THE ORIGIN OF LETTERS AND NUMERALS.

systems of the Phoenicians, Egyptians, Babylonians etc., even indicated the numbers 5, 6, 7, 8 and 9 by the first four groups of strokes, as || ||| = 5, ||| ||| = 6, | ||| ||| = 7, || ||| ||| = 8, and ||| ||| ||| = 9. There can be no doubt, therefore, that by ten Sefirot original: עשר ספירות (Eser Sefirot). In this context, the author interprets the mystical "spheres" or "emanations" as simple "countings" or digits. the Book of Formation original: Sefer Yetzirah meant 1, 2, 3, and 4 written in strokes, their number amounting, when added together, to ten ¹⁷⁾, and by nothingness original: בלימה (Belimah). Usually translated as "ineffable" or "nothingness" in mystical texts, the author argues here for its mathematical definition as zero., it meant zero, which, being a symbol for nothing, is the equivalent of nothingness original: בלימה (Belimah)—"nothing" in Hebrew. My belief is that originally the text must have had ten Sefirot and nothingness original: עשר ספירות ובלימה (Eser Sefirot u-Belimah) = ten digits and zero.

As, according to the Book of Formation, it is possible to express all numbers by the ten Sefirot ¹⁸⁾, we must demonstrate how all numbers, even those higher than nine, may be indicated by the ten strokes. The strokes to indicate numbers were anciently written vertically and horizontally as — ═ ≡ ≣. By means of the strokes and the zero, all numbers may be expressed, as they are expressed by the Arabic numerals. The numbers 10, 20, 30, 40, 50 .... 500 ... 5000 .... 50000 may be expressed as — 0, ═ 0, ≡ 0, ≣ 0, Ⲷ 0, . . . . . . Ⲷ 00, Ⲷ 000, Ⲷ 0000.

1907 for instance would be represented thus: — vertical stack of 9 horizontal bars 0 vertical stack of 7 horizontal bars ¹⁹⁾.

¹⁷⁾ Dr. H. Malter calls my attention to the following passage of Abraham Abulafia A famous 13th-century mystic and founder of "Prophetic Kabbalah." in Jellinek's Treasures of the Wisdom of the Kabbalah original: גנזי חכמה הקבלה (Ginze Chokmah ha-Kabbalah), Leipzig 1853, p. 20: "The mind of a child counts ten Sefirot which are included in four according to the forms of the emanations original: Atzilus in this way: 1, 2, 3, 4, from which the emanation [is derived] as such (as if the letters Yod and Aleph The letters representing 10 and 1. were written one after the other)." This passage proves that the true meaning of the Sefirot had been known to some Hebrew writers.
¹⁸⁾ See text, § 16.
¹⁹⁾ Some Pythagoreans used the strokes with the principle of position without a zero in the columns of an abacus (Dr. M. Cantor's Mathematical Contributions original: Mathematische Beiträge, page 202).