THE peculiar properties of numerical magic squares became involved from quite early times in philosophical speculations and in practical activities. 1 To philosophers, the squares seemed to promise the discovery (after appropriate analysis) of new relations between things and their properties. However, this application of the squares was relatively limited when compared with their use in magic. Here they were particularly important because the occult properties attributed to numbers-or to any other symbols derived from them -seemed to be enhanced in squares. In magical practices, a certain property might be ascribed to the square as such-for example the third-order square might be used as a talismanic symbol to promote easier delivery in childbirth. For this purpose, it was important that the property could be formulated generally-it did not have to relate to the numbers of any particular square. In philosophical speculations, the situation was different. In this case certain relations between specific numbers and particular kinds of matter (or their properties) were sought·In this way, numerical magic squares survived for centuries somewhere between magic, philosophy and 'proto-science,' particularly alchemy. They were never particularly prominent, remaining rather shadowy entities surrounded by superstition. It is not easy to trace them through the history of the sciences-particularly of alchemy, which itself was anything but an accessible body of knowledge. Nevertheless, we can discover some cases where magic squares affected the alchemical speculations and experiments of adepts in the remote past. With some simplification, this process can be described in two steps. In the first, significant links between the squares and philosophical principles were sought. Then the resulting hypothesis was applied to actual, or imaginary, experiments.
MAGIC SQUARES, PLANETS AND METALSAn important aspect of magic squares was their relationship with astrological and alchemical speculations. Squares were linked with planets via the metals, a practice which indicates the ancient origins of the squares themselves. By the seventh century A.D., the pairing of planets with metals was firmly established,2 though the roots of this beliefmust be sought in ancient Mesopotamian astrology. An interesting relationship between planetary gods and numbers was noted by Stapleton. 3 In the Harranian culture, the planet-metal pairing was institutionalized in temple worship, where idols of the gods were made of the corresponding metal (with the exception of mercury; here the metal was inside the statue in a small vessel). In Europe, a relationship between numbers (the order of the square), planets and metals was recognized somewhat later, in a magical context. Significantly, Saturn (lead) always appeared on one of the ends of the series. This obviously relates to the ancient belief that lead was the 'father of metals,' which can be traced to writings by Greek authors as early as the first century A.D. 4 Two centuries later, Zosimos maintained th...
