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Numbers are Meant for Counting, Right?
- Edited by Marco Pasi, Peter Forshaw, Wouter Hanegraaff
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- Book:
- Hermes Explains
- Published by:
- Amsterdam University Press
- Published online:
- 24 November 2020
- Print publication:
- 02 July 2019, pp 47-53
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Summary
Right. Unfortunately…! But what is counting, anyway? Surely, the word and the mental operations associated with it are not exclusively concerned with those maddening “problems” of leaking taps and the exact quantity of water they are liable to spill in a given amount of time; or with the number of miles it will take for a certain train to catch up with another one, taking into account their respective speed.
As a matter of fact, counting, for our distant forebears, did not apply exclusively to items belonging to the physical world. To put it differently, calculus was not necessarily understood as an abstract but useful tool for the study of nature, devoted to the task of reckoning, distributing, or classifying the elements of reality, as we know it. The agency of numbers was in fact extended to questions pertaining to the immaterial layers of being as well, inasmuch as numerical entities were perceived as governing central concepts of cosmology, such as harmony, measure, balance or proportion, which could also apply outside the limits of physical reality proper.
The question of knowing whether numbers actually exist separately on a plane of their own (mathematical “realism”), or whether they are no more than abstractions generated by the working of the human mind (“idealism”), is still being debated today among professional scientists and philosophers. Both stances, which the historical names of Plato (or Pythagoras) and Aristotle (fifth-fourth cent. BCE) have respectively come to stand for, can be traced back to classical Antiquity. From that period onwards, until well into the seventeenth century at least, numbers have often been closely related to the qualitative aspects of both cosmic and human nature.
This particular cultural attitude refers to a type of understanding of mathematics which imbues numbers with the capacity of signifying more than just the quantity they materially refer to. In this perspective, numbers are construed as manifesting effectively the invisible energies at work behind the veil of exterior reality, thus structuring and harmonising the physical world from inside (or from “above”). This view actually presupposes the idea (“neoplatonic,” in a very general way) of a multi-layered universe, in which numerical entities occupy a higher level of reality than the one corresponding to objects belonging to the ordinary physical plane.
34 - Mathematical Esotericism
- from V - COMMON THREADS
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- By Jean-Pierre Brach, École Pratique des Hautes Études, Paris
- Edited by Glenn Alexander Magee, Long Island University, New York
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- Book:
- The Cambridge Handbook of Western Mysticism and Esotericism
- Published online:
- 05 May 2016
- Print publication:
- 18 April 2016, pp 405-416
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Theology, Ethics, Cosmology
“Number symbolism” refers to a “qualitative” approach to number and mathematical objects in general. It is backed by what is known as “correlative thinking” and operates according to a network of analogies linking the quantitative values of mathematical entities to a vast array of correspondences throughout the many levels of the so-called Great Chain of Being. It is also a universal cultural phenomenon, likely to have existed from time immemorial. But it should not be confused with “numerology,” a term that has mainly come to designate contemporary methods of a pseudo-divinatory character, which do not concern us here.
Within Western culture, to which we shall limit ourselves in this essay, explicit considerations pertaining to “arithmology” (or qualitative number) first appear with the Greeks – insofar, that is, as extant documents are concerned.
Although it is clear that correlative thinking, mathematical symbolism, and the worldview they both depend on pertain to a type of archaic “wisdom” predating Greek civilization, it is nevertheless the case that the few truly arithmological texts that have come down to us date from no earlier than the late Hellenistic period. Still, one must take into account the fact that the name of Pythagoras (ca. 570–490 BCE) was already synonymous in Ancient Greece with a “philosophy of number.” It appears that the Pythagorean school, which vanished around the end of the fourth century BCE, never felt compelled to draw a clear distinction between mathematical research, as we would understand it, and mystical speculations about arithmetic and geometry. Both Proclus (412–485 CE) and Damascius (ca. 470–535 CE) ascribe to Philolaus of Croton (fl. ca 450 BCE), one of the main representatives of the early Pythagorean movement, a discourse on “theological geometry,” which correlates the respective angles of the triangle and square to the same number of masculine and feminine Olympian deities, to underline the sovereignty of the duodenary (3 × 4) associated with the supreme god Zeus. This appears to confirm the presence of symbolic perspectives from the beginning of the school, inasmuch as it is feasible to distinguish between supposedly “original” material and later, “traditional” developments.
What appears to us, accordingly, as a mixture of scientific and symbolic perspectives results in a general doctrine of cosmic harmony, partly expressed in mathematical concepts and correspondences that may have exerted a certain influence on Plato.
Mathematical Esotericism: Some Perspectives on Renaissance Arithmology
- Wouter Hanegraaff, Joyce Pijnenburg
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- Book:
- Hermes in the Academy
- Published by:
- Amsterdam University Press
- Published online:
- 20 January 2021
- Print publication:
- 21 August 2009, pp 75-90
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Since Augustine and the high Middle Ages until it began its decline at the end of the 13th century, the symbolism of numbers was known in Europe by terms such as “arithmetics,” the “mystery (or sacrament) of numbers,” or sometimes even the “mystical sense of number.” It was rediscovered during the Renaissance, and now came to be known as “mystical,” “formal” or “Pythagorean” arithmetics, or as the “mystical application of numbers.” As such, it was part of the revival of neoplatonizing tendencies and of the interest – albeit frequently biased, in this respect – in the works of Nicholas Cusanus (1401-1464).
Although Marsilio Ficino, the central representative of Renaissance Platonism, devoted some important discussions to an analogical or qualitative interpretation of numbers or of certain geometrical figures (both in his own works and in his translations of and commentaries on Plato), the triumphant return of number symbolism to the center of humanist preoccupations was primarily the work of his young fellow countryman Giovanni Pico della Mirandola (1463- 1494) and of the German Johannes Reuchlin (1455-1522). From 1486 on, with his famous Oratio on the Dignity of Man, Pico made an explicit attempt to establish arithmology as a “way of philosophizing” (institutio philosophandi, that is to say, as a method of doing philosophy by means of numbers), and even as a wholly independent current of speculation almost on the same level of importance as Neoplatonism, Aristotelianism, magic, or kabbalah. In such a context, “Pythagoreanism” ceased to be understood – as it had mostly been thus far – as a vaguely allegorical approach to mathematics, or a hermeneutical tool for interpreting the numbers in the Bible. Pico made a point of emphasizing that even if he was presenting this “philosophy by numbers” as something new, it was in reality an ancient tradition that had been highly respected by the “ancient theologians” and from there all the way up to Plato and Aristotle themselves. As is well known, he was planning a public debate presided over by the Pope himself, which should take place in Rome after Epiphany in 1487, in which he wanted to discuss no less than 900 theses written by him for the occasion.