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In general, with an abacus. Roman numerals for generally used for recording information, not for calculating with them. The article emphasizes how easy it is to

In general, with an abacus. Roman numerals for generally used for recording information, not for calculating with them. The article emphasizes how easy it is to add and subtract with Roman numeral notation, but everything else I've read emphasizes the Abacus even for that. After all, most people today calculate with calculators as well, and we have a snazzy Hindu-Arabic system for numbers.

hencq 6y ago
It's actually somewhat surprising to me that the Romans didn't invent the concept of zero, when they used the abacus for daily calculations. With the benefit of 20:20 hindsight you'd think that the concept of zero would follow quite naturally from the concept of an empty column on the abacus.
- Sharlin 6y ago
  But that's the thing about Roman numerals: you don't need a placeholder number to represent empty columns. And for "what is XVI subtracted from XVI" they could just use a word meaning "nothing", such as nihil or nihilum. The need for the concept of zero as we understand it really only arises together with a place-value system.
  - crazygringo 6y ago
    Thanks for explaining that clearly. I've always been so baffled by people who claim that some society didn't have a concept for zero, as if "inventing" zero marks some major advance in intelligence. Every culture has a concept of "nothing" which works for zero. The ancient Greeks debated over whether nothing was a number or not, but that's just a semantic splitting of hairs. At some point a symbol for nothing becomes useful so you invent a number-like notation for it. But that's just a matter of convenience. It's not some great conceptual leap.
    - dwohnitmok 6y ago
      I think that for the majority of people throughout history, numbers were inseparable from numerals, i.e. notation for numbers. This would explain why people are far more comfortable with the notion of real numbers (which despite their name are very very strange in a lot of ways) than imaginary and complex numbers. Even their names betray the difference. However, one has a common notation that everyone has learned whereas the other has a more confusing and less well-known notation. Therefore I think ancient arguments over whether 0 is a number (and acceptance thereof) are representative of a greater paradigmatic shift, similar in essence to the arguments over whether the square root of -1 is truly a "number." Viewed that way 0 is the first step in a journey of an understanding of numbers from purely counting discrete entities, to abstract parts of computation. So basically I would posit that it is in fact a great conceptual leap (just as the negative numbers are) that only seems like an obvious fluke of notation when every schoolchild has learned it.
      - crazygringo 6y ago
        I would clarify that to say numbers were inseparable from words for them. Writing has only existed a short time of our history, so numerals are pretty recent. And the "meaning" of zero as a number like others along a number line, rather than as mere notation for "nothing", I assume only ever became necessary with the invention of negative numbers. With addition, multiplication and division, zero simply does nothing or annihilates a number, and so doesn't need to be treated like other numbers. AFAIK, zero as a number arises first in figuring out how to "get to" negative numbers, e.g. what is two minus four (one, zero, negative one, negative two), where zero is required as a numeric concept. Negative numbers were a big step forwards. Zero, I still don't see it -- either it was just convenient notation for "nothing", or part and parcel of the shift to negative numbers. Unless I'm missing something in the historical record?
        IIAOPSW 6y ago
        You need zero for place based notation. Eg 210 is "two in the hundreds place, one in the tens place, none in the ones place." Place based notation gets you representation of multiples all the way to infinity. Otherwise you need to represent multiples with unique symbols like in Roman Numerals. Eg X means 10 no matter how many symbols are to the right of it.

hencq 6y ago

It's actually somewhat surprising to me that the Romans didn't invent the concept of zero, when they used the abacus for daily calculations. With the benefit of 20:20 hindsight you'd think that the concept of zero would follow quite naturally from the concept of an empty column on the abacus.

Sharlin 6y ago
But that's the thing about Roman numerals: you don't need a placeholder number to represent empty columns. And for "what is XVI subtracted from XVI" they could just use a word meaning "nothing", such as nihil or nihilum. The need for the concept of zero as we understand it really only arises together with a place-value system.
- crazygringo 6y ago
  Thanks for explaining that clearly. I've always been so baffled by people who claim that some society didn't have a concept for zero, as if "inventing" zero marks some major advance in intelligence. Every culture has a concept of "nothing" which works for zero. The ancient Greeks debated over whether nothing was a number or not, but that's just a semantic splitting of hairs. At some point a symbol for nothing becomes useful so you invent a number-like notation for it. But that's just a matter of convenience. It's not some great conceptual leap.
  - dwohnitmok 6y ago
    I think that for the majority of people throughout history, numbers were inseparable from numerals, i.e. notation for numbers. This would explain why people are far more comfortable with the notion of real numbers (which despite their name are very very strange in a lot of ways) than imaginary and complex numbers. Even their names betray the difference. However, one has a common notation that everyone has learned whereas the other has a more confusing and less well-known notation. Therefore I think ancient arguments over whether 0 is a number (and acceptance thereof) are representative of a greater paradigmatic shift, similar in essence to the arguments over whether the square root of -1 is truly a "number." Viewed that way 0 is the first step in a journey of an understanding of numbers from purely counting discrete entities, to abstract parts of computation. So basically I would posit that it is in fact a great conceptual leap (just as the negative numbers are) that only seems like an obvious fluke of notation when every schoolchild has learned it.
    - crazygringo 6y ago
      I would clarify that to say numbers were inseparable from words for them. Writing has only existed a short time of our history, so numerals are pretty recent. And the "meaning" of zero as a number like others along a number line, rather than as mere notation for "nothing", I assume only ever became necessary with the invention of negative numbers. With addition, multiplication and division, zero simply does nothing or annihilates a number, and so doesn't need to be treated like other numbers. AFAIK, zero as a number arises first in figuring out how to "get to" negative numbers, e.g. what is two minus four (one, zero, negative one, negative two), where zero is required as a numeric concept. Negative numbers were a big step forwards. Zero, I still don't see it -- either it was just convenient notation for "nothing", or part and parcel of the shift to negative numbers. Unless I'm missing something in the historical record?
      - IIAOPSW 6y ago
        You need zero for place based notation. Eg 210 is "two in the hundreds place, one in the tens place, none in the ones place." Place based notation gets you representation of multiples all the way to infinity. Otherwise you need to represent multiples with unique symbols like in Roman Numerals. Eg X means 10 no matter how many symbols are to the right of it.