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How bizarre. I was wondering if you and I had read the same post here; turns out we hadn't. The original answer that I read yesterday has since been removed by the mods for some reason. --- [-] ImOuttaThyme66 points 16 hours ago [Their number system.](http://storyofmathematics.com/roman.html) Mathematician in studying here with a side hobby of history. Sources are included throughout. You may recall from elementary school or personal perusing of Roman history books that they had their own numeral system with letters instead of their own numerals, excerpts of the Latin Alphabet. I is 1, C is 100, and so on. The Romans did decent with their numeral system. They could add, subtract, multiply and divide with their numbers. However, it was missing two very important principles, if that's the right word, that today's Arabic numbers have. The first is the idea of zero in mathematics. They knew the concept of nothing yes but they had no numeral for the number "zero." So essentially, try doing your own math homework without using the number zero in the one's place, the ten's place, and so on. Now, zero itself didn't come with Arabic numbers but they did come from an ancestor. [Origins of Zero](https://www.smithsonianmag.com/history/origin-number-zero-18...) Which led to the second problem with Roman numerals. Their numbers do not work on a positional system. Today's Arabic numbers, 0-9 work on a positional system. That is, we have the one's place, go left one digit, ten's place, left again, hundred's place, and so on. Each digit in a number is the base raised to a certain power. And this is what makes addition, subtraction, multiplication and division so easy to do with Arabic numbers, especially with the concept of zero, a placeholder to place in a certain space when a number has no "tens" or "hundreds" or "ones". Like 109. It has 9 ones, and 1 hundred, but no tens. Without zero, we couldn't be able to write it out like this. A little sidenote here, technically, the Romans did have a positional system. That is, the greater numerals were on the left and the lesser ones were on the right unless they were using two numerals to communicate numbers. So, it's not an explicit positional system like we do today, in which each digit means a certain number, they did order their numbers around based on size. Now, in fairness, the Romans simplified their numeral system a little over the years by adding two principles, subtraction and multiplication. What the Romans did was that whenever they placed a smaller number before a bigger number, those two numbers communicated a new number entirely by subtracting the smaller from the bigger. So for example, 109, CIX, the IX becomes worth 9 because X (10) - I (1) is IX (9). Multiplication, to indicate 1000's, they would put a line over the symbol, and that would be the same as multiplying it by a 1000. Let's do a little Roman math. For Roman numerals, 109 would be written out as CIX. Great, we get the amount communicated. Let's say we want to add 32 to this number in Roman numerals. 32 in Roman is XXXII. CIX + XXXII Immediately, there's a problem. We have to separate the various numbers. So CIX becomes C IX and XXXII becomes XXX II. Now we can add them together by going "Okay, IX plus I makes X, there's an I remaining, X joins the three other Xs so we now get CXXXXI." aka 141 in today's numbers. Let's imagine as if we did that with our numbers. Let's add 109 and 32 again. Only, we're adding 100 and 9 and 30 and 2. We know 9 + 2 makes 10 and 1. We know 10 and 30 makes 40. We have 1 and 100 remaining, there's nothing else to add them together so they stay like that. The resulting number becomes 100 and 40 and 1. Exhausting. So, addition is possible. Subtraction is also possible. You have to go through the entire grouping of bases to do it but it is possible. Multiplication is somewhat possible but very iffy, having to do all those grouping of bases manually. Division. Division was the hell of the Roman numeral system. The Romans did not have decimals. They had fractions but they did it in duodecimal form, that is, 12ths. They did not have a 1/10th. There was no talking about that explicitly, they preferred to do everything in 12ths. Now, this makes sense, 12 has many factors compared to 10. You can divide 12 by 1, 2, 3, 4, 6 and 12 itself whereas you can only divide 10 into 1, 2, 5, and 10. There are plenty of people who believe we should move to a duodecimal system. Then again, the French attempted installing a decimal system for time during the French Revolution. Maybe not all ideas are popular. Either way, Romans did not have very explicit fractions. They had the base fractions 1/12 through 12/12, then they continued on from there by dividing them further. Like 1/144 (1/12 * 1/12) or 1/8 (3/12 * 6/12). More information on Roman fractions can be found [here](http://dmaher.org/Publications/romanarithmetic.pdf). Another side fact of their fractions was that they always named them as fractions of something, such as 1/12 of as, which was a currency. Never 1/12 by itself. So, now that we've gone through the clusterfuck that is Roman numerology, we can pretty much understand why they didn't advance the mathematics field too much. It was functional for their time. The Romans still did many grand engineering feats that were no doubt developed from this number system. However, when it came to further mathematics such as calculus, which would finally be found by Newton and Leibniz independent of each other in the mid 17th century, you can't get any further when you don't have a positional system that makes adding/subtracting a lot easier, no numeral for the number 0, and your dividing tactics do not allow you to do decimals very well, especially when your numerals are 1, 5, and then powers of 10. Decimals could be made possible with these numerals yes but it would be insanely difficult to understand and is made so much easier when you assign every basic integer, like zero through nine for instance, their own numeral. And that's probably why the Romans didn't do very well in mathematical advancement. |