The Crystal

Looking back on two millennia of history of the sciences and arts, the crystal, understood as a natural phenomenon and as a cultural construct, appears to be the most prominent example of transitions, transfers, bridge-building, modelling and inspirations between the sciences and the arts throughout world cultures. The reason for this double career is that it seems to embody mathematics and geometry in an aesthetic way. Schelling calls the crystal "the spiritual in the material" (das Geistige im Materiellen) – the materialised form of a "spirit" that makes God's blueprint of creation coincide with the human faculty of knowledge. Mathematics itself is thereby declared a natural phenomenon or projected into nature. The crystal appears as a hinge between the knower and the known, confronting the epistemological subject-object dualism with the old philosophical questions of a monistic ontology.

Another bridging function between the arts on the one hand, and mathematics and the natural sciences on the other, was based on Pythagoras' theory of music in which the Greek philosopher claims that music, colours and forms could be translated into one another by means of numerical relationships (proportions). Johannes Kepler wrote a Pythagorean theory of music and a crystallography. His belief in these ancient models led him to conclude that the planetary orbits could not be circles, but only ellipses, because God could probably only have created the planetary system as a harmony of the spheres. He then wanted to test this fantastic idea empirically and constructed the Keplerian optics as well as the Kepler telescope in order to confirm his assumption in an empirical way. This moment in history marks the transition between aesthetic phenomena (music and crystal) and the empirical methodology on a mathematical basis.

The historical construct of the crystal, as conceived by Pythagoras, handed down by Plato and rationalised by Kepler, also sheds a remarkable light on the present sciences and arts, which are characterised by the digital number. The cosmos was imagined as a calculating machine whose mathematical operation with ratios produced the appearing world. In phenomena such as tonal harmony – crystals, the laws of leaf arrangement and aesthetic proportions in art – according to this creation myth, the self-calculating computation was evident and provable. The "celestial machine" (Boethius) produces an "inaudible sound", a generating, eternally updating calculation, whose mere epiphenomena are all earthly phenomena.

Since the early days of computer science (cybernetics, systems theory), the recursive calculus, the result of which is the starting point of a new calculus, has been the starting point of new topics such as self-reference, self-control, autopoiesis, algorithm, emergence, system formation and artificial intelligence. The emergence of life – as well as the self-organisation of social systems – is pursued from an approach that got its historical and metaphorical impetus from "crystal growth", a mathematically conditioned self-organisation of matter. We do not know whether the world is the product of an immaterial self-calculating calculation, but for virtual worlds up to the Metaverse, we can answer this question with a clear yes and without doubt. The question of the recognisability of the natural object by the subject awaits further research, to which both the sciences and the arts can contribute. Crystal, an object that tips erratically between subjectivity and objectivity / living and dead is well suited as a bridge that brings both approaches together.