Talk:Roman numerals/Archive 2

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Numerals Caused Slow Development

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
I thought that in the Roman era and the Middle Ages, people used the abacus for calculation and the numerals for writing them down. -- Error 00:34, 5 May 2004 (UTC)

Indeed. The very word "abacus" is a Latin one, though nowadays abaci are chiefly identified with East Asia. --167.206.188.3 07:38, 10 Oct 2004 (UTC)

A note about Unicode roman numeral symbols

Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Ⅷ Ⅸ Ⅹ Ⅺ Ⅻ are all in unicode.

But don't replace the ISO Roman numerals with them. Morwen says they have been deprecated from Day 1 and are there just for compatibility issues. WhisperToMe 17:20, 1 Jul 2004 (UTC)

Clocks?

This article was just cited in an Associated Press story today,with its mention of a supposed Roman ruler ordering a change from "IV" to "IIII",which as I understood it was older(subtractive notation being an innovation even if during classical times).However,the article refers to an "incorrectly" made clock...in Roman times there were sundials,but not clocks!(Could the ruler have been more modern?)--L.E./12.144.5.2/le@put.com

I just corrected (= deleted) this. IIII was very common before the middel ages. It was only in the middel ages that roman numerals where "standarized". When mulitiplication and division became important the rules listed on the page where developed. For a roman it was much more natural to actually write IIII than IV. Generally romans didn't like subtractions. And they even wrote IC for 99. It was a bit more normal to use IX than IV, but VIIII was still heavilly used. Maybe a new section ought to be added about Roman numberals as used in the ancient times. (That is: write so you are understod as the only rule it seems.) Many of these variations have survived because people tend to see them in old books and arcitetctual places. Anyone that understands norwegian might want to incorporate some of the information there about older practices from there.

Roman Arithmetic

For those that might be inclined, I have added an article on Roman arithmetic which instructs the reader how to perform addition, subtraction, multiplication and division operations using Roman numerals without converting them to Arabic numerals.

Once you get the hang of it, it is rather easy, but not as easy at using Arabic. denorris 05:24, 31 Aug 2004 (UTC)


That title is spelled wrong, and there was already a Roman arithmetic article. I guess they should be merged...have fun :) Adam Bishop 05:48, 31 Aug 2004 (UTC)
That is what I get for working late. Corrected denorris 06:03, 31 Aug 2004 (UTC)

Impact of Greek notation system on Romans: positional or non-positional?

The following was removed from the article:

But that can't be true because many Romans were educated in Greek whose astronomers used Greek numerals in such a positional notation system, including a special symbol for zero. The Romans could have simply transcribed the Greek version into Latin characters if they had a need for such a system.

The Greeks did not use a positional notation system.

Ptolemy (circa 85 - circa 165 AD) used ο (ouden) to represent nothing (Number Words and Number Symbols, Karl Menninger, 1969, pp 399) but this is only part of the necessary ingredients for a positional notation system.

In Greek numerals, a count of one is represented by α (mia) and a count of ten is represented by ι (de´ka).

A Greek positional notation system would have a count of ten represented by α (mia) in the tens column followed by ο in the units column (αο instead of just ι).

In a further example, the numerals to represent a count of eleven would have been αα. However, the ancient Greeks would have used ια just as the Romans used XI and not II.

I have shown in Roman arithmetic that it is possible to perform the four basic arithmetic functions (addition, substraction, multiplication and division) using Roman numerals without a positional notation system. No doubt the Greeks used similar approaches.

However, the Greeks did have a character to present each count from 1 to 10 (a decimal system) while the Romans only used 2 characters; one to represent 1 and the other to represent 5 (a bi-quinary coded decimal system). Regardless, they were not decimal positional notion systems. That had to wait for the concept of zero as a number in the 6th century.

--Denise Norris 19:00, Sep 22, 2004 (UTC)

