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TFA was written by someone speculating based on some half-remembered trivia and their own inferences, and is not based on solid evidence about how people actual

TFA was written by someone speculating based on some half-remembered trivia and their own inferences, and is not based on solid evidence about how people actually calculated (notice the lack of references). There is limited direct evidence of calculations per se still available today, but plenty of indirect evidence that people did not ever write down modern-style “arithmetic” using Roman numerals, but instead did calculation with tokens on some kind of counting board, or else calculated on their fingers. > Romans didn't use subtractive shorthand notation Not always as a strict rule as became a common standard centuries later, but there are numerous examples of this kind of subtractive notation from ancient times. Wikipedia mentions “For example, on the numbered gates to the Colosseum, IIII is systematically used instead of IV, but subtractive notation is used for XL; consequently, gate 44 is labelled XLIIII” You might enjoy https://en.wikipedia.org/wiki/Roman_numerals#Irregular_subtractive_notation https://en.wikipedia.org/wiki/Roman_numerals#Irregular_subtr...

lproven 4y ago
> (notice the lack of references). I do so note. I also note a lack of references in your explanation. Look, I am not picking sides here. I have no skin in this game, merely a very mild passing interest. You're presenting your own (AFAICS) hypotheses as facts, and so are they. The Wikipedia page merely suggests to me that innumeracy was a common problem across the Empire, and that people got it wrong a lot, in inconsistent ways. No?
- jacobolus 4y ago
  Your claim was that “Romans didn't use subtractive shorthand notation”. This is a trivially falsifiable claim: There are numerous examples of subtractive Roman numerals used in Roman times. Wikipedia describes several. > Wikipedia page merely suggests to me that innumeracy was a common problem across the Empire, and that people got it wrong a lot This is comical deflection from my point, which was that Wikipedia directly refutes your claim (repeated from TFA) with numerous references. People writing XL for 40 and XIIX for 18 and IC for 99 are not “getting it wrong”; they are using subtractive notation, which was both commonplace and well understood (but not standardized) at the time. The author of TFA didn’t do any research whatsoever about the topic and is speculating based on some half-remembered trivia. Which is fine, it’s a blog post on a personal website. But you shouldn’t pretend it is a reliable source. * * * More generally though, if you want to learn about my main claims upthread that a counting board was used by Romans in preference to anything like written arithmetic, here are some references: Chrisomalis (2020) Reckonings > In fact, among the thousands and thousands of Roman and post-Roman medieval Latin texts that survive, on a wide variety of media, none line up Roman numerals in columns for arithmetic, or use Roman numerals directly for arithmetical purposes. Admittedly, much of the material and literate record of of the Romans is lost, but there is no evidence to support the idea that reckoners in the Roman tradition ever did what we might imagine them to have done, which is to use Roman numerals as computational aids by writing them down and manipulating them. > This has not stopped Western scholars from trying to show that it could have been done. I know of no fewer than five attempts, largely independent of one another, to show how the Roman numerals could have been manipulated to perform basic arithmetic adequately (Anderson 1956; Krenkel 1969; Kennedy 1981; Detlefsen et al. 1976; Schlimm and Neth 2008). All of these are artificial—they use the structure of the system and then imagine different ways it might have worked. None of them directly present any evidence to show that they were used in this way, because there simply is no such evidence. > At best, even when the conclusion is not so bad for the Roman numerals, it’s ahistorical and strange to insist on these comparisons. We are so attached to the idea that numerals are for arithmetic that it’s very hard to stop and ask whether they were actually used for doing calculations in a given society. Turner (1951) “Roman Elementary Mathematics” https://penelope.uchicago.edu/Thayer/E/Journals/CJ/47/2/Roman_Elementary_Mathematics*.html https://penelope.uchicago.edu/Thayer/E/Journals/CJ/47/2/Roma... (who also describes Roman finger calculations) > The other method of working mathematical problems available to the ancient Roman would be the use of the counting board or abacus. That this was the standard instrument for any type of complex calculation is, I believe, a safe assumption, but an assumption based on surprisingly little direct evidence. The very word "abacus" which I have been using does not seem to have been found in this sense in classical Latin literature. The most common terms used are rather calculi (pebbles) for counters, tabula for the table; calculos ponere for undertaking a problem. The widespread metaphorical use of calculus is ample evidence of the universal and early use of the device, but precise evidence on its nature or on the way it was used is remarkably scarce.... If you are interested in the general topic of number systems let me recommend Menninger’s classic book Number Words and Number Symbols. Or you could try Chrisomalis’s other book Numerical Notation. Or Ifrah, The Universal History of Numbers. If you want to know about medieval European counting boards, look up Barnard (1916) The Casting-Counter and the Counting-Board. A neat paper about Greek use of tokens is Netz (2002) “Counter Culture” http://worrydream.com/refs/Netz%20-%20Counter%20Culture%20-%20Towards%20a%20History%20of%20Greek%20Numeracy.pdf http://worrydream.com/refs/Netz%20-%20Counter%20Culture%20-%...

