Review of incursive, hyperincursive and anticipatory systems-foundation of anticipation in electromagnetism

Abstract

The main purpose of this paper is to show that anticipation is not only a property of biosystems but is also a fundamental property of physical systems. In electromagnetism, the anticipation is related to the Lorentz transform. In this framework the anticipation is a strong anticipation because it is not based on a prediction from a model of the physical system but is embedded in the fundamental system. So, Robert Rosen’s anticipatory systems deal with weak anticipation. Contrary to Robert Rosen’s affirmation, anticipation is thus not a characteristic of living systems. Finality is implicitly embedded in any system and thus the final cause of Aristotle is implicitly embedded in any physical and biological systems, contrary to what Robert Rosen argued. This paper will review some incursive and hyperincursive systems giving rise to strong anticipation. Space-time incursive parabolic systems show non-local properties. Hyperincursive crisp systems are related to catastrophe theory. Finally it will be shown that incursive and hyperincursive anticipatory systems could model properties of biosystems like free will, game strategy, theorem creation, etc. Anticipation is not only related to predictions but to decisions: hyperincursive systems create multiple choices and a decision process selects one choice. So, anticipation is not a final goal, like in cybernetics and system science, but is a fundamental property of physical and biological systems.