4 ms·

Why would it be significantly harder than using some other system of numerals?

shultays 6y ago
They probably had algorithms for it, but even then it sounds challenging. Addition sounds easy and works mostly like how we do base 10 addition. I imagine they would first go for sub 5 part which is a bit exceptional and had to be manually. And then start grouping letters together like we do and create carries if they reach the next letter. Subtraction sounds harder. It sounds close enough to our base 10 system but borrowing from next digit is much more complicated. Like subtracting D-I (500-1). The answer is CDXCIX but I am not sure how I can go there. And now imagine this with more complex numbers But multiplication and division? in that weird base format? I won't even try Keep in the mind that they don't convert or even think numbers in base 10 system like we do.
- Grustaf 6y ago
  How numbers are written down does not necessarily correspond to how you do calculations. Given that 499 was called 499 I’m pretty sure they thought in base 10, so subtracting 1 from 500 would be trivial. Writing it down took a few more symbols but so what?
  - shultays 6y ago
    Hmm, I was assuming they didn't have a concept of base 10. If they do have it I wonder how they couldn't make the connection and write stuff in base 10 as well instead of a mixed base with weird rules Then I guess the real challenge is converting numbers around?
Sharlin 6y ago
Did you read the friendly article?
kccqzy 6y ago
When I was learning programming, one of the beginner's exercises was to implement addition, subtraction, and multiplication of natural numbers "by hand" (division wasn't covered). There you learn to formalize the grade school algorithms you know by heart into concrete code, a necessary mental process for beginning programmers. At the end of the session, the teacher asked us to try the same with Roman numerals. That was when I knew it's significantly harder.
Koshkin 6y ago
Well, you can try and then you'll appreciate the difference, I am sure. Even if implemented in computer hardware, operating with Roman numerals would either be slow or take many more transistors (or both). As to why in a philosophical sense, it is because the positional system was invented specifically as a computational device, which only happened many years after people learned how write numbers down. Optimization effort takes time, and a random solution is not guaranteed to be optimally suited for a particular application (such as performing calculations).
- 082349872349872 6y ago
  We all do the same thing. Our calculators work in binary, and we only do i/o in decimal. Their calculators (slaves who pushed pebbles, calculi, around) worked in a decimal place-value system (or used egyptian/russian peasant multiplication), and only the i/o was done in roman numerals.
  - Koshkin 6y ago
    Sure, but the essence of the discovery, which is in fact far from trivial, is that it was found possible to perform calculations by manipulating written symbols themselves (i.e words) rather than using pebbles or an abacus. (This is by the way how mathematical notation began - as the means of reasoning by performing formal manipulations with marks on paper.)

They probably had algorithms for it, but even then it sounds challenging. Addition sounds easy and works mostly like how we do base 10 addition. I imagine they would first go for sub 5 part which is a bit exceptional and had to be manually. And then start grouping letters together like we do and create carries if they reach the next letter. Subtraction sounds harder. It sounds close enough to our base 10 system but borrowing from next digit is much more complicated. Like subtracting D-I (500-1). The answer is CDXCIX but I am not sure how I can go there. And now imagine this with more complex numbers But multiplication and division? in that weird base format? I won't even try Keep in the mind that they don't convert or even think numbers in base 10 system like we do.

Grustaf 6y ago
How numbers are written down does not necessarily correspond to how you do calculations. Given that 499 was called 499 I’m pretty sure they thought in base 10, so subtracting 1 from 500 would be trivial. Writing it down took a few more symbols but so what?
- shultays 6y ago
  Hmm, I was assuming they didn't have a concept of base 10. If they do have it I wonder how they couldn't make the connection and write stuff in base 10 as well instead of a mixed base with weird rules Then I guess the real challenge is converting numbers around?

Sharlin 6y ago

Did you read the friendly article?

kccqzy 6y ago

When I was learning programming, one of the beginner's exercises was to implement addition, subtraction, and multiplication of natural numbers "by hand" (division wasn't covered). There you learn to formalize the grade school algorithms you know by heart into concrete code, a necessary mental process for beginning programmers. At the end of the session, the teacher asked us to try the same with Roman numerals. That was when I knew it's significantly harder.

Koshkin 6y ago

Well, you can try and then you'll appreciate the difference, I am sure. Even if implemented in computer hardware, operating with Roman numerals would either be slow or take many more transistors (or both). As to why in a philosophical sense, it is because the positional system was invented specifically as a computational device, which only happened many years after people learned how write numbers down. Optimization effort takes time, and a random solution is not guaranteed to be optimally suited for a particular application (such as performing calculations).

082349872349872 6y ago
We all do the same thing. Our calculators work in binary, and we only do i/o in decimal. Their calculators (slaves who pushed pebbles, calculi, around) worked in a decimal place-value system (or used egyptian/russian peasant multiplication), and only the i/o was done in roman numerals.
- Koshkin 6y ago
  Sure, but the essence of the discovery, which is in fact far from trivial, is that it was found possible to perform calculations by manipulating written symbols themselves (i.e words) rather than using pebbles or an abacus. (This is by the way how mathematical notation began - as the means of reasoning by performing formal manipulations with marks on paper.)