Some Personal Remarks on the Creative Potential of Space
(Towards an Einsteinian Turing machine)

Trevor Batten:

Paper originally published in the Proceedings CIRCUS
    conference Glasgow University 20-22 September 2001


Author Names and e-mail contact information:

Batten, Trevor 

email: trevor@tebatt.net


Abstract

The author believes that "art" should be an autonomous process
which can participate in a dialogue with the artist, -that
the computer is an ideal machine for realizing this dialogue
and that "conceptual space" provides not only the ideal
set of techniques for its construction but is also the ideal
environment for it to take place.

This position is expanded by suggesting that our everyday
understanding of space is in fact highly conceptual and
probably not at all related to our actual experience of
space.

If we are prepared to accept that space is primarily a conceptual
construct then we are able to enter the bizarre world which
theoretical physics has successfully exploited for many
years now.

We then discover that dimensions are not fixed, that space
can be folded, cut and joined and playfully manipulated
in many ways -and that the way these games are played might
be of vital importance because, even though the structure
of space is fairly flexible, the structure of the space
also has significance.

Not only can space represent a set of potential sensory images,
a system for storage or retrieval of data and a physical
or conceptual environment for us to explore - space can
also be used to process space in many ways, often dependent
on the spatial configuration of the elements involved.


However, even if one is not prepared to accept the more extreme
claims of the author, then parametrical space may still
prove useful in the construction and comparison of conceptual
models -by forming a framework within which systems of representation
can be developed which could allow artists and others to
present "subjective" ideas in a more formal way in order
to encourage exchange and discussion to take place within
a nexus of conceptual and physical spaces in an open and
yet "objective" way.	

	

1 Introduction:

1.1 The Ontological Computer

Although I can understand the commercial and political significance
of using digital technology to support interactive systems
-I do not consider "interactivity" as a useful basic principle
for structuring a discussion on relating creativity to digital
systems.

It is not true that computers automatically imply "Interaction":
One can easily argue the opposite -that automation means
the removal of outside interference -in effect, making the
"automated" process pre-defined and truly "autonomous".
Indeed, it is the need to pre-define the universe of operation
that make epistemology and ontology probably the most important
concepts within automation (even with "self-learning"
systems -which still need initial definition) .

It might also be interesting to reflect that what in England
is known as "Fine art" -is known in Holland (literally translated)
as "autonomous art". This suggests to me that not only is
it reasonable for art to be "automated" but also that it
should be free of the externally imposed need (by the artist)
to carry some form of artistic, political or propagandist
"meaning".

On the other hand, it is important not to be too dogmatic:
We have a intellectual tradition of divide and conquer and
are used to chopping up our experience of the world into
separate and manageable problems, but the computer is revolutionizing
our lives and is forcing conceptual and practical integration
in many areas which have long been considered separate.

Survival often seems to be a question of balance and so total
autonomy may be as dangerous and undesirable as being totally
under external control.

1.2 Art as Formalization

Although art can be seen as an expression of the artist -it
can also be seen as a set of creative techniques which help
to transcend the limitations of the individual artist (and
perhaps, by extrapolation, the audience). Contemplation
is important -and interactivity does have a role in contemplative
exploration -indeed, we often like to take unknown objects
in our hands in order to investigate them better from all
sides and from different perspectives. However, larger objects,
abstract ideas and historical processes are more difficult
to deal with in this manner and we have to resort to a more
metaphorical manipulation in mental space in order to integrate
the different conceptual positions.

So I would like to take up on Simon Penny's suggestion in
his position paper and explore the important and magical
concept of "space". A concept which often seems to taken
for granted while remaining largely undefined and yet almost
as ubiquitous as the computer itself.

If you cannot see the point, please do not worry -I am not
concerned with making points but with developing spaces.

2 The Nature of Space:

2.1 The Basic Definition of Space

I propose that "Space" is created and defined by the act
of defining a set of coordinates: It is the selection and
organization of the parameters (or dimensions) which provides
the link with epistemology and it is the experience of navigating
the resulting space which provides the link with ontology .

In other words, "Space" is simply an "address system" -A
way of "finding or retrieving lost, hidden, or invented
things" -exactly the way one uses a basic coordinate system
to find the university library on the map in a strange town
-or the way one can spontaneously stroll the streets in
search of serendipity.

This definition of space gives full credit to Descartes for
his development of analytical geometry and the coordinate
system. However, I intend to demonstrate that this system
can be extended far beyond what we (but possibly not Descartes)
might understand as being "Cartesian" limits.