lproven 4y ago

> (notice the lack of references). I do so note. I also note a lack of references in your explanation. Look, I am not picking sides here. I have no skin in this game, merely a very mild passing interest. You're presenting your own (AFAICS) hypotheses as facts, and so are they. The Wikipedia page merely suggests to me that innumeracy was a common problem across the Empire, and that people got it wrong a lot, in inconsistent ways. No?

jacobolus 4y ago
Your claim was that “Romans didn't use subtractive shorthand notation”. This is a trivially falsifiable claim: There are numerous examples of subtractive Roman numerals used in Roman times. Wikipedia describes several. > Wikipedia page merely suggests to me that innumeracy was a common problem across the Empire, and that people got it wrong a lot This is comical deflection from my point, which was that Wikipedia directly refutes your claim (repeated from TFA) with numerous references. People writing XL for 40 and XIIX for 18 and IC for 99 are not “getting it wrong”; they are using subtractive notation, which was both commonplace and well understood (but not standardized) at the time. The author of TFA didn’t do any research whatsoever about the topic and is speculating based on some half-remembered trivia. Which is fine, it’s a blog post on a personal website. But you shouldn’t pretend it is a reliable source. * * * More generally though, if you want to learn about my main claims upthread that a counting board was used by Romans in preference to anything like written arithmetic, here are some references: Chrisomalis (2020) Reckonings > In fact, among the thousands and thousands of Roman and post-Roman medieval Latin texts that survive, on a wide variety of media, none line up Roman numerals in columns for arithmetic, or use Roman numerals directly for arithmetical purposes. Admittedly, much of the material and literate record of of the Romans is lost, but there is no evidence to support the idea that reckoners in the Roman tradition ever did what we might imagine them to have done, which is to use Roman numerals as computational aids by writing them down and manipulating them. > This has not stopped Western scholars from trying to show that it could have been done. I know of no fewer than five attempts, largely independent of one another, to show how the Roman numerals could have been manipulated to perform basic arithmetic adequately (Anderson 1956; Krenkel 1969; Kennedy 1981; Detlefsen et al. 1976; Schlimm and Neth 2008). All of these are artificial—they use the structure of the system and then imagine different ways it might have worked. None of them directly present any evidence to show that they were used in this way, because there simply is no such evidence. > At best, even when the conclusion is not so bad for the Roman numerals, it’s ahistorical and strange to insist on these comparisons. We are so attached to the idea that numerals are for arithmetic that it’s very hard to stop and ask whether they were actually used for doing calculations in a given society. Turner (1951) “Roman Elementary Mathematics” https://penelope.uchicago.edu/Thayer/E/Journals/CJ/47/2/Roman_Elementary_Mathematics*.html https://penelope.uchicago.edu/Thayer/E/Journals/CJ/47/2/Roma... (who also describes Roman finger calculations) > The other method of working mathematical problems available to the ancient Roman would be the use of the counting board or abacus. That this was the standard instrument for any type of complex calculation is, I believe, a safe assumption, but an assumption based on surprisingly little direct evidence. The very word "abacus" which I have been using does not seem to have been found in this sense in classical Latin literature. The most common terms used are rather calculi (pebbles) for counters, tabula for the table; calculos ponere for undertaking a problem. The widespread metaphorical use of calculus is ample evidence of the universal and early use of the device, but precise evidence on its nature or on the way it was used is remarkably scarce.... If you are interested in the general topic of number systems let me recommend Menninger’s classic book Number Words and Number Symbols. Or you could try Chrisomalis’s other book Numerical Notation. Or Ifrah, The Universal History of Numbers. If you want to know about medieval European counting boards, look up Barnard (1916) The Casting-Counter and the Counting-Board. A neat paper about Greek use of tokens is Netz (2002) “Counter Culture” http://worrydream.com/refs/Netz%20-%20Counter%20Culture%20-%20Towards%20a%20History%20of%20Greek%20Numeracy.pdf http://worrydream.com/refs/Netz%20-%20Counter%20Culture%20-%...