Paul Klee marries the Turing Machine
-and they both end up taking a line for a walk in Computational Space:
The Turing Machine is a fundamental model for the computational process which was formulated by the
British Mathematician Alan Turing. Basically, a Turing Machine is a machine conceptualized as
operating in time and space: A "pointer" is assumed to move to a location in memory space, from
where a stored symbol is retrieved -this is then substituted by another symbol according to rules
also stored in the same machine. The new symbol is then written back into the memory space,
possibly in a new location. By such a process, the Turing Machine is continually changing its own
memory space -which in turn modifies its behaviour. If the processing rules are located in the
processed memory space -then the machine can modify its own rules of operation.
Paul Klee was a Swiss German Bauhaus artist who produced a two volume book of pedagogical notes.
The first volume "The Thinking Eye" describes how a single dimensionless, colourless (grey) point (
or dot) becomes an egg from which all Klee's work can be hatched:
In the imagination of the artist, the point is moved to form a line -such that the line can be subsequently expanded or bent to form solid or open shapes (lines and planes). The creation of a drawing can then be described as "Taking a Line for a Walk".
In the mind of the artist Klee, the point is able to move itself according to the will of its creator. However, the Turing Machine can only function when presented with more explicit and specific rules.
