Talk:Roman numerals/Archive 7

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Modern use of "barred" numbers?

@Bigdan201/Xcalibur In case you do come back, I've rewritten the section on (Roman??) vinculum numbers to clarify what "would" be the alternative forms available if we were to revive their use (although why we would want to do anything of the kind I still really can't think!!!). In case the question asked in the last topic heading is still not understood - we could do away with M altogether - OR we could keep it for CM and the low thousands, before we cut in at IV. In either case M gives us a thousand thousands, a million in other words, as ANY Roman numeral - even one including an M can be "barred" (multiplied by 1,000)! Oh dear, confusing myself now! Do try to get the hang of this sort of thing before you go trying to write rule sets, anyway. Otherwise it's a bit like me trying to write a new set of rules for football. In all kindness, and with all due respect, I do think this is your problem. --Soundofmusicals (talk) 08:42, 19 December 2018 (UTC)

Semi-protected edit request on 11 July 2018

In the summary, please correct "From the 14th century on" as "From the 14th century onwards". Thank you. 81.131.172.92 (talk) 08:01, 12 July 2018 (UTC)

 Done DRAGON BOOSTER ★ 08:31, 12 July 2018 (UTC)

Foolishness - nothing whatever wrong with original text - in fact tone of suggested phrase is stiffer and more pedantic (the last thing we want just here!) with no gain whatsoever in "correctness" or clarity. -Soundofmusicals (talk) 02:08, 14 July 2018 (UTC)

"IVPITER"?

Isaac Asimov, the well known science fiction writer - also wrote an entertaining book called "Asimov on Numbers" which seems to be the origin of the notion that the Romans avoided "IV" as the numeral for "4" in favour of the obsolete form "IIII" - long after other "subtractive" numerals had become more or less firmly established: because it resembles the Roman name for the chief deity, Jupiter (Roman spelling "IVPITER"). This has been long expunged from the article as speculation, but it is speculation by an outstanding writer (on mathematics and physics as well as fiction) and provided we identify it as speculation and give the source, it does seem rather plausible - at least I can't see any reason why it couldn't have been the reason! In any case, after a good deal of soul-searching I have "reinstated" it, in spite of some lingering doubts. What do others think? --Soundofmusicals (talk) 04:02, 3 January 2019 (UTC)

While it sounds like nonsense, as long as it's reputably citable nonsense, it is allowed to be in the article. But debatably the relevance to the core subject (Roman numerals) is weak enough for it to be removed anyway. Renard Migrant (talk) 13:54, 29 January 2019 (UTC)

Less nonsensical than other explanations - at least it doesn't notably clash with any known facts, even if we'd need an ancient or medieval source to take it too seriously. It is intriguing that the Romans avoided "IV" at the same time as using "XL" and other cognate numerals - in fact some readers look the article up specifically to see what we have to say on the subject - so there is perhaps no real harm in mentioning it, while attributing it to our source, and making it clear that it is at best plausible speculation. --Soundofmusicals (talk) 01:10, 30 January 2019 (UTC)

More medieval uses

'Je vous en rench .V^C merchis' (circa 1300).

I'd like to signal the medieval usage of C or M over the top of a number for 'hundred' or 'thousand'. Here's a French example from circa 1300. Also .iiii. and .iiij. can be found easily enough by searching for them on the French Wikisource, should you require them. If you want manuscript originals, I should be able to find some, but it'll take a little bit of time. Renard Migrant (talk) 13:52, 29 January 2019 (UTC)

If you have the time to do this properly - go for your life! The illustration of "iiij" is a most welcome improvement! --Soundofmusicals (talk) 01:15, 30 January 2019 (UTC)

Proposed replacement for descriptive section.

The following has been "tentatively" added to the article - bringing it here so we can discuss it point by point:

Current orthography

The modern era has seen the emergence of a standardized orthography for roman numerals, which permits only one permutation for any given value. While exceptions can be made (notably IIII instead of IV on clockfaces), the modern convention is widely recognized and adhered to, and may be described by the following ruleset:

• Repeated decimal numerals (I, X, C, M) are additive.
• Up to three (3) decimal numerals may be repeated sequentially per power (there may be up to four (4) non-sequential repetitions per power).
• Smaller numerals placed to the right are also additive.
• Smaller decimal numerals placed to the left are subtractive.
• Quinary numerals (V, L, D) may not be repeated.
• Quinary numerals may not be subtracted, only added.
• Only one (1) decimal numeral may be subtracted per power.
• 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).
• Addition may be by any amount that is equal to or less than the adjacent value (not greater).
• Powers of ten are dealt with separately, ordered from greatest to smallest and from left to right.
• Addition/subtraction operations are to be applied to the rightmost numeral per power.
• Fractions may only be added to the right of all numerals (not subtracted).
• Addition/subtraction should not be redundant (eg X should not be IXI).
• If there is no adjacent value, a numeral may be entered ex nihilo.
• Roman numerals are positive integers with pre-defined values.
• Placing a bar (vinculum) over a numeral multiplies it x1000.
• The vinculum is used for values of 4,000 and greater (it is not used up to 3,999).

Comment on the above

1. For starters - can anyone actually explain what any of the rules actually means? Not just for a newbie to Roman Numerals, but for me? I'm serious - I think I can decode "decimal numbers are additive" (although the existing text makes the same point in a far more intelligible way) but (just for one example) "a numeral may be entered ex nihilo"? or "Addition may be by any amount that is equal to or less than the adjacent value (not greater)". There is no point whatever in including any rule that is not clearly intelligible, surely? If it is only intelligible in terms of the existing description, then what do we gain by repeating it?

2. Modern use of Roman numerals does not normally include fractional values, nor do we in practice ever use them for numbers over 3,999 (although in both cases we could). A description of the historical use of Roman numerals for fractions and large numbers is already in the text, but neither question is one we could summarise in a "rule", and in any case does not belong in this section.

That might do for the moment from me! --Soundofmusicals (talk) 00:27, 21 November 2018 (UTC)

First of all, I suppose it's prudent to bring it to talk page to discuss first. I debated over which rules to include or exclude, and found they ranged from 12-16. I decided that it would be best for me to take an 'all-in' approach, then weed out any rules deemed unnecessary. I want comprehensiveness, clarity, and simplicity, and maybe elegance too -- if I can achieve that with less rules, then that's for the better.

ex nihilo rule: this is very technical and formal. it's basically telling an uncooperative computer program: 'if there's nothing in the field, you can add a numeral'. There was a similar thought behind my 'positive integers' rule: it's telling the evil computer program that it can't willingly misinterpret the numerals.

addition equal/less: this is defining that you can add a numeral that is equal or less, but not greater, e.g. IV can't be 1 + 5, it's 5 - 1.\

fractions: I put this in because it seemed correct, and it covered more ground. but you're right; fractions are not typically a part of modern usage, and my sources were rather thin on that point anyway. I'll confess, I was going for an aesthetic style here, but I can still achieve that without the fractions rule.

I think my rules are intelligible by themselves, although they may be excessive. I'm willing to reduce them as needed. It is relevant to note that all the rules you've criticized are also rules I've debated and considered expunging -- you seem to take less issue with my 'core' rules. I've taken the liberty of 'striking through' rules that I'd be willing to exclude from the section. Once again, I appreciate your willingness to confer. Xcalibur (talk) 02:05, 21 November 2018 (UTC)

eta: I struck through a few more rules. turns out, I can get this down to 11 rules, but I'm not sure if I can go much lower. Xcalibur (talk) 02:33, 21 November 2018 (UTC)

Another point: I don't want to replace the descriptive section. Rather, this can go alongside the 'basic decimal pattern' overview, as I believe they are complementary. Xcalibur (talk) 02:48, 21 November 2018 (UTC)

Just as well I put the following into a separate section so we avoided an edit conflict here! But, for the record the following section was added while you were replying to my comments. The basic problem with your "rules" is not that they include lines that are redundant or inapplicable - but that they are REALLY hard to understand - we're trying to help fellow humans who may not have pre-existing knowledge of the subject, but DO have a certain modicum of common sense - although I have seen (I suspect) every possible way of putting rules for a computer during the years I set it as an exercise for my programming students it is in every case something quite different! --Soundofmusicals (talk) 03:29, 21 November 2018 (UTC)

I thought they were clear enough. And as I said, this is meant to be complementary to the 'basic decimal pattern' section. there's no reason we can't have both a common sense overview and a technical ruleset side-by-side. Also, I'm building off the RS instead of inventing my own approach, which I think is significant. and to add on, I changed the strikethrough to italics for the addition rule, as I'd like to keep it. Xcalibur (talk) 04:06, 21 November 2018 (UTC)

Have a look at the "rules" suggested in the next section. Each rule here is self-explanatory - in the case of possible ambiguity an explanatory note is added, and finally, where examples are needed to complete the clarity they are added. --Soundofmusicals (talk) 04:21, 21 November 2018 (UTC)

References

Semi-protected edit request on 17 February 2019

"Roman numerals began to be replaced in most contexts by the more convenient Arabic numerals" to "Roman numerals began to be replaced in most contexts by the more convenient Vedic Indian numerals" Shah18shivam (talk) 05:12, 17 February 2019 (UTC)

 Not done. Please establish a consensus on the talk page before making this request. –Deacon Vorbis (carbon • videos) 03:07, 19 February 2019 (UTC)

Semi-protected edit request on 20 March 2019

I the roman number for 4 is not IIII, but IV. Edu.alc (talk) 16:03, 20 March 2019 (UTC)

 Not done: This is discussed in the article. IV is more common now, but IIII is the original notation and is still used in some places today (clock faces, in particular). ‑‑ElHef (Meep?) 16:44, 20 March 2019 (UTC)

Pointless "rn" template

The "rn" template does not seem to have any advantage over writing the numbers as plain text, like "MMCDXXV". On the contrary:

• It makes the text a lot harder to edit.
• It also formats the numbers as math, which may look rather bad depending on the reader's choice of text fonts, and on the device used. (On my screen, the letters of "MMCDXXV" are signifcantly taller and wider than those in "MMCDXXV".)
• Since editors cannot be forced to use it, articles that use that template will often have also numerals without it; which will look bad.
• On my screen at least, when the overline notation is used, the template does not leave any space between the letters and the overline; so that one can hardly tell the difference between X (or M, or V) with overline or without it.

