ONT Re: Data Models, Ontologies, Logic
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Note 18
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Jim,
Sorry if I behaved impatiently with you, but I could see
my client sitting here in my office starting to roll her
eyes at the little fab-fest we were having. She did not
cross my threshold for a dilletentation on the very idea
of having a purpose in life -- it's another office she'd
go to if she was having any difficulties about that, but
as it happens she already knows her purpose in life well
enough for the moment, and it is my paycheck to serve it.
So let us not kid ourselves any further now, but merely
pause to refresh our vows and recite the oath of office:
| I will never forget that the most important thing about the datum
| is how it refers to the objective world from which it is gathered,
| the way of all of signs being abstract partial samples of objects,
| by virtue of which sampling they denote the vaster reality beyond.
Before we go any further, I will need to tighten up my account
of one significant subtlety, with the lack of respect to which
I have allowed myself to relax into a looseness of description
that is customary in the field, but is just as inexcusable for
all that, and this would be nothing other than the distinction
between codes and realities, that is, between sign and object.
By way of fixing this problem, let me redescribe the
shape and sense of the data in the following fashion:
A data point u in the data space U is a k-tuple <u_1, ..., u_k>.
We conceive of the point u as arising from an objective point x
in the objective space X by way of a mapping m : X -> U that we
regard as a "coding", a "measurement", an "observation", or any
other appropriate sort of interaction with the "realities" in X.
So now the shape of the data, a space of signs, in the
Family Interaction case would be redescribed like this:
Chapter 1 (Revised). Shape of the Data
A data record u is an element in the space U, where:
| u = <u_0, u_1, u_2, u_3, u_4, u_5, u_6>.
|
| U = U_0 x U_1 x U_2 x U_3 x U_4 x U_5 x U_6.
|
| U_j = {0, 1, ..., c_j_max}.
|
| For j = 0 to 5, c_j_max is small.
|
| For j = 6, c_j_max is large.
I always like to reserve the letter "X" for the underlying reality in question
at the moment, in order to remind me of how little I ever really know about it.
You realize, of course, that I'll probably go back to being sloppy about this
distinction again at the very first chance I get.
Here is a picture of the situation, illustrating
a typical couple of data dimensions u_i and u_j.
o-----------------------------------------------------------o
| X |
| |
| o-------------o o-------------o |
| / \ / \ |
| / o \ |
| / / \ \ |
| / / \ \ |
| / / \ \ |
| o o o o |
| | | | | |
| | | | | |
| | X_i | | X_j | |
| | | | | |
| | | | | |
| o o o o |
| \ \ / / |
| \ \ / / |
| \ \ / / |
| \ o / |
| \ / \ / |
| o-------------o o-------------o |
| |
| | |
o-----------------------------|-----------------------------o
|
| m
|
o-----------------------------|-----------------------------o
| U v |
| |
| o-------------o o-------------o |
| / \ / \ |
| / o \ |
| / / \ \ |
| / / \ \ |
| / / \ \ |
| o o o o |
| | | | | |
| | | | | |
| | U_i | | U_j | |
| | | | | |
| | | | | |
| o o o o |
| \ \ / / |
| \ \ / / |
| \ \ / / |
| \ o / |
| \ / \ / |
| o-------------o o-------------o |
| |
| |
o-----------------------------------------------------------o
I am an hour or two overdue for my first cup of coffee,
so I will break, try to think about where we are going,
and get back in a while to discuss the details of this.
Jon Awbrey
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