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Those don't seem related to me at all. Quipu was an Incan record-keeping system that we don't understand well. Abaci are very ancient calculation devices that d

Those don't seem related to me at all. Quipu was an Incan record-keeping system that we don't understand well. Abaci are very ancient calculation devices that don't use writing. The oldest Mesopotamian and Roman versions were just a table with pebbles on it. And that's where we get the word for "calculate".

openasocket 9y ago
They aren't required, it's certainly possible to have a number system and not a writing system. But for anything where you need to do non-trivial arithmetic or accounting you can't just do all that in your head and memorize the results. You need some way of recording the results in a persistent way, even if it's just tallies carved into a piece of wood. And I imagine any culture that figures out a recording system for numbers would pretty quickly (in historical terms, so like years or decades) develop a writing system. I could be wrong of course, I haven't really formally studied ancient history. Aside: Is Quipu not a writing system? I thought there was some evidence indicating it was.
- panglott 9y ago
  Pebble-tables are fine for that, but don't leave a persistant record. Mostly when I hear "writing system" I think "linguistic writing system", a writing system for language, rather than "mathematical writing system". But IIRC a number of writing systems started off first as mathematical record systems before developing to encode linguistic information. Maybe a good example is cuneiform, which started off as tally marks in balls of soft clay stored in jars, for tax purposes, which developed symbols for encoding what kind of goods were being counted. Quipu may be similar, with more nascent development as a linguistic system.
jacobolus 9y ago
As far as I know the invention and use of counting boards went hand-in-hand with written (cuneiform) records. Or at least, we don’t have any evidence of earlier positional counting boards, only artifacts like tally sticks and piles of (non-positional) tokens. The Sumerian society that developed cuneiform numeration/writing was a large bureaucratic urban society built on complicated debt/taxation/social organization.

openasocket 9y ago

They aren't required, it's certainly possible to have a number system and not a writing system. But for anything where you need to do non-trivial arithmetic or accounting you can't just do all that in your head and memorize the results. You need some way of recording the results in a persistent way, even if it's just tallies carved into a piece of wood. And I imagine any culture that figures out a recording system for numbers would pretty quickly (in historical terms, so like years or decades) develop a writing system. I could be wrong of course, I haven't really formally studied ancient history. Aside: Is Quipu not a writing system? I thought there was some evidence indicating it was.

panglott 9y ago
Pebble-tables are fine for that, but don't leave a persistant record. Mostly when I hear "writing system" I think "linguistic writing system", a writing system for language, rather than "mathematical writing system". But IIRC a number of writing systems started off first as mathematical record systems before developing to encode linguistic information. Maybe a good example is cuneiform, which started off as tally marks in balls of soft clay stored in jars, for tax purposes, which developed symbols for encoding what kind of goods were being counted. Quipu may be similar, with more nascent development as a linguistic system.

jacobolus 9y ago

As far as I know the invention and use of counting boards went hand-in-hand with written (cuneiform) records. Or at least, we don’t have any evidence of earlier positional counting boards, only artifacts like tally sticks and piles of (non-positional) tokens. The Sumerian society that developed cuneiform numeration/writing was a large bureaucratic urban society built on complicated debt/taxation/social organization.