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Counting by cutting in half

Chedanaka

छेदनक

The commentators do not write the human maximum as digits. They say it is the number with ninety-six cuttings - halve it ninety-six times and you reach one - which is how a tradition without place-value written large says two to the ninety-sixth.

A chedanaka is one halving. A number's chedanakas are how many times it can be cut in half; the number with ninety-six is 2^96, and the human maximum is given as that number less one, so that it has exactly ninety-six and not ninety-seven. The view lays the ninety-six out as a staircase, each tread a doubling, and the top tread is the twenty-nine digits.

The same device measures other things in the texts: the ranks of the innumerable are built by repeated squaring and cutting rather than by writing digits, which is why the atlas can say how those ranks relate without ever printing a figure for one.

Twenty-nine digits: the most humans there can be at oncethe commentators on Prajñāpanā 3 and the Jīvābhigama: the number with ninety-six cuttings2^96 − 1, checked by arithmetic; everything above this rung is beyond counting2^12^82^162^322^642^96ninety-six doublings, each tread one chedanakaTHE MOST HUMANS BORN OF THE WOMB, AT ONCE79,22,81,62,51,42,64,33,75,93,54,39,50,335two to the ninety-sixth, less one - so that it halves exactly ninety-six timesTHE RUNGS ABOVE, WHICH NO STAIRCASE REACHEShell-beings: innumerably many times more than thisgods: innumerably many times more than the hell-beingssiddhas: infinitely many times more than the godsthe nigoda, among the plants: infinitely many times more than the siddhas
Twenty-nine digits: the most humans there can be - Chedanaka highlighted

Measurements and counts

One chedanakaone halving
Ninety-six of them2^96
The human maximum2^96 − 1
Why less oneso that it has exactly ninety-six cuttings

Connected

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समयं गोयम! मा पमायए

Do not be heedless, Gautama, for even a single samaya.

Uttarādhyayana Sūtra 10