Thousands of templates have been created by well-meaning programmers, but very few -- maybe only a couple of dozen -- are really a positive contribution. Each new template intrinsically makes editing more complicated, and thus scares potential contributors away. Most templates make editing harder, not easier, even for editors who understand them. A template must have HUGE advantages to overcome those two big disadvantages. I don't see that in the "rn" template.
All the best, --Jorge Stolfi (talk) 07:44, 18 April 2019 (UTC)

The specific "Roman Numeral" font is very useful indeed, with its slightly different and embolded letters. In this article, at least, we actually want them to stand out, and the template is the easiest way of consistently producing this effect. I can't see that Roman Numerals in another article, where they are probably much more "incidental", necessarily look "untidy". A classic example of a "good" template, in fact. The template may make the article a little more difficult to edit - perhaps we need a little note somewhere about cut'n'pasting the template and inserting the specific number. I do all my templates this way, to be honest. Sorry to disagree so comprehensively - but it's bound to happen now and then. What do other editors think? --Soundofmusicals (talk) 10:07, 18 April 2019 (UTC)

I missed the point about "barred" numerals, like XXVCDLIX (25,459) not displaying well in some fonts. In my experience they are just fine in most fonts, but if they are bad in some others we may have to fix this (probably with another template, I'm afraid! --Soundofmusicals (talk) 10:16, 18 April 2019 (UTC)

Capitals vs lowercase

The article should explain that Roman numerals are usually written in upper case because lower case letters were developed only in the Middle Ages. In medieval manuscripts, in fact, they are often written in lower case, like mcdxxi. This style is still used in some contexts, such as numbering the "extra" pages added before a book (title page, table of contents, etc.) and numbering items in lists "i)", "ii)", etc. Italic font is often used in these cases. --Jorge Stolfi (talk) 07:51, 18 April 2019 (UTC)

It already does. We discuss lower case Roman numerals in the Middle Ages section (the logical place, really) and there make exactly the point you are asking for. We'd really have to mention them here and bringing it up eslewhere would produce all kinds of duplication and forward referencing. (IMHO) Sequencing the information in an article like this is not straightforward, however, things logically cross over a bit. Possibly no 100% foolproof way round this --Soundofmusicals (talk) 09:57, 18 April 2019 (UTC)

Oops, I missed that. Sorry. --Jorge Stolfi (talk) 00:17, 19 April 2019 (UTC)

No worries - s/he who never made a mistake never made anything! --Soundofmusicals (talk) 08:00, 19 April 2019 (UTC)

Remarks on early history

About the historical section:

• "One hypothesis is that the Etrusco-Roman numerals actually derive from notches ..." It should be emphasized that this theory is largely conjectural. So the paragraph should start as "In 1983, Foobarevsky advanced the theory that the Etrusco-Roman..."

• "Likewise, number four on the stick was the I-notch that could be felt just before the cut of the Λ (V), so it could be written as either IIII or IΛ (IV)." This part of the theory seems rather questionable. It seems to be trying to explain the subtractive notation, that may not have been used for centuries. No?

• This page presents an interesting view of the early symbols. In that theory, the symbols for 10 and 50 were not "a crossed double notch" and "a three converging notches" (or "a V and a I together"), but rather the symbols for 1 and 5 modified by one extra stroke. Likewise the symbol for 100 was not "three crossing notches" or "an X and a I combined", but the symbol for 1 modified by two extra strokes.
  There does not seem to be evidence that this is how the writers then "saw" those symbols; but it is the sort of simple and straightforward system that someone would have devised, in the absence of any previous tradition.
  The pattern breaks down for the symbols that are given there for 500 and 1000, though. So maybe those symbols came from a different source, at a different time?

• That blogpost also implicitly suggests that the "apostrophe" notation ("CIↃ" etc.), as well as the capital Greek letters Φ or Ψ, are not original, but merely corrupted forms of the original symbols shown there (crossed circle and half of it).

• In modern usage, roman numerals are commonly printed in the so-called "Roman" font, with serifs; and that is how they look like in ancient Roman monuments. However, the serifs are almost surely an accidental product of the medium. When letters are chiseled in stone, the way to give the strokes a "clean" look, and make all letters stand evenly on the baseline, is to finish (or begin) each groove with a short transversal strike of the chisel.
  In printed books, on the other hand, serifs were adopted since the beginning to make the letters more distinguishable in spite of uneven inking, worn type, paper blemishes, etc.; that was the origin of "Roman" fonts. (Another approach for that problem, but only for lowercase letters, was the "Italic" style, that used modified curvy shapes for the same purpose.)
  The point is that, in the computer age, there is no reason why Roman numerals should be typeset in special font (Roman, with serifs), rather than on whatever font is used for normal text. For Wikipedia, in particular, readers who prefer skins with sans-serif fonts (like I do), serifed roman numerals look weird and ugly.
  I would be very surprised if the Romans themselves put serifs on the numbers when writing them by hand (on papyrus or on waxed tablets). And I seem to remember several ancient stone inscriptions of a more modest character (like gravestones) where the numerals, like ordinary text, did not have any serifs.
• By the time Rome became an Empire, they certainly needed to write down numbers larger than 3999 (or 4999) for military and civilian administration. Most such writing was on papyrus or waxed tablets, and hence most ofit has been lost. But there should be at least a few surviving examples. If so, it would be nice to cite those explicitly, rather than vague statements like "at some time, the convention developed...".

All the best, --Jorge Stolfi (talk) 01:37, 19 April 2019 (UTC)

The text of the history section of this article is very old (more or less as ab initio - that it as the article was originally written, years before I ever had to do with it) unlike other sections that have been edited and added to many times since then. It is very hypothetical, and could very well be better phrased. I'll leave that to you for the moment, anyway --Soundofmusicals (talk) 07:48, 19 April 2019 (UTC)

Alas - apart from inscritions on stone (and most of THOSE are lost) most "old" written examples of Roman numerals in daily use come from Medieval and later times and are not very helpful in this context. --Soundofmusicals (talk) 08:00, 19 April 2019 (UTC)

Python algorithm

Maybe there should be a section for programmers, with code to read and write Roman numerals. Here is my attempt, in the Python3 language. Or should it go to some other place, like Wikisource?
(I am sure that there is already a python library somewhere that performs this function; and I have not used all fancy python tools like regular expressions. However, the point is to show the algorithms, in a way that even programmers who are not fluent in python can easily understand, and reimplement in whatever languages they like.)
--Jorge Stolfi (talk) 06:13, 20 April 2019 (UTC)

There WAS one once I think. Go back in the archives of old versions of the article and have a look. I once (MANY years ago) taught beginning programmers in good old BASIC (GOTOs strictly forbidden) and something similar was one of the fairly early assignments I used to set. Great fun - especially when (as sometimes happened) someone came up with a novel approach! Personally I tend to feel better in its own article, if at all. --Soundofmusicals (talk) 23:26, 20 April 2019 (UTC)

More doubts about Asimov's "IVPITER" theory

The Colosseum article states that only entrances 23 to 54 survive. So how did Asimov know that entrance 4 was "IIII" not "IV"?
He could not have been referring to 24,34,44,54, because his "IVPITER" explanation would hardly apply to ""XXIV".
(By the way, is the "4" on those gate numbers also "IIII", or "IV"?)
Did Asimov base his claim on some old description of the Colosseum, from a time when gate 4 was still standing? Or was he repeating a claim made at such a time?
Besides, if the Romans had superstitious qualms about "IV", how did Julius Caesar write his own name?
I now suspect that Asimov's theory today would be twitter-level material...
(Let's assume that the Romans did in fact use "IIII" on Colosseum gate 4, but not on gates 14,24,...,74, nor on gates 9,19,...,79. My own "twitter theory" to explain that anomaly is that "IIII" is still short enough to be easily readable, and required only a little more chiseling than "IV", so they did not bother to use the latter (and common folk probably did the same in their writing, for the same reasons). Whereas "IX" is clearly much better than "VIIII" in all respects (and common folk probably wrote "9" that way too, for the same reasons). Once they decided to use subtractive notation for 9 (and 19,29,39,..79), it would be natural to use it also for 14,24,34,...,74. Besides, while "IIII" is still sufficiently readable, "XIIII", "XXIIII" etc are increasingly less so.)
(But here is another "twitter theory", free if you buy the first one: maybe the Romans tended to avoid "IV" for 4 because it could be mistaken for the abbreviation of Latin names like "IVLIVS", or some other Latin word like "IVVENES", and that could have created confusion -- in letters and such, if not at the Colosseum gates. Such confusion between numbers and abbreviations could not arise for any other subtractive numerals. It could have arisen for "VI" and "I" -- but there was no alternative way to write these two.)

Various thoughts on that one but I'll stick to the strictly relevant. (We are supposed to be about improving the article here, not running a forum). We originally accepted Asimov rather uncritically, along with a lot of other peculiar theories - then someone pointed out it was only a theory and it got wiped - then finally I re-inserted it myself, while making the point it is complete surmise, albeit reasonably intelligent surmise. The main reason I did this, to be honest, is that is has gained a surprisingly wide currency (lots of people believe it is "true") - and we need to mention it, even if just to say that it "ain't necessarily so". --Soundofmusicals (talk) 23:55, 20 April 2019 (UTC)

"We are supposed to be about improving the article here, not running a forum" Indeed, but I could not resist. 😊 As an excuse: those two "twitter theories" of mine should show that Asimov's is very flimsy, and requires more support, for or against. I agree that it should be left in the article, with emphasis on "speculation". --Jorge Stolfi (talk) 02:35, 21 April 2019 (UTC)

Glad you agree about one thing, at least! --Soundofmusicals (talk) 14:29, 21 April 2019 (UTC)

Too many changes in one go!

Let's work from the top down - what exactly is wrong with the lead section "pre-edit". Drastic changes to an article need a consensus. So far you have made statements - some of which I have disagreed with. We probably need to get other people's considered opinion on each point - just barging in with a massive re-write, with nothing more than your opinion and my disagreement is not the way to go. --Soundofmusicals (talk) 14:09, 21 April 2019 (UTC)

• It was not a massive rewrite, just a reordering of the material and small changes to your text. Please take the time to understand the changes before reverting other people's work. There is no rule in Wikipedia about doing "too much work" on an article. --Jorge Stolfi (talk) 14:15, 21 April 2019 (UTC)
• I see that you have reverted again my work without eve bothering to check it. Please restore my version, and then we can discuss why do you think that it is worse than the previous one. Thank you. --Jorge Stolfi (talk) 14:24, 21 April 2019 (UTC)

I'm afraid you have it back to front. Changes to an established article need to be discussed first - attempts to "blast through" like this with no consensus for the changes is not the way to go. Let's work through each section one by one. The lead section should (among other things) not confuse the reader with detail that can only confuse "out of context". Subtractive notation (in itself a very simple concept, but one that causes much undue confusion) is far better treated in context - we don't need the unnecessary and confusing forward reference to it that you add to the lead. Let's look at that first. And as I said - let's get some "third opinions" if we can. We do need to reorganise something coherent for a "third party' to negotiate, however. --Soundofmusicals (talk) 14:39, 21 April 2019 (UTC)

Again, there is no such rule against "too much work", or having to get permission from other editors before improving an article.
In the substance, my changes were minimal -- and, I would way, for the better. The changes to your section were mostly wording and formatting. Most of my work was sectioning and reordering the existing material, without changing it.
Since you give the values of symbols in the lead section, it is important to warn the reader that there is more to the system than just that table.
Again, if you have concrete objections to some of my changes, at least revert only those changes.
--Jorge Stolfi (talk) 14:51, 21 April 2019 (UTC)

Lead section

Here is a detailed "blow by blow" of your additions to the lead - just for starters.

