[om-list] Dimensions in knowledge space

[Thomas L. Packer at home]

Rajeev

    About numbering dimensions ...

    That's an interesting question, but I don't think there's any reason to
worry.  We would start with a few "primitive" dimensions and keep track of
them forever, but then we would add more abstract dimensions every time we
needed them, and keep track of the important ones.

    I think if you realise that the term "dimension", in this context, is
simply taking the place of many ideas that have different names in other
contexts, such as "classes", "classifications", "units", "metrics", etc.,
and there is no upper-bound for the number of classes you can create is
there?  There is no need to limit yourself, except with you talk about
implementation constraints and trade-offs, such as working memory size, hard
drive space, and search-time, etc.  You can make as many dimensions as you
need, and you relate them to the ones you've already created so you don't
loose track of them and so you can make effective use of them.

    Chris Angell had a similar concern a few years ago when I told him about
this idea.  I think it was a little mind-boggling to consider that something
as fundamental as "dimensionality" (where there are only three or four that
most people think about) could be instantiated so many times to describe so
many things.  And I'm not sure if I made it better or worse by saying that
we could not only use lots of dimensions in a static model, but we could
also use "disposable dimensions", dimensions which are only around long
enough to make a calculation, and then thrown away.

    This happens all the time in other contexts.  Think of math classes and
analytic geometry: when you have a new word problem involving this or that
calculation involving these or those units of measurement, what are you
doing?  You are creating a whole new set of dimensions and relating them to
each other.  In a fully unified model of knowledge, all of those dimensions
could potentially be related to each other constantly, i.e. perpetually, and
therefore would become part of the same large set of dimensions, i.e. parts
of the same model.

    For example, remember Newton's Law of Cooling (or whatever it was
called): I'm not just talking about adding temperature as a function time,
and thereby having added two dimensions to the model.  I'm talking about
adding the temperature of every point in space as a function of time, or
more simply the temperature of every object of interest as a function of
time, and therefore we would be adding as many temperature dimensions as we
have objects needing their temperature described.

    But it's just the nature of this beast.  In one application, where the
knowledge representation is based on variables and named constants (i.e.
quantity without explicit quality), you create variables all the time, and
they are relatively efficient to use, and to throw away when you are done
with them.  In an optimised system that uses dimensionality (which in my
mind is just adding quality to quantity, and then allowing you to related
qualities), one would tend to use them for everything.

    As the Mormon hymn goes, "There is no end to knowledge ... There is no
end to space..."

    ;-)

tomp

~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Víðar sum quem nihil obstat.
www.Ontolog.Com
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----- Original Message -----
From: "MrM0j0r15n Rajeev the kanehbosm" <electrickanehbosm at hotmail.com>
To: <om-list at onemodel.org>
Sent: Monday, 02 September, 2002 13:35
Subject: [om-list] Dimensions in knowledge space


>
> Hello Mr Butler and other friends,
>
> I have a question regarding your discussion on dimensions in knowledge
> space. My questions is, wouldnt, any "non-normative" KRS based on
dimensions
> of quality, immediately degenrate into an infinite dimensional knowledge
> space ? How does one utilise the useful concept of dimensions without
going
> overboard ?
>
> For, eg, if OM were to be used in say political analysis, we might arrive
at
> a point where we need to "ask" OM, of how one event is similiar to another
> event. In my opinion (uneducated), we would now need an additional
dimension
> just to formulate such a question. Going in this direction, where can we
> find the upper limit on the number of dimensions required ? Also, even if
we
> were to consider only "primitive" dimensions, then the formulation of such
a
> question would amount to writing a program or a very complex state
machine.
> Is this opinion of mine baseless ?
>
> Also, Luke, has mentioned that the personal organizer is based on a graph
> formalism (what i understood). So, searching for relationships among
objects
> is the same as spreading "activations" from both objects and looking for
> places where the activations meet, especially those places that have some
> conceptual relevance to the question posed to OM. Luke, could you explain
> how this formalism is different from frame representation ?
>
> thank you
> insanekane
>
> PS: have any of u seen Chocolat ?
>
>
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