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Topic: Tetraktys

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Pythagoras

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	Middle Platonism [Internet Encyclopedia of Philosophy]
		Through this influence of the One upon the Dyad numbers are generated, i.e., the Decad, which in turn generates all other numbers.
		The most important of these primordial numbers is the tetraktys, numbers one through four, the sum total of which is ten, the Decad.
		The tetraktys also was interpreted by Plato as generating the four mathematical dimensions, with the number one corresponding to the point, two to the line, three to the plane, and four to the solid.
	www.iep.utm.edu /m/midplato.htm (8719 words)

	SEP: Pythagoras
		The tetraktys, which is the harmony in which the Sirens sing” (Iamblichus, On the Pythagorean Life, 82, probably derived from Aristotle).
		The tetraktys, literally “the four,” refers to the first four numbers, which when added together equal the number ten, which was regarded as the perfect number in fifth-century Pythagoreanism.
		Certainly the acusma which talks of the sirens singing in the harmony represented by the tetraktys suggests that there might have been a cosmic music and that Pythagoras may well have thought that the heavenly bodies, which we see move across the sky at night, made music by their motions.
	plato.stanford.edu /entries/pythagoras (10517 words)

	[No title]
		Tetraktys and II 312n, 463 andn, 599, 621
		As explained in Isis Unveiled (I, xvi.): The mystic Decad, the resultant of the Tetraktys, or the 1+2+3+4 = 10, is a way of expressing this idea.
		The One is the impersonal principle 'God'; the Two, matter; the Three, combining Monad and Duad and partaking of the nature of both, is the phenomenal world; the Tetrad, or form of perfection, expresses the emptiness of all; and the Decad, or sum of all, involves the entire Kosmos.
	www.theosophy-nw.org /theosnw/ctg/te-th.htm (7358 words)

	Number symbolism in the Mediterranean before A.D. 1000: a select bibliography
		"The Tetraktys: The Cosmic Paradigm of the Ancient Pythagoreans." Parabola 24.3 (1999): 38–43.
		Haase R. "Ein Beitrag Platons zur Tetraktys." Antaios 11 (1969): 85–91.
		Schwabe, J. "Arithmetische Tetraktys, Lambdoma und Pythagoras." Antaios 8 (1967): 421–49.
	www.kalvesmaki.com /Arithmetic/Number%20Symbolism.htm (7551 words)

	Harmonics, Music, Pythagoras and the Universe
		Rocks or stones as frozen music may derive from the habit of Greek mathematicians using movable pebbles to calculate (caculus means pebble or stone, as in calx, stone used in gambling).
		In the Pythagorean tradition the *tetraktys* of the dekad was demonstrated with such pebbles as unit markers.
		Dried beans were also used as calc to calculate but as the Pythagoreans knew, if defrosted by digestion could lead to noisy flatus down below.
	ray.tomes.biz /alex.htm (14270 words)

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