In practice, the implications of this simple definition are
so great that I can only briefly run through some of them
here -hopefully sketching a rich area for further research.

2.2 The Concrete-Abstract nature of Space

An image is generally represented by the computer as a two
dimensional raster, we are also used to reconstructing physical
space with the help of our sensory-motor system. So it seems
that as well as being a system for storage and retrieval
of data, a physical or conceptual environment to get lost
or found in -space can also be represented in terms of sensory
(tactile, visual and perhaps even aural) imagery.

On the other hand, one of the most baffling aspects of multi-dimensional
conceptual space is the problem of relating it to our commonplace
experience of three-dimensional space -and the difficulties
of imagining how extra dimensions would fit in.

It is generally assumed that coordinates must intersect at
right-angles to each other -but it might be interesting
for us to relax this condition in order to experiment with
other systems which may initially seem useless, stupid and
maybe even impossible.

If (for example) "Colour" can be usefully represented by
a three-dimensional conceptual model -then surely "colour"
must also be a three-dimensional part of our physical universe.
Likewise, concepts such as "smell", "texture", "speed",
or "density", etc. -these too must fit into
the "dimensions" of the physical universe -just as easily
as they can form parameters of a conceptualized universe.

Our traditional concept of three-dimensional physical space
cannot be derived directly from our own sensory-motor system.
The coordinate systems generated by our eyes, ears and other
sensory systems all seem to function slightly differently
from each other -although there may also be similarities
between them.

Our eyes map space mainly (but not exclusively) through binocular
focusing while our aural system uses phase-shifted (time
delayed) signals to locate sources within sensory space.

Our arms and legs also help us to move around and explore
space -but these limbs are connected in limited ways by
different joints that move in complex but specific ways.
The control parameters of our motory system must surely
be based on our physical body -and yet even the simplest
study of robotics must demonstrate that our sensory-motor
space is much more complex that the simple three dimensional
system of physical space which we are conditioned to believe
in.

I strongly suspect that our concept of physical space is
dependent on ancient Greek/Egyptian measurement of flat
surfaces (possibly originating in the yearly demarcation
of arable ground in the Nile valley) -and that these ancient
mathematical methods have been passed down (often demonstrated
on the flat surface of paper or slate) until we have (regrettably)
come to believe that Euclidean space is the only (possible)
reality.

2.3 The Intuitive nature of Space

Wittgenstein has remarked that we must remain silent over
that which we cannot speak about.

We may therefore suspect that many problems may indeed prove
insolvable simply because we have no suitable language to
express and explore them adequately. Apart from the problem
of inventing things which do not exist, the search for a
suitable language (in the widest possible sense of the word)
is made even more difficult by the way languages, models
and description methods often impose their own ontological
and grammatical assumptions onto the subject -easily making
them subtle tools for biased propaganda rather than neutral
media for research.

Perhaps some form of underlying "political", conceptual or
aesthetic "bias" cannot be entirely removed from any conceptual
system -but by explicitly expressing the underlying model
in terms of the chosen parametrical system the basic assumptions
are more openly expressed and is therefore more open to
challenge and debate.

When the underlying structure of the representational system
becomes more explicit -it can be related more easily to
other similar spaces. By facilitating comparison and mapping
between systems, a richer, more diverse dialogue becomes
possible without compromising individual positions or degenerating
into mutual incomprehensibility . 

2.4 The Creative nature of Space

If we can accept that "space" is more a conceptual than a
physical phenomenon -then we become free to construct it
in any conceivable way.

Presumably, each individual constructs their own egocentric
mental space which is why we sometimes have difficulties
mapping the psychological space of others into our own conceptual
space!

If "space" is defined and created by the coordinate system
then it seems that a taxonomy of coordinates, including
a study of the consequences for the different types of space
they generate, would be the first step towards an understanding
of conceptual space.

2.5 The Mnemonic nature of Space

At this point, I would like to mention "The Art of Memory"
by Frances Yates -a fascinating book on the (spatial) use
of Mnemonics as an aid to memory before written language
and printed books made human memory largely redundant as
a way of preserving large chunks of information.

Within the context of "content" and its potential relationship
to "form" Yate's book is extremely important because it
clearly demonstrates a wide range of cultural implications
(ranging from the architecture of the theater to the interaction
between scientific and mystical thought) directly related
to the practical use of mnemonics.

I believe it is a great loss that much of that which is discussed
in her book is now largely outside our cultural awareness
and perhaps even our understanding -simply because the basic
techniques of memory described are no longer required to
function as essential techniques for preserving cultural
heritage.

