Patrik Christen

Patrik Christen

Self-modifying code has many intriguing applications in a broad range of fields including software security, artificial general intelligence, and open-ended evolution. Having control over self-modifying code, however, is still an open challenge since it is a balancing act between providing as much freedom as possible so as not to limit possible solutions, while at the same time imposing restriction to avoid security issues and invalid code or solutions. In the present study, I provide a prototype implementation of how one might curb self-modifying code by introducing control mechanisms for code modifications within specific regions and for specific transitions between code and data. I show that this is possible to achieve with the so-called allagmatic method - a framework to formalise, model, implement, and interpret complex systems inspired by Gilbert Simondon's philosophy of individuation and Alfred North Whitehead's philosophy of organism. Thereby, the allagmatic method serves as guidance for self-modification based on concepts defined in a metaphysical framework. I conclude that the allagmatic method seems to be a suitable framework for control mechanisms in self-modifying code and that there are intriguing analogies between the presented control mechanisms and gene regulation.

Patrik Christen

Having a model and being able to implement open-ended evolutionary systems is important for advancing our understanding of open-endedness. Complex systems science and newest generation high-level programming languages provide intriguing possibilities to do so. First, some recent advances in modelling and implementing open-ended evolutionary systems are reviewed. Then, the so-called allagmatic method is introduced that describes, models, implements, and allows interpretation of complex systems. After highlighting some current modelling and implementation challenges, model building blocks of open-ended evolutionary systems are identified, a system metamodel of open-ended evolution is formalised in the allagmatic method, an implementation self-modifying code prototype with a high-level programming language is provided, and guidance from the allagmatic method to create code blocks is described. The proposed prototype allows modifying code at runtime in a controlled way within a system metamodel. Since the allagmatic method has been built based on metaphysical concepts borrowed from Gilbert Simondon and Alfred N. Whitehead, the proposed prototype provides a promising starting point to interpret novelty generated at runtime with the help of a metaphysical framework.

Sebastian Fix, Thomas Probst, Oliver Ruggli et al.

Combinatorial evolution - the creation of new things through the combination of existing things - can be a powerful way to evolve rather than design technical objects such as electronic circuits. Intriguingly, this seems to be an ongoing and thus open-ended process creating novelty with increasing complexity. Here, we employ combinatorial evolution in software development. While current approaches such as genetic programming are efficient in solving particular problems, they all converge towards a solution and do not create anything new anymore afterwards. Combinatorial evolution of complex systems such as languages and technology are considered open-ended. Therefore, open-ended automatic programming might be possible through combinatorial evolution. We implemented a computer program simulating combinatorial evolution of code blocks stored in a database to make them available for combining. Automatic programming in the sense of algorithm-based code generation is achieved by evaluating regular expressions. We found that reserved keywords of a programming language are suitable for defining the basic code blocks at the beginning of the simulation. We also found that placeholders can be used to combine code blocks and that code complexity can be described in terms of the importance to the programming language. As in a previous combinatorial evolution simulation of electronic circuits, complexity increased from simple keywords and special characters to more complex variable declarations, class definitions, methods, and classes containing methods and variable declarations. Combinatorial evolution, therefore, seems to be a promising approach for open-ended automatic programming.

Olivier Del Fabbro, Patrik Christen

Control was from its very beginning an important concept in cybernetics. Later on, with the works of W. Ross Ashby, for example, biological concepts such as adaptation were interpreted in the light of cybernetic systems theory. Adaptation is the process by which a system is capable of regulating or controlling itself in order to adapt to changes of its inner and outer environment maintaining a homeostatic state. In earlier works we have developed a system metamodel that on the one hand refers to cybernetic concepts such as structure, operation, and system, and on the other to the philosophy of individuation of Gilbert Simondon. The result is the so-called allagmatic method that is capable of creating concrete models of systems such as artificial neural networks and cellular automata starting from abstract building blocks. In this paper, we add to our already existing method the cybernetic concepts of control and especially adaptation. In regard to the system metamodel, we rely again on philosophical theories, this time the philosophy of organism of Alfred N. Whitehead. We show how these new meta-theoretical concepts are described formally and how they are implemented in program code. We also show what role they play in simple experiments. We conclude that philosophical abstract concepts help to better understand the process of creating computer models and their control and adaptation. In the outlook we discuss how the allagmatic method needs to be extended in order to cover the field of complex systems and Norbert Wiener's ideas on control.

Patrik Christen, Olivier Del Fabbro

We recently presented the so-called allagmatic method, which includes a system metamodel providing a framework for describing, modelling, simulating, and interpreting complex systems. Its development and programming was guided by philosophy, especially by Gilbert Simondon's philosophy of individuation, Alfred North Whitehead's philosophy of organism, and concepts from cybernetics. Here, a mathematical formalism is presented to better describe and define the system metamodel of the allagmatic method, thereby further generalising it and extending its reach to a more formal treatment and allowing more theoretical studies. By using the formalism, an example for such a further study is provided with mathematical definitions and proofs for model creation and equivalence of cellular automata and artificial neural networks.

Patrik Christen, Olivier Del Fabbro

As a discipline cybernetics has a long and rich history. In its first generation it not only had a worldwide span, in the area of computer modelling, for example, its proponents such as John von Neumann, Stanislaw Ulam, Warren McCulloch and Walter Pitts, also came up with models and methods such as cellular automata and artificial neural networks, which are still the foundation of most modern modelling approaches. At the same time, cybernetics also got the attention of philosophers, such as the Frenchman Gilbert Simondon, who made use of cybernetical concepts in order to establish a metaphysics and a natural philosophy of individuation, giving cybernetics thereby a philosophical interpretation, which he baptised allagmatic. In this paper, we emphasise this allagmatic theory by showing how Simondon's philosophical concepts can be used to formulate a generic computer model or metamodel for complex systems modelling and its implementation in program code, according to generic programming. We also present how the developed allagmatic metamodel is capable of building simple cellular automata and artificial neural networks.

Patrik Christen, Olivier Del Fabbro

Many computer models such as cellular automata and artificial neural networks have been developed and successfully applied. However, in some cases, these models might be restrictive on the possible solutions or their solutions might be difficult to interpret. To overcome this problem, we outline a new approach, the so-called allagmatic method, that automatically programs and executes models with as little limitations as possible while maintaining human interpretability. Earlier we described a metamodel and its building blocks according to the philosophical concepts of structure (spatial dimension) and operation (temporal dimension). They are entity, milieu, and update function that together abstractly describe cellular automata, artificial neural networks, and possibly any kind of computer model. By automatically combining these building blocks in an evolutionary computation, interpretability might be increased by the relationship to the metamodel, and models might be translated into more interpretable models via the metamodel. We propose generic and object-oriented programming to implement the entities and their milieus as dynamic and generic arrays and the update function as a method. We show two experiments where a simple cellular automaton and an artificial neural network are automatically programmed, compiled, and executed. A target state is successfully evolved and learned in the cellular automaton and artificial neural network, respectively. We conclude that the allagmatic method can create and execute cellular automaton and artificial neural network models in an automated manner with the guidance of philosophy.