SUO: RE: Discussion Period on Motion by Matthew West
Dear Jon,
See comments below.
Matthew West
Principal Consultant
Shell Information Technology International Limited
Shell Centre, London SE1 7NA, United Kingdom
Tel: +44 20 7934 4490 Other Tel: +44 7796 336538
Email: matthew.west@shell.com
Internet: http://www.shell.com
> -----Original Message-----
> From: Jon Awbrey [mailto:jawbrey@att.net]
> Sent: 01 September 2003 20:23
> To: West, Matthew R SITI-ITPSIE
> Cc: SUO; Jim Schoening
> Subject: Re: Discussion Period on Motion by Matthew West
>
>
> o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
>
> 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.
MW: So far so good.
>
> 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.
> 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.
>
> 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.
> 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.
>
> 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: Sounds good. In the limit it can be reified-system-at-an-
instant.
>
> 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.
MW: Indeed. I think we have this covered.
>
> 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?
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.
>
> Jon Awbrey
>
> o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
>
>