• Wow. Can you entertain for a moment the idea that others can have different opinions, and maybe even improve your text?
  The head section is supposed to be a summary of the important points of the article. For some topics like iron, whose head section is a whole page, the bar for deserving a place in that section is rather high. But this head section is very short, so there is no reason to omit significant information that can be conveyed in one sentence. Please think of why readers will come to this page, and what the head section should do for them...--Jorge Stolfi (talk) 19:02, 21 April 2019 (UTC)

You seem to be deliberately missing the point. The idea is to get a better article, not evaluate different opinions - I honestly thought better of you. OK lets wait for a consensus that says your opinion takes precedence. Do this, please - as the onus is on you, as the promoter of the change(s). There is no set length for a lead section, but it is supposed to be a succinct summary, not a mini article, especially it a case like this, where the article covers a lot of incidental topics, by no means all of which are sufficiently "central' to need tratment in the lead. --Soundofmusicals (talk) 20:27, 21 April 2019 (UTC)

• I have run into this sort of situation several times, on both sides. It is natural to disagree, and to be upset when someone else changes your texts, or when someone discards your hard work. Those are human reactions, and not reasons to think badly of the other side.
  If you check my edits to the "Method" section, you will see that I have been much more limited in the second round, for respect to your opinions. Could you please show the same consideration for mine? --Jorge Stolfi (talk) 22:50, 21 April 2019 (UTC)

• However, the symbols "I", "X", and "C" could also have negative values (−1, −10, and −100), depending on their conext.

1. This seems to be a vague hint about "subtractive notation". In itself it is flat misleading - the Romans didn't have "minus numbers" or "negative values" as such. For someone totally new to RNs it is "forward referencing" and conveys no information whatsoever - to most readers, who either understand RNs or think they do it raises, even endorses, preexisting (and possibly mistaken) ideas they might have, which it is the function of the rest of the article to correct or perhaps debunk. All in all, NOT a helpful addition to the lead.

• Indeed it is a warning that the table is not all there is to it, and that those values might have to be subtracted rather than added, depending on the context. The Romans definitely knew subtraction, and that is how they understood "IV" and "XL", ever since they invented that notation. For readers who don't know how Roman numerals work, that is information -- important information. For those who already know, that sentence cannot possibly cause disagreement or confusion.
  If you object to the minus signs, we can omit them; but once you give the table, there simply must be a warning that the numbers may have to be subtracted, rather than added, to get the number's value. --Jorge Stolfi (talk) 19:02, 21 April 2019 (UTC)

On what grounds "must" we - isn't this sort of language doing what you accuse me of? As for subtraction, the minus sign hear indicates a minus quality, which was not something the Romans used. "IV" assuming we are counting UP indicates "the number before five" rather than "five minus 1". Think of Roman numbers as a series and you might start to get hold of the basic idea. I've never likes that "subtractive" term - it seems to have been devised specifically to make a simple concept difficult. --Soundofmusicals (talk) 20:27, 21 April 2019 (UTC)

• We must not give the reader information that would be quite misleading because it is incomplete. The table is great, but if there is no warning about subtractive cases, it effectively gives wrong information to the reader who does not know how the system works.
  Anyone who can count will know that taking one sheep away from 10 sheep leaves 9 sheep. The shepherds and farmers in that region surely understood that simple math, well before they started writing numbers down. The idea that subtraction is an "advanced" concept, and that therefore they must have though of "IV" as "one before five" but not "one less than five", is speculation that borders on nonsense, probably confusing language with ideas. (Like debating whether black is a color or rather the absence of color. Or whether zero should be considered a "natural" number.).
  Besides, you said yourself that the first goal of the article should be to explain the system as it is used today, not as it was developed (which seems to be mostly speculation at this point) or how the Romans used it. Thus it is immaterial how the pre-Etruscan pheasants or the Romans understood "IV", or whether they used negative numbers. For that goal, and for the modern reader, the sentence I wrote is perfectly fine. So would be a sentence that says "should be subtracted" rather than "have negative values", if you prefer. --Jorge Stolfi (talk) 22:50, 21 April 2019 (UTC)

• Examples of roman numerals are "XXX" (meaning 30), "LXXVIII" (78), "XIV" (10−1+5=14), "MMXVII" (2017), and "MCMXCIX" (1999). Since the Middle Ages, lowercase letters have also been used, as in "viii".

Not in the lead. Until we have had a look at the way RN symbols are used, examples like this are not meaningful for a reader with no background, and impart no information to a reader who has seen RNs "in action" already.

• Yes, examples are definitely needed in the lead. Think of the reader who does not know what RNs are. Those examples alone will tell him half of what the body of the article has to say, and help him better follow the explanation.
  That is simply good teaching practice: show a couple of examples first, then teach the general theory. --Jorge Stolfi (talk) 19:02, 21 April 2019 (UTC)

This is an encyclopedia - not a school lesson. But even then, your examples are questionable - especially the XIV one, which implies that one is subtracted from ten and then added to five! (NOT the same thing! --Soundofmusicals (talk) 20:27, 21 April 2019 (UTC)

• Well, the original explanation of how the system works was already a quite bit beyond "encyclopedic" and well into the "school lecture" territory. A purely encyclopedic article would start describing the subtractive notation in two paragraphs, leaving the additive system for the "Alternative" section — and without speculating on why 9 is written "IX" instead of "VIII".
  However, a Wikipedia article should try to explain the topic to the likely readers in the way that is most effective for them. Thus it should use any devices that may help achieve that goal. Examples would certainly help a significant subset of the readers.
  As for the "XIV" example, would you accept "(10+(5-1)=14)"? That is as close as one can get to the way a modern reader will parse "XIV".
  And it is fitting, even to Wikipedia, to justify the subtractive notation (as in your original article) by pointing out that "VIIII" is more cumbersome than "IX"; not just when reading, but also (and probably more importantly) when writing, or chiseling in stone. --Jorge Stolfi (talk) 22:50, 21 April 2019 (UTC)

• Roman numerals remained in current use throughout Europe long after the decline of the Roman Empire, through all the Middle Ages. From the 14th century on, they began to be replaced in most contexts by the more convenient Arabic numerals; however, this process was gradual and stretched into the Renaissance.

3. This paragraph is notably clumsier than the existing text. The point we are making is that although we have been using "modern" numerals since the 14th century, their replacement with Roman numbers happened very gradually - AND CONTINUES IS SOME CONTEXTS TO THIS VERY DAY!!! (Otherwise we would have no practical need for an article like this at all!!!)

• Note the word "current". Maybe it should be replaced by "everyday" or "practical". The point that the head section should make is that the Roman numerals were the only system used in Europe by common folks, for counting and measuring things until the 1300s; and ANs replaced them in those uses gradually, in a process that stretched into the 1600s or later. But today they are not used for those purposes, except for a couple of very limited contexts where they barely get up to a dozen or so. In most current uses, they are chosen only because of tradition (like in volume and chapter numbers -- where they are losing ground too) or for style, to impart a "classic" or "monumental" air to something.
  And of course Wikipedia would need an article on them even if they were completely extinct -- like it has one on Egyptian numerals. --Jorge Stolfi (talk) 19:02, 21 April 2019 (UTC)

• The use of Roman numerals for practical purposes has since ceased, and today they are adopted, for reasons of tradition or style, only in a few non-critical contexts—like volume and chapter numbers in books, hours in clock faces, and dates in monuments.

4. This is far from a meaningful summary of current uses of RNs. Apart from the fact that their use has NOT ceased at all (point of the article). Reasons why they are adopted? This is simply not matter for an encyclopedia - and does not (or should not) occur elsewhere in the article. There are (we might surmise) many "reasons" why they have not totally died out - but these are all speculation. Tradition? Style? perhaps, but many others too. Scientists and mathematicians also find them useful on occasion. Many other uses might look like empty affectation - but the that would be a value judgement. On the whole NO!

• About "ceased" or not, see the point above.
  Of course an encyclopedia should try to explain why something is used. Like, why nails are used in some situations, and woodscrews in others. That is not a value judgement, but a summary of the contexts in which those numbers appear (or fail to appear), and the objective advantages and disadvantages of using them in each context.
  The article must inform the reader somehow that there is no rule or practical logic mandating roman numerals on clocks, monuments, or Olympiads; and that people chose to use them in those contexts purely for reasons of tradition or style. (Or to obfuscate the public, like in copyright notices of movies. Didn't the original article say that? Now, that is a value judgement...)
  The only cases where Roman numerals are used for non-stylistic reasons (and that too should be said in the article) is when it is handy to have two separate series of numbers that are visually distinct.
  * One example is numbering pages of "front matter" like TOC, title, abstracts, etc. that are attached to the front of a book or thesis, so that page 1 (Arabic) is the start of the actual text. But those numbers (which are always in lower case -- hence the reason for saying that in the lead) rarely get over a dozen or so.
  * Another such use is in nested lists, where the two styles are used in different levels, so that the items get numbers like IV.3.a or 3.C.ix. But clearly the advantage here is slight to negative, especially if the numbers can get above a dozen.
  That was also the reason for their use in chemistry, but the same caveats apply. --Jorge Stolfi (talk) 19:02, 21 April 2019 (UTC)

Why does the article "need" to explain "why", when any such explanation would be speculation? You could put some o this sort of thing in a blog (or even an academic book or article, but we either avoid speculation, or assign it to a source, in a context like this. --Soundofmusicals (talk) 20:53, 21 April 2019 (UTC)

• Again, that is not speculation by us. It is a fact that people nowadays choose to use RNs on clocks, monuments, Olympiads, conference issues, chapter and volume numbers, or even monarchs and generations, for no objective reason or official imposition; and they could choose to use Arabic numerals instead on all those cases, and often do. Even the chemists will commonly write "iron(8+)" rather than "iron(VIII)", and IUPAC now numbers the columns of the periodic table with ANs rather than RNs. Even those two "practically motivated" uses that I mentioned above could use ANs instead of RNs, with no loss. (Front pages could be numbered "F1", "F2", etc., and similarly for nested list items "3.2.1 or "3.B.§1" etc.)
  It is also unquestionable that most of those uses continue only for reasons of tradition or style. Even when there are bureauratic regulations or standards that specify RNs, the reasons why they do so are not practicity, but tradition or just arbitrary choice. I am pretty sure that one can find plenty of "reliable" sources, like manuals of design, that say so.
  That fact is useful information that definitely belongs in the article, much more so than Asimov's speculations about why the Romans didn't use "IV" on the Colosseum. Think of the reader who wonders why some contemporary clocks and monuments still use RNs, and comes to Wikipedia hoping to find the answer. --Jorge Stolfi (talk) 22:50, 21 April 2019 (UTC)

• The largest number that can be properly written in the basic Roman number system is 3999. Although the Romans and Medieval writers had several ways to denote larger numbers, they do not mesh well with the basic system, and are no longer relevant today—except for reading some ancient texts.

