Talk:Roman numerals/Archive 6

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Definitely Not Decimal? Not.

A revision comment states that the Roman Numeral system is definitely not decimal. Simple inspection would seem to say that the system is decimal (based on powers of 10). The basic symbols all represent either powers of ten, or five times a power of ten. A Roman Numeral can be visualized as its decimal digits, and omitted zero placeholders (which are unnecessary because the magnitude is explicitly indicated by the choice of symbols). It's not like the symbols represent dozens and gross, or other truly non-decimal quantities. True one might be able to construct restrictive definitions of "decimal system" which would exclude Roman Numerals, but that wouldn't seem to qualify as "definitely". Given the obviously decimal nature of the system, I don't see why one would need an explicit source for using the word, especially in one of the deletions.--SportWagon (talk) 18:12, 25 February 2009 (UTC)

Attempting to find web citations found this unfortunate garbage where, in the middle of the page, they seem to encourage very young readers to do things like VL. [1]--SportWagon (talk) 18:36, 25 February 2009 (UTC)

Here's someone who agrees with the "decimal" concept.[2]--SportWagon (talk) 18:36, 25 February 2009 (UTC)

web search does indicate most people contrast "Roman Numerals" to "decimal", however. That is, when they say "decimal" they mean more than what we mean by "decimal".--SportWagon (talk) 18:36, 25 February 2009 (UTC)

Another programmer who agrees with much of what we say. [3].--SportWagon (talk) 18:53, 25 February 2009 (UTC)

A "Math Forum" (not forum in that sense...)[4]. Contains further references.--SportWagon (talk) 18:57, 25 February 2009 (UTC)

I was the one deleting the "decimal" remark: thanks for your comments. I must admit that I have not yet checked the links you give, but if Wikipedia has to be consistent as a whole, this article must agree with Decimal (and with Decimal representation). In those articles, and for what I know in the current use of the word (when talking about numeration systems), a decimal numeration system is before anything else a positional system, that is, one in which each digits gets a meaning depending on where it is in the representation of a number. So in "13" the digit "3" denotes three units, while in "31" it denotes three "tens", and so on. So merely the fact that some of the symbols used in Roman numerals denote powers of ten is not sufficient to qualify it as "decimal". Thanks, Goochelaar (talk) 18:59, 25 February 2009 (UTC)

I'll leave it to kwami to choose some appropriate compromises. It seems like the word we want might have disappeared from the English language as "decimal" has taken on extra implications. Ignoring pedantic interpretations of "decimal", the now omitted paragraph following the table should simplify readers' thinking. (And true, one can just as easily say our attempted use of "decimal" is the pedantic one...)--SportWagon (talk) 19:12, 25 February 2009 (UTC)

Egyptian numerals and Chinese numerals are examples of decimal systems which are certainly not positional because they use different symbols for every power of ten. — Joe Kress (talk) 19:41, 25 February 2009 (UTC)

Declaring that decimal must imply positional seems pedantic because it insists one cannot understand a broader definition of a term in different contexts. However, the way you used "decimal" can also be considered pedantic because it would appear that "the decimal system" and "decimal numbers", even just "decimal" are commonly understood to imply the currently widespread positional system. That is it requires the reader to not make common assumptions. I will keep out of the editing for now.--SportWagon (talk) 20:58, 25 February 2009 (UTC)

"Decimal" means base 10, just as "binary" means base 2. That's all it means. We speak of languages as having decimal, vigessimal, etc. systems, but spoken languages are neither positional nor do they have a zero. Other than the auxiliary base 5 (presumably due to the limits of visual processing of iterated symbols), Roman numerals are analogous to the decimal numbering system of the Latin language. If our decimal article is wrong, then it needs to be corrected. The intro to this article clearly states that Roman numerals are decimal but not positional. Though a check with a dictionary is all that should be needed, I added a ref from Ifrah. As far as compromising with people who do not understand the concepts involved, that would be like stating that whales are fish as a compromise with people don't know the difference. kwami (talk) 21:15, 25 February 2009 (UTC)

Kwamigami, thanks for your good work on this article, but I must disagree. First of all, the reference you give uses the words "a decimal system in which the number 5 is an auxiliary base" not about Roman numerals, but about a previous, archaic, conjectural numbering system an hypothetical herdsman might have developed in order to tally his animals; in fact, it follows "(and the numbers 2 and 5 are alternating bases)". Second, we might as well say that it is a "quinary", or base 5, system. Third, even if we find and agree on a source that describes Roman numerals as decimal under a broader definition of "decimal", we should immediately modify Decimal and Decimal representation (we have to be able to link the word "decimal" in this article to one of those articles).

You are right about languages, but we are not covering Latin language here; only this numeration system as used then and now in several countries with several different languages (in fact, nowhere is told anything about the Latin names for composite numbers, that is, different from 1, 5, 10 etc.).

As this is an encyclopedia, we are forced to be careful about the meaning we attribute to the words we use (even when this looks like pedantry). Goochelaar (talk) 23:45, 25 February 2009 (UTC)

It is nothing close to being a base 5 system. 25, 125, 625 etc. do not fall out as being simple representations the way C and M, and larger powers of ten do. The use of base 5 is merely a means of shortening what are conceptually decimal digits.--SportWagon (talk) 23:55, 25 February 2009 (UTC)

You are onto something here. The use of a representation of 5 is merely a means of shorting what is essentially a unary system. And the use of a representation for 10 is merely a means of shortening what is essentially a unary system. At no point is it decimal or quinary. The fact that symbols exist for V and X actually specifically exclude it from that - V and X are both 10 in decimal and quinary. It's the point at which the system rolls over and starts using other representations. V, X, L, C, etc... are merely convenient representations for large number of I's. By tradition, of course, you put these in order, and you use the representation that takes the smallest amount of space (so no VV or IIIII). But that doesn't make it decimal. Having a representation for 0, 1, 2...9 and then rolling over to 10 at the end makes a system decimal. If I rolled over to my own representation of 10, such as X, or A, I would not have a decimal system. Math in Roman numerals looks nothing like decimal math. It looks like unary math. Because Roman Numerals are unary.98.95.203.214 (talk) 03:35, 29 September 2011 (UTC)

Yes, Ifrah was speculating on the origins of the system, but what he ended up with was a decimal system "exactly the same as in the Roman system". As for language, my point was that if decimal means base 10 when describing numeral systems in language, it means base 10 when describing numeral systems in writing. I've seen no reason to believe that the word "decimal" changes definition depending on which medium we're discussing. SportWagon is right. There is no *VVV for 15, or *LLLL for 200, which is what Ifrah meant by 5 being "auxiliary". Roman numerals are base 10, therefore decimal. kwami (talk) 00:24, 26 February 2009 (UTC)

Roman numerals aren't decimal. They're unary with extra symbols thrown in so that you don't have to write out ridiculous number of I's, which are themselves stacked on each other in a unary fashion. The fact that these special symbols, which, in actuality, are simply representations for a large amount of unary I's, are usually based on powers of 10 doesn't make the system decimal. If it were base-10, it wouldn't have a representation for 10. No base-10 system has its own representation for 10. 10 is the place where the system rolls over and starts re-using other representations. So, in fact, having its own representation for 10 is one thing that would actually definitively exclude it from being base-10. And having its own representation for five doesn't make five an "auxillary base". Base 5 doesn't have a 5. 5 is 10 in base-5. Roman numerals are, again, base-1. — Preceding unsigned comment added by 98.95.203.214 (talk) 03:22, 29 September 2011 (UTC)

There are two main definitions. The historically primary definition deals with fractions, as decim means a tenth, but since at least 1684 the phrase "decimal fraction" has been used to disambiguate. Roman numerals are not decimal in this sense, since the fractions were duodecimal. But no-one uses Roman fractions anymore; for nearly everyone, we're talking about the non-fractional part. The second definition, per the OED, is "decimal numeration, the numerical system generally prevalent in all ages, of which 10 forms the basis; i.e. in which the units have distinct names up to 10, and the higher numbers are expressed by multiples or powers of 10 with the units added as required." There is ambiguity with decimal referring to decimal point & decimal places, etc., but the intro is clear enough for the reader to follow.

To be precise, Ifrah says that "the successive order of magnitude [used by the hypothetical herdsman] are exactly the same as in Roman system", not the system itself about which he only says that "the graphical forms for the figures ... are closely comparable with those in the archaic Roman and Etruscan systems". More importantly, the paragraph

The number system of the Latin language was decimal. That is, one said "one thousand and two hundreds and thirty [and] four". When writing a Roman number, the thousands, hundreds, tens, and units in the chart above are strung together the way they are spoken: M (one thousand) + CC (two hundreds) + XXX (thirty) + IV (four), for MCCXXXIV. Thus eleven is XI, 32 is XXXII, and 45 is XLV. Note that the subtractive principle is not extended beyond the chart, and *VL is not used for 45, as it does not correspond to the spoken language.

cannot stay as it is. Of course, in Latin one did not say "one thousand etc."; if anything "mille etc." Moreover, we cannot bring Latin language into this, because it would immediately contradict what is being said: "eighteen" is in Latin "duodeviginti", that is, "two-from-twenty", which would suggest such an expression as *IIXX, and similarly for 19, 28, 29 and so on. In order to find a solution acceptable to everybody, I suggest rewriting the former along the lines of

A practical way to write a Roman number is to consider it as if it were written in the modern decimal number system, and string together separately the thousands, hundreds, tens, and units as given in the chart above. So, for instance, 1234 may be thought of as "one thousand and two hundreds and thirty [and] four", obtaining M (one thousand) + CC (two hundreds) + XXX (thirty) + IV (four), for MCCXXXIV. Thus eleven is XI, 32 is XXXII, and 45 is XLV. Note that the subtractive principle is not extended beyond the chart, and *VL is not used for 45.

Would this be acceptable? (The problem would still remain to make this article and those on decimal notation not contradict each other.) Goochelaar (talk) 01:11, 26 February 2009 (UTC)

Yeah, that's better. I'd forgotten about duodeviginti. I'll go ahead and change it. kwami (talk) 02:17, 26 February 2009 (UTC)

The new paragraph is about what I thought could be asserted. The advice also helps for reading Roman Numerals. Why not say "numeral" rather than "number"? When you begin to move towards insisting that decimal comes from "tenth" rather than "ten", you also start to call some explanations of the term "decimal system" into question. Strange, web searches for "decemal" find first references to "decemal point". Oh well. Would some remaining uses of the term "decimal" in this page be better changed to references to "powers of 10", or possibly "base 10"?--SportWagon (talk) 03:21, 26 February 2009 (UTC)

We could probably come up with different wording, but I don't see the point. Decimālis means 'pertaining to decima, which means 'tenth' or 'tithe'. The earliest usage I can find is for writing fractions x.xxx rather than xx/xxx. However, that is only one use out of several, and when people speak of decimal numeration, it has nothing to do with fractions, just as it has nothing to do with tithing. —kwami (talk) 04:11, 26 February 2009 (UTC)

It seems that it would be more accurate to consider Roman Numerals a unary system with extra symbols thrown in so that you don't have to write out a ridiculous amount of I's to represent larger numbers. But these extra symbols are simply stacked on each other in a base-1 fashion. Decimal implies that it's base-10, which it's clearly not. Having a convenient symbol for 10 doesn't make something base-10. In fact, base 10 actually obviously doesn't even give 10 it's own symbol. That's one thing that sets it apart from more primitive systems.98.95.203.214 (talk) 03:09, 29 September 2011 (UTC)

Frequency of use of "additive" forms

1. Change "* Roman inscriptions, especially in official contexts, sometimes use "additive" forms such as IIII and VIIII for "4" and "9" instead of (or even as well as) subtractive forms such as IV and IX. Both methods appear in documents from the Roman era, even within the same document." to
"* Roman inscriptions, especially in official contexts, seem to show a preference for additive forms such as IIII and VIIII instead of (or even as well as) subtractive forms such as IV and IX. Both methods appear in documents from the Roman era, even within the same document."
When the text was separated into bullet points[5] "seem to show a preference" was changed to "sometimes use", contrary to the source.
2. The switch to bullet points has left the first two statements apparently unsourced. We need to provide the same ref for all three, e.g. <ref name="OCD">{{cite encyclopedia|first1=Joyce Maire |last1=Reynolds |first2= Anthony J. S. |last2=Spawforth|title=numbers, Roman|encyclopedia=[[Oxford Classical Dictionary]]|edition=3rd | editor1-first= Simon |editor1-last=Hornblower |editor2-first= Anthony |editor2-last=Spawforth |publisher=Oxford University Press|date=1996|ISBN = 0-19-866172-X}}</ref><nowiki> for the first ("*Roman inscriptions") and <nowiki><ref name="OCD" /> for the next two (*Double... and *Sometimes...).