We have a misunderstanding here, no doubt due to my poor wording — I will attempt to reword the paragraph to take your confusion into account. You are correct that basic Greek numerals are not positional. Nevertheless, Ptolemy used a sexagesimal (base 60) positional system copied from Babylonia but using non-positional Greek numerals for each digit (0–59), as the following explanations by experts show.
[The sexagesimal system] was taken over by the Greeks (one may guess by the Hellenistic astronomers) from the Babylonians as a convenient way of expressing fractions and (to a lesser extent) large numbers, and of performing calculations with them. It is the first place-value system in history [Babylonian and Greek]. In the translation and notes I use the convenient modern 'comma and semi-colon' notation [devised by Otto Neugebauer in the 1930s], in which 6,13;10,0,58 represents 6 × 60 + 13 + 10 × 60–1 + 0 × 60–2 + 58 × 60–3. Ptolemy uses the system only for fractions, and represents whole numbers, even when combined with sexagesimal fractions, by the standard Greek (alphabetic) notation. The translation follows the mixed notation (thus the above number would be written 373;10,0,58 in the translation, and τογ ι ο νη in Greek [all except the isolated ο have an overbar]. — G. J. Toomer, Ptolemy's Almagest (1998), pp.6-7.
The sexagesimal place value notation, including a symbol for zero, is of course of Babylonian origin. By its adoption in Greek astronomy it also became the standard method in Indian, Islamic, and western European treatises and tables. The method of writing the single digits is insignificant. The alphabetic notation is used in Greek and Arabic texts, Roman numerals in Latin, Hindu numerals in Sanskrit. The essential point, common to all, is the place value notation and the use of a zero symbol. The modification of this notation to decimally written numbers as well, which took place in India, produced the "Hindu numerals" which we use now and which appear in slowly increasing frequency in the later Middle Ages in Arabic as well as in Byzantine and Latin texts. For the computational methods this is of very little importance since it does not matter in what form the individual digits are written. — Otto Neugebauer, A History of Ancient Mathematical Astronomy (1975), p.1113.
Neugebauer implies that writers did use Roman numerals for the individual digits in a sexagesimal system!
Joe Kress 01:19, Sep 25, 2004 (UTC)
This is an article on Roman numerals, so unless it has a proven impact the Roman numeral system, perhaps this discussion should be moved to Greek numerals.
Also, Ptolemy was a Roman Empire era scholar. Clearly his work did not influence the development of Roman numerals. I would imagine that an article on Roman Era Math would be better suited to discuss the influence of Ptolemy rather than Roman numerals.
My specific objection was the conclusion (badly worded or not) that Roman's had a positional notation system simply because the it is assumed the Greek's had one. Both conclusions are un-supportable. The specialized use of Babylonian sexagesimal counting by Ptolemy in Roman/Greek society is akin to the use of calculus in modern society.
--Denise Norris 07:43, Sep 25, 2004 (UTC)

Flipped C

I don't get how the flipped C works. Can someone explain it better? lysdexia 08:00, 10 Oct 2004 (UTC)

What I was told in Latin class boils down to this: originally, the Romans used the Greek letter Phi (Φ), which was unused in their own alphabet, to denote the number 1,000. To denote half its value (i.e., 500), they halved the letter Phi, resulting in the regular "hardware representation" I+reverse C, which in turn was standardised into D. Reversed-C on its own I've never seen (but that doesn't mean it may not exist). This, by the way, contradicts what the first paragraph says about I+reverse C being an old representation of M, I think someone's got it confused with D. Correct this? — Cwoyte 14:01, Dec 3, 2004 (UTC)

The reverse-C is the "apostrophic C" [U+2183]. The notation (|) for 1000 is likely to be the origin of the M symbol, rather than M-for-mille. Each level of bracketing multiplies the represented value by 10: ((|)) = 10,000; (((|))) = 100,000. Half symbols were used to represent half the value: |) = 500 [hence D]; |)) = 5000, |))) = 50,000. However, there may be no evidence for numbers greater than 100,000 were represented in this way -- the overbar being used instead (later?): single overbar (with small drops, [ on its side) for x 1000; full-three sides for x 100,000. The overbar multiplication was apparently not applied to I,V, L (?).

I have really been looking for fractional notations: The reverse-C appears as '1/4' in some contexts.

It is useful to remember that arithmatic was performed on Abaci, not with the written numbers (as we would with Arabic/Indian numerals). Roman numerals are a direct representation of what is on the Abicus. --Sawatts 11:56, 8 Dec 2004 (UTC)

Barney is Satan?

I highly doubt that this joke could possibly qualify as encyclopedic. Can we remove it and its associated redirect Barney is Satan? -- Antaeus Feldspar 17:50, 10 Nov 2004 (UTC)

I agree. As far as I'm concerned, go ahead and delete it. — Cwoyte 14:01, Dec 3, 2004 (UTC)

Actually, I took the step and edited the Barney bit out. As for the Barney is Satan redirect, I do not know how to remove that. — Cwoyte 22:12, Dec 5, 2004 (UTC)

I've added the Barney is Satan redirect to Wikipedia:Redirects for deletion and {{rfd}} to the redirect (although it doesn't appear due to a bug). — Joe Kress 19:26, Dec 7, 2004 (UTC)

Romans used arabic numbers in lists?

