How to tell if an ancient culture had zero
How would you know whether an ancient culture had zero?
John D. Cook explores the challenge of inferring a number system from fragmentary evidence, using spreadsheet column labeling as a modern example of bijective base-26. He explains that distinguishing between base-5 and bijective base-5 requires large samples or contextual clues, and notes that Benford's law could theoretically help but is less practical than finding numbers with known meanings.
If you found only 20 numbers, for example, you could hardly conclude ☘︎ never appears at the beginning of a number just because it doesn’t come at the beginning of any number you’ve seen.
- idoubtit
The question is the title is left unanswered by this shallow article. At least it's not AI slop since there are spelling mistakes ("You’re best hope").
> Say you’ve found 17 numeric symbols. You might infer that the writing used a base 20 system
Reals numerical systems are much more diverse than that. For instance, Babylon used a base 60 (hence our minutes and hours). But there were much less than 60 numeric symbols, since they had a symbol for 1 and 10. So 2 symbols for a base 60!
> never appears at the beginning of a number, you might infer that is a zero
In the later times Babylonians had a kind of zero, but it was very limited, only used to point the lack of a number between two, i.e. "2∅1" but never "21∅∅" which was written "21" (so numbers were ambiguous if the context didn't give the magnitude).
And Babylonians had floating numbers. So "4" could also mean 4/60.
What I mean is that Babylon had a zero, but it only covered a part of the positional modern zero. They could not write 0 - 3. And if their zero had been fully positional, there would have been numbers beginning with it, i.e. sexagecimals floats.
- jamesjolliffe
Is this the perfect clickbait title for nerd sniping?
One of the best I can recall.
- lisp2240
Zero has two roles: as a positional placeholder and as a cardinal value (nothingness or net-zero). This only addresses the former.
- gmuslera
Looks like translating a positional numbering system from ancient cultures than ruling out or not if they had the concept of zero. It may be a single use symbol, here is nothing, instead of being part of bigger amounts. Numbering systems doesn't have to be positional (nor go too far).
- thaumasiotes
> If you knew somehow that some symbol corresponds to 20, then you’d know they didn’t use base 20 because base b doesn’t have a single symbol for b.
Well, this is plainly false.