Just an opinion BUT: While "seems to show a preference" follows our (very prestigious) source word for word, we are not constrained to use the precise wording of our sources - in fact to do so too slavishly, too often would be risking the breach of copyright. In any case we very often (and quite rightly) use alternative wording conveying the same or even very similar meaning. "Sometimes use" is certainly not in any sense contrary to our source's "seems to show a preference", in fact if the latter is true, then our current text is fully verified (although the reverse is not the case, there is no reason why it has to be, we are not verifying Hornblower and Spawforth, but this article)! It is arguable, in fact, that we should be concerned more with what definitely IS, rather than what SEEMS (given that only a tiny proportion of Roman inscriptions can possibly have survived) and that our version is (pace the Oxford University Press) more genuinely encyclopedic and free from speculation. Not being arrogant here - the OUP has of course more authority than us, and is freer to speculate than we are!

As for the desire to separately cite three very closely linked bullet points to the same source - this appears to me, in this context, to be gross over citation. --Soundofmusicals (talk) 23:42, 18 June 2017 (UTC)

In fact the wording of this section was, on checking it - FAR too close to the original source - I have re-written this. No longer quite so positive about the need for multiple references for those bullet points - although we'd do this with "ref name" rather than repeating the whole screed three (III) times? --Soundofmusicals (talk) 03:53, 19 June 2017 (UTC)

"Sometimes" is too weak, suggesting "occasionally", "rarely" or "in a few instances", contrary to the source. "Commonly" would match "seems to show a preference" better. Many inscriptions have survived; altogether "this must run into the hundreds of thousands",[6] of which 3550 in Britain alone have been collated. 79.73.240.200 (talk) 15:03, 19 June 2017 (UTC)

If "sometimes" seems "too weak" then "commonly" may well be too "strong" - at least too definite. What about "not infrequently"? See how it now reads anyway. --Soundofmusicals (talk) 19:03, 26 September 2017 (UTC)

Modern "Continental" use revisited!

Looked into this in considerable detail several years ago now - can't say we reached a "consensus" as no one else joined the debate but... various "modern uses" of RNs are extremely rare in English speaking countries, but relative (very relatively!) more common in other countries. This use seems to be very patchy, almost local rather than national, far from standardised, and in fact pretty much totally unformulated. At one stage we even had a "little list" of sample countries/cities etc. where particular "odd" RN usages occurred. Sure, our notes here look vague - but then any accurate description of the situation is bound to be vague. It's a vague situation, for heaven's sake! Photographs rather than "text" quotes are not just the best reference we can have here - but pretty much the only references we are likely to find (and I've looked, believe me!). Deleting the whole section because it describes a vague (even shifting!) situation would seem to be a shame - leaving it with disfiguring and misleading tags that are highly unlikely to ever be resolved an even bigger shame. NOT what constructive cn tagging is for at all - it's plainly never going to "improve the article". Now if you have an idea for a better (probably even vaguer?) wording then by all means let us have it! ---Soundofmusicals (talk) 12:18, 26 September 2017 (UTC)

You could say that RN are sometimes used in Europe in a certain way and say something like "an example from an Italian road sign is depicted at right", but the wording "some countries" implies that there is a particular list of countries. If there were such a list, it would have to be provided.--Khajidha (talk) 13:41, 26 September 2017 (UTC)

Maybe something like this: "In continental Europe, the usage of Roman numerals is somewhat more common than in Anglophone countries. There are several contexts in which they may be used, but such usages are not standardized. Each usage described in the following text is supported by an example (with location), but the same usage may also occur elsewhere."--Khajidha (talk) 14:22, 26 September 2017 (UTC)

With respect - this seems a bit like "waffle". But the phrases that attracted the original CN tags were basically just elegant variation - what about just leaving out "In several European countries" and leaving this to be implied by the context? At least, have a look at how it reads now. Is this just as clear, without raising expectations of a list? --Soundofmusicals (talk) 18:53, 26 September 2017 (UTC)

IC=99 revisited

We start the explanatory part of this article with a straight description of the "correct" modern way of writing a standard, easily recognisable and unambiguous Roman numeral for any number. Better, really, to leave any mention of one of the many "non-standard" forms (not a few of which have been actually used historically!) to the "Alternative forms" section that follows. If we tried to list every "wrong" form that might seem to have a logical basis then we'd end up with a very long and extremely confusing article, that would not only be far less useful but liable to infinite extension as one editor after another "discovered" a new form. All this in explanation of my reverting a good faith edit illustrating a "correct" form by contrasting it with "incorrect" ones. --Soundofmusicals (talk) 02:05, 28 September 2017 (UTC)

Reading back though earlier comments I cam across this earlier explanation for the same idea - which may be even more persuasive?

"Rules" should be kept as simple as possible - no need to detail, for instance, usages that break them, such as IC instead of XCIX. Otherwise we could easily be asked to list every "wrong" Roman number ever propounded, which would run to an article many times the length of this one! Our own age, being inherently more "scientific" and much given to efforts to standardise and avoid ambiguity - actually uses Roman numerals in an unprecedentedly "consistent" way, many of our "rules" used to be broken fairly often (see the following section!!) In any case, the purpose of setting firm rules is really just to give the "new player" a guide that will enable him/her to translate a "standard" Roman numeral into a (so-called) "arabic" number and vice versa - not to list every possible pitfall for the unwary. -Soundofmusicals (talk) 01:05, 22 February 2014 (UTC)

Referencing system in this article needs to be made at least internally consistent!

While I was working on the Vinculum section I wanted to add a reference - tried to do this so it was consistent with the references already in the article and noticed that these have been added at hazzard in an least two different formats. This needs to be rectified by bringing them all into the same system - and a proper bibliography included. May do it myself (if I "get a round tuit") - failing my finding that precious object some other editor may like to make it his/her project? In my view, it matters little which of the several referencing systems we use, provided one is chosen and used consistenly. --Soundofmusicals (talk) 05:53, 30 September 2017 (UTC)

Question(?) about variant subtractives.

We have fought hard and long to maintain a simple and unambiguous set of "rules", enabling someone new to Roman numerals to construct a universally intelligible RN equivalent to any "Arabic" number, or to read the numeric value of any "standard" RN built by someone else. This, or something very like it, just HAS to be the basis for an encyclopedia article on this subject. All else dismay, and confusion, not to mention wailing and gnashing of teeth.

It is, unfortunately, necessary to go on to list common exceptions and errors - to make sense of inscriptions and other uses that break one or other of the "rules", and to point out that historically our modern "rules" were (and are?) rather frequently broken.

It is important to keep the two sections totally separate - adding exceptions to the basic "rule list" is can only cause confusion. So that while we may well argue that we don't need to even mention "IC" as a possible way of writing "99"" - if we are going to mention it we need to have it under our exceptions headings. --Soundofmusicals (talk) 02:40, 14 October 2017 (UTC)

The above basically duplicates remarks I have already made above - PLEASE come to talk first... --Soundofmusicals (talk) 02:43, 14 October 2017 (UTC)

I have not examined the article recently but I agree that the 12:31, 13 October 2017 edit is not desirable because it disturbs what should be simple examples in the first section. If sourced, the information might be suitable in some later section devoted to details. Per WP:NOTHOWTO the article is not intended as a definitive guide for writing Roman numerals, ancient or modern. Johnuniq (talk) 02:55, 14 October 2017 (UTC)

How about this (in place of the current "rule")?

I placed before V or X (and only these numerals) indicates one less, so four is IV (one less than five) and nine is IX (one less than ten)
X placed before L or C (and only these numerals) indicates ten less, so forty is XL (ten less than fifty) and ninety is XC (ten less than a hundred)
C placed before D or M (and only these numerals) indicates a hundred less, so four hundred is CD (a hundred less than five hundred) and nine hundred is CM (a hundred less than a thousand)

Personally I think it adds only confusion - but it does cover the "obvious question". --Soundofmusicals (talk) 03:02, 14 October 2017 (UTC)

My version was neater, but something needs to be said about this. --Khajidha (talk) 10:08, 14 October 2017 (UTC)

Whoops! Just noticed I had made a mistake. It should have said that subtraction cannot be used if one number is more than 10 times larger than the other, not 100. --Khajidha (talk)

The point is that the "rule" needs to be stated as such - exceptions have their very own section (under "Alternative forms"). Don't mean to be a testy old man - but could you please explain what part of this you think is wrong? --Soundofmusicals (talk) 19:01, 15 October 2017 (UTC)

1) The subtractive notation is not an exception, it is part and parcel of the standard method of writing Roman numerals. 2) Without somehow noting that subtraction is only used with numerals that are within a certain range of value from each other you are leaving things undefined. The point of the "Roman numeric system" section is to show people how to write any number in Roman numerals, without this note you have not taught them how to write numbers such as "99". Based on the previous text they have no reason to choose between "XCIX" and "IC". --Khajidha (talk) 18:20, 16 October 2017 (UTC)

PS - You previously wrote ""Rules" should be kept as simple as possible - no need to detail, for instance, usages that break them, such as IC instead of XCIX. ", my edit isn't explaining IC it is explaining XCIX. I'm not trying to explain usages that break the rules, I am explaining what the rules are so that you will know that XCIX is the one that follows the rules.--Khajidha (talk) 18:23, 16 October 2017 (UTC)

"IC" is an "exceptional" (many would simply say an "incorrect") use of subtractive notation - so it is mentioned under "Alternate forms" as an example of what we DON'T (usually) do, rather than a description of what we DO do (write the "ninety" and the "nine" separately - i.e. XCIX). Only the "correct" (or standard) form is mentioned in the initial description, as explained umpteen times above. The existing text of our description (provided it is taken literally, and why wouldn't it be?) gives nobody any rational reason to suspect that "XCIX" might also be written "IC". "I" can only precede "V" or "X", and "X" can only precede "L" or "C". That's the rule, and that's what the text says. AT the top of this section I suggested a more emphatic way to say this, but as you say it is a bit prolix and I don't think the emphasis is really necessary. If we want to list exceptions, then logically we can't do that until we've established what they're exceptions to. --Soundofmusicals (talk) 02:20, 17 October 2017 (UTC)

It did not previously state that these were the only subtractions allowed. Without that there is no rational reason not to think that IC would be a valid form.Khajidha (talk) 11:07, 17 October 2017 (UTC)