I wonder what the sentence

When describing members of a list, first A, B, C, D tended to be used, then 1, 2, 3 then i, ii, iii, iv.

intends to say.

Romans certainly didn't use 1, 2, or 3. The arabic numbers entered europe long after the fall of the Roman empire. According to Georges Ifrah, Universalgeschichte der Zahlen, the Codex Vigilanus from 976 C.E. is the oldest european work containing arabic numbers.

The sentence seems to require some historical context. Given the fact that this context is not given, I suggest to remove the sentence. --Kune 22:40, 2005 Jan 27 (UTC)

Is MIM ok for 1999?

The article said:

Some rules regarding Roman numerals state that a symbol representing 10x may not precede any symbol larger than 10x+1. For example, one should represent the number "ninety-nine" as XCIX, not IC. However, these rules are not universally applied.

The last sentence is wrong. MIM for 1999 is not kosher, any way you look at it. So I removed the last sentence. Egil 07:31, 3 Feb 2005 (UTC)

That last sentence reflects that fact that - "kosher" or not - some people do it anyway. Since the role of Wikipedia is not to proclaim what's right, but to describe what's done, I've restored a slightly modified version of that statement. Tverbeek 15:20, 3 Feb 2005 (UTC)

I beg to disagree. There is no reason to report usage that is patent nonsense, unless in very particular cases. The statement However, these rules are not universally followed is just as bad as the previous one. As far as I know, the only usage of 'MIM' and 'IMM' is by people who haven't even bothered finding out what roman numbers really are. The 'pedia should report correct information. Your sentence gives the impression there is doubt about what the correct usage is. This is misleading. And if you feel the need to state that "People do not always bother following rules", it should be done in the context of human behaviour in general. -- Egil 17:23, 3 Feb 2005 (UTC)

One point of that section is that the question of "correct" usage isn't as simple as you state. Not only has usage varied somewhat with time and place, the Romans themselves exhibited some inconsistency in their usage, and a degree of personal preference seems to have been involved. Certainly we can and should spell out the usage that's most prevalent, but since no one can find the original RFC or ISO standard for them, the position that there is an indisputable standard for "correct" usage - and that you have it - seems hard to justify. Tverbeek 20:52, 3 Feb 2005 (UTC)

The usage XIIX for 18 is attested in actual usage in medieval times, and I think IC for 99 is also. People who actually wrote and read these numerals could communicate unambiguously with a slightly more flexible version of "The Rules", so who are we to be throwing around epithets such as "patent nonsense"? My guess is that "The Rules" were written by printers round about the time that they standardized spelling. Tverbeek is right. Cbdorsett 07:09, 6 Feb 2005 (UTC)

I came across a photo of an ancient inscription with the numeral XIIX (the tomb of Secundinus on the Via Appia). Does anyone know of an ancient example of the use of IC, IM or XM? --Zundark 14:03, 6 Feb 2005 (UTC)

"There was no need for a zero" ...?

The are lengthy learned discussions on this talk page about zero; I haven't read it all, so this may be silly: I think the comment "There was no need for a zero." on the entry "Zero" in the long table of numerals should go; it seems to arise from a confusion of the digit zero and the number zero: The was no need for a digit zero, as e.g. CI clearly means 101, not 11, 110, 1001, or whatever. But the entries in this table are not digits; they are numbers (e.g. 1999). A Roman farmer owning zero cows had as much (or as little) need for the number zero as a modern farmer. -- But perhaps the table should be a table of digits, or rather should be split into two tables?--Niels Ø 10:40, Apr 22, 2005 (UTC)

Jove?

The clause

Originally, it was common to use IIII to represent "four", because IV represented the god Jove (and later YHWH).

needs context or explanation. I assume this is a taking-the-name-of-the-lord-in-vain kind of thing, but it's too vague as is. Besides, the whole reason we use Rx for recipe instead of just R] is because Rx resembled the symbol for Jove. So why write Rx but avoid IV? kwami 05:07, 2005 May 17 (UTC)

5000 - Isn't it an overlined V?

According to a book I have the value for the 5,000 roman numeral is \frac{}{V}?

RyanJ

The overlined V (V) for 5000 is shown under Alternate forms, but it was a relatively recent development during the Middle Ages. The other forms shown were those actually used by the Romans, which were still popular throughout the Middle Ages and Renaissance. — Joe Kress 16:54, 23 July 2005 (UTC)