "configuration space", but because
I start with non-deterministic systems from the outset
I don't make that distinction.
MW: So far so good.
JA: One thing that we are talking about when we say "the system"
is a thing that can be in various states, and a thing that
can pass through a line or a sequence of states.
MW: Agreed.
JA: In that case, we can say that the state is a complex property of this
system-thing. We say that the system is in the state x in the set X,
and there are projection maps p_j : X -> R, just taking R as a typical
example, and that we think of as "measuring" x in X with regard to the
property corresponding to p_j, and giving us a real number.
MW: I think I'm still with you.
JA: So I think I have a way of understanding the statement that
a state is just a complex property of a system. Some people
will call that system-thing the "reified system".
MW: It is that which takes on the state.
Yes, the picky point that I think some people are trying to make is that
the data of experience or the results of measurement are what we really
have on hand, whereas the system-thing is in the bush, as it were, at
some remove from immediate impressions, the object of possibly many
and possibly competing hypotheses that we form to explain why the
data are as they are.
JA: They will say that it is nothing but a "hypostatic abstraction" that
personifies the measurements we make and that enter our experience
and that are the only real things that we ever know of this system,
but I don't see the harm of positing such objects, so long as we
stay conscious of what we are doing.
MW: One of the things I like about 4-dimensionalism is that it is very unfussy
about what objects there are. If it is some extent in space-time, you can
have it. Why you are interested is up to you. So we are allowed systems.
Seems eminently reasonable to me.
MW: The time chunk of the system that possesses the state is the relevant
possible individual, that is itself a temporal part of the whole life
of the system.
JA: Almost. Let me try. Instead of a reified-system-at-an-instant,
the thing that is in the state x in X, you want to talk about a
"time chunk" as the thing that has the properties p_j that afford
a basis for defining the state x in X, along with all of the other
properties that the system has at that moment?
MW: Sounds good. In the limit it can be reified-system-at-an-instant.
Check.
JA: In practice, both empirical and theoretical practice,
we commonly approximate continuous trajectories with
discrete sequences of states, and computational work
pretty much forces us to start with discrete and even
finite cases, so it's best to have concepts that cover
both indifferently, at least, until push comes to shove.
MW: Indeed. I think we have this covered.
Whew!
JA: Given the variety of different ideas about data models
that we've seen, it might also help if you could say
a few words about how you see them.
MW: The structure and meaning of data, is the few words version.
A longer version can be found in:
http://www.matthew-west.org.uk/Documents/princ03.pdf
JA: I could not download or read this successfully,
and I think my Adobe reader is pretty current.
Do you have another format?
MW: The site seems to have been having some delays which have made
connecting and downloading difficult. It seems ok now though.
MW: I have just generated a PDF V1.3 version of the document,
complete with bookmarks for the TOC. Try that. If it
still doesn't work I can e-mail it or a Word document.
Will try again.
Jon Awbrey
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