More to the point - it did not mention any other subtractives so there was at least a very strong implication. "Rules" can be complete without lists of possible "errors" (the idea of "right and wrong" here is very fuzzy, but that is another matter). As it stood there was no reason whatever to suppose that other "subtractives" were "allowed", except a preconceived idea that there might be. --Soundofmusicals (talk) 20:16, 17 October 2017 (UTC)

As I wrote above, per WP:NOTHOWTO the article is not intended as a definitive guide for writing Roman numerals, ancient or modern. If a very good source discusses the points in contention, the conclusion from the source would be WP:DUE, but if such a source is unavailable there is no point wondering what the exact rules are. In fact, there are no exact rules, and never were. There were just customs that are very likely to have varied from time to time and from place to place. Johnuniq (talk) 03:21, 17 October 2017 (UTC)

I agree that this is not a point we can be too pedantic over, but this is really another question (done to death over the years, if you read earlier comments). Fortunately we now have several sources describing the customs followed in current everyday use of Roman numerals - which is what we describe in the "Roman numeric system" section. Without going into exhaustive detail we add a further description of some of the commoner variants under "Alternative forms". What I have been concerned about here is keeping the "alternatives" in their place rather than adding confusion to our statement of the "rules". --Soundofmusicals (talk) 23:23, 17 October 2017 (UTC)

Rewrite of the basic description section

Getting as far away from the "handbook" approach as possible while providing something clear and understandable, I have tried a straight systematic listing - detailing the pattern that runs though all Roman numerals. Hopefully this will be seen as systematic, succinct, and specific. The dreaded and much misunderstood "subtractive" notation is explained from the top down - as originating as a shorthand and clearer way of writing "4" and "9" and thenceforward applying to "40" and "90" and "400" and "900". Numerals that follow a different pattern or differ in some other way are left for the "Alternative forms" section that follows, if only to keep this one simple. --Soundofmusicals (talk) 01:59, 19 October 2017 (UTC)

Dot separator usage

With respect to Slavic languages, AFAIK, the correct date and century notation using the dot is to use the dot to indicate ordinality, but only with hindu-arabic notation; whereas the roman numerals are used almost exclusively to indicate ordinality, and one should not write a dot after the roman notation, e.g. a date should be written as "4. IV 2009.", "18. vek/век/stoleće", "XVIII vek/stoleće".

Cannot really google this (now), but pretty sure.109.121.97.69 (talk) 07:14, 27 May 2018 (UTC)

"IIIIII and XXXXXX" for 6 and 60? What?

  "Sometimes V and L are not used, with instances such as IIIIII and XXXXXX rather than VI or LX"

How the hell does that even work? You write "I, II, III, IV, V, IIIIII"? If "IIII" is too long for 4, why would one EVER write 6 as "IIIIII"? It totally ignores the existence of "V", you might as well use straight tally marks and make it "I, II, III, IIII, IIIII" and then "IIIIX, IIIX, IIX, IX, X". That would make more sense than writing out 6 lines for six, you'd never have to write more than 5 marks. Same goes for "XXXXXX". If anyone has ever written this, it was mistakenly. If it wasn't for the fact that it's "cited" I'd just delete this as obvious vandalism. If there is a textbook out there that once taught this to students...well, I'm glad the students probably never needed to know Roman numerals for everyday life. Maybe it was someone who had this textbook as a student that mis-wrote the copyright numerals on "The Last Time I Saw Paris", which caused the copyright to expire ten years sooner than it should have and the studio to loose copyright status on the film? AnnaGoFast (talk) 23:09, 16 December 2017 (UTC)

Believe it or not we are simply reporting on what the ancient Romans occasionally did. These are actual examples - quoted in the sources cited. Whether it makes sense or not is hardly the point - one could argue (and probably be right!) that being inconsistent in the use of a numeric system defeated the object of the exercise, maybe that was the reason for the decline and fall of the Roman Empire (lol) - in fact none of the "alternative forms" reported here are recommended for modern use of Roman Numerals - if they are to mean anything they have to be applied consistently. Which is why we start out by stating the proper "rules" for writing unambiguous ones. --Soundofmusicals (talk) 00:54, 17 December 2017 (UTC)

It makes sense once you remember that Roman Numerals and Tally Marks are related and share a common ancestor. V and L were newer innovations that meant you only needed to write I or X 4 times in a row. The medieval inconsistencies were mostly attempts to make things clearer and easier to read. III and IIII were hard to tell apart so eventually they adopted the accounting version where 4 became IV and 9 became IX.

i.e.

IIIIIIIII = 9 Sheep in Roman Pre-history

VIIII = The 9th Legion during the Roman Empire.

viiij = 9 dragoons in France in the 1600s

IX = Chapter 9 in a book in the 1800s.

- Ikmxx (talk) 01:55, 16 May 2018 (UTC)

Not quite as simple as that - subtractive forms coexisted with "additive" ones for centuries, in fact millennia! Roman numerals have never been officially standardised (and still are not, of course) - we have quite deliberately avoided personal theories regarding "usual" and "variant" forms unless we have been able to find a reliable source. Have a look at what the article currently says, anyway, and comment on that rather than what people have said on this page. That's how articles get improved. --Soundofmusicals (talk) 02:10, 17 May 2018 (UTC)

I'm not proposing any change, I'm just saying that in both the usual and the variants (even the strange variants), all the various innovations people added over the centuries start making sense once you see them in context, the numbers are written in a way that a person in the writer's time period would easily understand. It's not the writer from centuries ago trying to be clever, or a modern "obvious vandalism". I guess my comment was more directed at AnnaGoFast than you. There's no reason to discard Roman Numbers in everyday life because of inconsistencies that happened centuries ago, especially if you remember how a number system having (easily-decipherable) differences over a couple thousand years pales in comparison to how much a language, like English, changes over the same period. On the subtractives, yes people knew they existed the whole time, but it was mostly only used by medieval accountants who used what is now the standard version Ikmxx (talk) 00:52, 28 May 2018 (UTC)

No beef with most of what you are saying, of course, although accountancy and the need for consistent and accurate numerals certainly didn't begin in Medieval times! "What is now the standard system" has in fact been around for a very long time indeed, although not everyone has always used it to the same degree of exactitude. Ignorance, carelessness, perhaps even pure cussedness? The point is that in an article like this one we are much more preoccupied with recording the facts rather than promoting theories about "why", or even "to what precise degree", and this is why we have very little of the kind of matter you mention. I am glad you think we have this about right (at least that is how I interpret "I'm not proposing any change". These talk pages are really about changes we either have just made, or are thinking about making - see WP:NOTAFORUM (says he - making what amounts to a forum post himself)!! Hang in there --Soundofmusicals (talk) 06:39, 28 May 2018 (UTC)

Semi-protected edit request on 11 July 2018

This edit request to Roman numerals has been answered. Set the |answered= or |ans= parameter to no to reactivate your request.

103.52.12.58 (talk) 15:40, 11 July 2018 (UTC)

Not done: it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format and provide a reliable source if appropriate. --Danski454 (talk) 15:44, 11 July 2018 (UTC)

Use in TV and film

I'm not convinced that the use of roman numerals in TV and film is "an attempt to disguise the age of films or television programmes", given that things which have zero chance of ever being repeated in full - the news, sports coverage, Question Time etc - also have it in roman numerals. Having said that I don't have any alternative explanation. MFlet1 (talk) 16:16, 3 February 2012 (UTC)

Agree it sounds unlikely to me too, but it has a citation and doesn't say it too forcefully and you haven't anything implying otherwise or even a very good story for anythig different, so I'm afraid what you say comes under WP:Original research and can't go in. Dmcq (talk) 17:38, 3 February 2012 (UTC)

Fair enough. MFlet1 (talk) XII:XXXVI, VII February MMXII (UTC)

Which is easier to read? MIM or MCMLXXXXVIIII? The second is the same value, but more convuluted. After 2000, Roman numerals disappeared from copyrights. But they're now reappearing. Will (Talk - contribs) 05:53, 7 August 2018 (UTC)

MCMXCIX is actually the way the BBC wrote 1999 of course. --Soundofmusicals (talk) 12:23, 8 August 2018 (UTC)

PLEASE keep on topic

This article is about Roman numerals - not (for instance) the landmarks of London. "Links" to relevant articles are adequate for things like the proper name of "Big Ben". The point made in the relevant paragraph was always very simply that the number "4" in Roman numerals on a clock face is usually "IIII" rather than "IV" but that there are exceptions - and we actually mention the most famous of those exceptions (really just to make the point that there is no firm rule - just an old tradition). That's quite enough, really. A history lesson is just not required - at least not one about what is in the context of this article pretty much totally irrelevant. We have always pointed out FWIIW the "popular" name is incorrect - but even that is verging on the irrelevant. Someone should do an essay (if no one has already) about "keeping on topic".

"Examples" (e.g. of modern uses) are just that - if we tried to make them comprehensive they'd go on for ever and get more and more trivial as they went. This has actually happened more than once, and to more than one article in Wikipedia. Look at the history of "Auld Lang Syne! This sort of thing needs to be watched - lest they grow into the bulk of an article without adding any real information at all. A citation in a reliable source is important (in fact we probably need to be stricter in this regard than we have in the past) - not just to establish veracity, but also notability. If it is so much part of common knowledge that it doesn't need a citation there is at least a chance that it doesn't even warrant our mentioning it! --Soundofmusicals (talk) 23:00, 10 August 2018 (UTC)

Having said all that - the new "academia" entries scrape in, and can be left - at least as relevant and notable as several other items! But we do need to watch that this doesn't get out of hand - a time may well come for a weeding! ---Soundofmusicals (talk) 23:20, 10 August 2018 (UTC)

BUT I have tweaked and relocated them to fit better into the existing article! BTW do we have anything in Wikipedia about school sport? Tried hard to find a good link without success - could this be a reflection of what our "American Cousins" might term "jocks" and "geeks" (athletes and intellectuals) among students? --Soundofmusicals (talk) 00:04, 12 August 2018 (UTC)

Completed "description" (substitute for so-called "rules")

This clears the way for anyone wanting to add a "set of rules" (IMHO such rules are in practice highly problematic and best avoided here) by removing reference to the old idea of reading a Roman numeral by counting up the elements. Comments welcome!! --Soundofmusicals (talk) 01:39, 12 August 2018 (UTC)

Redirect from Latin numerals

The redirect from Latin numerals to this article is infelicitous, as the numerals used in the Latin language are not treated here, nor should they be, as the term Roman numerals usually refers to the figures I, V, X, L, C, M, etc., and not to the Latin words they originally represent. So why has my new article about those words under the title Latin numerals been repeatedly removed? --Abderitestatos (talk) 00:27, 31 August 2018 (UTC)

@Abderitestatos: note the hatnote on this article: "Latin numerals" redirects here. For counting in Latin, see Latin § Numbers. I think we're taking "Latin numerals" to be a synonym for "Roman numerals", and your new content goes beyond the scope of that to list numbers in the Latin language in various forms... only the "Roman numerals" column in your table is on-topic for "Latin numerals" if they're synonymous. Think about how to best integrate this into the existing content. Add it to an existing article if there's room; if not then you should put navigation links to your new page from the point where readers are most likely to look for it, per WP:Summary style. Also how does it fit in relative to List of numbers in various languages? Maybe title it Numbers in Latin if you can't fit it into an existing article. wbm1058 (talk) 01:49, 31 August 2018 (UTC)

By way of reference here is a version of the page that Abderitestatos is thinking about. Best, Barkeep49 (talk) 02:10, 31 August 2018 (UTC)

With all due respect to Abderitestatos the problem here is very simply that he is misusing the word "numeral". Roman (or Latin) NUMERALS refer unambiguously to the form and use of "the figures I, V, X, L, C, D, and M". Latin NUMBERS (ūnum, duo, trēs, quattuor, quīnque etc., with their variant forms) are something else and belong elsewhere viz. a dictionary definition of numeral "a figure, symbol, or group of figures or symbols denoting a number". Wbm1058's advice seems very sound - would suggest that in fact most if not all of the information in the article proposed by Abderitestatos can already be found in the Latin article, but in any event has no relevance here. --Soundofmusicals (talk) 04:06, 31 August 2018 (UTC)

A numeral is a word that designates a number, and if you search for "Latin numerals", you shall find many entries treating Latin words for numbers, but almost none that use this expression synonymously with "Roman numerals", so the redirect was never really justified anyway, whereas an article about the numerals of the Latin language fits exactly under that title. --Abderitestatos (talk) 10:26, 31 August 2018 (UTC)

wikt:numeral gives both meanings:

A symbol that is not a word and represents a number, such as the Arabic numerals 1, 2, 3 and the Roman numerals I, V, X, L.
(linguistics) A word representing a number.

