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Roman Numerals edit
I've read somewhere that Roman numerals were partly responsible for slowing the development of science and math. This was purely because they are harder to deal with, and it takes even a trained user longer to add, subtract, multiply and divide numbers written in Roman numerals that it does someone using Arabic numerals. This greater barrier to entry, as it were, resulted in less research.
Is this true? -- ansible
Maybe yes, maybe not: they certainly could not interact with "our" computing system because of lenght (in chars) of single numbers, which is variable too. For instance: number 77 is expressed in arabic with two chars only, while LXXVII needs six. But the worse is that number 78 needs seven chars (LXXVIII).
But this does not mean that there are operations that you cannot perform with them too. If you try to calculate a square root of some number, you will get the same result with both systems. Maybe obviously this would require a different use of the space.
On the other side, every calculation in roman numbers requires a logical scheme that is different from arabic system. I could not say which is the best: if you are latin-minded (and you are consequently used to decline words, verbs and other object of same frequency making use of a sort of "on-the-fly" developping), you will find it as natural as today we find arabic ones, the longer time only depending on writing.
I think that it is only that arabic system was used by phoenician merchants in the whole Mediterranean area well before that Rome had an influence over a similarly extended territory. A fact is that Rome created the widest empire of ancient world using its numbers, and another fact is that we use arabic system; opinions might evaluate whether it is better for us, but keep in mind that we were born "within" this mentality.
I do think however, that it would be quite complicated to eventually revert our system now :-)
In Latin class I had learned the exact opposite of what Ansible suggested. From what I understand, the Roman numeral system is supposedly really easy to count on your hands with. Essentially, the Roman numerals were quicker to add and subtract with, whilst Arabic numerals are easier to mulitiply with. Just some thoughts... --BlackGriffen
- I can kind of see how Roman numerals would be easier to learn how to count. But there's a lot more science needs than simple counting. It's multiplying and division that seem to be overly difficult in Roman numerals. I remember in 3rd grade, learning how to divide using Arabic numbers was hard enough. What are even the rules for doing manual division with Roman numerals? Does anyone even know anymore? -- ansible
- As far as I remember, there is no different operational method with roman numbers, since it should be only a matter of graphical rendering, or I didn't meet this point in my studies. The concept of division should be the same in both methods. Roman system has a different approach to rendering, requiring not to consider a linear sequencial scale (as in arabic ones) but a more complex thought about "notable" numeric entities: 99 is in arabic only the number after 98, in roman it is the one before one hundred (closer relevant entity), and is "IC" (really, I am not aware it is wrong, being more purely latin minded, and I have many books with that form too - just checked). A rendering like LXXXXVIIII would be the first result in our current mentality, but a second thought is required to better describe it in latin concepts (so LXXXXVIIII is a wrong form, correct being only IC - or the other one proposed in article).
- With arabic numbers you have to learn by heart some concepts like fixed relationships: series of adding or multiplying factors (like 2,4,6.8.... or 3,6,9,12,.... or 4.8.12.16,.... and so on) will be recalled from your memory when you compute the separate parts of a multiplying operation. In roman maths, you will constantly evaluate concrete "weight" of numbers, so you will get your result with less use of memory and deeper instant analysis.
- With romans you need to realise "where" in the proportion of values your number is located: is 98 closer to 50 or 100? Am I talking about something that is of (this) kind of proportion or of (this other kind)? Idea is: main identifiable concept = one hundred, my number differs from that of II less (so it's on the left = IIC), while let's say 105 is more than one hundred by 5 (so it's on the right = CV).
- Obviously this is easier to perform with sums, and it is true that main progresses in main scientific disciplines were achieved by arabs (just think of astronomy). I wouldn't however agree it simply slowened progress: Roman system might have been better structured to complete a mentality which put humanist sciences before technical sciences, but today's progressed world belongs more to latin civilisation than to arabian one.
I do not believe that the difference between operating with Roman or Arabic numerals is just a question of getting used to one or the other, as some of the above posters seem to imply. A positional number system like the Arabic one(with a symbol for the zero, which the Romans didn't have, and which marks a significant difference) is much more handy for performing all kinds of operations thana system like the Roman. In fact, the Romans did not do any long divisions or stuff like that with their symbols, but they used an abacus for calculations, and an abacus is basically a positioning system.
By the way, the Arabic numbers should really be called Indian numbers, that's where they originally came from, although they were introduced into Europe by the Arabs.
In reply to the last post, I think the progress in the Western world owes much more to the Arabic digits than to the Roman humanistic legacy....
I would like to quote Georges Ifrah from "The Universal History of Numbers":
Anyone who reflects on the universal history of written number-systems cannot be but struck by the ingeniousness of this system, since the concept of zero, and the positional value attached to each figure in the representation of a number, give it a huge advantage over all other systems thought up by people through the ages. -Calypso
- Oh - so the West was able to 'progress' using Arabic zero while the Arabs were not? Just a query from a specialist in the western humanities. Let's not start this silliness. Culture is considerably more complex than ease of computation. --MichaelTinkler
I certainly agree that culture and 'progress' are complex topics. It seems to me, though, that the tools (physical and mental) that are available to people drastically change their outlook on the world. Mathmatics is the basis of science and technology, and arithmetic is the starting point of it all. It seems to me that entire new opportunities became available to us, when we switched numbering systems. However, I'd like to have some references before I write up an encyclopedia article about it. Are there any good studies of history where fundamental practices changed because of better math? Like some example from military history, where someone, because they were able to figure out their logistics better, were able to win some battle. --ansible
- Sure it's important, but given that everyone from India to Iceland had the use of the numeral system by some date, we're in Sapir-Whorf fallacy zone to use it as much of an explanation. And what about the Central American zero? There are scholars who insist that the invention of double-entry accounting (Venice, late middle ages) is really what does it for the West. My only goal here is to suppress sweeping, universalistic statements about the zero changing the world. It did so, but very, very, very slowly. --MichaelTinkler
Of course culture is terribly complex, and I certainly did not want to reduce the success of Western culture (or, let's say, the current dominant position of Western culture in economic terms) to the adoption of a certain numerical system. In any case, the main point of my previous post is that the Arabic numerals are intrinsecally better for doing mathematics than the Roman numerals are. --Calypso
- Take a look here above: most of the words you use have latin or greek roots. Maybe this is stats, still it's not economy. I agree that the explanation of this concept might be better shown in arabic numbers, but I still prefer a latin "idea", than a fair perfect result.
- Greetings