The world’s oldest 3x3 magic square, discovered/invented in Ancient China and now known as Luoshu 洛書/ ‘Document [from the River] Luo’, was endowed by Chinese tradition with unprecedented dignity and placed at the very heart of Chinese thought. The bewitching geometric-numerical imagery of Luoshu, open to a great many different visions, when reading-interpretation becomes the final moment of the very act of perception, turns this Chinese mandala into a real eye trap. With its disturbing persistence, it resembles the magically attractive ‘Zahir’ from Borges’ short story of the same name.
Among the most diverse ritual and ideological instrumentalizations of the Luoshu magic square (from the sacred emblem of cosmic harmony to the requisite of a geomancer), the mobilization of this esoteric figure for the arithmetization of the cornerstone of all Chinese philosophy, the fundamentally non-verbalizable Tao, is dominant. The coding of the dao by the number 15 is reinforced by its spatialization, so that the entire “Document [from the river] Lo” appears as a map of the various trajectories of the Tao within this nine-field square. Moreover, the coincidence (in number 15) of differently composed sums appears as an inscrutable variety of paths leading to the same goal - the final implementation of Tao.
By virtue of the validity of the equality 15 =mod10 5 the magic sum of the Luoshu square (Const15) immutably, although covertly (in the form of a number 5), centers the entire Luoshu configuration. This secrecy of the magical constant (the latter is absent in the entire observable space of the “Document [from the river] Lo”) refers to the hidden “back-side” of Luoshu numbers, represented by the number 10 (in its role as a modulus of comparison in the arithmetic of residues modulo 10).
Judging by the directly visible, so to speak, ‘front’ part of the magic square of order 3, it is allowed to count only up to nine in it. But the already absent-present magic sum (number 15), breaking the seemingly inescapable circle of arithmetic of residues, brings to light the comparison module (number 10) as Luosh’s hidden ‘truth’, which alone gives meaning to the entire nine-cell construction. Awareness of this truth is the first step in the transition to the ‘register of truth’ of this extraordinary gestalt. The subsequent connection to it of problems focused by the Pythagorean theorem radically expands Luoshu’s ‘register of truth’.
The geometrized arithmetic of the Luoshu magic square, which is a unique spatial-numerical fixation of the seemingly fundamentally non-objectivable Tao (i.e., combining the apparently incompatible) marks the possibility of a paradoxical union of Heraclitus with Pythagoras, successfully realized by the Chinese tradition.