Numeral is an ambiguous term – that's a disambiguation page. Numeral (linguistics), the article about the word, is parenthetically disambiguated.

That would suggest Latin numerals (linguistics), with Latin numerals possibly turned into a disambiguation.

Disclosure: I was pinged into this discussion because I created the redirect on 4 September 2014 after another editor added a hatnote on 30 August 2014. The title-case version Latin Numerals was created on 31 May 2012.

I don't have a strong opinion on which meaning is primary, and as Latin numerals shows only a small number of page views, I don't object to putting the new article on that title, with a hatnote there to navigate back to Roman numerals. – wbm1058 (talk) 13:16, 31 August 2018 (UTC)

No real objection to this - the value to this article of the redirect was probably always very small - especially if there is to be a clear hatnote back to it from that heading. More concerned about a projected article that would do no more than duplicate matter that ought to be (and to at least a large extent already is) part of the Latin article. In any case it doesn't belong here, please! --Soundofmusicals (talk) 19:51, 31 August 2018 (UTC)

Hi, since the article has already been reinstated and reviewed I've opened up a discussion on the talk page of the Latin numeral article with some suggestions. I've absolutely no objection to their being a separate article on numerical expressions in Latin language from a lexical perspective, which far exceeds the scope of this article, which is a much better vehicle for info about the development of the characters and their usage throughout history to the present day. Definitely an appropriate fork from/between both the article on Latin (language) and from Roman numerals. With avoidance of cross posting in mind I humbly suggest having the conversation about improvement of the related article on its own talk page. Many thanks. Edaham (talk) 03:19, 1 September 2018 (UTC)

Stylized versions like Apple ][

What about making a note about stylized versions of Roman Numerals like Apple ][?

Topher67 (talk) 06:26, 23 September 2018 (UTC)

Overline notation (vinculum)

This is only one of several expedients used by the Romans and/or later users of Roman numerals to express numbers larger than 3000, and is treated in this context. It most certainly doesn't belong in the lead, as if it were a "standard" feature. --Soundofmusicals (talk) 05:52, 2 October 2018 (UTC)

XC vs LXXXX

Most people use XC for ninety. There is, however, an exception: some may use LXXXX depending on the situation under them. For example, MCMXCIV and MCMLXXXXIV are the Roman numerals that represent 1994, although the earlier is used far more often. Now, how often is XC used vs LXXXX? Angela Maureen (talk) 11:58, 17 March 2014 (UTC)

As explained in the article, "XC" is the "normal" way of writing 90 in Roman numerals (by the same principle as IV for 4, IX for 9, XL for 40, and so on). Many people (like teachers, for instance) would say, in fact, that IIII for 4, VIIII for 9, XXXX for 40, and LXXXX for 90 etc. are just "wrong", because they break the rule that you don't put four "same" characters in a row. We hesitate to be quite so positive about it in an article like this - because over the centuries people have not always "spelled" Roman numbers "correctly". They used to spell ordinary words lots of funny ways too. Books, printing, and now the internet, have made us much more fussy about correct spelling. Some "incorrectly spelled" RNs are more (historically) common than others - many, many years ago IIII was quite a common variation for IV (you still see it on clocks), and "CM" (900) used to be (at least occasionally) written as "DCCCC". I have never actually seen LXXXX used for 90 - although that doesn't mean it has never been used, and of course it is obvious what number it stands for. The reason is that at a quick glance it is so easily confused with LXXX (80). "MCMLXXXXIV" seems a very strange way to write 1994. Can you see why?. --Soundofmusicals (talk) 09:17, 18 March 2014 (UTC)

(IMHO) the best way to explain it is that the numerals with 4 of the same (LXXXX, XXXX, VIIII, IIII) were the "correct" version before the subtractive versions(XC, XL, IX, IV) gained popularity in the early-modern period, with the added readability benefits. Ikmxx (talk) 02:26, 16 May 2018 (UTC)

But "subtractive" numerals were common in Roman times - certainly by the time of the Emperor Augustus if not earlier. The avoidance of "IV" in favour of "IIII" may well (although we deleted it in the article years ago for lack of a good citation) be connected with "IV" being an abbreviation of "IVPITER". Hence forms like VLIIII for 44! --Soundofmusicals (talk) 11:34, 23 October 2018 (UTC)

A "time" for "IV" and "IX" relacing (to a large extent) "IIII" and VIIII"?

I really don't think we're ever going to find out "when" this happened - especially as it seems both forms remained common for centuries. But even if we could determine who invented "subtractive notation" and when - this would belong in the "History" section rather than being an essential part of the bare descriptive part. Perhaps this bit needs a little rewrite? I'll think about it. --Soundofmusicals (talk) 02:40, 6 November 2017 (UTC)

I believe the current subtractives are from medieval accountants in the 1200s-1300s onward and became common in the 1700s, don't have a source right now though. My own theory is that older subtractives before that were just people writing numbers the way they said them out-loud, a common practice but not a true "rule". — Preceding unsigned comment added by Ikmxx (talk • contribs) 01:08, 16 May 2018 (UTC)

An interesting notion - although unfortunately it doesn't tally with old inscriptions (see thread above). --Soundofmusicals (talk) 11:36, 23 October 2018 (UTC)

Edits made very late at night!!

Was it just unicode playing up on my computer? If so some people may be wondering what I was on about! On the other hand a crude "reversed C" (for example) is still better than a box with numbers in it - if that's what some computers make of precise unicode values! And I didn't find all the equivalents either! - Never mind - if this is just a massive cockup it should at least be amendable with a simple revert! -Soundofmusicals (talk) 15:57, 31 October 2018 (UTC)

Just had a look at the article on my great-nephew's computer - looks as if it WAS basically a quirk of mine! On the other hand everything still displays exactly the same in both versions, so it doesn't matter very much (I Hope).-Soundofmusicals (talk) 07:22, 1 November 2018 (UTC)

The above IS little me (no matter what signbot thinks! Had a look at this article, as I said, on another computer, without thinking that he was logged in to Wikipedia under his own account. Comes of two editors sharing the same house. --Soundofmusicals (talk) 21:17, 31 October 2018 (UTC)

Rules for Roman Numerals

I see alot of debate on this talk page. I'd like to contribute my understanding of Roman numerals to help clear up misconceptions.

First of all, the numerals were not quite standardized in antiquity. In particular, the Romans applied the subtraction rule to higher numbers but not to lower numbers. For example, they would use IIII instead of IV, but would use XL instead of XXXX. This inconsistency between lower and higher numbers can be seen in the Colosseum -- this is not a RS or anything, but may help illustrate: [7] There were other exceptions as well, so that particular numbers may have been written in different ways, eg IIIIII for 6, or XXXXXX for 60.

In contrast to this, modern usage of Roman numerals is standardized. Also not a RS, but this comment is helpful [8] and here's a useful RS: [9]

Based on available sources & information, here is my attempt at a modern ruleset:

Powers of ten are dealt with separately. Addition is to the right and subtraction is to the left, relative to the adjoining value. Adjoining values are ordered from largest to smallest, from left to right. The adjoining value is defined as a numeral which is an additive multiple of five or ten, to which you may add up to three equal digits in repetition, and subtract by only one digit. Subtraction and repeated addition must be based on ten (I, X, C, M). You may only add one multiple of five (V, L, D), and subtract by no less than one tenth of the adjoining value. Addition/subtraction must be less than the adjoining value, except that equal non-auxiliary numerals may be added in accordance with the additive rules. Adjoining values may not be subtractive (though they can be subtracted from), and addition/subtraction must be applied to the rightmost adjoining value. Addition/subtraction should not be redundant (eg X is not written as IXI). Roman numerals are assumed to be positive integers. For larger numbers, you add a bar over the numeral to multiply x1000.

Therefore, 4 = IV; 8 = VIII; 9 = IX; 14 = XIV; 19 = XIX; 39 = XXXIX; 45 = XLV; 49 = XLIX; 99 = XCIX; 1844 = MDCCCXLIV; 1999 = MCMXCIX; 2018 = MMXVIII.

I think many misunderstandings are perpetuated by the differences between non-standardized classical use, and standardized modern use. Hopefully this clears things up. Let me know if there are any questions, or corrections/additions to be made. My ruleset went through a few different reworkings. It may not be ideal, but it should work as a foundation. Xcalibur (talk) 19:52, 2 August 2018 (UTC)

As an afterthought: I realize this is WP:NOTAFORUM. However, I believe this information could be useful as a guide to explaining the subject matter with greater precision and clarity, and could be a starting point for changes to the article. Xcalibur (talk) 08:27, 1 August 2018 (UTC)

Always a good idea to read an article before bothering with the talk page! To be positive about the "not a forum" business - always feel free to comment on an article, but do (please) base any comments and suggestions on the article itself. Just to point out that confused and controversial talk pages are often appended to what may be in itself a very good article indeed (in part, perhaps, because the discussion on the talk page was so productive). Not all talk page comments get reflected in the relevant article (which is a very good thing - as some very silly comments are preserved on various talk pages). I think if you read the article you will find that all the matters you raise are dealt with there, if not quite in the same wording or arranged in the same way. --Soundofmusicals (talk) 11:36, 2 August 2018 (UTC)

Of course I read the article first. Yes, much of what I said about rules and differing conventions is mentioned in the article, however, it could be laid out more specifically. For example, in this old revision: [10], there is a set of bullet-point rules under the first section. My idea is to create a set of rules which, if followed, would always give you the correct modern form without any ambiguity. I realize Original Research is not allowed, but I'm sure it can all be sourced. I also think we could more fully explain the differences between ancient/historical and current conventions, rather than just mentioning several exceptions. For example, I think the Roman tendency to only apply the subtraction rule to higher numbers may be worth noting. btw, pardon my multiple edits, I couldn't resist tweaking and improving my work. Xcalibur (talk) 13:30, 2 August 2018 (UTC)

More glad than I can say we're both talking about the article as it has evolved - always an advantage if we're both talking about the same thing!

"A set of rules, which if followed etc." is something we have tried more than once - we had endless "what if" and "why can't I" complaints - it became evident that many of our readers objected to us "laying down the law", or even denied that there WAS a set of rules at all. Then someone pointed out the guideline at WP:NOTAMANUAL. The whole "What Wikipedia is not" project page is well worth looking through in this context.

