Institute for Computing and Information Sciences, Radboud University Nijmegen,
Heyendaalseweg 135, 6525 AJ Nijmegen, Netherlands
Abstract. Self-programming systems are capable of producing theirown constraints. However, what a program produces is already implicitlypresent in its initial set of instructions. The capability for tranformationalcreativity turns out to be a crucial factor for self-programming. In orderto create new constraints, room has to be made available first through areduction of existing constraints.
Keywords: self-programming, constraint, exploration, transformation,artificial creativity.
What causes a program’s execution? Is it the design of the program, or the sys-tem on which it runs? In order for a program to execute as intended many timesover, a stable enviromment is required in which instructions are flawlessly con-verted into physical operations. Computers take care of exactly that: they havebeen meticulously designed to maintain stability against noise and interaction,except for the operations of the program they provide an environment for. Sys-tems have a natural tendency to degrade and fall apart, and computers serve toconstrain the physical surroundings of a program. They are the embodiment ofperfect unnatural mechanism, not only faster and more precise than the humanmind, but also of a kind of dullness that we humans aren’t capable of sustainingfor a long period of time . A program, then, is a set of ordered instructionsthat further constrains the executions that are possible on a computer. In or-der to guarantee that the execution goes as intended by the programmer, theprogram should be in a maximally constrained state.
If programs are essentially ordered sets of instructions, then for a system to be
self-programming it has to be capable of producing its own instructions. Thatis, new constraints that affect its operation. But if a program is a maximallyconstrained system, to what extent were these changes not already part of theoriginal program? Have we encountered a paradox? Either the new constraint isalready present in the program, and therefore not new. Or it is created by theprogram itself - in which case it is not a constraint, since the system could notbe constrained any further. It appears that some constraints need to be brokendown first.
Thinking Outside the Box: Creativity in Self-Programming Systems
Combination, Exploration and Transformation
The ways in which constraint can be broken corresponds to the kind of cre-ativity involved in the process. When dealing with computational creativity, adistinction is often made between combinatorial, exploratory and transforma-tional creativity . These types differ in the level of surprise that is generatedby an idea. Combinatorial creativity is the discovery of a statistically unusualoccurrence. Exploratory creativity is the discovery of a new idea that had beena possibility all along. And transformational creativity has to do with ideas thathad previously been thought impossible.
It is argued that combinatorial and exploratory creativity can be modeled
with computer programs, for example when a program iterates through a list tolook for an optimal solution. As for computational transformational creativity,it can be disputed whether it is capable of inventing anything radically new.
Ultimately, the search space of a program is still determined by its programmer.
Unlike humans, if a program transforms its search space, this new space wouldstill be part of the original program.
By definition, a deterministic program explores a single trajectory. This tra-jectory is maximally constrained in order to guarantee the achievement of anintended outcome (Figure 1a). That is, the constraints of the space are implicitin the constraints of the program. No room is left for new constraints that werenot already implicitly present within the original constraints of the program.
And with that, there is also no room left for transformational creativity andself-programming.
Fig. 1: Schematic illustration of constraints affecting the execution of a program.
This is in agreement with the notion that for tranformational creativity to
occur, partial independence from intentional control is a prerequisite . How-
Thinking Outside the Box: Creativity in Self-Programming Systems
ever, if the level of constraint were to be lowered below the maximum, that wouldleave room to create new constraint. Constraints can be lessened or removed bya number of causes that infere with a program’s execution. Examples of thesemay include programming errors, deviations in the physical embodiment, in-teraction by users or other programs, or (pseudo-)randomized functions. Suchfactors have in common that they can be noisy and unpredictable to a certainextent, features which can be employed to lessen the amount of constraint on aprogram. Consequently, instead of a constricted path there now exists a spaceof possibilities in which multiple paths are available, depending on the cause ofinterference and how it affects the program (Figure 1b).
Such a deconstrained space allows for the system to self-program new con-
straints. New, because the resulting path is not completely determined by thealgorithm, but also by how the space is tranformed by the interplay betweenprogram and the deconstraining interference. What appears to be noise disturb-ing the computational process, actually provides a breakdown of constraint thatis necessary for transformational creativity and self-programming to occur .
A deterministic program uses exploratory creativity to change its state. A self-programming system needs to be capable of transformational creativity, whichin turn requires a breakdown of constraint in order for new constraint to comeabout. This breakdown is established by deviations from the maximally con-strained path that the algorithm was intended to follow, which are henceforthnot part of the program itself.
In the end, the mere capability of changing its constraint is not sufficient for
callling a system self-programming; they also need to be changed in a meaningfulway. Creativity, contrary to random exploration, requires purpose . So whilebugs, errors and random numbers provide a means to get out of the box, theydo not specify where to go next, nor how to get there. An interesting side-effectis that the reduction of constraint causes a system’s operations to become lesswell-defined. This makes the system lose some of the qualities that we tend to at-tribute to a computer program . As a system becomes more self-programming,it becomes less of a program itself.
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