The interaction between technological, conceptual, cultural
and social change remains an important but difficult subject
for study. In my view this book presents an excellent set
of demonstrative case histories.

3 Processing Space:

Although the use of space as a multi-dimensional "address
system" suggests a rather static use -there are a wide range
of strategies for creatively manipulating the conceptual
space.

One can think of such techniques as:

3.1 Enumeration (combinations and permutations)

Although the decimal system is now in common use there are
many other numerical systems which use a different number
base than ten. One can think of technical systems such as
binary and hexadecimal, but also other systems such as feet
and inches (base 12) or the sixteen ounces in a pound weight.

The number of the dimensions of a space and the number of
points within each dimension correspond to the number of
bits used and the numerical base in a specified number system.
So "counting" (in whichever numerical base one chooses)
is simply an "enumeration" of all the points contained within
the specified space (or, in other words, a combination of
all the parameter intersections involved). Because of this
-changing the dimensions of a space is really equivalent
to changing the number base used to enumerate the states.

It seems that the number of dimensions used to define a space
are actually rather arbitrary.

3.2 Set Manipulation

Points, lines, planes and volumes can all be represented
as a hierarchy of increasingly complex sets of sets of points.

By considering a set definition to be equivalent to a parameter
of conceptual space -all the techniques for forming combinations
or intersection of sets should also have equivalent operations
in terms of space.

3.3 Folding the Space

Proximity and connectivity between points are essential factors
regarding "communication" between points -both in terms
of movements through space -or the exchange of messages
and information.

Space can be "folded" by changing the order in which the
coordinates are interpreted (for example, swapping the interpretation
of colour parameters so that {red, green, blue} becomes
{blue, red, green}. Such manipulations of the space will
change the relative positions of the points addressed by
the system, so that in this case the transition required
to get from "red" to "dark green" will be changed within
the modified colour space.

As a result of changing the space in this way, some points
will become closer to each other while others will become
more distant -thus modifying the navigational and communicative
characteristics of the space involved.

3.4 Analytical geometry

The techniques of Analytical geometry (originated by Descartes)
allow the calculation of trajectories and their intersections
in space, the estimation of minimum and maximum (optimal)
points (or values) of curves, the area of surfaces and the
content of volumes.

These techniques have proved valuable in Cartesian space
so presumably they might also be interesting to play with
in multi-dimensional conceptual space.

3.5 Matrix Multiplication

Matrix Multiplication is currently used to efficiently transcribe
objects to new positions in physical or virtual space. It
also plays an important role in image processing and neural
nets.

A matrix is a small section of space -so space can be used
to process space.

3.6 Cell Automata

Cell Automata have applications (as static cells) in image
processing, modeling diffusion systems and in simple artificial
life systems. However, in the form of movable finite automata
they can become independent "agents" capable of carrying
out autonomous background tasks -such as searching for information,
checking agenda changes and booking your hotel room..

Groups of automata can also collectively form environmental
ecologies which can evolve into more complex systems by
a process of natural selection.

Connected together in the form of neural networks with feedback,
simple automata also can become capable of processing poorly
defined information and developing a wide range of self-learning
processes.

Such automata not only process space but are themselves defined
in terms of their spatial organization.

3.7 Pattern Matching

Perhaps it is not unreasonable to assume that "pattern" is
a quality involving (statistical?) regularities (and perhaps
irregularities) in the organization of space and that the
recognition of "pattern" plays an important role in cognitive
processes.

4 Structure and Meaning in Space:

In discussing the relationship between structure and meaning
we seem to be faced by a strange dichotomy -because structure
often has a meaning and meaning generally implies some form
of structure.

I will try to give some pointers towards different ways in
which conceptual spaces might contribute towards dealing
with problems concerning meaning and structure -which at
the same time might help to clarify the relationship between
the two:

4.1 Look-up Tables

The Mnemonic use of memory described by Yates may represent
the first historical use of mental "look-up tables". 

The technically linear space of the computer random access
memory, can easily be addressed in terms of any number of
conceptual dimensions which the computer can then automatically
convert to a one-dimensional offset in order to find the
correct position in digital memory. Printed tables such
as bus time-tables, temperature charts and currency converters
work on the same principle as digital look-up tables, although
they are usually restricted to fewer dimensions than the
maximum the computer can handle.

Multi-dimensional addressing can be an efficient way of storing,
retrieving and converting data.