What we have evolved to instead of just listing rules and exceptions is a description of how Roman numerals work - this won't please everyone, but it is not only more immediately comprehensible for our hypothetical reader who has never heard of Roman numerals before, it looks more like an encyclopedia article than a "how-to" manual. The basic basic "decimal tally" principle is pretty simple - and once you grasp that you don't need "rules". As I think you have already discovered, RN "rules" were always honoured more in the breach than the observance - and not only in Roman and medieval times but even to the present scientific age, when we have an unprecedented tendency to standardise everything.

Have you thought of a personal blog about Roman Numerals, or perhaps numeral systems? Might just be more like what you want to do. Anything you do here will be edited over until all traces of your brilliance has been lost. Been there, done that. --Soundofmusicals (talk) 01:20, 3 August 2018 (UTC)

Totally off topic - but don't be in too much of a hurry to press the "Publish changes" button. It's always a good idea to try "Show preview" instead until you have worked out just what you want to say (I can't talk when it comes to multiple edits myself, but they ARE confusing for others). And while this isn't a forum, and we are allowed to edit "old" talk posts it is fraught, and a good policy to put all our talk remarks into new posts - all kinds of reason for that to, which I won't insult your intelligence by enumerating! :) --Soundofmusicals (talk) 01:20, 3 August 2018 (UTC)

Of course, comments should be sequential, and Show Preview is useful. Again, I didn't mean to clog up the edit history, I just kept finding ways to improve on the ruleset, and my multiple edits were only in that context.

The description is adequate, but I think the article can be expanded to cover changing conventions, including a precise definition of the modern convention. I think documenting the modern convention accurately would not necessary violate WP:NOTAMANUAL, as long as we document the information without an instructional approach, i.e. we can list a set of rules, but not a step-by-step guide for writing a numeral with examples.

Yes, I noticed quite a bit of consternation over what is or is not allowed. In my estimation, that's because the stated rules were not comprehensive. My idea is to introduce an airtight set of rules that can answer every hypothetical question. The thought experiment I used is: what if you had an evil computer program, which had to obey rules, but would try to give you the wrong output at every opportunity? How could you create a ruleset that would force the evil program to give you the correct numeral? That's how I thought of it. Done correctly, it would address any and all complaints, especially with the explanation that historical usage of Roman Numerals often defies convention. Overall, it would make the article more informative.

I'm not worried about the prevailing winds of editing. Wikipedia may seem chaotic, but in fact there is an informal meritocracy at work here: good edits tend to stick, low quality edits tend to get reverted or rewritten. Xcalibur (talk) 08:52, 3 August 2018 (UTC)

Another alternative - what about starting a new article (!) called "Rules for construction Roman numerals". Just an idea. Have to say personally I can't see that anything of the kind would be much use for this article. Another alternative would be having a good "web-surf" through the already existing sites about RNs elsewhere and add their URLs to the external links section. --Soundofmusicals (talk) 09:57, 3 August 2018 (UTC)

I don't think an entire new article is warranted. Unambiguously describing the current convention is both relevant and informative -- why wouldn't it be useful for this article? It could be a new subsection under 'Roman numeric system'. We could include new links as well, it doesn't have to be either/or. Xcalibur (talk) 11:23, 3 August 2018 (UTC)

Perhaps even better to detail exactly how the current section is ambiguous, irrelevant or uninformative? Run something of the kind past us. any ambiguous passages and how you would take away the confusion, any irrelevant passages (which will of course have to go) - and uninformative passages (no place for them in an encyclopedia!) Perhaps just delete the Alternative forms bit? Sorry for getting a little ironical but I am a testy old man in the evening of his days and you need to make allowances. When I was much younger (incidentally long before there was such a thing as a HOME computer) I used to set my beginning programming students the exercise of writing a few lines of BASIC that would translate between Roman and "Arabic" numerals, up to 3,999. (No GOTOs allowed!) They were consistently surprised how few lines of code it could be done in. The enterprising ones used to add a routine that corrected common errors, or added an extra place (say, "Q" for 5,000). Explaining the system to a human is rather a different matter - but I honestly believe we don't do such a bad job already. --Soundofmusicals (talk) 21:38, 3 August 2018 (UTC)

It's fine, you can carry on if you wish. I would like to point out that this is not a personal criticism against you or your efforts.

This is not a zero-sum game, I can add new content without deleting/rewriting old content. The current section is adequate, but it still leaves room for uncertainty, and can be expanded and improved further. There are many questions and debates on this talk page relating to how Roman Numerals should be written, so there's plenty of interest in the matter. I was thinking of creating an 'Orthography' section (unless there's a better term for it), and providing a ruleset for the current convention, while pointing out that exceptions/alternate forms are still used today. Would that be agreeable? Xcalibur (talk) 09:09, 4 August 2018 (UTC)

As you hint - I don't "own" this article any more than you do. Not meaning to be unduly cynical - I may be coming across as defensive which is not really my intention - but believe me we have been down the "set of rules" path before, and as I have said, we found it very problematic. And not just because our rules "weren't comprehensive enough" I think in retrospect many readers found them TOO "comprehensive" - the more that got added the more ambiguous they got.

On the other hand I am pleased you want to discuss this here rather than just barging in with something off the top of your head (it happens). Why not work something up in your sandbox? Just copy the current article there and put in whatever tweaks/additions you want without actually disturbing the "public" article. Then invite me (and anyone else you like) to have a look at your efforts. No one would be more delighted than me if you can come up with something that really improved the article! Try to keep it descriptive, and like an encyclopedia, and do avoid the "manual" bit. Most of that project page was written by the founder of Wikipedia, and is really fundamental to what this encyclopedia is all about. --Soundofmusicals (talk) 10:45, 4 August 2018 (UTC)

I understand. However, I believe that all the previous controversy was caused by imperfections in the proposed rules. My ambition is to create a flawless ruleset for Roman Numerals, which if applied, allow only one possible iteration of any whole number. I'll cook something up in the near future, and link the subpage draft when I'm ready. Xcalibur (talk) 11:15, 4 August 2018 (UTC)

Sorry - yes - go for you life! --Soundofmusicals (talk) 21:37, 4 August 2018 (UTC)

Hi, it's been some time since I last checked in here; I got quite distracted by other things. Now I'm back with new & improved sources, enough to justify a new section covering both ancient ambiguity and the modern ruleset. I've only got preliminary notes in my namespace right now, but I'll be expanding that into a draft, and eventually incorporating the material into the article. Here are the sources I've found:

[11][12][13]these sources cover modern rules fairly well. while not the most reliable, they're better than a blog or reddit post.
[14] updated link. a more reliable source for modern rules.
[15] pp. 54-63 of this RS has great coverage of the history of roman numerals, and their flexible/ambiguous use in classical antiquity.
[16] "Note on Roman Numerals" this article is the best source I've found yet, highly reliable, and covers both modern rules and historical exceptions.

I think my section will be divided into an overview of historical use, and then a modern ruleset.

My current draft of the rules is as follows: 1. Repeated decimal numerals (I, X, C, M) are additive. 2. Up to three (3) decimal numerals may be repeated sequentially per power (there may be up to four (4) non-sequential repetitions per power). 3. Smaller numerals placed to the right are also additive. 4. Smaller decimal numerals placed to the left are subtractive. 5. Quinary numerals (V, L, D) may not be repeated. 6. Quinary numerals may not be subtracted, only added. 7. Only one (1) decimal numeral may be subtracted per power. 8. *Subtraction must be by 1/5 or 1/10 of the adjacent value (i.e. the next lower decimal numeral relative to the adjacent value). 9. Addition may be by any amount that is equal to or less than the adjacent value (not greater). 10. Powers of ten are dealt with separately, ordered from greatest to smallest and from left to right. 11. Addition/subtraction operations are to be applied to the rightmost numeral per power. 12. Addition/subtraction should not be redundant (eg X should not be IXI). 13. Roman numerals are positive integers with pre-defined values. 14. If there is no adjacent value, a numeral may be entered ex nihilo. 15. Placing a bar over a numeral multiplies it x1000.

This is an update on where things stand at the moment, feel free to provide feedback. ETA: updated my draft. Xcalibur (talk) 13:36, 30 October 2018 (UTC)

Possible simple rules: for each power of 10 n, there are two symbols, one representing 10ⁿ and another representing 5×10ⁿ. For each decimal digit from highest to lowest, the digits 0-9 are translated to the "digits" (nothing),I,II,III,IV,V,VI,VII,VIII,IX where I is the 10ⁿ symbol, V is the 5*10ⁿ symbol, and X is the 10ⁿ⁺¹ symbol. These are then written in the same order as the decimal digits. The symbols for values greater than 1000 have multiple designs, see below.Spitzak (talk) 16:28, 30 October 2018 (UTC)

That's an interesting theoretical approach! However, my main concern here is avoiding Original Research; as a result, I'm working from Reliable Sources which back up my content. I also want to write the ruleset in such a way that it addresses common questions and points of contention. Xcalibur (talk) 02:19, 31 October 2018 (UTC)

Tempted to just go back to my very first response - how (and please be specific) is any of this not very much better covered already by the descriptive approach currently there. The rules (at best) only make any sense at all if you're already pretty familiar with RNs anyway - introducing confusing jargon like "additive" and "subtractive" outside an explanatory context for instance - or insisting that we NEVER repeat a symbol more than three times when almost every RN clock face does exactly that! I've said this over and over, but we DID have a ruleset very like the one you propose (based, I suspect, on the same sources) and it produced no end of confusion and dismay. Many sources come up with "facts" that are just not so, and which we need to avoid. Just one example is that RNs changed a lot during the Middle Ages. Superficially this is true, but the only "medieval" changes we have not pretty much completely ditched in favour of a return to "classical" (Roman) usage is lower case letters with a final "j" ("viij" for eight for instance) - and even then the classical VIII is far more common - and a continuation of the gradual easing of the avoidance of "IV". (I am increasingly coming to the conclusion that this avoidance MUST originally have been because to a Roman it looked like an abbreviation of "IVPITER"). On the other hand the Romans used the other subtractives (IX for nine, XL for forty etc.)! (Viz. the gates of the Colosseum!), so it was never an avoidance of subtractives as such or because they hadn't invented them yet! The current article is not brilliantly referenced - and pinning down a reliable source for some of the things we assert may be an exercise very well worth the bother - but there is an awful lot of surmise and guesswork out there - much of it very definitely contrafactual. --Soundofmusicals (talk) 14:15, 31 October 2018 (UTC)

The description is a solid introduction to Roman Numerals, but it still leaves questions unanswered; eg why are combinations like IC, IIX, IXX, VL, XXXX (to name a few) not 'legal'? There's room to expand on this with a comprehensive section on orthography (in addition to the fundamentals). As long as we're describing how the rules work, rather than demonstrating in how-to fashion, it should be fine. While rules caused consternation in the past, I'm convinced that this is because they were incomplete; a complete, accurate ruleset should go over just fine, and I believe that's what I have conceived. Yes, we have to be careful in how we use sources, which is why I'm working from the common ground shared by multiple RS. In addition, the section could explain the principles of ancient and medieval usage alongside the modern convention, eg how flexible and ambiguous was the ancient convention? (answer: very), and how did usage change during the medieval era? (although the history section already covers this to an extent, and we'd have to work around that).

