Logic Trees, Magic Squares, Magic Circles and Magic Square of Squares

JF Ptak Science Books LLC  Post 1238

[Associated posts: The Mother of all Renaissance Logical Graphs, The Knight's Tour, Porphyry and Boethius and Census Art and the Display of Quantitative Data, 1860.]

Well now:  I don’t know what the provocation or inducement is here to hurtle this axe-swinging monk to attack Porphyry’s Tree¹, though it would be interesting in a forensic sort of way to know what the tree’s section might reveal. The “tree” was a diagrammatic creation of a 3^rd century Syrian mathematician/logician/philosopher named Porphyry who-- much taken with Aristotle (and with the Categories in particular)-- developed a systematic approach to the organization of thought in diagrammatic form.

What’s inside a tree of logic and memory?  Is there a  xylem-y/phloem-y stuff besides a three-dimensional representation of the structure of organizational thinking?  Or is the 2-dimensional rip a fatal blow to other dimensions, and like Eddington’s Turtles, it’s a simple slice of Flatland all the way down?  

Perhaps Porphyry’s tree rings would look like this, a magic circle or spiral, which would make some sense, and would bring to bear an associated use of turtles—or tortoises, I should say.  It turns out that perhaps the very first use of the magic circle, rolling back its origins through the Islamic world to India and to Persia and then to Japan,  and then finally to China where, in about 2000 BCE, the magic square appears in an image with the Emperor Yu,  inscribed on the back of a tortoise.

 

[Magic circle source:  Abraham Rees Encyclopedic Dictionary , printed 1805-1815. The originals are available from our blog bookstore.]

Notes:

1. This image appears in the rare Destructio sive eradicatio totius arboris Porphirii : magni philosophi ac sacrae theologiae doctoris eximii Augustini Anchonitani ordinis fratrum Heremitarum Sancti Augustini, cũ quadã decretali eiusde, published in 1503.