5. Is it? We may come to a similar conclusion, but this, again, is only confusion in a lead section. And what's this "properly" business anyway? There's no "properly" about it, really, as there's no fixed set of rules that's universally followed - there wasn't in Roman times, there certainly wasn't in Medieval times, and there really isn't nowadays either, albeit we tend to be more dogmatic about such things nowadays than used to be the case. Again - the actual question is well covered (as it should be) in the article - but it doesn't need vague foreshadowing here. And if you actually want to write 4,000, nothing to stop you writing "MMMM", or "IV" (overstruck). The real reason for not doing so is not that you "can't" but that there is no need! --Soundofmusicals (talk) 15:55, 21 April 2019 (UTC)

• Strike the word "properly" if you must, but there is no question about what the "basic Roman number system" is -- namely, the subtractive notation applied consistently at all powers-of-ten.
  Again, there is no reason to omit from the head the information that Roman numerals cannot be used in practice above 3999, because, being outside the "common" system, people would not understand them. That fact alone is reason to not use RNs for things that could go higher than that, like street numbers, zip codes, pages of an encyclopedia, products in a catalog, etc..
  And that information in the head would also serve the reader who knows RNs for the common uses, but comes to this page because he wants to know how one would write 7235 in them. --Jorge Stolfi (talk) 19:02, 21 April 2019 (UTC)

The first rule of all is to make sure that all information is entirely factual. There IS a "way" to write any number whatever in Roman numerals - provided you are prepared to go outside the usual (modern) system. The problem is, why would you? Since it is arguable that RNs are used in quite enough contexts, without wanting to invent more. Most people have real problems reading year numbers in RNs! --Soundofmusicals (talk) 20:53, 21 April 2019 (UTC)

A compromise lead section

I am still unconvinced we NEED an examples/common modern uses paragraph IN THE LEAD. But what about something like this? Our examples, instead of being picked at random, are in themselves instructive - treating the two contexts in which practically everyone has seem Roman numerals! And, incidentally, giving an early example of subtractive notation, and an instance of its avoidance. If we were to add this to the current lead one would want (perhaps) not to re-use the "current year" trick, but find another example in the main text. Does this meet your objections?

Many common uses nowadays assume that low values are to be used - for instance the familiar hour numbers on a Roman numeral clock face, that are confined to the series from 1 to 12. Like this:

I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII

It is however traditional on a clock face to represent the number 4 (usually IV, signifying "the number before five") as IIII (signifying "four units").

On the other hand very large numerals usually indicate year numbers. Years in the last century started with the notation MCM (for 1900) signifying "a thousand, and a hundred less than another thousand". For example 1912 would be written MCMXII. This century's year numbers start more simply, as MM (for 2000). Thus the current year is MMXXIV. In practice modern Roman numerals are almost never used for a number larger than the current year.

• Those would be great examples in the lead section, thanks! May I suggest a slightly different text:

---

Roman numerals are still commonly used on clock faces, where the hours from 1 to 12 may be written as

I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII

The notations IV and IX can be read as "one before five" (that is, 4) and "one before ten" (that is, 9), respectively. On some clock faces, however, 4 may be written IIII, and (very rarely) 9 may be written VIIII.

Roman numerals are also often seen on monuments and buildings, denoting year numbers. For example 1912 would be written MCMXII; the notation MCM here signifies "a thousand, and a hundred less than another thousand" -- that is, 1900. Years in the current century start more simply, as MM (for 2000). Thus the current year is MMXXIV. In practice, modern Roman numerals are almost never used for a number larger than the current year.

---

--Soundofmusicals (talk) 21:56, 21 April 2019 (UTC)

The lead section

There is a useful sequence to the lead section that we want to keep if we possibly can.

1. The "definition" paragraph: what ARE Roman numerals?

2. A VERY brief history: basically - they persisted for centuries, and we still use them for some things.

3. Examples: just the two most commonly seen ones, lots more later on in the article. The examples we picked are both "public ones" - clock faces and year numbers. If we decide we want some more examples here they would be best in their own sentence rather than sandwiched in with the years!

Welcome attention had led to these three becoming "crossed".

And while concision is important - the new "table" of Latin characters used for RNs was not very clear, and I have restored the old one for the moment (although we may very well devise another that is as easy to read but more concise.

Finally - given that clock face numerals are so pervasive and that they do make the best possible "first example" we actually use "IIII" instead of "IV" in this context - just a brief note to this effect will head off the obvious question at the pass!

--Soundofmusicals (talk) 23:24, 22 April 2019 (UTC)

This contents is fine with me. I would like to be a bit more precise with the history (the only system in use in Western Europe until the 1300s, except in Greek texts; sporadic use for numbers in general seems to have continued until the 1600s-1700s, but died there, surviving only for the specific contexts.).
As for "IIII" versus "IV" in clocks, it does not matter which is in the list and which is in the following text; but, for the sake of readers, I think it is better to be consistent, to make the paragraph easier to read and understand. So either "IIII" and "VIIII" in the list, and "IV" and "IX" as alternatives, or the other way around; not mixed.
Also, I would write "many clocks" rather than "most clocks", unless we have some reliable source with statistics. Perusing images on the internet, I see many with "IV". Maybe "IIII" is 80%. Also, maybe those "IV" are "amateur" clockfaces (e.g. computer graphics ones); on the other hand, it may also be a regional thing, e.g. British/American clockmakers like "IIII", but not those in other countries. Or vice-versa. Anyway, "many" seems safer.
By the way, the life of Roman Numerals for general counting seems to correlate with the life of Latin as the language of formal writing, which also started to be replaced by vernaculars in the 1300s and mostly died out in the 1600-1700s. Except that, in those later centuries, authors generally opted for Arabic numbers for general counting even when writing in Latin. --Jorge Stolfi (talk) 14:52, 23 April 2019 (UTC)

I'm pretty certain that there are *FAR* more clock faces with IIII and IX than with VIIII, so I certianly would not use VIIII in any example!!!Spitzak (talk) 23:20, 23 April 2019 (UTC)

So I would use "IV" and "IX" in the example (as in the Big Ben!), and then note that in many clocks have "IIII" instead of "IV", and some may/mught/could have "VIIII" instead of "IX". --Jorge Stolfi (talk) 09:32, 24 April 2019 (UTC)

Here is an example of Roman numerals used for general counting in the 1400s (Johannes de Sacrobosco, John of Holywood, Tractatus de sphaera):

Aufer vigesimam secundam partem de circuitu terræ: et remanentis tertia pars hoc est octingenta et clxxxi stadia et semis et tertia unius stadii erit terreni orbis diameter sive spissitudo.

"take away the twenty second part of the circuit of the Earth: and the third part of what remains, that is, eight-hundred and CLXXXI stades and a half and one third stades, would be the diameter or thickness of the terrestrial globe."

That is, diameter = circumference x (1 - 1/22) / 3 = circumference/3.1429...). The site I got that from translated "octingenta et clxxxi" to 80181. It seems that in the Middle Ages the "stade" (Latin stadium, Greek stadion) was 185 meters; the correct diameter of the Earth, as we know now, would be 68775 stadii, so that seems to be the correct reading. --Jorge Stolfi (talk) 15:25, 23 April 2019 (UTC)

Removed possible original research

I removed this paragraph with no source, because it seemed to the the original theory of some editor:

Another possibility is that each I represents a finger and V represents the thumb of one hand. This way the numbers between 1–10 can be counted on one hand using the order: (P=pinky, R=ring, M=middle, I=index, T=thumb N=no fingers/other hand) I=P, II=PR, III=PRM, IV=IT, V=T, VI=TP, VII=TPR, VIII=TPRM, IX=IN, X=N. This pattern can also be continued using the other hand with the fingers representing X and the thumb L.

The proposed hand signal for "IV" seems to have been invented to explain a notation that may as well have been devised only much later, and only to save strokes in whring. As a hand gesture, it saves nothing. I find it hard to believe that the farmers of 800 BCE Latium would use such unnatural system. But we may reinstate this text if someone provides a notable source for this theory. --Jorge Stolfi (talk) 22:38, 24 April 2019 (UTC)

Well done! After a rather shaky start (requesting information that was already there) you may now be well up with the few people who have actually read this whole (let's face it, somewhat useless) article from beginning to end. I am tempted to give you a barnstar to that effect. Honestly, aren't you getting rather bored with it too? 😀 --Soundofmusicals (talk) 00:02, 25 April 2019 (UTC)

The article is far from useless; in fact it is quite important! Wikipedia is not meant to be just a manual of useful recipes!
I have edited a bit the article on Etruscan numerals, which clarified a lot of things about the history of Roman Numerals. It makes some parts of this article superfluous, because it is clear that the Romans inherited the number notation from the Eruscans, including the symbols. The Romans may only have added the subtractive notation, presumably as a hack to save time and space. (However there is one Etruscan site that uses it too. It is described in Heems, but I did not have time to read the details. It may be back-influence of the Romans to the Etruscans.) So the speculation about hand gestures and tally sticks belongs there, not here. Have a look. --Jorge Stolfi (talk) 13:34, 25 April 2019 (UTC)

Actually an excellent way of learning about a subject - trying to improve its Wiki article (and preserve it from vandals, wild and wooly O.R. and other degenerative forces). I have been fiddling with the edges a little, as you have probably noticed, but my initial interest has been wearing very thin lately, to be perfectly frank. One thing I notice about your expanded history section is that it is very short on citations - do (please) try to find some if you can. R.S. sources (mostly books and things) are best of course - but in a case of an article like this it is arguable that ANY source (even one that would not be fully acceptable as "reliable" in more academic circumstances) can be at least a little bit better than nothing (at least it proves you didn't make anything up). Nothing wrong with directly quoting sources (especially reliable ones) - but do make it clear that you are directly quoting. --Soundofmusicals (talk) 23:16, 25 April 2019 (UTC)

I added only the first 7 paragraphs of the "Origins" section. Sources are not needed if the statements are taken from linked-to articles. That is the case, for example, of the two paragraphs that describe the Greek and Egyptian numerals; or that states that several civilizations had preceded the Romans in the Mediterranean.
The two statements that needed a source (and are so marked) are the claim that the Roman numerals were not imported from those earlier civilizations (which seems to be false, because the Etruscan numerals page says that they were derived from an older Greek system, the Attic numerals); and the claim that the systematic subtractive notation was a Roman innovation over the Etruscan system (which seems unwarranted, because there are too few surviving examples of Etruscan numerals to tell one way or the other). I will try to fix those.
Other statements were in the original article; I only rearranged them. A couple of them seemed uncertain and had no source, and are now so marked. --Jorge Stolfi (talk) 05:05, 26 April 2019 (UTC)

If there is a (good) reference in another article (linked or not) for a particular point - all the more reason to duplicate that reference here, surely! Even if only to head off the "reference police" who are perfectly capable of assuming that text not obviously referenced is O.R. and deleting it out of hand. As a rule it is a far, far better thing to have the odd unnecessary reference than to omit a useful one. --Soundofmusicals (talk) 11:26, 26 April 2019 (UTC)

"Basic rules"

Much against my own first reaction, I eventually agreed to a change the section heading at this point to include the word "rules". But given that our description of the current convention is to be described as a set of "rules" we need to be very careful about seeming TOO "free and easy" - (nor do we want to lay down the law too prescriptively either of course - and I would resist describing an unusual form as "wrong" or "incorrect" - at this point we simply don't mention "funnies" at all). I think we already had the balance about right before the last "usually/generaly/often" ridden edit. Too much "moderation" and compromise at this precise juncture could get wish-washy to the point of being flat confusing. The "Alternate form" section is the one we can let loose with alternatives - and then we need to include only examples that have (or still sometimes are) been used. The "rules" are (or should be) a fairly unambiguous template enabling a reader to read a conventionally constructed Roman numeral - or to construct one from any "Arabic" number that will be readable by anyone with a grasp of the system. --Soundofmusicals (talk) 05:10, 28 April 2019 (UTC)

"Alternate forms"

Can anyone find an instance of "IIXX" for 18? (or of "IIX" for 8 for that matter). We do seem to have one for "XIIX", which does at least "fit" the fundamental rule that units, tens etc are separate. Are we really so sure about linguistic justification for ANY of these clearly very closely related forms? Just let's be on our guard against inadvertent O.R. - this is a point where a named reference (like the one at the note about a certain science fiction writer's speculation the classical avoidance of "IV", perhaps). Just because it look plausible doesn't mean in necessarily belongs (except, just maybe, as a clearly labelled "speculation") in an encyclopedia article. And just because what may be the "least rare" form a variation takes may not fir out explanation quite so well isn't a reason to make an artificial distinction between what's so very obviously essentially the same variation. --Soundofmusicals (talk) 05:40, 28 April 2019 (UTC)

Google finds dozens but mostly medieval; see below. From Roman times, I found a dozen or so, but usually from the periphery of the Empire, and it is not clear whether they are errors, or mean "22" rather than "18". Below is one from Rome ~230 CE.
That claim "duodeviginti made Romans write IIXX" is not mine; it came from some book.