I found another source (to go along with the websites on the first bullet point), and I've added a rule: ~~'Fractions may only be added to the right of all numerals (not subtracted).'~~

Once I'm further along in cooking up the section, I'll post the userspace link. Xcalibur (talk) 08:45, 1 November 2018 (UTC)

There's more to it than just finding websites. As you will have noticed, they differ quite widely, and even contradict each other.
Roman numerals have never been (and continue not to be) standardised in the way that the metric system, or the international games of rugby football or cricket are. It might be possible for an international institution to be formed for the purpose of devising a "standard" form for RNs, and formulating rules for the consistent application of this standard, but in fact this has never been done. Not in Roman times when they invented the things - not in the chaos of medieval times, and certainly not since. Some of us might say that this is a shame, others that it is actually rather sweet. In any case it is a fact, which you can't get away from.
Strictly then, just as anyone can edit a Wikipedia article, anyone can write any combination of letters from the Latin Alphabet (or other set of symbols for that matter), call it a Roman numeral, and designate the number it represents. As with the efforts of many Wikipedia "editors" the result may in some cases be less than helpful, but he will NOT be breaking any "law" in doing so, in the sense that a grocer supplying 75g of sugar and calling it a kilogram, a bowler tampering with the properties of a cricket ball, or a rugby player tackling an opponent by grabbing him round the neck, might be said to be breaking a law of just weights and measures or fair play.
There are in fact two senses in which a so-called "standard" Roman numeral like "XCIX" (for 99) might be said to be "better" than a "variant" form like "IC". One is just that it is simply more usual. If you like, rather more likely to be what the standard would be, if there was one. Secondly, it just fits better with the system - the use of our "arabic" numerals to write the series "95, 96, 97, 98, 99, 100" has an equivalence to the equally logical (if more cumbersome) "XCV, XCVI, XCVII, XCVIII, XCIX, C". Writing out this series (as, for instance to number the pages of a book) in any other way would be bizarre. On the other hand Roman numerals are not quite the everyday matter they were once upon a time - we might need a moment's reflection to see that XCIX is 99 - but at the same time and in the same way IC is clearly also 99 - no ambiguity.

Very well let's imagine what an ideal set of "rules of the game" might look like. Some of this mirrors some ideas of your own of course.

The first "law" of RNs (from which all the others stem) would describe the simple set of primary symbols (I, X and C) with a "tally" or repeating value of 1, 10, and 100. M (1000) is a special case of course and needs its own rule(s). We would really have to add examples to make this clear.
The next law would describe the "intermediate symbols" (V, L, D) with a fixed, "non-tally" or non-repeating value of 5, 50 and 500. Again, a set of examples - or extensions of the examples from rule 1 would be necessary if this was to be intelligible, much less clear.
The third law would need to describe how the "units" of a RN are denoted by I, V and X. Any arabic number not ending in a "0" (i.e. having a "unit" component) will end in one of the roman numeral tally combinations to a unit value. This is, for whatever it might signify, the law broken by IC. Any arabic numer ending in "9" can only be represented by a Roman numeral ending in "IX".
The next law might generalise the other decimal places (tens, hundreds, and in a way thousands) and that they follow, in the simplest possible way, the same pattern.
Somewhere in all this we would include a law of "subtractives" - making it clear that any repetition of a "primary" symbol more than three times is unnecessary, albeit the Romans seem to have had a (possibly pious or superstious) aversion to "IV", so that "IIII" does occur.

We're getting there, I think? Now just to pause here, what part of this does our description not cover? And what other "laws" do not follow from this description? Isn't the description in fact easier to follow, especially for a beginner? Sorry if I have "gone on" a bit but my other more succinct explanations don't seem to have hit any particular mark. --Soundofmusicals (talk) 12:16, 1 November 2018 (UTC)

If "IC" is not allowed, then the rules can be simply stated by showing the 10 patterns that are allowed for each decimal digit. The rules you are suggesting are far more complicated than just listing the valid resulting set. Then list a few common exceptions that some consider invalid and others allow, such as "IIII" and "IC".Spitzak (talk) 19:49, 1 November 2018 (UTC)

But there is, in fact, a modern convention for Roman Numerals. it's not something enforced by any institution, and exceptions are made (especially the use of IIII on clockfaces, which is for aesthetic effect). but I think it's safe to say that there is a standard modern form, and I have the RS to back up that claim. While anyone can make up any rule or value, they cannot provide backing as I can.

Again, top-down theoretical approaches are interesting, but AFAIK not adequately backed by sources, which creates an issue with OR. also, the rules should be intelligible without having to provide examples along the way (and this would run into the NOTAMANUAL issue you brought up previously). While having 15 rules may seem complicated, they are individually very direct and straightforward, and taken together they should be foolproof and unambiguous. They address why combinations like IXX, IIX, IXI, LL, MMLC, or ILV are not permitted. They also prevent the hypothetical 'evil computer program' I mentioned earlier from doing things like adding or subtracting in the wrong direction, putting values out of order, etc. I think a precise ruleset can exist alongside the 'basic decimal pattern' section (which is perfectly fine as an introduction). Xcalibur (talk) 08:06, 2 November 2018 (UTC)

Pardon me, still fiddling with this -- I removed the fractions rule (decided it was unnecessary and not within scope), and added a new source (mathforum) with plenty of relevant info. eta: I must correct myself, there is some support in my sources for a theoretical, pattern-based approach -- enough to back up the current intro, but not enough to be comprehensive. PS: looking over my ruleset, there's a few that serve as elaboration but are not required. I could whittle this down to 12 rules, would that be better? Xcalibur (talk) 10:11, 2 November 2018 (UTC)

The fewer "laws" the better - but don't you think that no "laws" whatever might be better still? True, there is a convention, which can be much more easily (and usefully) described (as we already do) rather than formulated, in fact any such formulation, from the examples you suggest, is going to cause far more confusion than it dispels. We already mention the more common "variants". Why, exactly, we need to explain why each of these is "wrong"? On what grounds can we even talk of "right" and "wrong" on such a topic as this? I have thought of introducing a section (or perhaps a new article) on "Roman arithmetic" - this would demonstrate the usefulness (to the ancient and medieval people who used RNs for arithmetic) of keeping hundreds, tens and units separate rather than crossing them over (as, for instance, "IC" does). I can't see that anything like that would improve the article, mind you. --Soundofmusicals (talk) 21:13, 4 November 2018 (UTC)

Like I said, previous formulations were incomplete, which is why they led to confusion. I'm convinced that my formulation is the one that will work. I want to add it because there are many questions about roman numerals, such as, why can't I do this? or, which of these forms is 'better'? You can see some of those questions on this very same talk page. therefore, I think a comprehensive formulation of current orthography would expand upon and improve the article. I also want to more explicitly describe how flexible the Romans themselves were in their usage -- while they generally added to the right and subtracted to the left, much else was ambiguous. For example, one of my sources mentions the use of IXCS for 89 1/2! (S being semi, or 6/12).

As for math with Roman numerals, I bring you more sources: [17][18][19] that should be plenty to work from.

eta: just realized that my third source supports the tally hypothesis, and mentions that the quinary numerals (V, L, D) were invented by the Etruscans and borrowed by the Romans, and in turn, cites this source: [20] this could be useful material for the history section. Also, it may be worth mentioning that Roman Numerals are a biquinary decimal system, that is, base ten with five as a sub-base. Xcalibur (talk) 10:04, 5 November 2018 (UTC)

Yes, I know you think the more rules the better - also the more "coined" technical terms the more impressive. On the other hand you know that I disagree quite strongly on both accounts. I succumbed some time ago to "subtractive" - but in my opinion it would be good to avoid even that one! This is a popular, general encyclopedia and I really do think that the current text (as you admit, a "sound introduction") is pretty much what is actually required. We are in the business of being helpful, not of mining for the maximum "impressiveness", or (heaven forfend) of covering every possible "base" (pun intended) touched on by every other online cite. --Soundofmusicals (talk) 22:18, 5 November 2018 (UTC)

My aim here is not to impress or be overly technical. additive/subtractive, while not the most basic concepts, are not too difficult either. I have, in fact, taken a step back from coining terms and tried to make the rules self-explanatory; I've also whittled them down to 12 for the sake of brevity. This is not a zero-sum game, there's room for both a basic overview and a precise explanation, they can be complementary.

Over the course of digging for sources, I've found room to expand upon not just orthography, but also history, mathematics, and biquinary decimal design (to be precise, biquinary uses 2 and 5 as sub-bases, and Roman Numerals emphasize the 5). Even if you're apprehensive about my ruleset, I hope you can see the value in increasing coverage and providing the requisite sources. Xcalibur (talk) 05:30, 6 November 2018 (UTC)

Yes - "subtractive" is one I use myself, as I mentioned, and even "additive" is fair enough - but some of the others... Just quietly, I think we can do without "biquinary", for instance. Much more helpful to explain clearly what we mean in ordinary words.
Adding citations (provided they are good ones, of course) is always a good move. There is an awful lot of nonsense out there, unfortunately. Avoid repeating wild surmise and truism with little or no basic=s in fact. If in doubt, leave it out!
What about some of the "rule" information you miss being added as footnotes? These can be very handy for elucidating points without "breaking the thread" of a connected explanation. No objections to anything that makes what is already there more understandable and less confusing. (Rather than vice versa.)
The "History" and "Hypothesis" sections have remained the same for many years and may well benefit from a bit of a re-write. Although they were there long before I came to the article I do like the way they avoid presenting debatable (and debated) matter as "fact".
Remember the suggestion I made a while ago for you to create a sandbox version of the article which you could tweak to your hearts content and invite anyone interested to have a look at? I have done this a number of times - in every case most productively. You probably know as well as I do how to do this - but if you need 'walking through" it by all means ask me, perhaps on my own talk page. --Soundofmusicals (talk) 10:40, 6 November 2018 (UTC)

I generally agree, which is why I wrote my ruleset in plain terms. Where I used a more technical term, such as 'quinary numerals', I added (V, L, D) to make my meaning clear. When we describe the biquinary decimal design of Roman Numerals, we'll not only pipe to the relevant page, but also explain it in plain terms (as it's a fairly esoteric topic, and even I was a little unsure about subradices at first, though I think I've got it now). RS are important, which is why I've emphasized the sources built on firm ground (the scholarly books and article in particular). You make a good point about footnotes, I may in fact add one in order to include the extra clarifications (duodecimal fractions to the right, positive whole integers, ex nihilo). While the history section is not bad, it could use revamping, especially in light of the relevant information I've dug up. And yes, userspace is a good thing -- I'll post the link when ready. Xcalibur (talk) 11:13, 6 November 2018 (UTC)

At first I wanted to renovate, but now I'm not so sure. The current section covers matters fairly well, but could still be expanded. I think the sheer amount of variation in ancient usage could be documented further, e.g. LXXXXVIIII / IC for 99, and IXCS / SXC for 89 1/2. Also, my source indicated that while the vinculum could be used to multiply x1000, it was more commonly used to distinguish numbers from letters. I'm thinking about dropping my modern ruleset in with a brief introduction and sourcing (I'd link my userspace page, but it's a bit cluttered right now), then deal with other issues when I get to them. Xcalibur (talk) 09:48, 20 November 2018 (UTC)

Went ahead and BOLDly added it in. Let me know if there are any questions/comments/concerns. Xcalibur (talk) 10:33, 20 November 2018 (UTC)

That list of rules seems ridicuolusly complex. There are only 10 patterns allowed so more than 10 rules means you are not describing it efficiently. I think the confusion is that "IX" should be considered part of the 1's, not a 10's digit. As far as I can tell the first section describes the rules perfectly and much much clearer. There are exactly 2 patterns with subtractive digits so the use of 5 or 6 rules to talk about them is overkill.

