Copyright 2009 David Dodds

Metaphors are concepts. Concepts cannot be put
into computers directly because concepts, their
actuality, is not understood as it occurs in the
human brain / mind. What we can put into
computers is some description of the concept,
some facsimile or representation of the concept.

This is done in a form that is amenable to being,
in turn, represented with a collection of ones and
zeros. (and even then there are not actual 1's and
0's in the computer but only (electrical) 'charges'
and 'potentials'. which are DISPLAYED as ones
and zeros when they are output to humans for
their consumption. (Well of course we humans
look at text (words, numbers and punctuation,
etc ) and such (like 'graphics' / 'pictures') which
are collections of those 1's and 0's.

(so those 1's and 0's that we do see are
interpretations or representations of the charges
and not what is actually there.)

In the (content of)
awareness of the individual human there is a whole
host of (layers of) interpretation of (bio-electrical)
'potentials' which have arrived in the brain from
bodily sensors and activities which have occurred
in some parts of the brain and are attended
to / received by other parts of the brain.
Awareness / consciousness does not occur
in / at a single neuron it is a distributed thing, just
as the light from your light bulb does not only
come from a tiny point but rather (simultaneously)
from the whole emitting surface of the light bulb.

Metaphors are concepts and occur in a number of
neurons simultaneously. We can place
representations of these metaphor concepts into
a computer. Each such metaphor occupies more
than one bit, byte or word in the computer memory,
as data and program. Just as this collection of bits
can operate as a single ensemble, as an executable
model in the computer, we humans can utilize a
collection of (perhaps not sequentially co-located)
neurons.

A model of a 'black hole' utilizes some number of
memory locations, memory transfers, and processing
in the arithmetic / logic circuitry of the computer to
effect the activity of modelling the 'black hole'. Just
as we know we cannot drink the tea in / from a
hologram of a (filled) teacup, we also know that the
model of the 'black hole' is not (itself) an actual
'black hole'. This is true of our modelling of gravity
well, aircraft, motorcycles as well.

The model might be completely mathematical, based
on equations and such. This kind of model is often
hard for non-technical people to visualize and so
to be useful (to them) these mathematics need to
be converted either into words or pictures (or both).

We will look at MathML
[http://www.w3.org/TR/2003/REC-MathML2-20031021]
as a means of both
representing equations and mathetical stuff and
as means of depicting / displaying them in a 'pretty'
manner for human's eyes to appreciate.
Furthermore, by associating the MathML content
with ontological knowledge, in the form of XML
OWL ontologies and the OMC Processing Connection
Service (PCS), we will see how, in a sense, the
equation, as depicted via MathML may 'have
some understanding' of its (own) meaning.
A simple example of this is that 'the equation'
(actually the computer system which implements
it) understands / recognizes that it is a 'second
derivative' [which is a kind of mathematical
operation or entity, and it is used to perform
specific numerical tasks].

While it is possible to display a static drawing
of a 'black hole' with various graphic formats it is
possible to animate the rotation / swirl of the
event-horizon depicted in such a drawing by using
SVG. The lines and such that SVG produces may
be governed by mathematical equations which
describe the physics of the 'black hole'. In so far
as the mathematics are accurate then so too is
the animation of the drawing produced by that
SVG. Since SVG is an XML namespace it is able
to display the numerical results of equations etc
represented in MathML. The SVG language also
has a metadata element defined in it and this
allows SVG to participate with an XML OWL
ontology so as to give (ontology based) meaning
to one or more items in an SVG 'picture' (ie an
SVG file). Don't confuse merely attaching a (to
humans only) 'meaningful label' (merely a text artifice)
to SVG 'picture' components : with the recognition
and association of ontological elements with those
SVG 'picture' components.

In the same way we call a virtual machine a single
thing, we can call the collection of data and
programming for the above 'black hole' modelling
a single thing too (a single model). It might be said
that this single model is a (representation of a)
'concept'. By having a collection of models in an
inventory it is thereby possible to have a modelling
of some aspects of human cognition / thinking.
The key point is that it is a modelling and not
cognition / thinking itself.

A girl's dollhouse is a model of a house, a physical
metaphor of a house. Its physical existence and its
implemented metaphorical elements allow it to be
used in quasi-houselike ways, but (the nature or
details of) its metaphorical implementation does
preclude one from living in it oneself. Models and
metaphors are useful for some things with regard
to that which they model or are metaphor of, but
since they are not the (real) thing itself aspects of
use / interaction (with the model or metaphor) are
precluded which are not precluded in use /
interaction with the real thing. In order for a
metaprogramming system to make correct use of
such models or metaphors then the
metaprogramming system must take into account
knowledge of what is to be precluded (as above).
[continued next posting]