History
Abjectio novenaria (Latin for "casting out nines") was known to the Roman bishop Hippolytos as early as the third century. Ibn Sina (Avicenna) (908–946) was a Persian physician, astronomer, physicist and mathematician who contributed to the development of this mathematical technique. It was employed by twelfth-century Hindu mathematicians. in the 17th century, Gottfried Wilhelm Leibniz not only used the method extensively, but presented it frequently as a model for rationality: "By means of this, once a reasoning in morality, physics, medicine or metaphysics is reduced to these terms or characters, one will be able to apply to it at any moment a numerical test, so that it will be impossible to be mistaken if one does not so desire...".
Synergetics, R. Buckminster Fuller claims to have used casting out nines "before World War I." Fuller explains how to cast out nines and makes other claims about the resulting 'indigs,' but he fails to note that casting out nines can result in false positives.
The method bears striking resemblance to standard signal processing and computational error detection and error correction methods, typically using similar modular arithmetic in checksums and simpler check digits.
Read more about this topic: Casting Out Nines
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“Those who weep for the happy periods which they encounter in history acknowledge what they want; not the alleviation but the silencing of misery.”
—Albert Camus (1913–1960)
“If you look at the 150 years of modern China’s history since the Opium Wars, then you can’t avoid the conclusion that the last 15 years are the best 15 years in China’s modern history.”
—J. Stapleton Roy (b. 1935)
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—T.S. (Thomas Stearns)