4.2 Information and Identity

Interpreting "Information" requires detecting both essential
differences in transmitted signal and in determining the
"significance" of these differences.

Subtle variations in similarity and difference also form
the basis for identity and identification.

By specifying the dimensions we can specify exactly in which
areas there are differences and which areas there are similarities.
Comparisons between parameterized spaces should be a relatively
simple process -especially in potentially confusing situations
where some parameters are almost identical and others are
radically different (i.e. when dealing with problems involving
such questions as "Are modern media similar or different
to traditional media?").

If we can represent the same phenomenon in different conceptual
spaces -which represent the various conceptual contexts
(or domains) in which the subject may be manifest -then
a nuanced and well-founded discussion should be facilitated
if we can map between these different representations.

4.3 Association

The advantage of "space" as opposed to a "set"
as a representational metaphor lies in the fact that the
"coordinates" of space intersect and are not nested -so
navigation through the semantic space becomes much simpler.

The idea that the points in space can have a "meaning", combined
with the idea of "moving" from one position or location
to another via a series of connecting parameters, suggests
that when working with ordered space the "association" of
similar concepts or ideas should be more efficient than
with unordered sets.

i.e. in space, all the "red" objects will be found along
the "red" dimension -and all the "round" objects along the
(round) shape dimension. So we can easily guess where a
"nice red juicy apple" will be found -and what might be
next to it, in different directions -if we know the nature
of the space involved.

Obviously, large variations are possible (based on functional,
cultural, pyschological, perceptual or historical differences)
in the nature of the conceptual space which might be constructed
around the point labeling (or defining) the concept "apple".
Although the manipulation of space may be "objective"
-the definition of space can be completely "subjective".

4.4 Geometry and Topology

Within a space, one may refer to the "geometry" of the space
-i.e. characteristics which reflect the connectivity between
points within that space. For example, are the connectivity
rules homogeneous (as on a flat surface) -or are there variations
depending on (local) circumstance -such as the differences
between the number of "shortest routes" demonstrated by
great and small circles on the sphere? Can all the points
be connected to all the other points as on a Mobius strip
or are there barriers in between? These kind of questions
are vital in determining the "geometry" of a space.

Comparisons between spaces are generally considered to be
questions of "topology" -which essentially asks if one space
can be "converted" into another by "conceptually" stretching
or compressing (but not tearing) either of the spaces.

A comparative topology of multi-dimensional space should
be a valuable tool for the understanding of conceptual similarities
and differences across temporal, media or disciplinary boundaries.

4.5 Grammar and Language

If all the possible "primitives" of a language are ordered
in a conceptual space, then the "grammar" of that language
could be seen as representing the "connectivity rules" determining
how one point in space may be connected to (or combined
with) another. So the construction of a "compound" is then
relative to the movement, or trajectory, through the specified
space under control of the relevant grammar.

The concept grammar thus becomes linked to the concept of
topology.

If "language" becomes primarily involved with "movement"
in space -then presumably "interpretation" will be concerned
with reconstructing this "ballet" in conceptual space -in
order to discover its significance.

4.6 Complexity

One form of complexity is generated by "nesting" of concepts
or terminology.

In other words, the formation of a "Gestalt"-when a compound
in one system becomes a primitive in another system -or
a complex space becomes represented as a single point within
an encompassing (meta)space.

An interesting manifestation of this "nesting" is when the
nature of the space/point changes depending on which level
one is looking at. Examples might be the difference between
the computer as experienced by a programmer and as experienced
by a non-technical "user" -or the difference of effect when
applying a steam engine as a static source of industrial
power within a factory or making it mobile on a set of rails
-which, in turn, might be rather similar to the difference
between a stand alone computer and one in a network.

One may suspect that "great philosophical texts" are often
written at times of change -sometimes on the basis of a
sense of loss regarding what is passing -but also because
we often only become conscious of things when they change.
If the multi-dimensional parameters of social and technological
change could be represented within a single set of interconnected
conceptual spaces then the description and study of the
interaction between these processes might be much easier.

5 Sculpting in Space:

Presumably, it would simplify comparison and understanding
of a wide range of phenomena if many conceptual and physical
processes could be described in terms of operations involving
conceptual space.

Furthermore, we could probably describe these operations
as belonging to the following categories:

5.1 Construction/definition of space

Involving either the construction of conceptual models based
on existing phenomena or the invention and investigation
of new spaces which have no known parallel elsewhere.

5.2 Operations on or within space

Involving "cognitive" operations within a space or the generation
of new spaces through the modification of existing conceptual
spaces.

