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The referenced article mention this in passing without giving a reason. But didn't Pythgoras use musical whole number ratios like 2:1, 3:2 and 4:3?If so he must
by nyc111 8y ago
The referenced article mention this in passing without giving a reason. But didn't Pythgoras use musical whole number ratios like 2:1, 3:2 and 4:3?If so he must have considered 1 and 2 to be numbers.
- dr_dshiv 8y agoSorry to be lazy about citation. Here [1] is a peer reviewed article with better internal citations about Pythagorean mathematical perspectives on 1 and 2. It has been argued [2] that the Pythagorean numbers were quite different from numbers as we think of them in arithmetic. The One (or Oneness), for instance, is more than the number one. However, because these views extended to at least 10, it isn't an argument for disincluding 1 & 2. (BTW, [2] is probably the best thing I've ever downloaded from Kindle. Highly recommended. Be sure to read introduction.) [1] Caldwell, C. K., & Xiong, Y. (2012). What is the smallest prime?. Journal of Integer Sequences, 15(2), 3. [2] Guthrie, K. S., & Fideler, D. R. (Eds.). (1987). The Pythagorean sourcebook and library: an anthology of ancient writings which relate to Pythagoras and Pythagorean philosophy. Red Wheel/Weiser.
- nyc111 8y agoThanks for the references. I could only find this online which looks similar to what you have by the same authors: https://cs.uwaterloo.ca/journals/JIS/VOL15/Caldwell2/cald6.pdf https://cs.uwaterloo.ca/journals/JIS/VOL15/Caldwell2/cald6.p... Looks very interesting. Reading it now.
- dr_dshiv 8y agoGiven that the Pythagoreans believed that "all is number" and worshipped "Oneness", I'd be surprised if they didn't consider one to be a number