WORKSHOP: LIMITS, CHOICE AND EXPRESSION
The starting point for the workshop is the question:
"How is it possible to express oneself through the medium
of the computer considering that, in principle, all possible
pictures are potentially defined by the number of points on
the screen and the number of colours available?".
One may consider the following related points:
i. The possible similarity to human language systems where a
large but still limited range of words seemingly allow
infinite expressions of meaning.
This invites the following questions:
a. How are can a limited repertoire be expanded to cover
a wide range of meanings?
(i.e. the number of possible statements be maximalized)
b. How important is the interpretation process?
(i.e. does the manipulation of meaning increase the
number of possible statements?)
c. Is verbal language a valuable model worthy of further
ii. The possibility that all systems are in some ways limited
and the limitations of the computer may be similar to those
of traditional media like painting (where one is also limited
by canvas size, palette, size and shape of brush stroke,
art history etc..)
Certainly it is possible to categorize different types of
limitations found in daily life:
a. Physical Limitations:
i.e. some variations are physically impossible.
b. Conceptual Limitations:
i.e. some variations are possible but we haven't
thought of them yet.
c. Perceptual Limitations:
i.e. many variations are possible but we can't
distinguish them from others.
d. Moral or Aesthetic Limitations:
i.e. some variations are possible but we choose not
to use them.
e. Logical Limitations:
i.e. any variation which if it were possible would
contradict our system of belief and understanding
about the world around us.
i.e. variations which may be impossible within our
belief structure but may be possible outside it.
NOTE: With the exception of Moral/Aesthetic Limitations,
which may be consciously made, it is very difficult to
determine how valid the limitations are.
i.e. We are surprised when an impossible variation
is proved (by experience) to be possible, but it is
virtually impossible to know if a variation is
possible or not before it is proved to be possible.
iii. The different (but equally valid) aesthetics of sterile,
accurate and controllable digital systems compared to messy,
inaccurate and relatively uncontrollable analogue systems.
i.e. Analogue system: continuous space
�like a topographical map where
valleys gradually become mountains.
�variation is implicit and must
explicitly removed if undesirable.
Digital system: discontinuous space
�like a political map where
countries have abrupt borders.
�variation is absent and must be
explicitly included if desired.
(within limits of resolution)
iv. The difference between physical and conceptual actions
(i.e. the absence of a perceived physical action changing
the image may force one into more abstract modes of thought)
II. TOWARDS SOME THEORETICAL SOLUTIONS:
i. Combinations and Grammars
a. Combinations in Time and Space
A easy way of increasing the number of possible
statements that can be made with a limited repertoire
is to copy the basic elements and to re�combine them
in Time and/or Space.
i.e. the images may be limited but their behavior
may be complex and varied in time.
(morse code, digital sound sampling, etc.)
i.e. the elements may be limited but they can be
repeated in complex patterns in n�dimensional space.
(parallel port, colour bit�planes, Weaving, etc.)
NOTE: The Space is often limited (i.e. the number of bits
in a computer system, the number of pixels in a screen)
so the patterns remain restricted by the number and
length of the dimensions of the space and the number of
One assumes that Time is infinite and therefore there
are an infinite number of patterns in time that can be
constructed even from a minimal repertoire of two
basic elements. Practical and Perceptual Limitations
may still be valid here too.
b. Perceptual and Conceptual Categories
Although we can mathematically calculate the number of
patterns that can be generated by any given number of
repetitions of a basic repertoire, there may be a
considerable difference between the theoretical number of
patterns possible and the number of patterns actually
As noted earlier �some patterns may be indistinguishable
from others and the number of effective patterns reduced.
(i.e. is that line 36.5 or 36.6 cm. long?
is that note 366 or 367 hertz?)
Some patterns will form conceptual relationships with
(i.e. Some patterns may be rotations, mirrorings, or
colour isomorphisms of each other)
Depending on the circumstances the conceptual
categories may increase or reduce perceived differences.
c. Filters and Grammars
For practical or Aesthetic reasons, some combinations
of basic elements or processes may be unacceptable.
(i.e. a large box can't be placed inside a smaller box,
Certain colour combinations may be unpleasant, etc.)
The rules determining which combinations are acceptable
and which are not are generally (in linguistic terms)
known as "Grammars". In order to work Grammars usually
require some kind of "Grammatical Categorization" of
the basic elements (or "Primitives") in order to specify
those categories of element which may be combined and
those which may not.
