Ad Quadratum is a convenient and profound technique in which continuous scaling of size can be given to square shapes, either from a centre or periphery. The differences in scale are multiples of the square root of two [sqrt(2)] between two types of square: cardinal (flat) and diamond (pointed).
When a square’s diagonal touches opposite sides sides of a larger square, the two squares differ by sqrt(2) and a square becomes a diamond or visa versa. By repeating this effect a continuum can be generated to form the large patterns found in sacred buildings such as the Vedic Angkor Wat, Christian Gothic cathedrals, Islamic Dome of the Rock and even Stonehenge. The technique is therefore very ancient yet still used. Subjectively such buildings express a high degree of visual order by employing what is called a geometrical progression. Objectively, such patterns appear to convey cosmic principles known to ancient builders but largely forgotten recently.
It is said that we are transiting from the Age of Pisces to the Age of Aquarius in a backward precession through the 12 zodiacal signs. Examining the numbers that define these Ages is one of the core themes of this book. The basic premise is that stories – some of them handed down orally since Neolithic times – enable us to identify the inner spiritual aspects within our material world and participate in the evolution of human consciousness foretold by ancient myths. The author is greatly influenced by G.I. Gurdjieff and his Law of Seven, albeit with revisions of his own.
Readers such as myself, for whom mathematics is not their strong suit, need not be daunted by the many sets of figures presented in this book. They are important as supporting evidence for the theories presented, and their comprehension is made easier by the use of diagrams. Moreover, the fractions and ratios are often related to musical octaves and the Do-Re-Mi music-reading system.
Here I start by publishing an important diagram that shows how the earliest known references to musical tuning (early 4th millennium BC) on clay cuneiform tablets, using “regular numbers” whose factors are products of only the numbers 2, 3 and 5, led to the cosmological vision of their gods, the primary god, Anu, being a balanced mix of all three numbers as 60 but also called ONE. This is the source of their Sexagesimal or base-60, still employed in measuring angles and time called minutes and seconds. All comes from ONE.