• (1692) Vera Ac Germana Detecto Clandestinarvm Deliberationvm (left page, after the parag break.)
• Acta publica inter invictissimos gloriosissimosque&c. ... et Ferdinandum II. Romanorum Imperatores... (date in signature; several in this book)
• Italia Epigrafica Digitale, XII.5.1 (Novembre 2017), Roma – Inscriptiones Latinae: CIL, VI 40000 e seguenti, Parte I "IIXX Prim[igeniae, cur(atori) viae Latinae novae?]" 218-245 CE
• Malone, Stephen James (2005) Legio XX Valeria Victrix... PhD thesis On page 396 discusses many coins with "Leg. IIXX" and notes that it must be Legion 22. The footnote on that page says:

The form IIXX clearly reflecting the Latin duoetvicensima 'twenty-second': cf. X5398, legatus I[eg II] I et vicensim(ae) Pri[mi]g; VI 1551, legatus leg] IIXX Prj; III 14207.7, miles leg IIXX; and III 10471-3, a vexillation drawn from four German legions including 'XVIII PR' - surely here the stonecutter's hypercorrection for IIXX PR.

So there you have (1) influence of the language leading to "wrong" numerals IIXX, although meaning 22 not 18; and (2) a contemporary "smart" stonecutter who saw "IIXX" on the order and thought that the client, poor dunce, meant 18. Just to make the confusion confusier...

--Jorge Stolfi (talk) 07:22, 28 April 2019 (UTC)

Unicode characters: NOT, please

I just added all of the Unicode characters for Roman numerals: why were they not previously included? I know in the past they have been. ―Justin (koavf)❤T☮C☺M☯ 18:19, 4 May 2019 (UTC)

The people at the Unicode Consortium themselves recommend against using those symbols in ordinary contexts. As explained in the linked article Numerals in Unicode#Roman numerals, those composed symbols were added to Unicode in order to allow Roman numerals to be typeset in vertical Asian texts. In horizontal text, the plain Latin letters should be used instead.
Check also the pics in the Roman abacus article. The Romans did not write those apostrophus symbols as single letters either...
However, this article did need a section about the Unicode block. Added now. --Jorge Stolfi (talk) 11:32, 5 May 2019 (UTC)

A new "general rules" section?

I am wrestling with the idea of changing the name of this section - after trying so hard to get away from "rules" the idea of calling the section, descriptive rather than prescriptive as it is, "rules" grates a bit. On the other hand... give me time and I might accept this one, on reflection I can see advantages.

I am still adamant about "counting to ten", rather than nine. There are ten beads in each column of a the simplest form of an abacus (which works on the principle of a child's counting frame) and it is the fall of the tenth bead that triggers the "carry" to the next column. All else confusion and false carries. The resulting overlap between the last character in one column and the first one in the next is actually a product of the absence of a "place-keeping zero". It is logical enough, and answers the possible question "what about 10 then", which seems much more likely than "doesn't 10 already belong in the next place?". Having established the pattern, its repetition should be clear.

I'd also like to see us finish talking about the initial iteration of the "pattern" (including our simple explanation of subtractives) before going on to the second and third. Much easier to see how the pattern is repeated if we already understand its basic form and logical structure.

On reflection, I can live with giving several justifications for subtractives, although on the whole I'd prefer not to hammer this one so heavily.

Anyway - just to save time - I'll stick a new version of the next section into the article. If you have any serious difficulties with it we'll revert to the older version, and come back here to iron out a final version. --Soundofmusicals (talk) 07:04, 22 April 2019 (UTC)

• And I still feel very strongly about starting out the description with 1 to 9 only.
  There is no reason to go up to 10 at that point. The reader already knows from the lead that "X" measn 10 and "IX" means "1 before 10". Going up to 10 can only confuse the reader, because the most important point that he must learn -- even before learning what the "digits" are -- is the fact the RNs (in any version) are just a strict base-10 system.
  Namely, that the very first thing one must do, to read or to write them, is break the number into thousands, hundreds, tens, and units; each being a multiple from 1 to 9 (ONLY) of the corresponding power of 10.
  As for the abacus, what you are describing is the modern Western kindergarten abacus. (Which is definitely going to confuse children, more than help them, when teaching numbers.)
  Japanese abaci have 4 beads + 1 bead in each column, so they can count from 0 to 9 and carry is mandatory. Chinese abaci have 5 beads + 2 beads, so each position can count up to 15. That reduces the need for carry in chained operation; but since their number system is strictly decimal too, digits higher than 9 must be cleared at the end.
  That's only to show that the design of an abacus cannot be used to claim that counting to 10 at the units is natural. Some abaci are like that, but some aren't.
  More relevant is the Roman abacus that Romans actually used to do their math. It did not have 10 beads per position. Each position (a column) was divided into two parts, one to hold 0 to 4 "1" beads, the other to hold 0 or 1 "5" bead -- so each position could have a value from 0 to 9 (not 10). (Then, to the left of the units column, there was a column with a slot for 0 to 5 "1" beads and a slot for 0 or 1 "6" bead, allowing to count from 0 to 11 -- for fractions, which were base-12 rather than base-10; and yet another column with three smaller slots, for finer fractions.)
  --Jorge Stolfi (talk) 03:36, 23 April 2019 (UTC)

Been giving this a fair bit of thought - starting to wonder if this isn't a relatively minor point and trying to convince myself that I'm being a bit of a beast persisting. I am really a humanities person rather than a maths/science one and I admit I usually think of a children's counting frame when I hear the word "abacus" - I have never worked out how a "real" abacus, like a Roman (or modern far-eastern) one, actually works. To me the tenth digit of a place has always been the one that "carries" - and hence sort of overlaps - especially in the case of RNs, which are NOT exactly the same as Arabic numbers. The basic abacus is of course the ten fingers of our two hands (the origin of the decimal system, when all is said and done!) In Arabic numbers (and any other system with a "zero") we essentially count our ten fingers as 0,1,2,3,4,5,6,7,8,9. In Roman numbers there IS no zero, so we count them as I, II, III, IV, V, VI, VII, VIII, IX, X.

More to the point perhaps - can you live with the rest of the section as it stands. It is effectively now more a tweaked version of your text rather than thw original. --Soundofmusicals (talk) 04:11, 23 April 2019 (UTC)

I must insist again that the "X" be left out of the "units" sequence, and ditto for C and M in the tens and hundreds. Those extra "digits" only obscure the fairly simple base-10 structure of the system and will only confuse the reader, not help him. The "finger count sequence" is not a well-defined concept, and anyway its not relevant at all: neither to the bare logic of the system, nor to its history (that is not at all how it developed among the Etruscans, who passed it ready-made to the Romans), nor to the purposes of this section (since every reader will be totally familiar with the Arabic system, and does not need to have a base-10 system explained in terms of finger counting). Moreover, in surviving Roman abaci, each position can count only from 0 to 9, not from 1 to 10; which is one more bit of evidence that the Romans themselves would say that the "units" went only up to 9.
--Jorge Stolfi (talk) 20:01, 7 May 2019 (UTC)

What is wrong with "additive notation"?

What is wrong with "additive notation"? It goes together with "subtractive notation" (that is surely not a term that the Romans would use!), and has been used to contrast not only "IX" with "VIIII" but also the Roman system with the Etruscan, Egyptian, and ancient Greek ones. See the source. --Jorge Stolfi (talk) 21:13, 7 May 2019 (UTC)

Just looked it up in the dictionary - there is a secondary meaning there for "appertaining to addition" - but it usually means an "additive" in the sense of (say) artificial sweetener added to "low sugar" food, or the lead compounds they used to add to fuel. In this context it is thoroughly strange for an uninitiated reader - in fact it looks as if someone just stuck it in as an apparent opposite to "subtractive". I honestly don't like subjective either, but it does barely scrape in as it is explained "in line", doesn't have a different common meaning to cause confusion, and doesn't have an obvious one word plain language equivalent. I just don't like jargon like this (and I am not alone - see WP:Jargon). This is not a technical article, where jargon is unavoidable, and if it was, our MOS makes it clear it should be minimised, and explained. Which I would have thought is just common sense. --Soundofmusicals (talk) 23:08, 7 May 2019 (UTC)

I am baffled. Why is "additive" jargon, but "subtractive" is not? --Jorge Stolfi (talk) 23:34, 7 May 2019 (UTC)

More generally, can you explain what kind of reader you think this article should cater to, and what its purpose should be? Sometimes it seems that the article is trying to teach small children, sometimes it seems to be trying to tell people what is the "right" way to write RNs, or to advance one particular way of looking at them ... --Jorge Stolfi (talk) 23:46, 7 May 2019 (UTC)

Manuals of style are not to be taken lightly, even if they seem at times to be trivial or overly pedantic. They are important in giving coherence and common usage to any work of composite authorship. In this case the rule in Wikipedia's MOS - that jargon should in general be avoided, except in technical articles where it cannot really be avoided, seems eminently sensible - I am flabbergasted that you could possibly have difficulties with this. And while both "additive" and "subjective" are equally jargon in the senses they are used here, they are none-the-less different cases, as I tried to explain in my last post. As for our intended audience - it must always be primarily a general reader with little or no background in the subject. By no means all such people are children. --Soundofmusicals (talk) 00:53, 8 May 2019 (UTC)

I totally support the recommendations about jargon, and much of my editing elsewhere it in fact replacing jargon my more accessible prose.
However, the recommendations are against using jargon to explain something; not against telling the reader about existing jargon. In fact, a Wikipedia article must mention and explain any such jargon that general readers may encounter out there.
Which is precisely how and why "subtractive notation" was introduced in the article, and why and how "additive notation" should be too.
As for the readership, please try to be more specific. Surely you must agree that every reader who wants to understand Roman Numerals -- including schoolchildren -- will be totally familiar with base-10 number notation, and arithmetic operations?
I can't imagine such readers getting confused if they are told that the possible units in a Roman numeral are I to IX; on the contrary, I think they may be quite confused reading that they are I to X.
And surely they will not be put off by being told how those two notations are called, when it is necessary to name them?
All the best, --Jorge Stolfi (talk) 01:24, 8 May 2019 (UTC)

Contrary (IMHO) to our MOS - both terms are not only explained but repeatedly hammered at several places in the article. While this remains the case you might want to let this one rest? In any case I have no intention of editing out any mention of either term in the current version of the article. -Soundofmusicals (talk) 05:26, 8 May 2019 (UTC)

First footnote

This has been restored to its original form in an effort to keep to simple statements of fact - rather than seeming to mind-read the ancient Romans - as someone justly remarked, we don't actually know WHY they did anything. If common sense does indeed suggest a motive, then let the reader provide it him/her self. --Soundofmusicals (talk) 10:01, 12 May 2019 (UTC)

When did the additive notation became archaic/deprecated/wrong?

