Underlinings (#52)

Florian Cramer:

The Pythagorean project consists of the extraction and application of a universal numerical code that organizes both nature and art. This code allows the creation of a correspondence between macrocosm and microcosm and describes harmony, in the sense of beautiful numerical proportions, as the guiding principle of the world. And for the first time, it allows the computation of nature and art. Any natural and symbolic system can be broken up into numerical proportions and values which in turn may be compared to the numerical proportions and values of another observed system. It is this principle of universal similarity and correspondence which Eco calls the “hermetic paradigm” and sums it up under the maxim “sicut superius sic inferius,” “as above, so below” to describe a correspondence of macro- and microcosm. In Pythagorean and later hermetic thinking, numerical proportions can be universally equated to geometrical proportions and musical intervals. Letters, likewise, can be computed as numbers and set into relation to the numerical intervals which are thought to be the foundations of the cosmos. Pythagorean thought therefore first coined and systematically expressed the idea that a symbolic-mathematical source code underlies the universe and describes nature and culture alike.




“… despite the connotations of the word ‘twin’, a dodecahedron actually has 5 twins. […] But here’s something deeper that Ocneanu claims to have proved, in unpublished work. Suppose you take one of these twins. It, too, will have 5 twins. One of these will be the dodecahedron you started with. But the other 4 will be new dodecahedra: that is, dodecahedra rotated in new ways. […] How many different dodecahedra can you get by continuing to take twins? Infinitely many! This image by Roice Nelson shows the vertices of a dodecahedron, its twins, the twins of its twins, the twins of the twins of its twins, the twins of the twins of the twins of its twins, and the twins of the twins of the twins of the twins of its twins …”