Crystals fascinate us with their clear shapes and with their sensual attributes such as color, luster, hardness, etc. and by their variety of substances. Each of these aspects corresponds to a field of study within scientific crystallography: crystal morphology studies possible and actual shapes, crystal physics their physical attributes, and crystal chemistry studies the elements they are composed of and their influence on color, shape, etc..
Conventional crystallography «explains» most of the phenomena by the way in which small particles join to form lattice-like structures. How does this relate to Rudolf Steiner’s emphasis on the role of cosmic/spiritual configurations of forces in the forming of crystals?
Crystal morphology and physics study attributes which correspond to singular directions within the crystals: flat crystal surfaces are situated at well-proportioned angles to each other (law of the constancy of interfacial angles); the level of hardness and the optical attributes (in double refraction, for example) are not the same for all directions, etc. This means that the study of the inside of crystals leads to qualities that are connected to the outer shape but point far beyond its finite limits. Each crystal has a handle of singnlar directions which span all of space. Suitable, idealized crystal shapes prove to be symmetrical, that is, they can be brought into self-coincidence by rotating them about axes with 60, 90, 120 or 180 degrees. They can also often be mirrored on the planes which join two axes.
Conventional crystallography interprets these directions as a consequence of the lattice-structure. The building blocks of these lattices are atoms, ions or molecules. This concept enables crystallographers to develop a subtle picture of how the macroscopic attributes relate to the micro-structure. However, for these studies to be precisely (mathematically) applied, one must assume that the various crystal lattices are infinitely large - that they span the whole of space. As a consequence of this, it appears that only one aspect of crystal formation is grasped by the infinite lattice. Its other, necessarily complementary aspect needs to be sought in projectively enhanced morphology. The latter enables one to think the idea of a formative force which spans the whole of space to its logical conclusion. In addition, it will be shown that projective concepts may be relevant for the interpretation of X-ray diagrams of crystals.
In this sense, the two main ways of studying crystals - structure theory and morphology - prove to be complementary. Structure theory expresses variations of substance and local principles, whereas morphology expresses forming and global principles. The two fields thus form a solid fundament for crystallography and mineralogy permeated by an anthroposophic approach.
N1 -Crystals fascinate us with their clear shapes and with their sensual attributes such as color, luster, hardness, etc. and by their variety of substances. Each of these aspects corresponds to a field of study within scientific crystallography: crystal morphology studies possible and actual shapes, crystal physics their physical attributes, and crystal chemistry studies the elements they are composed of and their influence on color, shape, etc..
Conventional crystallography «explains» most of the phenomena by the way in which small particles join to form lattice-like structures. How does this relate to Rudolf Steiner’s emphasis on the role of cosmic/spiritual configurations of forces in the forming of crystals?
Crystal morphology and physics study attributes which correspond to singular directions within the crystals: flat crystal surfaces are situated at well-proportioned angles to each other (law of the constancy of interfacial angles); the level of hardness and the optical attributes (in double refraction, for example) are not the same for all directions, etc. This means that the study of the inside of crystals leads to qualities that are connected to the outer shape but point far beyond its finite limits. Each crystal has a handle of singnlar directions which span all of space. Suitable, idealized crystal shapes prove to be symmetrical, that is, they can be brought into self-coincidence by rotating them about axes with 60, 90, 120 or 180 degrees. They can also often be mirrored on the planes which join two axes.
Conventional crystallography interprets these directions as a consequence of the lattice-structure. The building blocks of these lattices are atoms, ions or molecules. This concept enables crystallographers to develop a subtle picture of how the macroscopic attributes relate to the micro-structure. However, for these studies to be precisely (mathematically) applied, one must assume that the various crystal lattices are infinitely large - that they span the whole of space. As a consequence of this, it appears that only one aspect of crystal formation is grasped by the infinite lattice. Its other, necessarily complementary aspect needs to be sought in projectively enhanced morphology. The latter enables one to think the idea of a formative force which spans the whole of space to its logical conclusion. In addition, it will be shown that projective concepts may be relevant for the interpretation of X-ray diagrams of crystals.
In this sense, the two main ways of studying crystals - structure theory and morphology - prove to be complementary. Structure theory expresses variations of substance and local principles, whereas morphology expresses forming and global principles. The two fields thus form a solid fundament for crystallography and mineralogy permeated by an anthroposophic approach.
Crystals fascinate us with their clear shapes and with their sensual attributes such as color, luster, hardness, etc. and by their variety of substances. Each of these aspects corresponds to a field of study within scientific crystallography: crystal morphology studies possible and actual shapes, crystal physics their physical attributes, and crystal chemistry studies the elements they are composed of and their influence on color, shape, etc..
Conventional crystallography «explains» most of the phenomena by the way in which small particles join to form lattice-like structures. How does this relate to Rudolf Steiner’s emphasis on the role of cosmic/spiritual configurations of forces in the forming of crystals?
Crystal morphology and physics study attributes which correspond to singular directions within the crystals: flat crystal surfaces are situated at well-proportioned angles to each other (law of the constancy of interfacial angles); the level of hardness and the optical attributes (in double refraction, for example) are not the same for all directions, etc. This means that the study of the inside of crystals leads to qualities that are connected to the outer shape but point far beyond its finite limits. Each crystal has a handle of singnlar directions which span all of space. Suitable, idealized crystal shapes prove to be symmetrical, that is, they can be brought into self-coincidence by rotating them about axes with 60, 90, 120 or 180 degrees. They can also often be mirrored on the planes which join two axes.
Conventional crystallography interprets these directions as a consequence of the lattice-structure. The building blocks of these lattices are atoms, ions or molecules. This concept enables crystallographers to develop a subtle picture of how the macroscopic attributes relate to the micro-structure. However, for these studies to be precisely (mathematically) applied, one must assume that the various crystal lattices are infinitely large - that they span the whole of space. As a consequence of this, it appears that only one aspect of crystal formation is grasped by the infinite lattice. Its other, necessarily complementary aspect needs to be sought in projectively enhanced morphology. The latter enables one to think the idea of a formative force which spans the whole of space to its logical conclusion. In addition, it will be shown that projective concepts may be relevant for the interpretation of X-ray diagrams of crystals.
In this sense, the two main ways of studying crystals - structure theory and morphology - prove to be complementary. Structure theory expresses variations of substance and local principles, whereas morphology expresses forming and global principles. The two fields thus form a solid fundament for crystallography and mineralogy permeated by an anthroposophic approach.