While the subtractive notation ("IV", "IX", "XL", etc) has been predominantly used since Roman times, I am not aware of any authority of any kind having ever determined that the additive notation ("IIII", "VIIII", "XXXX", etc.) was "wrong", "non-standard", "archaic", "deprecated", etc; or restricted to "IIII" on clocks. (Brutus may have had hated Julius Caesar for many reasons, but his use of "XVIIII" for 19 must not have been one of them.) In fact, people have continued to use the additive version, sporadically, for as long as they used the numerals.
Maybe modern primary school teachers are responsible for the view that those numerals are "not good" in some sense?
So, are there textbooks of the like, from more than 100 years ago, which say that the Roman number system is the subtractive version and not the additive one; or any instance of someone complaining about the use of the additive version, besides schoolteachers?
All the best, --Jorge Stolfi (talk) 01:54, 8 May 2019 (UTC)

Can any of the above be related to something in the article that needs changing? I thought this was pretty much what we have always had to say. Even "irregular", in the subheading "Irregular subtractives" is in inverted commas. --Soundofmusicals (talk) 05:16, 8 May 2019 (UTC)

Nothing specific yet, but it would be proper to add such a reference if it exists. "Some school textbooks published in the 20th century have characterized the additive notation as 'wrong' or 'archaic'.<ref>..."

That would be VERY subjective, unhelpful and unnecessary - I think the simple statement at the beginning of the "Alternate forms" section about there being no absolute or "legislated" standard is quite enough - especially as an introduction to specific examples (as it is). --Soundofmusicals (talk) 06:04, 15 May 2019 (UTC)

If there are such textbooks, that would be a FACT about the history of RNs that definitely should be mentioned. Needless to say, I would strongly disagree with those textbooks. --Jorge Stolfi (talk) 10:18, 15 May 2019 (UTC)

There are very good reasons for detailing the current convention (no "funnies" or strange usages whatsoever) and encouraging its use (like avoiding confusion and ambiguity as far as possible). The fundamental questions most of our readers want answered is "how do I write (a given number) in RNs?" and "what does MCMXCVIII mean". Back in the days when everyone was brought up on RNs as the main (or only) way of writing numbers, one could probably afford to be a bit more flexible, as people had enough background to decipher an unusual number. As it is many people can only read RNs at all up to about XXXIX, and have no idea of year numbers (especially those of the latter decades of the last century). As I think I have mentioned elsewhere, Cecil Adams is NOT a very good source - his fixation on forms like IIMM for 1998 - which incidentally have no classical or medieval authority whatever, verges on a plea for "free expression". --Soundofmusicals (talk) 06:04, 15 May 2019 (UTC)

I think that the written record from Roman times to the 1700s and beyond clearly shows that (1) there is a huge gap in usage frequency between "weird" forms like "IIXX" or "XIIX" and the additive notation, and (2) while there is also a huge gap between additive and subtractive, the former has always been accepted as valid and has been used occasionally by many educated authors, without guilt or scorn.
Therefore I think it is actually wrong to try to bias the description in the sense of making the additive notation seem 'wrong' or 'obsolete' or 'less important' etc.
The fact is that "VIIII" and "IX" are both valid ways to write 9 in Roman numerals. The article should not try to hide that fact or bias the reader towards what we think is the "right" way to write RNs.
Once again, Wikipedia is not meant to be a teaching aid for kindergarten. Readers are supposed to be adults and teenagers, who will not be terrified if the article tells them that there are several ways to write the same number. In fact, 99% of those readers who do not know how RNs work will come here to learn how to read them, not how to write them; and therefore they must be taught how to read "VIIII" too, because they will occasionally run into it. --Jorge Stolfi (talk) 10:18, 15 May 2019 (UTC)

But the article already gives a succinct little summary of most of the common "variants" - largely in your words too, I think. Mixing this in with the "usual usage" or leading with it before we had described same would be less helpful, however you look at it. That's what I meant when I asked you how this "argument" (not that we are differing very much anyway) bears on the wording of the article. The answer to the question at the head of this thread is of course "never, and we don't say it!". No guilt or scorn here, and as far as I can see no "seeming" to say the opposite of what we do say. Not that it hasn't been fun - but I don't think further iterations of this silly circular argument are very useful. --Soundofmusicals (talk) 12:50, 15 May 2019 (UTC)

Have a look at my edit of the "section lead" for "Alternate forms". Does this still give (you) the impression we are implying that "typical modern use" is the only "valid' way of writing RNs? --Soundofmusicals (talk) 13:29, 15 May 2019 (UTC)

I have split that into "Use of additive notation" and "Rare variants", per discussion above.

I can live with this - but see my most recent post! --Soundofmusicals (talk) 13:35, 18 May 2019 (UTC)

"Valid" Roman numerals?

Some "variant" Roman numerals are genuine variant forms - they have classical and/or medieval warrant, and are unambiguous (it's obvious exactly what they mean). Some were actually used in classical or medieval times but are ambiguous (IIXX could mean 18 or 22) others are (sort of) decipherable but seem to be modern "one-offs". But NO Roman numeral, "standard" or "variant", is really more "valid" than any other - since there is no fixed or universal standard by which any of them might be validated. Just a funny old man being paradoxical or something that warrants an explanation? Just wondering. --Soundofmusicals (talk) 13:33, 18 May 2019 (UTC)

Semi-protected edit request on 5 May 2019 - remove speculation

Change "However, the numerals for 4 (IIII) and 9 (VIIII) require too many strokes (a nontrivial concern when chiseling them in stone), take up too much space, and are easily confused with III and VIII, especially at a quick glance. At some early time the Romans started writing them as IV (one less than 5) and IX (one less than 10), respectively."
to "At some early time the Romans started often writing IIII as IV (one less than 5) and VIIII as IX (one less than 10), respectively."
First, talk of strokes and chiseling is speculation. Unsourced, it is WP:OR and even if it was sourced, it would be guesses that there was only one reason for the shift, that the shift originated with carvers, and that it's easier to chisel complex characters than simple characters with slightly more strokes overall. We don't know why it happened; there are no sources contemprary with the shift that discuss it and we cannot read their minds or raise their ghosts.
Second, we must not give the impression that the shift was uniform; the Romans did not shift from using one style to another, they shifted from using one style to using two. 79.73.240.196 (talk) 18:40, 5 May 2019 (UTC)

 Done – Þjarkur (talk) 18:50, 5 May 2019 (UTC)

It is indeed easy to become beguiled by the persuasive, but none-the-less purely speculative arguments of some of the more imaginative sources "out there" - we do need to maintain "encyclopedic detachment" and avoid unnececcary speculation. Good point, well taken. On the other hand the purpose of this section is to supply the much requested set of unambiguous rules - and we cannot really escape the need for a little incidental speculation, well qualified as such by words like "probably", "usually" and "generally". Anyway, I have once more edited this section in an effort to preserve the benefits of all editor's insights. --Soundofmusicals (talk) 23:58, 5 May 2019 (UTC)

@Soundofmusicals:, thank you for removing the speculation. Regarding clarity, you might enjoy considering the use of the simple Roman counting board. Made of wood or scratched in the dirt, it had separate columns for each digit or merely power of ten, signified by numerals or merely appropriate collections of pebbles. It might have a horizontal line halfway down. Try a few additions or subtractions on it. I was soon convinced that shopkeeper and customer, creditor and debtor, or a pair of traders using Roman numerals and a board could quickly agree a result with no literacy, barely any numeracy and not necessarily even a language in common. It's a marvel of clarity - so long as additive numerals are used. Subtractive numerals massively complicate its use.

I don't suggest using this insight in the article; I mention it to strengthen your resolve not to include assumptions that more extensive domain knowledge can quickly undermine. 79.73.240.196 (talk) 12:45, 19 May 2019 (UTC)

I agree with user LXXIX.LXXIII.CCXL.CXCVI: we should not speculate why people usually write "IX" instead of "VIIII", no matter how obvious that may seem. On the other hand, we can note that those notations requirefewer strokes and take up less space, without stating that it may have been the reason. By themselves, those measurements are not OR, because they are strictly mathematical and trivially verifiable.
--Jorge Stolfi (talk) 19:44, 7 May 2019 (UTC)

All civilisations are limited by the state of their science and technology!

