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> goes so quickly that it's possible for the person calculating to cheat an onlooker Indeed, the biggest advantage of paper arithmetic is that it leaves a writ
by jacobolus 5y ago
> goes so quickly that it's possible for the person calculating to cheat an onlooker
Indeed, the biggest advantage of paper arithmetic is that it leaves a written record: each step in the algorithm can be checked for mistakes afterward. It is otherwise significantly slower and not inherently more accurate than a counting board.
The other advantage that paper arithmetic has is that it can be easily reproduced in printed books, making learning more advanced techniques more accessible / easier to spread to anyone literate, without requiring an expert teacher.
(And finally, paper arithmetic [eventually] has the advantage that it can be more conveniently extended and generalized to include more kinds of operations and structures, in a way that is easier to explain and teach than adding new kinds of counting board rules. Paper arithmetic is a more natural precursor for symbolic algebra than counting-board calculation.)
The big disadvantage of paper arithmetic is that it depends on widespread literacy and cheap access to paper (or similar material). In a context where paper is expensive or unavailable, written arithmetic is not very compelling.
- dredmorbius 5y agoChalk (or charcoal) and slate (or other rewritable surfaces) were common before paper was cheap. Greek and Roman students typically used wax-coated boards and scratched them with styli. The surface could be heated or rubbed to restore its unmarked form.
- jacobolus 5y agoYes that is true, but if you don’t have a permanent written record of the computation, that takes away a lot of the advantage of written arithmetic. You may as well just use your counting board.
- dredmorbius 5y agoNot permanent, but a record that could be shown as the computation was performed, and until the slate itself was erased. Obviously, where a permanent record is desired, permenent media would be used. My point was that there were cheap alternatives to parchment and paper for quick work.
- jacobolus 5y agoA wax or clay tablet or flat patch of dirt and a stick, piece of bark or wood and charcoal, etc. don’t have enough advantage for anyone to bother organizing their accounting or calculation system around them. They are on the whole inferior to the existing system. Trying to introduce them to people 2000+ years ago might have a chance, but it would be a tough sell. The thing that really spread Hindu numbers around the world was access to paper.
- dredmorbius 5y agoIs there any evidence / record that Hindu / Arabic numerals and paper co-dispersed?
- jacobolus 5y agoI am not an expert. My impression is that in India “Hindu” numerals and arithmetic were developed using some kind of erasable board, but among Arabic speakers (and later Europeans) the spread of Hindu numerals went along with paper as a prerequisite technology. This looks relevant https://cpb-us-e1.wpmucdn.com/sites.ucsc.edu/dist/f/704/files/2019/05/Islam.atCenter.JWH_.09.pdf https://cpb-us-e1.wpmucdn.com/sites.ucsc.edu/dist/f/704/file... Here is a relevant looking book: https://yalebooks.yale.edu/book/9780300089554/paper-print https://yalebooks.yale.edu/book/9780300089554/paper-print In e.g. Britain, the transition to Hindu numerals did not occur until 1600–1800, depending on the place.
- jacobolus 5y agohttps://doi.org/10.1017/jbr.2017.59 https://doi.org/10.1017/jbr.2017.59 is interesting
- dredmorbius 5y agoThanks.
- dredmorbius 5y agoIt's probably worth noting that Fra Luca Bartolomeo de Pacioli's dates are c. 1447 – 19 June 1517, shortly after Gutenberg and about 50--100 years after cheap papermaking (comparatively) first reached Europe. It's hard to have double-entry bookkeeping without books. I'm unsure if he used Arabic or Roman notation... Though the dedication page of Summa Mathematica in fact does include recognisable Hindu / Arabic numerals: https://en.wikipedia.org/wiki/Summa_de_arithmetica#/media/File%3ALucas_de_Burgo%2C_Dedication_page%2C_%22Somma_di_aritmetica%22_Wellcome_L0006607.jpg https://en.wikipedia.org/wiki/Summa_de_arithmetica#/media/Fi... Wikipedia's article has several illustrations, but none of the actual bookkeeping notation itself, which is ... a curious oversight. Continued on the double-entry bookkeeping article as well FWIW. https://en.wikipedia.org/wiki/Luca_Pacioli https://en.wikipedia.org/wiki/Luca_Pacioli