5.3 Comparisons and Mapping between spaces

Involving operations concerned with comparisons between (potential)
similies, simulations and metaphors but also mapping or
translations between different conceptual domains -possibly
relating such things as physical and mental phenomena, social
and technical effects, the modeling of trans-disciplinary
problems, the interpretation of technical data or the mapping
and interpretation of sensory data.

6 Using Space as a Creative Generator:

6.1 Extrapolation

At school, I remember being fascinated and impressed by the
way in chemistry the "Periodic Table of Elements" allowed
the characteristics of elements to be specified, through
extrapolation of the characteristics found in the table
-even though some of these elements had not yet been discovered
in what is generally referred to as the physical universe.

Presumably, such extrapolations could be applied more extensively
and systematically to assist in the creative generation
and manipulation of new systems of knowledge or universes
of experience.

6.2 Mapping

Another important creative strategy is to transfer, or map,
a technique from one medium or context into another -but
what represents the essence of a technique when it has been
removed from its context?

I guess this is basically a question of abstract topology.

6.3 Communicating

The conceptual nature of space makes it an ideal tool for
explicitly representing subjective or non-existent phenomena
thus "objectifying" them -thus facilitating their exploration
and investigation by others -by permitting one to move more
freely between existing and invented systems without getting
confused as to which is which.

By mapping our individual conceptual spaces into more explicit
systems we enable others to enter and map our private mental
space into theirs. If this is a mutual process then participants
can contribute to the creative dialogue by developing a
collective "dance in space" which as it grows becomes a
new universe of referential experience for those involved
-and possibly a point of reference for others. 

7 Expanding Space:

7.1 Touring the Automated Space

The "Turing machine" is a basic conceptual model of the computer.

Basically, it moves through memory, and re-writes the symbols
found there according to pre-defined rules which govern
both the transformation of the found symbol and the new
position in memory where the new symbol should be stored.

7.2 Einsteinian Time/Space

Space generally suggests the idea of movement while, in turn,
movement (presumably) generates space.

The concept of movement begs the question of what causes
the movement? Is it, for example, internal "animism" (some
kind self motivating force or will) -an external agent (operating
in terms of an interactive device) or something else (as
yet unexplained).

Physics distanced itself from animism a long time ago -so
the "passive" conceptual space favoured by physics may not
easily relate to social systems which are assumed to involve
"actors" with internally organized free will.

However, Einsteinian Time/Space specifies that an object
moving through space modifies the space as it moves.

So, if we consider the memory utilized by a Turing machine
as a (one-dimensional) space -then we may suspect that it
is also a (one dimensional) Einsteinian Time/Space machine!

Although this sounds pretty obscure and exotic -we should
remember that originally time/space was intended as a representation
of gravity, so it may be so that it simply represents a
"force field" such as may be found in daily life in the
form of gravity or magnetism, etc...).

It may also be possible that people are more influenced by
(mental) force fields than by "free will" -so perhaps an
Einsteinian Turing machine could prove an effective medium
for the exploration of the dynamics of psychological space.

However, conceptual force fields are not limited to individual
psychology -perhaps they can also be used to model social
questions such as the relationship between "technological/commercial
push" and "creative/consumer pull".

7.3 Dialectical Parameters and the Logic of Aesthetics

Although parameters are generally considered to be linear
-it is also possible to construct space on the basis of
"dialectical" parameters (expressing a scale
of positions between two apparent opposites -such as static/dynamic,
rational/intuitive, conceptual/physical, etc.).

If we could imagine a dialectical Meta-space, such that each
point within the space represents (or specifies) sets of
axioms (specified by the dialectical coordinates of the
meta-space) -then each of those points would represent a
(formal, semi-formal or even informal) conceptual system
with various characteristics.

If this "dialectical Meta-space"
can be accepted, then "Aesthetic choice" might be seen as
being a basically arbitrary choice (i.e. it cannot be derived
via any rule based system) -which is (nevertheless) capable
of generating "rule based systems" which have "logical"
(i.e. derivable) consequences for those operating within
such a system. Analogue to systems derived from formal axioms,
modifying these arbitrary choices will generate a new system
different from that generated by previous sets of choices. 

If this is true, then we should preserve these aesthetic
(cultural) alternatives as carefully as we preserve biological
variation. In order to preserve conceptual diversity, it
is essential that we do not allow the "Flat" space of western
culture and the way it excludes alternatives to seduce us
into degenerating into aesthetic , conceptual and cultural
homogeny.