For each power of 10, there are 4 "digits": I,IV,V,IX (list others here). The pairs are called "subtractive" digits as they are one less than the second part of them.
The value of the number is the sum of all the digits.
When writing choose the largest digit less than the remaining value first. This produces the shortest number. Also it means they are written from largest power to smallest, which is also necessary so the subtractive digits are not ambiguous.

Spitzak (talk) 19:50, 20 November 2018 (UTC)

If we wanted to do this by "rules"

I do not want to be too dismissive of the sincere attempts to reduce this to "rules" but what exactly would be specifically wrong with this as a "ruleset"? Each rule is intelligible in itself, and builds on the one before it. Any technical terms are explained on their first use. While each rule should be reasonably succinct, this must not reduce it to incomprehensibility. Some rules require a note or two to render them clear.

1. Roman numerals are an informal convention for expressing numbers, closely based on classical usage in the Roman Empire. The following rules are an expression of this convention.

2. Counting in Latin is primarily decimal (Hundreds, tens and units). Reflecting this, in Roman numerals each power of ten: is notated separately, from left to right, as with standard "Arabic" numerals. Each power has its own specific notation - thus:

i. Units are expressed by the symbols I (=1) and V (=5)

ii. Tens are expressed by the symbols X (=10) and L (=50)

iii. Hundreds are expressed by the symbols C (=100) and D (=500)

3. Multiples of the base symbols for each power (I, X, C) are built in the form of a tally, thus:

i. I=1, II=2, III=3

ii. X=10, XX=20, XXX=30

iii. C=100, CC=200, CCC=300

This basic addition by tally is called additive notation.

4. For each power of ten there is an intermediate symbol represent 5 of the base tally symbols.

i. V=5

ii. L=50

iii. D=500

These numerals are called quinary numerals

5. A quinary numeral preceded by the base numeral for its power represents 4 (5-1) of the base symbols for each power.

i. IV=4

ii. XL=40

iii. CD=400

This is an instance of "subtractive notation". The only "regular" exception to this rule is that 4 (IV) is usually represented as "IIII" on clock faces.

6. A quinary number is followed by a tally of the base numerals for its power to represent the remaining values for that power.

i. VI=6, VII=7, VIII=8

ii. LX=60, LXX=70, LXXX=80

iii. DC=600, DCC=700, DCCC=800

7. The base symbol for the next power up preceded by the base symbol for each power represents 9 (10-1) of the base symbols for each power.

i. IX=9

ii. XC=90

iii. CM=900

For the purpose of this rule "M" is used as the base symbol for the thousands, but M(=1000) is a special case - there is, for instance, no standardised quinary numeral for 5000. The modern use of "M" as an additive symbol in (say) MMXVIII has no classical precedent - while Roman numerals are not in practice used nowadays for numbers larger than 3,999 (MMMCMXCIX).

8. No combination of symbols that is redundant with a regular numeral described in any of the preceding rules is "regular" in terms of these rules, although in some cases it may exist as (for example) an inscription.

Examples - additive quinary numerals (VV=X=10), double subtractive numerals (IIX=VIII=8), ambiguous or self cancelling numerals (IXI=X?=10). Similarly, the consistent use of subtractive notation renders the repetition of any symbol more than three times redundant, so that such notation is regular only in the exceptional case of clock faces.

I am NOT suggesting, incidentally, that the above would be in any way superior to the existing article text, but if we have to have rules let them at least be sequential and comprehensible!

What about appending (as an appendix) something like this to the article, as an afterthought? --Soundofmusicals (talk) 03:00, 21 November 2018 (UTC)

While those rules are pretty good, they're also rather theoretical in their approach. My rules are very direct and convenient for answering any questions (eg why isn't this allowed?). Perhaps this is a difference in opinion. More importantly, my ruleset builds off the content I sourced, rather than a creative approach (which veers towards Original Research). eta: my rules are not random, I attempted to create a logical and stylistic sequence. I can always adjust that if necessary. Xcalibur (talk) 04:15, 21 November 2018 (UTC)

On the contrary, these rules are very down to earth - unlike yours they include examples, and they are not random but in sequential order. The first rule MUST be a basic definition, or anything following is without context and therefore meaningless. Each following rule MUST build on the one before, anything else will be "forward referencing". It is normally very good encyclopedic style to be succinct - but not to the extent of being cryptic, which all your rules are to a greater or lesser extent. Finally, adding to (or building onto) an RS rather than paraphrasing or summarising it is OR by definition. I'm trying very hard to be fair, but... By the way, what about a totally new section for rules, going at the end of the article as an appendix - a suggestion I've made more than once. At least this would avoid the confusion that would arise from putting the two totally different (in fact contradictory) approaches on top of each other. --Soundofmusicals (talk) 04:38, 21 November 2018 (UTC)

Incidentally attempting to have a rule to specifically cover every possible "mistake" would require about twenty kazillion rules (it just isn't practicable). Rules describe "correct" usage - usage that breaks the rules is wrong by definition. But look at my rule 8. What does not that cover? --Soundofmusicals (talk) 04:49, 21 November 2018 (UTC)

I essentially am paraphrasing, I'm taking information from my sources and expressing it in a new way. I think a conceptual approach not backed by sources is much more problematic for OR. As for defining, that's why I emphasized that this is complementary -- the previous section covers the basics, while mine introduces formal rules. I agree, my section would be difficult by itself, but as an elaboration it should be fine. I did in fact approach this logically, starting with a basic rule, then elaborating further, and grouping closely related rules together. I don't think an appendix is necessary for this, and the two different approaches are not in fact contradictory -- they are complementary, as they both describe the same system by differing but consistent means. To expound a bit further, people often ask why they can't use certain permutations of roman numerals, eg: why is 19 XIX and not IXX? Why is 45 XLV and not VL? Why isn't IC allowed? With my ruleset, I could point them to the 'rightmost' rule, the 'quinary addition' rule, or the 'subtraction' rule to answer their query. There is something to be said for a rule-based approach that only permits the proper permutation.

To respond to your latest edit, I believe I have specifically covered every possible mistake, and in far less than twenty kazillion rules -- more like 12-16. If you can come up with a single permutation of roman numerals that my ruleset doesn't cover, I'd be interested. This is an open challenge! Xcalibur (talk) 05:19, 21 November 2018 (UTC)

Using more than 10 rules to make 10 different patterns is obviously inefficient. I think the introductory section already gives the rules. To be pendantic here is my set of rules, designed to be as short as possible:

The following "digits" are available: I=1, IV=4, V=5, IX=9, X=10, XL=40, L=50, XC=90, C=100, CD=400, D=500, CM=900, M=1000.
To write a number, choose the largest digit less or equal to the number, write that, subtract it, and repeat with the remainder. This means the digits are always sorted from largest to smallest, which is necessary to make the "subtractive" digits such as IX unambiguous.
You cannot write a number larger than 3999.
All the exceptions basically add more "digits" to the available set.

But honestly I think the introductory section is quite enough. Spitzak (talk) 05:05, 21 November 2018 (UTC)

So do I, obviously! Good to have you here Spitzak! Your rules are the right ones to tell a computer how to handle Roman numerals, just bye the bye. Although my Computer Programming I students found some other ways that also worked, if less efficiently. Oh for the days of my misspent youth!--Soundofmusicals (talk) 05:41, 21 November 2018 (UTC)

Inefficiency would be a concern if this were a basic overview or introduction. However, my approach is designed to be comprehensive, allowing only a single permutation per value. Given this, 12-16 rules is quite reasonable. As I said above, this is intended to be an elaboration on the 'basic decimal pattern' section, not a replacement. Xcalibur (talk) 05:24, 21 November 2018 (UTC)

A bit of an edit clash! But answering you, Xcalibur - I have still, after reading through ALL your comments on this page very patiently, still not seen a decent argument from you as to why the existing text does not fully subsume any sensible "set of rules"! Every time I have asked you to specify things we could do differently all you seem to be able to say is that the section is "pretty good". If it is pretty goo I suggest we leave it as it is. If we MUST have a formal ruleset in addition then why not have it in an appendix, where it will cause minimal confusion? Asking this yet again in the hope of getting some reaction from you on the subject. Sorry if I'm becomin a bit testy but even my patience has its limits! --Soundofmusicals (talk) 05:41, 21 November 2018 (UTC)

I'm not trying to be contrarian or make things difficult. I simply want to contribute something of value. The current section is in fact pretty good for the purpose of a basic introduction. My section, on the other hand, emphasizes precise rules that answer any and all doubts. Two different sections for two different goals, that's my idea. In my previous comment, I mentioned some common mix-ups: IC, IXX, VL, to name a few. I think my ruleset does a better job of explicitly responding to these queries; as opposed to the intro, which is better at providing an easily understood general guideline. So as I said, they're complementary. I'm not vociferously opposed to relegating the rules to an appendix, but I don't think it's necessary, especially since the section is fairly concise. Xcalibur (talk) 05:53, 21 November 2018 (UTC)

Xcalibur - if I didn't think you were basically well-meaning I wouldn't have put up with all this for a moment! I am starting to wonder, but that is another matter altogether. BUT if usage that clearly breaks a rule needs another rule to validate it then we are like the oozelum bird, going in infinite concentric circles up our own fundamental orifices. The usages you exemplify as needing a specific rule to "explain" all break existing rules about keeping the powers of ten separate and restricting subtractive notation to the very limited possible set of permissible forms (4&9, 40&90, 400&900). Assuming we have a rule, then "why" is not really a valid question, is it? Or the invariable answer is "because that's the rule". And then we get the further question "then why have rules?" - round and round, as I said. And a kazillion is a pretty fair estimate. And no, your rule set doesn't even start to define every possible crazy permutation. Not that it needs to try! :) --Soundofmusicals (talk) 06:11, 21 November 2018 (UTC)

I don't think the current section clearly disallows those 'incorrect' variants I mentioned. I think a more exacting clarification can be done without creating an endless loop, as long as all possible sources of confusion are adequately covered, which they are. I would argue that yes, my ruleset covers every possible permutation, both crazy and sane. Xcalibur (talk) 06:20, 21 November 2018 (UTC)

Well, I think that either deliberately or otherwise you're missing (avoiding?) the point - we don't need to specifically disallow what is implicitly not permitted. To put it another way, enumerating what is permitted is pretty simple, whereas a futile attempt to enumerate everything that is NOT permitted is just that, futile. In fact attempting to do so gives "what is not permitted" a legitimacy we have to avoid. No possible set of rules can cover perpetually circular questions. Why is [any non-standard RN] "wrong" and [any standard one] "right"? As I said "because the first form breaks the rules and the second conforms with them". If that is not a completely adequate answer our rules are meaningless. Which brings us back to the reason for this article NOT explaining how RNs work in the form of a set of rules, but rather as a descriptive account. Since lots of people DO deny that there is a set of rules at all (and, since they have a point - since in a sense there isn't!) then best, as I have said enough times by now I hope, that we avoid the whole "rules" thing. --Soundofmusicals (talk) 07:58, 21 November 2018 (UTC)

I maintain that my ruleset does completely enumerate what is and is not permitted; and the current introduction, while being useful, does not address all concerns. Moreover, I've provided RS stating that there is a modern convention governed by rules, and my content is directly derived from these. That should be enough to support inclusion, especially since the section is of reasonable size. In regards to your edit summary stating in effect that you will not budge on this, and further discussion will require dispute resolution: While I could go up the ladder, I would rather that not be necessary. Therefore, I will give you time to come around.

