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So wait... math was never really done long hand in ancient times, but calculators (the abacus or any other form) were used instead? In some respects, that make

So wait... math was never really done long hand in ancient times, but calculators (the abacus or any other form) were used instead? In some respects, that makes sense. Paper like materials were never cheap and long-hand math uses a whole lot of paper. Bead calculators makes sense. I'd be curious to see if there's a correlation to "cheap" paper being plentiful right before the invention of complex math like Algebra. With a quick 5 minute peek, "cheap" paper came from China to the middle east in the ~8th century. Algebra was recorded in the 9th in the middle east. So... eh, maybe. Requires more reading, but it's interesting. Sounds like an interesting infrastructure like correlation to technology.

thaumasiotes 6y ago
> math was never really done long hand in ancient times, but calculators (the abacus or any other form) were used instead? No. I provided an example of peasant multiplication in my response sidethread. (Well, "yes" if you mean using paper. Paper is hard to get. But you can multiply without needing a special tool; the algorithm is commonly executed by using piles of rocks and pits in the ground.) The abacus is a more advanced technology that took time to develop. (It does appear early in some form; see https://en.wikipedia.org/wiki/Abacus#History https://en.wikipedia.org/wiki/Abacus#History )
jacobolus 6y ago
Yes this is largely correct. Calculation was not done with Roman (or Sumerian, Egyptian, Greek, ...) numerals per se, but mentally, with fingers, with piles of tokens, or with a counting board. But we are talking about moving tokens around on some markers drawn on the ground (or on a piece of cloth or animal skin or wooden board or whatever), not beads on rods like a Suanpan/Soroban used in East Asia today. My speculation is that many ancient game boards (e.g. backgammon, mancala) were also (or originally) counting boards. (The Roman phrase 'calculos ponere' literally means 'place pebbles', as on a counting board; this is where our word 'calculate' comes from. To settle accounts with someone was to 'vocare aliquem ad calculos' or 'call them to the pebbles') You should think of written numbers as a historical serialization and storage format. Something like the XML or JSON of the ancient world. And just like a modern computer, ancient computers first deserialized data to a more convenient internal representation for intermediate processing. Arithmetic really took off in Europe with the advent of printed books (easier to teach written arithmetic tricks via books, whereas counting-board tricks were largely passed down orally and by demonstration) and of course with cheaper paper and widespread literacy. The big advantages written arithmetic has vs. counting boards (despite being slower and having a steeper learning curve) is that all of the scratch work remains visible, which makes it easier to check for mistakes. Roman numerals are a more direct representation of the state of a counting board which takes less practice to learn, especially for illiterates.
- jackcosgrove 6y ago
  That's interesting that the root meaning of calculate is pebbles. I'm sure it's unintentional, but pebbles as a mnemonic for calculus is pretty good. Take the counting stones and pulverize them into dust and you get calculus.
  - thaumasiotes 6y ago
    The word is derived from calx [limestone/chalk]. Calculus is then a "little rock" -- the -ul- or -cul- infix is a diminutive form. (Analogous to "doggy" vs "dog" in English.) > pulverize them into dust While we're on the subject, the Latin for "dust" is pulvis. ;D

thaumasiotes 6y ago

> math was never really done long hand in ancient times, but calculators (the abacus or any other form) were used instead? No. I provided an example of peasant multiplication in my response sidethread. (Well, "yes" if you mean using paper. Paper is hard to get. But you can multiply without needing a special tool; the algorithm is commonly executed by using piles of rocks and pits in the ground.) The abacus is a more advanced technology that took time to develop. (It does appear early in some form; see https://en.wikipedia.org/wiki/Abacus#History https://en.wikipedia.org/wiki/Abacus#History )

jacobolus 6y ago

Yes this is largely correct. Calculation was not done with Roman (or Sumerian, Egyptian, Greek, ...) numerals per se, but mentally, with fingers, with piles of tokens, or with a counting board. But we are talking about moving tokens around on some markers drawn on the ground (or on a piece of cloth or animal skin or wooden board or whatever), not beads on rods like a Suanpan/Soroban used in East Asia today. My speculation is that many ancient game boards (e.g. backgammon, mancala) were also (or originally) counting boards. (The Roman phrase 'calculos ponere' literally means 'place pebbles', as on a counting board; this is where our word 'calculate' comes from. To settle accounts with someone was to 'vocare aliquem ad calculos' or 'call them to the pebbles') You should think of written numbers as a historical serialization and storage format. Something like the XML or JSON of the ancient world. And just like a modern computer, ancient computers first deserialized data to a more convenient internal representation for intermediate processing. Arithmetic really took off in Europe with the advent of printed books (easier to teach written arithmetic tricks via books, whereas counting-board tricks were largely passed down orally and by demonstration) and of course with cheaper paper and widespread literacy. The big advantages written arithmetic has vs. counting boards (despite being slower and having a steeper learning curve) is that all of the scratch work remains visible, which makes it easier to check for mistakes. Roman numerals are a more direct representation of the state of a counting board which takes less practice to learn, especially for illiterates.

jackcosgrove 6y ago
That's interesting that the root meaning of calculate is pebbles. I'm sure it's unintentional, but pebbles as a mnemonic for calculus is pretty good. Take the counting stones and pulverize them into dust and you get calculus.
- thaumasiotes 6y ago
  The word is derived from calx [limestone/chalk]. Calculus is then a "little rock" -- the -ul- or -cul- infix is a diminutive form. (Analogous to "doggy" vs "dog" in English.) > pulverize them into dust While we're on the subject, the Latin for "dust" is pulvis. ;D