Aesthetic research, involving a study of the (aesthetic,
logical and practical) implications of systems derived by
aesthetic choice -practiced on both a practical (artistic)
level and a theoretical (meta-) level -could make a significant
contribution to a better understanding of the relationship
between theory and practice.

7.4 Art in Space:

I suppose music has always been involved, more than most
of the other art forms, with (abstract) movement within
sensory and conceptual space -and with the link between
the two.

Maybe the complexity of the mapping involved was why the
ancient Greeks valued music so much. Possibly this complexity
is related to the reasoning behind the attempt of Xenakis
to liberate musical sound, many years ago, by changing to
a set of parameters based more on the science of physics
than on traditional music. What a pity this attempt failed
-presumably because his attempt to apply parametrical conceptual
space to an artistic process became too strongly associated
with aleotoric serialism to receive the full attention which
it perhaps deserved.

Although the removal of artificial (mechanical) instruments
in the production of music is almost unthinkable, -until
fairly recently, the production of visual art has been almost
entirely by hand and because the cinematic and theater arts
have largely focused on content and story telling -the implications
of parametrical conceptual space were presumably irrelevant
outside the field of music -until computer systems began
to force the issue.

Unfortunately, the rejection by contemporary culture of almost
any type of formalism -or universally accepted meta-language
-encouraged by the cultural split between science and art
has not prepared the art world in any way (with the possible
exception of music and dance) for the advent of the computer.
In fact, exactly the opposite -it is only the De-formalization
of the computer, and the denial of its essentially formal
nature, which has made it acceptable to the art world.

Considering the consistent and extremely successful use of
parametrical conceptual space by the practitioners of physics
over a considerable period of time, it is strange and regrettable
that although words such as "parameter" and "space" have
crept into the language of cultural theorists, there appears
to be very little concerted effort to develop a real understanding
of these terms and their implications for the creative arts
outside the reincarnation of renaissance pictorial space.  

7.5 Simulation:

Science is strong on the testing of models but is (with a
few exceptions -such as the abstract formal systems found
in mathematics and logics) generally weak on "scientific"
methods for the construction of models -which is generally
left to the "intuition" of the scientist.

Art is rather weak on the testing of models (often pragmatically
testing them by relying on the sympathetic "intuition" of
the public) -but it has developed (both collective and individual)
artistic strategies for the generation of artistic models
(i.e. specific genres and works of art).

Simulation allows direct (ontological) experience of a model
(without epistemological mediation). The simulation of complex
ontologies is probably a major link between art and science
-which, because computer simulation increases the participatory
(experimental) aspect of science -will probably become even
more significant in the future.

8 Conclusions 

I strongly suspect that practical investigation will confirm
that parametrical conceptual space can be a valuable tool
for the non-reductionist analysis of complex and perhaps
paradoxical systems -allowing structural (topological) comparisons
between different universa of practice or experience which
can also be applied (if desired) within the context of a
generative framework for dynamic creative systems.

How much more efficient it would be if we could describe
a wide range of mental and physical phenomena within a single
language -without detracting from the fundamental nature
of the phenomena involved by forcing upon them an unsatisfactory
structure as the price to pay for the integrating translation.
I believe that "parametrical conceptual space" is flexible
enough to allow us to do this -because the space can be
tailored to fit the phenomenon being described or modeled
-and not vice versa.

If "intelligence" can be reduced to the ability to create,
manipulate and map conceptual space -then we would have
at our disposal a powerful conceptual medium for exploration,
understanding and manipulating the interrelations between
structure and meaning. 

"Parametrical conceptual Space" may be an essential paradigm
for dealing with content within the context of integrated
research into creative user systems. If we are to connect
the dots and find the patterns in a useful and meaningful
way then we shall need the space to do it.

References

Rene Descartes []


References:

-Simon Penny: Position paper "Circus Synergy Theme: Interactivity
and the Future of Creative Practice": http://www.circusweb.org/synergies/Syn-Interactivity&Future.pdf

-"Art of memory", Frances Amelia Yates: London, Pimlico, 1992.

-Non-Euclidean Geometry: http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/Non-Euclidean_geometry.html#47

-Relativity Theory (Albert Einstein): http://www.britannica.com/eb/article?eu=117375

-Iannis Xenakis: http://headwize.com/articles/steven_art.htm

-A Dialectic of Audible Space by Ian Stevenson: http://headwize.com/articles/steven_art.htm

-An Atlas of Cyberberspaces:Information,Space,Maps: http://www.cybergeography.org/atlas/info_maps.html