6 ms·

This is an interesting perspective, but you have to assume that deprecating the system happened for a reason, probably due to ergonomic disdvantages. For simple

This is an interesting perspective, but you have to assume that deprecating the system happened for a reason, probably due to ergonomic disdvantages. For simple counting tasks, unary tally marks are still fashionable. Edit: I never used an abakus or the like, but maybe that's what roman numerals are the analogy to, and it got overcome with long division and the like.

jacobolus 8y ago
There are certainly advantages to the more abstract positional Hindu–Arabic number system (or e.g. the ancient Mesopotamian system for writing sexagesimal numbers which also positional). I am not trying to dispute that. A symbolic positional system saves space on the page. It makes recorded numbers more difficult to falsify later. Doing scratch work on paper leaves a better record of calculations (the position of a counting board is inherently ephemeral) which potentially makes it easier to spot errors. It is easier to describe pen and paper arithmetic in printed books which helps spread knowledge more easily than an oral tradition. It extends more easily to larger or (after the advent of decimal fractions) smaller numbers without needing an inordinately large number of different symbols. It is more easily extended by the use of pre-computed tables of function values, and especially by slide rules and similar devices. Once we start decimalizing our metrical system it becomes very regular to work with many different measurements in a consistent way. Perhaps most importantly the use of writing leads naturally to the development of symbolic algebra and ultimately simpler formulations of higher mathematics. But we can carefully describe the advantages and historical process of replacement etc. without unfairly disparaging the more direct representation.
- posterboy 8y ago
  MCM requires subtraction, two directions, 1900 is additional, maybe multiplicative if you want to be strict, either way only one direction. I'm not sure what's "more direct", either is linear. I might even think of 15:45 as a quarter before 4 [1]), but I'd argue that subtraction is conceptually a level higher. Nevertheless, high level representation might be an advantage. Maybe an interesting parallel viz. cognition is the 19.95 pricing scheme that's apparently proven to be confusing to the consumer. I'm just not sure which numeral system suffers more from that. [1] which marks an isogloss between east and west germany, the latter saying "dreiviertel vier" - three quarters four; German also has a weird order for decimal place reading: 121=hundred-one-twenty
  - jacobolus 8y ago
    Well MCM is not how Romans would write this except in rare cases. That one did not become a standard form until Medieval Europe. MDCCCC is absolutely a more direct representation of the counters on a counting board than 1900. Each letter precisely represents one counter and its position. But if you want, you can make a counting board with a line down the middle and use one side for negative values, in which case MCM would be a pretty direct representation of that. (It is unclear whether this was the origin of such numerals; we don’t have a whole lot of evidence about how calculation on ancient counting boards was done, because it was largely part of oral culture.)
- Koshkin 8y ago
  Speaking of fractions: https://www.quora.com/How-were-decimals-and-fractions-used-in-the-Roman-numeral-system https://www.quora.com/How-were-decimals-and-fractions-used-i...

jacobolus 8y ago

There are certainly advantages to the more abstract positional Hindu–Arabic number system (or e.g. the ancient Mesopotamian system for writing sexagesimal numbers which also positional). I am not trying to dispute that. A symbolic positional system saves space on the page. It makes recorded numbers more difficult to falsify later. Doing scratch work on paper leaves a better record of calculations (the position of a counting board is inherently ephemeral) which potentially makes it easier to spot errors. It is easier to describe pen and paper arithmetic in printed books which helps spread knowledge more easily than an oral tradition. It extends more easily to larger or (after the advent of decimal fractions) smaller numbers without needing an inordinately large number of different symbols. It is more easily extended by the use of pre-computed tables of function values, and especially by slide rules and similar devices. Once we start decimalizing our metrical system it becomes very regular to work with many different measurements in a consistent way. Perhaps most importantly the use of writing leads naturally to the development of symbolic algebra and ultimately simpler formulations of higher mathematics. But we can carefully describe the advantages and historical process of replacement etc. without unfairly disparaging the more direct representation.

posterboy 8y ago
MCM requires subtraction, two directions, 1900 is additional, maybe multiplicative if you want to be strict, either way only one direction. I'm not sure what's "more direct", either is linear. I might even think of 15:45 as a quarter before 4 [1]), but I'd argue that subtraction is conceptually a level higher. Nevertheless, high level representation might be an advantage. Maybe an interesting parallel viz. cognition is the 19.95 pricing scheme that's apparently proven to be confusing to the consumer. I'm just not sure which numeral system suffers more from that. [1] which marks an isogloss between east and west germany, the latter saying "dreiviertel vier" - three quarters four; German also has a weird order for decimal place reading: 121=hundred-one-twenty
- jacobolus 8y ago
  Well MCM is not how Romans would write this except in rare cases. That one did not become a standard form until Medieval Europe. MDCCCC is absolutely a more direct representation of the counters on a counting board than 1900. Each letter precisely represents one counter and its position. But if you want, you can make a counting board with a line down the middle and use one side for negative values, in which case MCM would be a pretty direct representation of that. (It is unclear whether this was the origin of such numerals; we don’t have a whole lot of evidence about how calculation on ancient counting boards was done, because it was largely part of oral culture.)
Koshkin 8y ago
Speaking of fractions: https://www.quora.com/How-were-decimals-and-fractions-used-in-the-Roman-numeral-system https://www.quora.com/How-were-decimals-and-fractions-used-i...