SUO: Re: Discussion Period on Motion by Matthew West
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Matthew,
Deleting points covered, and continuing.
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.
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-determinstic systems from the outset I don't make that distinction.
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.
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.
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".
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: 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.
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: You can of course decompose the system and the state.
JA: Just as a subset of X corresponds to an indicator function q : X -> B,
where B is the boolean domain -- here, q is the sort of thing that is
convenient to think of as a "proposition about X" -- constraints on
paths p : R -> X can often be expressed through the intermediary
of other functions that one builds up from X, R, and B.
JA: Now, my question is: Can I think of a possible_individual as being
associated with such a path p : R -> X through such a state space X?
MW: I'm not quite sure if you are talking about a continuous changing function here
or not. We can do that to. We talk about a spatio-temporal extent having
a property distribution, which can perhaps be described by a function.
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.
JA: In the beginning, X is really the state space of the
whole system. It can be a tricky matter to say whether X
decomposes into some form of composite, but let's start with
the easy case, where X = X_1 x ... x X_k, a cartesian product
of component state spaces X_j for j = 1> to k, and X_j is the
state space of the j^th component subsystem. Then let us
suppose that we are talking about one of these ostensibly
independent components, and read what I asked above with
X_j in for X.
JA: Rephrasing the question: Can I think of a possible_individual as being
associated with such a path p : R -> X_j through such a state space X_j?
MW: Equally it is important that the model should have a way of
saying anything. It is the inability to state what you mean
accurately that leads to the abuse of data model structures to
accomodate data with an implicit meaning.
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
I could not download or read this successfully,
and I think my Adobe reader is pretty current.
Do you have another format?
Jon Awbrey
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