Abstract
In the course of modern history, science and magic have gradually become separated into a pair of binary opposites. While acknowledging what the “pure reason” of modernity considered to be a supernatural action, science nevertheless attempted to explain the latter in terms of a regular method of a direct cause-effect connection as a method in natural science, promptly arriving at a conclusion of either anomalous effect (as in magic) or anomalous cause (as in mantic). But can what is called magic still be considered a science—a science of hidden relations that are nevertheless, and in accord with Charles S. Peirce’s pragmatic maxim, capable of producing real effects? Surely John Deely (2001) acknowledged Peirce’s vision as rooted in science rather than mysticism. This chapter uses one of the Tarot cards called the Magician as an index of overcoming a schism between the dual opposites when positioned in the conceptual framework of semiotics that allows us to elucidate the meaning of this sign (Fig. 12.1).
This essay is a modified and updated version of the earlier 2008 paper titled “The Transversal Communication, or: Reconciling Science and Magic” published in the journal Cybernetics and Human Knowing, Vol. 15, No. 2, pp. 33–48. See Semetsky (2008) in references, I acknowledge the original publication with gratitude.
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In the earlier publication titled “Interpreting Peirce’s abduction through the lens of mathematics” (Semetsky 2015) I suggested a vectorial diagram on the complex (Gaussian) plane as a model for knowledge structure incorporating abduction as an unconscious inference. Peirce called such a mode of thought instinctive reason. The Magician’s semiotic reason can be modeled by means of geometry on the complex plane using imaginary numbers—dubbed magical by physicist and mathematician Sir Roger Penrose (2004)—coupled with real and together forming complex numbers. The imaginary number i as a square root of minus 1 does “appear to play a fundamental role in the working of the universe” (Penrose 2004: 67) including, as implied by the Whiteheadian one world without and within, the working of the human mind. Leibniz called them amphibian: in-between being and nothingness. As Lou Kauffman points out, it is “remarkable that domains imaginary with respect to arithmetic are virtually real with respect to geometry” (1996: 293). Raising a complex number to the n-th power multiplies its angle by n. It was Riemann who merged projective geometry with the idea of complex numbers. On the Riemann’s “number sphere” zero and infinity are but two opposite poles. In quantum mechanics, zero (vacuum) is a source of infinite energy.
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Semetsky, I. (2019). Science, Magic, and the In-Between: Whence Logic. In: Danesi, M. (eds) Interdisciplinary Perspectives on Math Cognition. Mathematics in Mind. Springer, Cham. https://doi.org/10.1007/978-3-030-22537-7_12
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