We (very properly) avoid trying to mind read the Romans - and we don't know why they chose to do anything for which they had a choice. Point is, there are lots of areas they didn't have the same choices we have. In particular they HAD to use a different notation for each place - because the very concept of the "place keeping zero" - which enables us to write the numbers 1, 10, 100, 1,000 and so on all with a single numeric symbol - was not known to them (nor the ancient Greeks, Egyptians, Etruscans etc.). Hence this passage:

Since the concept of "place keeping" zeros was unknown in Europe before the 11th century C.E. different symbols had to be used for each power of ten, but a common pattern was used for each power or "place".

is "valid" - and not only that, but valuable! Hence my restoring it. --Soundofmusicals (talk) 11:28, 19 May 2019 (UTC)

That makes it seem very straightforward. But consider Greek numerals. The main system of the classical period used nine different symbols for 1 to 9, another nine for 10 to 90 and another nine for 100 to 900. The representation of a number in Greek thus looks very different from a Roman one, having no repetition of characters, and especially if all powers of ten are employed, more like an Arabic one. The lack of a zero does not have the inexorable force suggested by the passage you've restored. 79.73.240.196 (talk) 12:24, 19 May 2019 (UTC)

The "inexorable force" applies to the characters used. They MUST necessarily be different for different powers of ten, and ARE different in all numeric systems, including the Greek one, that lack place keeping zeros (all else confusion, not to mention wailing and gnashing of teeth). Place keeping zeros do NOT, however, have any force whatever (inexorable or otherwise) over "inter-place patterning" - which is indeed a point of distinction between Roman and Greek numerals. Is this clear? I am considering rephrasing slightly - although this may just mean changing a conjunction, and I remain unconvinced for the moment it is necessary. --Soundofmusicals (talk) 03:32, 20 May 2019 (UTC)

Sorry, but that is a totally unsubstantiated -- and probably wrong -- guess as to WHY they used different symbols for units, tens, etc.
First, they inherited the system from the Etruscans, who may have got it from the Greek, who may have got it from the Egyptians. The only innovation of the Romans was the subtractive notation.
Therefore, the reason why they used different symbols for different powers of 10 is the same reason that the English write the same sound as "too", "to", or "two": because that is how it has always been done, nothing more.
Therefore, Roman numerals did not have a symbol for the digit zero because they did not need one. Not because they did not have the "science and technology". More on that below.
--Jorge Stolfi (talk) 07:36, 20 May 2019 (UTC)

The notion that "zero" was an immense scientific discovery is a myth, maybe originated in the humanities where people often fail to distinguish ideas from words. The Babylonians used a positional system of notation, base-60, using the same digit symbols in every position. Originally they omitted zero digits, like the Romans, so a number like "16" could also mean "106" or "160" or "10600", and one had to use context to interpret them (just as one needs context to read the word "read" in English). But eventually they developed a sign for "zero digit", and the system became as good as the Arabic one, only still base-60.
I don't know whether the Hindu got the idea from the Babylonians, or vice-versa, of they were independent developments. But the Maya too developed, all alone, a positional base-20 system, with the same digits in all places and a symbol for zero.
If you think of it, the big idea is to use the same digits for all powers of the base: once you try to do that, the invention of a zero digit is almost automatic.
The lack of a symbol for the digit zero does not tell us whether the Romans understood that zero was a number, too. In the English language, zero is still not a number: people say "I bought two horseS, I bought one horse, I didn't buy any horses" (not "I bought zero horses"). But that of course does not mean that the English do not have the concept of zero; because language is not thought, and words are not ideas. Same goes for the Romans.
On the other hand, the Romans did lots of computations for accounting and engineering, so they must have understood zero and negative numbers in some fashion. And the Roman abacus could record zero as naturally as any other number. (In fact, the Roman abacus was totally positional, with the same digits in all positions -- which went from 0 to 9, not from 1 to 9 or 1 to 10!).
In conclusion: the claim that the Romans did not use a zero digit symbol "because they did not know the concept of zero" is unwarranted, and very likely wrong.
--Jorge Stolfi (talk) 07:36, 20 May 2019 (UTC)

Excuse my barging in here - but while everything you say here may be perfectly true the fact remains that notation representing a place keeping zero (even if it is just a dot, or even a space or gap) is a prerequisite for using the same notation for different powers of whatever base you are in, unless one accepts a degree of ambiguity. I can't see how anything can get round this one.
Just to clarify, Jorge Stolfi, the problem may be a matter of your mixing up the idea of "zero" in the sense of "nothing as a number", and a piece of notation representing an empty column on an abacus. It is the second of these (what we have been calling a "place keeping Zero") that really is an important discovery. To dismiss it as self evident raises the question of why it took so long to take hold in Europe, even after it had been introduced from elsewhere. WWIReferences (talk) 11:13, 20 May 2019 (UTC)

I do not like the claim that "lack of a zero forced them to use different digits for each power of ten". As pointed out in the other examples (Babylonian and Mayan) it appears that the idea of using zero as a placeholder does not occur until somebody tries to use the same digits for each position. It is probably more accurate to claim the reverse: "because the digits for each power of ten are different, no zero is needed". I really don't like some of the bloat being inserted into this article, that is one of them. Stick to the fact "the digits for each position are different, so no zero was needed or used". Also there is a lot of confusion about zero as a placeholder, verses the actual number "zero" as being a real number. It does look like the concept of zero and negative numbers being the same as positive numbers can arise earlier and completely independent of a zero place-holder, which apparently is a bit harder to invent.Spitzak (talk) 19:00, 20 May 2019 (UTC)

The nearest thing to a "Roman numeral" for zero, (N) was also a medieval "invention", and as Spitzak correctly points out, a different thing to a place keeping zero anyway. Is anyone really suggesting that the Romans had the concept of a place keeping zero, but chose instead to employ different notation for each power of ten? With all respect, this is plain daft. At best, it is highly misleading to suggest that such a case is possible. The very idea was unknown in Europe before the 11th century - many years after the end of the Roman era - is anyone disputing this fact? Is it not helpful and relevant to mention it at this point? --Soundofmusicals (talk) 21:50, 20 May 2019 (UTC)

No, no! The Romans (and Europe until the 1300s) did not "invent" a place-holding zero because they did not need it. They inherited the different-digits-for-each-place system from the Etruscans, and, as long as they stuck to that, a zero digit would have been a stupid waste of time.
Again, a zero digit symbol only makes sense after one has decided that using the same digits at all places would be better than the Roman system. Like the Babylonians did.
And, even after one has chosen to reuse the digits, there is another option. The Chinese number system uses the same digit symbols 1-9 (一二三四五六七八九) in all places, but, instead of place-keeping zeros, uses a separate symbol to identify the places: "四万三百七" = "four myriad three hundred seven" = 40307, "四万三千七" = "four myriad three thousand seven" = 43007, "四千三百七十" = "four thousand three hundred seven ten" = 4370. This system is in fact handier for large approximate numbers, like 40000 = "四万". --Jorge Stolfi (talk) 00:03, 21 May 2019 (UTC)

The question is whether the article should state

Since the concept of "place keeping" zeros was unknown in Europe before the 11th century C.E. different symbols had to be used for each power of ten, but a common pattern was used for each power or "place".

Perhaps you think this claim is blatantly obvious. However, WP:OR is clear; Any material that is challenged or likely to be challenged must be supported by a reliable source. Material for which no reliable source can be found is considered original research. It is not merely likely to be challenged; it is challenged. Reasoning from principles such as "All civilisations are limited by the state of their science and technology" is irrelevant.

What's more, that sentence makes quite extraordinary claims.

1. Different symbols had to be used for each power of ten.
2. This was because the concept of "place keeping" zeros was unknown in Europe before the 11th century C.E.

That's false. Not only is there an infinity of other ways of representing numeric values, the Roman decision to use their method cannot and should not be ascribed solely to the absence of zero.

It seems as if you think it necessary to explain why Roman numerals developed as they did. It's not. Indeed, it's problematic in many ways: it's speculative, unverifiable in the ordinary sense and the WP:V sense, and bloats the article when carried out directly as here or indirectly by the accretion of far too many examples and counter-examples for an encylopedia article (this is not a scholarly monograph or blog post). You seem to have spent time protecting the article against unwarranted insertions. Please don't go over to the dark side! 79.73.240.196 (talk) 22:59, 20 May 2019 (UTC)

What we are actually trying to do at this point is to describe the way Roman Numerals work. For the moment - until we are all on the same wavelength and can reach a consensus, there is probably no alternative to just cutting all mention of place keeping zeros at this point, unless we can do so without raising contention over causation, either one way or the other. The Romans certainly didn't use different symbols for different powers of ten to avoid place keeping zeros, as the original text implied. I hope we can all agree on that one, at least. --Soundofmusicals (talk) 00:45, 21 May 2019 (UTC)

XVIXIII ( "sixteen thirteen") for 1613.

This is not a "variant", even a "rare one" - but a plain error. "XVI" cannot stand for "MDC", as it does here, however "liberal" one wants to be. The engraver who put this on the padlock clearly had no idea how RNs for large numbers work. Not that surprising - he was an artisan rather than a scholar, - and even in the seventeenth century it had been many years since RNs had been the usual way of writing numbers. There is therefore no need to divide it from the following paragraph, which is about "real mistakes". --Soundofmusicals (talk) 22:18, 20 May 2019 (UTC)

That is neither a "variant" nor an "error"! The writer obviously just choose to write the year as "sixteen thirteen" (two numbers) rather than "one thousand six hundred thirteen" (one number). If that is to be called an error, then the English phrase "sixteen thirteen" is an error too.
We must not use the word "error" too freely. There is no official standard, right? All we can say is that some numeral is very rare, and some people may consider or have considered it and error (like that stonecutter). The citizens of that Irish town presumably did not think of XVIXIII as an error. --Jorge Stolfi (talk) 00:20, 21 May 2019 (UTC)

I don't think we will ever be of one mind on this one - but then do we have to be? After all we don't actually directly call it an "error" in the article text - just imply that it might be. What do you think? As for the opinion of the seventeenth century Irish citizenry about the engraving on the padlock (assuming any of them even noticed it at all, much less that it is a bit weird) can we presume what they thought either way? And does it even matter? --Soundofmusicals (talk) 00:48, 21 May 2019 (UTC)

Link direct to actual article names, please!

It is very murky practice (for many reasons) to link to a "redirect" page rather than directly to the article itself. Not all DAB pages, for instance, have "(disambiguation)" as part of their name. If you link IXL as IXL (disambiguation) You will actually generate an error message "(Redirected from IXL (disambiguation))". --Soundofmusicals (talk) 13:20, 18 May 2019 (UTC)

Linking to a redirect is normal and recommended in the Manual of Style - see MOS:REDIR. Thus IXL (disambiguation) works as intended now and will continue to work as intended in this article even if IXL is ever renamed IXL (disambiguation), whereas IXL might then take the reader to some specific article such as the old IXL article. The "Redirected from ..." message is informative and explains that Wikipedia has worked as designed; it's not an error message. 79.73.240.196 (talk) 16:30, 19 May 2019 (UTC)

The case described at MOS:REDIR (referring to a hypothetical redlink) is quite different. A more relevant reference would WP:DPL, which clearly states:

...links should go directly to the appropriate article

The renaming and merging of articles can indeed cause linking problems - but these are likely to be exacerbated rather than alleviated by linking to redirects rather than a plain and existing article name. Whether all disambiguation pages should have (disambiguation) as part of their name is quite another question, of course. In the case of XXX and IXL I can see no impelling reason to do this - for various reasons.--Soundofmusicals (talk) 03:58, 20 May 2019 (UTC)

WP:DPL is indeed pertinent. You quote a small part; let's look at the entire sentences.

Ideally, article namespace pages should not link to disambiguation pages, except when the ambiguity of a term is being discussed (as in hatnotes mentioning that a term has other meanings); instead, links should go directly to the appropriate article. Where an article intentionally links to a disambiguation page, that link should be through a "Foo (disambiguation)" redirect, to make it clear that the link is intentional. (my emphasis)

This article does intentionally link to disambiguation pages IXL, XXX and XL because the ambiguity of a term is being discussed (they "have other connotations besides their values as Roman numerals", it "more often than not means" something else). The links should be to "Foo (disambiguation)" redirects, i.e. IXL (disambiguation), XXX (disambiguation) and XL (disambiguation). Please could you restore the links and the perfectly correct comments <!--PLEASE DO NOT "FIX" THE DISAMBIGUATION--> inserted by Narky Blert (talk · contribs), whom you will see from their contribution history and talk page to be something of an expert in this matter. 79.73.240.196 (talk) 17:30, 20 May 2019 (UTC)

@Soundofmusicals: WP:DPL is a WP:WikiProject page. It does not set out any guidelines; rather, it reproduces parts of some guidelines.

