ONT Re: Qualitative Understanding Of Complex Systems
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QUOCS. Discussion Note 1
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JA = Jon Awbrey
MW = Matthew West
Matthew,
I was just going through our earlier discussion, pulling out the
systems bits and putting them under this more descriptive heading,
partly to abstract the more generic aspects of the LIS application,
partly to link back up with John Sowa's observation about the 3-adic
aspects of control systems, which I was shocked that everybody hadn't
heard of, since it was one of the first things I learned about control,
going back to the days when folks stuck a grid in the old gasbags that
used to run everything from our paleoradios to our eolithic computers,
thus converting 2-odes to 3-odes.
I'm still just collecting bits and pieces of ideas, though,
and it will take a bit more of that before I can see my way
through to begin developing the systems material any further.
JA: I have a general interest in intelligent control systems,
but I never found those 3d/4d discussions very helpful.
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.
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: As long as I've followed you, that sounds OK. And you could associate
a temporal part of that possible individual as a member of each state
in the state space that it passes through.
I found the rue/bled car example helpful on this point, so let me
fold it into the dough of the text, so that I can come back to it
and study it more carefully later on:
MW: Let me try to explain with an example. Let us
say that MyCar is red from Jan 2003 to May 2003
after which it is blue. A 3D description of that
might look like:
3D: (HoldsDuring Jan2003 May2003 (red MyCar)
4D: A 4D approach to saying this would be:
(TemporalPart State1 MyCar)
(Begins State1 Jan2003)
(Ends State1 May2003)
(red State1)
MW: The key difference between these is the way that time is handled.
3D: In the first (3D) description it is the proposition (red MyCar)
that is true for a time.
4D: Whereas in the 4D version the statement (red State1) is always true
(not just during some period). The time is built into the objects
about which assertions are made rather than being tacked on afterwards.
This is what makes an ontology 4D.
MW: Another thing you can see is that the first example does not
use explicitly temporal parts of an object. The second one
does (State1 is a temporal part of MyCar). Using temporal
parts explicitly is a hallmark of a 4D approach.
JA: Remark. In the beginning, X is really the state space of the whole system.
It can be a tricky question 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: Not sure if I understand the difference here. It looks like
X is a state space, and X_j is a state space, and a possible
individual could be seen as taking a path through it, i.e.
temporal parts of the possible individual would take up
states in the state space.
Will get back to this later in more detail.
The short schrifft is that the structure
of the most fitting state space for the
phenomenon or problem has to be teased
out of the data in discovery fashion
and not just imposed ad hoc. But
not every possible state space
factors into a direct product
of component spaces quite
so facilely. There are
things that are called
"semi-direct products"
that come up a lot,
just for example.
In physics this often comes up under the heading of "many-body systems",
say, 3-body systems, and whether their dynamics factors into separable
pieces where you can just think about independent 2-body interactions,
working in pairwise fashion toward the whole, or not. Sound familiar?
As often as not --
you cannot.
Jon Awbrey
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