Operators, the Lego‐bricks of nature: Evolutionary transitions from fermions to neural networks

Abstract

When Darwin wrote his ‘On the origin of species…” (1859) he focused on evolution as a property of living organisms in interaction with abiotic and biotic elements in the world. This viewpoint is still dominant amongst biologists. For particle physicists and cosmologists evolution refers to a larger scale, ranging from quarks and atoms to galaxies, stars and planets (i.e. Pagels 1985, Hawking 1988). To close the gap between such different viewpoints, a wide range of perspectives on an interdisciplinary understanding of system development has been published (i.e. Teilhard de Chardin 1966, von Bertalanffy 1968, Varela 1979, Prigogine and Stengers 1984, Laszlo 1996). As an integrative concept, the construction of nature from a hierarchy of system layers forms a central tenet in general system research and the stepwise construction of this layered hierarchy can be regarded as an interdisciplinary evolution theory. Surprisingly, the literature offers no unequivocal rules to recognise a multilayer hierarchy in nature. This presents an obstacle for interdisciplinary approaches to evolution. Searching a solution to part of the above hierarchy problem, the present paper is dedicated to the analysis of a special kind of layering in natural systems, which is based on transitions between ‘building block’ systems. To identify these building blocks, and the transitions from building block x at level A, to building block y at level B, the focus of this study is further limited to ‘hypercydic dynamics’ and ‘containment’. On the basis of these criteria, a hierarchy is created which shows no possibilities for ‘bypasses’. It connects hadrons to atoms, atoms to cells, and cells to neural networks. Implications of this hierarchy for system studies and evolution are discussed.