(i.e. a sentence requires a noun-phrase and a verb-phrase)
A grammatically correct combination of symbols is termed
"A Well Formed Formula". Traditional Linguistic Grammars
can decide if a sentence in a given language is correct
or not but are not very useful in the actual construction
of the sentence.
Conditional Filters can be used to remove unwanted
combinations of elements.
(i.e. Make Combination �IF Combination NOT Satisfactory
THEN Reject Combination AND Make New Combination)
Unfortunately the rules to reject unwanted combinations
may be difficult and sometimes complex.
Procedural Grammars can be considered as a set of
switches structuring the performance of a set of
EITHER Modify size
(case a) increase height
(case b) increase width
(case c) increase both
(case d) increase neither
OR Move position
(case a) move x
(case b) move y
(case c) move both
(case d) move neither
OR Change Colour
Transformational Grammars are sets of transformation
rules which are so defined that they always generate
Well Formed Formulas (WFF's).
(i.e. Any combination of symbols generated by a specified
grammar are termed WFF's of that grammar, so one has to
define the grammar so that it can only generate acceptable
Transformational Grammars obviously consist of a set of
transformational rules and look something like this:
x �> xx
xxx �> yxx
This Grammar would generate a strings like this
yyxx or xyxx
depending on it being read from the left or the right
(which would normally be implicit in the system).
Transformational Grammars are generally used for
artificial languages and have not yet been able to
generate all the grammatically correct sentences of
a natural language (i.e. English, French, etc.) and
it may be impossible for them to do so. They are easy
to implement in the "LISP" programming language.
ii. Organization and Interpretation
(i.e. The creation and definition of Space)
The concept of variation implies that there is something
that can be varied.
(i.e. a "Control Knoop" that can be turned to increase or
decrease something, such as height, volume, speed, etc.)
So in order to experiment with combinations and/or
variations of basic elements we shall need to define
our basic elements and decide what we can do with them.
i.e. do we have simply a set of images?
(select image a, b, or c)
do we have a set of elements and locations?
(set element x at location y)
do we have a set of procedures?
(change colour, size or position of figure)
Obviously, the way we select or define our basic elements
has implications for what we can do with them. Our basic
decisions in fact define a "Universe (or Space) of
Possibilities". It may be interesting to observe closely
how our decisions affect the dimensions (or "Parameters")
of the space we are defining.
III. TOWARDS SOME PRACTICAL EXPERIMENTS:
i. An Introduction To Computer Programming:
ii. Some Practical Exercises:
-enumerating the repertoire (coding?)
-random generation of image
-defining some basic repertoires and their variations
(parameters of space)
-controlling the variations
-deterministic clocks (functions)
-feedback and self controlling systems
IV. TOWARDS SOME THEORETICAL MODELS:
It is apparently
easier for humans to modify their external environment than their own
internal physiological system.
Perhaps "Art" is "one" way of manipulating the external environment
in order to modify our internal operations as a result of their
reaction to the environment.
What is "information"?
Are there different categories of "information"?
What is the relationship between directly experienced
"source information" and "synthetic information" which
is derived by some kind of processing? (Jonah)
Is not all "information" the result of some form of processing?
V. THE CONCRETE RESULT:
An introduction to programming in machine language, given by one
of the students, gave a practical insight into how interpreting
binary codes as operating instructions enables a limited basic
repertoire to be bootstrapped into complex behavior patterns.
One may strongly suspect that it is indeed the interpretation
process, by encouraging shifts into different "domains of
discourse" which generally permits the basic repertoire to
Although the students worked hard to master Basic programming
techniques, only one group produced interesting results based
on variation of the circle.
Again it was interesting to note that although the program was
based on drawing concentric circles (at different locations)
the circle parameters quickly became subservient to those of
the controlling loop structure (i.e. Increase or Decrease of
radius, size of Increase/Decrease and colour of circle). This
would appear to demonstrate once again how creating a "higher
level of language" transcends the original limits of the basic
repertoire �obviously not in a technical sense (of physically
extending the repertoire) but in an organizational sense of
introducing new ways of ordering the original material).
The students who remained until the end of the workshop were
generally more interested in their own explorations (which in
some cases can be expected to continue beyond the workshop)
than in the limited theoretical starting point, however it did
prove to be a useful introduction in many ways.
The student who posed the original question was too confused by
technical practicalities to develop the theme further within the
workshop. However she has promised to digest the experience and
to present her thoughts at a later date.
Amsterdam, March 1995