As to Spitzak: I appreciate your input here. I think your rules are very efficient, and are ideal for programming. However, I think the rules should focus on human (mis)understanding, and moreover, they should reflect the RS. Xcalibur (talk) 08:17, 21 November 2018 (UTC)

I think I've identified the crux of the matter.

You say: the basic intro is enough, we don't need rules, the rules aren't real anyway, and they lead to confusion.

I say: the rules could expand upon the intro and improve understanding of the subject matter; I've provided RS backing up the modern convention (which is what counts on here); all previous confusion was a result of the rules not being documented correctly, which is a problem I believe I've resolved.

I think my rationale is more than adequate, and I see no reason why I shouldn't add the section. Do you assent to my content, or do you oppose? As I said, I'll give you time to change your mind, but I'm willing to take this to other venues if you insist. Xcalibur (talk) 05:46, 23 November 2018 (UTC)

I'd like to reiterate that I have the RS to back up this content, including a scholarly journal, which should be enough. I see no reason why I shouldn't put the material up -- at the very least, we can make it more visible and find out what other readers/editors have to say. Xcalibur (talk) 11:08, 25 November 2018 (UTC)

As I've said - if you're unhappy, go to arbitration. Not being nasty here - it's just the next step. This, honestly, the best way of getting a few more opinions as to whether your "rules" would be a useful addition to the article. So far, the few "extra people who have butted in have all been very negative about them. --Soundofmusicals (talk) 03:26, 26 November 2018 (UTC)

As you wish. I made a good-faith effort to come to terms here, but since you're not having it, I'll have to take the next step sometime in the near future. Xcalibur (talk) 12:11, 26 November 2018 (UTC)

Absolutely NOT a matter of "terms' and "negotiation". I have very sincere doubts as to whether you have at any stage been entirely in "good faith" - but in any case that is not the point either. Among other things - we "assume" good faith, whether we really think it is there or not. This discussion has been from the beginning pretty one-sided, as almost nothing you have brought up has any bearing on the essential point - which is whether the changes you propose would make a more useful article. We already cover "barred" or "over-struck" (in Latin terms "vinculum") Roman numerals - they are most certainly not in modern daily use - or the current year would not be MMXVIII, but IIXVIII. Finally - the handful of contributions to this discussion from "outside" have been rather scathing about your "rules" - certainly none have been supportive. Consensus is therefore strongly against you. Throughout this whole thing I have been as patient as I can, but the point was reached long ago when any further (largely ignored) comments from me are a waste of both our times. My suggestion that you go to arbitration is not meant in any negative sense - I am still, believe it or not, trying hard to be as helpful and kindly as I can. --Soundofmusicals (talk) 01:25, 8 December 2018 (UTC)

I don't know why you wouldn't assume good faith, given my constructive efforts. I believe my submission would make the article more useful and informative, as it 1. answers many common questions directly, and 2. sums up content offered by RS. the overline rule is supported by my sources, which is why I included it. You make an interesting point about the vinculum, although my sources do say you can use it to write 7,000 as VII, although M is preferred under 4000. An interesting quandary, which will take some fine-tuning (but I'm sure that can be resolved). The only other contributor to this discussion simply disagreed with my approach in preference to another, but did not get substantially involved; while I see the value in Spitzak's logical method, it is not (to my knowledge) backed by RS, while my ruleset is (which is what counts here). In any case, this hardly qualifies as consensus, and should not be labelled as such -- this is primarily a disagreement between us two. Finally, I do not intend to goad you in any way, I'm simply trying (in vain it seems) to resolve our differences at a lower, informal level, as this should be preferable for all concerned. I will only go through formal channels if you insist. Xcalibur (talk) 16:58, 8 December 2018 (UTC)

Of course, it's quite easy to resolve. IV (4000) is the lowest overline value permitted. I, II, III are not eligible, and M is used instead. It all fits together seamlessly, I just need to express this in an elegant manner and add it to my rules. It seems you've been useful after all -- I hadn't noticed that issue, and your critique helped me tighten a loose screw. Xcalibur (talk) 02:16, 9 December 2018 (UTC)

I found another source, not the most reliable, but very informative: [21] Xcalibur (talk) 05:40, 9 December 2018 (UTC)

(IV) or M(V)? orthography issue

While discussing my ruleset with Soundofmusicals, a relevant point was brought to my attention -- what is the proper use of the vinculum, or overline? It quickly became evident that within 3,999, M is preferred to I. But what about higher figures? Should 4000 be written as IV or as MV? Likewise, should 6000 be rendered as VI or VM? Is one form preferred for the subtractive, and another for the additive? Or is it in fact entirely ambiguous? While I've found plenty of source material backing most of my rules, I haven't been able to get to the bottom of this -- the RS are too vague, and others are contradictory. On all other points, there is consistency and agreement, and this seems to be the final ambiguity to sort out. Perhaps a knowledgeable individual can clear up this matter, or at least point me in the right direction. Xcalibur (talk) 16:22, 9 December 2018 (UTC)

The "wrong direction" you took was right at the beginning - as I tried to point out at the time, and as I, with infinitely more patience than you had any right to expect, have repeated in different words and from various "directions" over and over. Mostly you have either simply ignored what I said altogether (proving yourself one of that tribe who learned to write but never really mastered reading) or you have answered a minor point by distorting what was actually meant. Accept that even angels (which I, alas, am not) tend to get fed up when they are compelled to repeat themselves ad infinitum, and receive no reasonable (in the sense of "conforming to reason") answer at all.

Published sets of rules for constructing RNs are legion (pun), but these (even those in "reliable sources") contradict each other freely and fundamentally - some sets permit forms that others reject as "wrong" - giving not one but several "valid" versions of sundry "problematic" numbers. There very simply is no set standard from which a valid working set of rules compatible with all of the published versions could be assembled.

The article (which incidentally you still haven't read) very specifically and for very good reasons avoids giving a set of rules at all (like many of our very best sources). Much better is what we have - read it PLEASE, or if you have already read it try to understand it. And don't try to come back with something like "I have read it, and I do understand it", because you have proved otherwise practically every time you have posted here. If I am wrong - then do me the courtesy of explaining where and how.

To take just one of your "meanders" - have you EVER seen a Roman Numeral in an inscription or a "document" ANYWHERE for a number larger than MMXVIII (or whatever the current year was or will be at the time)? Well, answer that please. You won't find it. Nowadays we simply don't use "big" RNs for anything but year numbers. So a system that will give us a valid RN for the year for "only" another 1,980 years or so needs expanding? I trow not. Enough of this silliness.

To answer your question, incidentally, a number like 2,345,678 CAN, if you really want to do such a thing, be rendered as MMCCCXLVDCLXXVIII. A very large number - written in this system (which at least one eminent historian doubts the Romans ever used!) consists of two parts - the "overstruck" section which is mutiplied by 1,000, and the remaining odd digits (representing any hundreds, tens, and units). But for goodness sake (to censor the earthier phrase I typed in first) why would anyone USE what is actually an incredibly cumbersome numeric system for anything like that? --Soundofmusicals (talk) 13:23, 10 December 2018 (UTC)

Just by the by - your latest source (Paul Lewis) HAS read the article, and what's more he understands it! Note that he also answeres your problem. BUT we try to avoid sources that have clearly read what we have said - this is known as "circular citation"! --Soundofmusicals (talk) 13:43, 10 December 2018 (UTC)

I don't mean to impinge upon your patience. I'm more than willing to read, and have read plenty of material in the course of research. I'm not ignoring your points, and I wouldn't accuse you of ignoring mine -- rather, I think there's a fundamental difference of opinion here, and our attempts to communicate have not bridged that gap. Nevertheless, I appreciate your willingness to conduct civil discourse.

You claim that sources on modern rules for RNs are all at random and contradicting one another. If that were the case, I'd make no attempt at a ruleset. But it's not true at all; if you review my cited sources, you'll see that they are quite consistent and in agreement with one another (and this applies to other sources I haven't linked). This broad agreement among RS makes it possible to formulate a ruleset and publish it here. I've pretty much nailed it down, almost every aspect of the system is defined, except for this one issue of adding/subtracting thousands in large figures of 4000+.

I read the article. I approve of the 'basic decimal pattern' section, and do not wish to replace it. I wish to complement it with an alternative approach, one that is more technical and precise, which can answer all doubts and concerns (as opposed to the 'decimal pattern', which serves as an introduction). As we discussed earlier, there used to be rules in this article, but they were removed due to the confusion they caused. I say they caused confusion because they were flawed and incomplete; with my comprehensive ruleset, no such issues will arise.

Yes, I've seen very large RNs using the vinculum, they are not commonplace, but do appear in some sources. I wish to treat the subject as comprehensively as I can.

Neither you nor Mr. Lewis answered my question. In the source I linked, he uses BOTH forms, adding 1,000 with an M and an overlined I. Other sources seem to be ambiguous as well -- that's why I want to figure out whether there's a convention, or whether I should create a rule explicitly leaving it ambiguous.

Circular citation is a cause for concern, but afaik he doesn't explicitly reference this article, so it should be fine. Either way, I've got enough RS to justify my addition. Xcalibur (talk) 15:32, 10 December 2018 (UTC)

Just to reiterate, as this is significant: there is a consensus among RS backing my ruleset, and that is my primary justification. Xcalibur (talk) 16:33, 10 December 2018 (UTC)

While I'm at it, my secondary justification: there is room to improve this article with a precise, comprehensive, rule-based treatment, in addition to the existing introduction. Xcalibur (talk) 17:49, 10 December 2018 (UTC)

I do not think a "ruleset" that, in effect, results in 3 repeats of 10 patterns, should take that many "rules". That is my primary objection to your "ruleset". The introductory section is far better and just lists the possible patterns without trying to make a huge set of rules that when intersected produce this tiny set of permutations.Spitzak (talk) 17:17, 10 December 2018 (UTC)

I understand where you're coming from, and I respect your efficient, logical approach to this. However, I think there are benefits to a precise, detailed elaboration alongside a general introduction. While there is in fact some support for your method in the sources, my ruleset is the best representation of the RS consensus. Xcalibur (talk) 17:57, 10 December 2018 (UTC)

Spitzak is not (so far as I can see) suggesting that we substitute a simpler set of rules - he is pointing out that there is no need for ANY formal set of rules at all - especially not in the form of a list of "usages to be avoided". I am sure he will forgive my paraphrasing his posts, and correct me if necessary. The best external sources, in fact, tend not give one! Where they do give a "set of rules" of the kind you advocate they are far from "agreeing" with the "cover all possible bases" approach you have suggested, which you don't seem to even understand yourself (otherwise what's the point of your latest line of questioning?) Nor do they even agree all that closely with each other - especially if we eliminate obvious cases of literal duplication. In fact the very best sources (dictionaries of Latin) mostly just list all alternatives without choosing any one as more "correct" that the others. What we have (once more suggesting that you R-E-A-D it! - and, assuming that it is inadequate in some way, tell us how!) is a description of the "normal" forms generally used nowadays - followed by a non-prescriptive list of (mostly) historical "variant forms". Our aim here is n-o-t to tell our readers what they may or may not do - but to give the simplest possible description of what is nowadays usually done, followed by enough of the exceptions that they can at least recognise these if they encounter them, and "read" them - i.e. work out their numeric value in Arabic numerals. "Who dares do more does nothing", if we may paraphrase Shakespeare in this regard. --Soundofmusicals (talk) 00:14, 17 December 2018 (UTC)

It's come to my attention that I need to revise my ruleset. In addition, I'm busy at the moment. Once all that is squared away, I'll get back to this discussion. Xcalibur (talk) 19:04, 17 December 2018 (UTC)