The relevant guideline is WP:INTDAB. I quote: "Links to disambiguation pages from mainspace are typically errors. In order to find and fix those errors, disambiguators generate a wide array of reports of links needing to be checked and fixed. Because these reports cannot distinguish instances where an editor has made such a link with the intent to point to the disambiguation page, the community has adopted the procedure of rerouting all intentional disambiguation links in mainspace through "Foo (disambiguation)" redirects. This makes it clear that such links are intended to point to the disambiguation page." (emphasis added).

WP:HOWTODAB says the same thing. I quote: "To link to a disambiguation page (rather than to a page whose topic is a specific meaning), link to the title that includes the text "(disambiguation)", even if that is a redirect" (emphasis in the original).

I fix several intentional links to DAB pages a day; either because a new direct link has been added, or because an editor has removed the "unnecessary" link through the (disambiguation) qualifier, in e.g. a see-also section or a hatnote. (There's also a bot, not mine, which specifically targets errors of this kind in hatnotes.) On occasion, I've reverted and corrected both 10-year veterans and admins who didn't know the rule. Narky Blert (talk) 18:51, 20 May 2019 (UTC)

Well, what do you know! I suppose if that's the rule... --Soundofmusicals (talk) 16:27, 23 May 2019 (UTC)

"Rare variants" section

Just to prove I am not immovable - I rather like the way this section has panned out. Thank you for your good work, Jorge! Some things I might have put differently but what the fuss! --Soundofmusicals (talk) 01:31, 1 June 2019 (UTC)

"M" (=1,000)

"M" seems to be a Medieval numeral - the Romans used other ways to indicate numbers of 1,000 and over. Most unlikely, in fact, that they used "MM" or "MMM" either. The use in a modern (Latin) edition (and/or a Medieval manuscript) of a classical author of "MMMM" is not necessarily how the original author expressed that number, which makes a reference that assumes the fact rather murky. In order to make a point about the "validity" of "four in a row" or "additive" notation, we have the examples "IIII", "XXXX", and "CCCC" - might this not be enough? These examples make the point equally well - there are plenty of them, and we avoid the doubt surrounding "MMMM". --Soundofmusicals (talk) 02:42, 30 May 2019 (UTC)

Indeed I have a source that says that use of M for 1000 started in the second century AD. So we need to be careful everywhere (not just in that sentence) to avoid the implication that the classic Romans used "M".
However, "Roman numerals" is not just "numbers used in the Ancient Roman Republic". If "MMMM" was generally accepted as 4000 in medieval times, we can still say that it has been widely accepted as valid. If the Pliny MMMM is a medieval interpolation, we should perhaps use a medieval source. --Jorge Stolfi (talk) 07:19, 30 May 2019 (UTC)

Of course if anyone actually used "MMMM" it would mean 4,000 - what else could it mean! But even if this were the case, "MMMM" is a special case in this list of examples, and quite distinct from (say) "CCCC". While there is a subtractive alternative ("CD") for "CCCC" - there is only a purely hypothetical subtractive alternative to "MMMM" (as it might be "MQ", if Q unambiguously stood for 5,000 which sadly it doesn't). In the absence of a subtractive form for 4,000 then "MMMM" is not "additive" in the same sense as "XXXX" or "CCCC".
But isn't the primary point we are making here the fact that "additive" numerals were widely used? Even with the "MMMM" example removed this is still what we say - giving a (very healthy) set of undoubted and undisputed examples that have ample classical warrant. As it is we don't have symbols for 5,000 and 10,000 so you could "legitimately" have a indefinitely long string of "MMMMMMMMM"s!
There ARE sources that claim the Romans didn't use "M" at all. Not doubting your source for a moment - but sources on this subject contradict each other like crazy - as I'm sure you have noticed. I don't feel that this is worth our working up a lather over really - do you? --Soundofmusicals (talk) 10:33, 30 May 2019 (UTC)

That source continues "The M was an abbreviation ... and was never used by the Romans as a numeral". 92.19.26.27 (talk) 15:19, 1 June 2019 (UTC)

There you are then. --Soundofmusicals (talk) 23:50, 7 June 2019 (UTC)

DCD for CM = VIV for IX

Someone thought that pointing this out was "vandalism". Writing 900 as 500+400 is indeed the same as writing 9 as 5+4. A clear example of the different powers of ten following the same pattern. --Soundofmusicals (talk) 23:49, 7 June 2019 (UTC)

Do you get any evidence of this?

—Your's sincerely, Soumyabrata 04:32, 10 June 2019 (UTC)

Read the article - especially the section headed "A base 10 system".

To summarise the (very basic) logic here:

I, II, III, IV, V, VI, VII, VIII, IX, X = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

The equivalent pattern for the tens is the same

X, XX, XXX, XL, L, LX, LXX, LXXX, XC, C = 10,20, 30, 40, 50, 60, 70, 80, 90, 100

Also the hundreds:

C, CC, CCC, CD, D, DC, DCC, DCCC, CM, M = 100, 200, 300, 400, 500, 600, 700, 800, 900, ::1000

So in conventional RNs CM=900 (just as IX=9)

If "DCD" was how we wrote 900, then on that pattern 9 would be VIV.

The article is if anything even clearer --Soundofmusicals (talk) 06:54, 10 June 2019 (UTC)

Wikipedia is not a publisher of original thought

—Your's sincerely, Soumyabrata 07:37, 14 June 2019 (UTC)

Very true indeed - by all means call us out on anything "original" in the above (hint; there istn't anything of the kind there). --Soundofmusicals (talk) 10:20, 14 June 2019 (UTC)

Not going to "battle on alone" any further on this one - if no one else is interested in defending it I will quietly "bin" it. A shame in a way, but we've all got more important information to defend. --Soundofmusicals (talk) 23:47, 16 June 2019 (UTC)

Incidentally "your's" isn't English - we don't appostrophise words that are already possesives (viz. his, hers, ours, theirs etc.). AND it's easier, as well as more standard, to sign with four "tildes" (these things "~").

What do you mean!?

—Your's sincerely, Soumyabrata (talk) 14:33, 24 June 2019 (UTC)

Problem with Greek source

Concering Greek numerals, it says,

"Η" for 100, etc. (the Greek word for 100 was however ἑκατόν, starting with E)

It's true that ἑκατόν starts with epsilon, but in Archaic and Classical Greece eta (Η) often stood for the aspiration (which is why it means that for us), so ἑκατόν would have been written ΗΕΚΑΤΟΝ. Hence Η being 100. — Preceding unsigned comment added by Adnphph (talk • contribs) 19:37, 16 June 2019 (UTC)

Is there a consensus on this? All Greek to me, but the original text before the edit based on this one probably needs reinstating? --Soundofmusicals (talk) 09:46, 19 June 2019 (UTC)

OK, someone's done it! Thanks are due, I suppose, but in general changes like this should be run here first (see next). --Soundofmusicals (talk) 19:51, 27 June 2019 (UTC)

Coin illustrations

While the addition of an illustration of Louis XIV's coinage is impressive - on reflection it is overdoing it a bit - and I have reverted to the original illustration as a bit less overpowering, while making the point equally well. --Soundofmusicals (talk) 03:39, 30 June 2019 (UTC)

Latest very elaborale and thoughtful edit of the "introduction" to the basic decimal nature of RNs

My own thoughts on this one (I know I said I was going to do let you have the first shake, but I'm relenting). These are not, perhaps, in the best order - I'm just hammering them out one by one, as I think of them.

• 1. "Decimal" counting means counting to ten (NOT nine). In a "place" system we "shift place" after nine and return to the first numeral followed by its place marker, but with Roman Numerals ten is naturally the "last unit" as well as the "first ten" (they're the same thing!). Otherwise we couldn't do the "subtractive 9" as "IX", for instance. This is perfectly consistent in a "non-place" system, no matter how untidy it might look in a place system. --Soundofmusicals (talk) 11:45, 18 April 2019 (UTC)

Sorry, I defintely disagree. The Roman numerals were clearly "decimal" in the same sense as the Arabic and Chinese ones: that is, for each power of ten there are only NINE symbols, that do NOT include a symbol for the next power of ten. In a decimal system one counts by one only up to NINE, then one shifts to a count of tens plus a separate count of units.
That was very clear in the original system, that used only I and V for units, X and L for tens, etc.. There was no question that "X" was "one tenful", not "ten units".
To read (or operate) with a Roman numeral, the very first step is to break it into its four parts - thousands, hundreds, tens, and units. (Once one understands that, doing arithmetic with Roman numerals is not much harder than with Arabic ones.) But the "X" in "XVI", "CCX", or "LXX" is part of the tens group, not of the units group; and so is "X" alone.
A reader who does not know Roman numerals will be very confused if you tell him that the units part can be "I, II, III, ... , VIII, IX, or X". The units part can be only I to IX in the modern system, or I to VIIII in the original one. Note that, with this definition, there is no ambiguity in the parsing -- as there would be if one included "X" as a possible value for the units part. --Jorge Stolfi (talk) 23:55, 18 April 2019 (UTC)

In a non-place numeric system like RNs there we extrapolate at our peril to "place" systems. "One tenful" and "ten ones" are not mutually exclusive, but two ways of looking at the same number - which the old Romans undoubtedly do here. Otherwise the subtractive 9 (IX), which is very clearly a "units" numeral, would never have occurred to them. Of course the Romans "broke their numerals down" to places (hundreds, units, and tens) - that is the main idea our introduction actually introduces. Bur even doing this, "Roman arithmetic" remains very fiddly indeed! Just try long division! For serious calculations they use an abacus incidentally. --Soundofmusicals (talk) 07:43, 19 April 2019 (UTC)

Long division is hard even in Arabic numerals. In Roman numerals, once you realize that they are just base 10 with the digits 0-9 written in silly ways, it is only a bit harder. You must do exacly the same steps and reasoning.
The hardest part is finding each digit of the divisor; namely, dividing A by B given that A is at most 9 times B. That is hard in Arabic too. That requires guessing a digit d, multiplying it by B and adjusting the guess if the product is greater than A, or if A-d*B is B or more.
To do that one must know the multiplication table of the digits by heart. In Arabic there is only one such table. In Roman there are 10 tables (units x units, units x tens, ...), but they only differ by the letters -- so you need to learn only the units x units. If you know that IX times VI is XXXVI, you also know that IX times LX is CCCLX, and that XC times LX is MMMDC.
On the other hand, Roman numerals have one huge advantage over Arabic: there are no numbers beyond 3999 😀.

A point is being missed here that modern "decimal" counting uses ten (not nine) different digits, as it includes a zero, and so allows representation of numbers of arbitrary magnitude simply by place shifting rather than needing distinct figures for each ten-step. In this case, nine is effectively the tenth number (as we start from zero - fencepost error much?), and ten itself is represented with a zero... in the units column, and a one in the tens column, being the equivalent (at least, when clearly followed by a zero) of an X. Similarly five + zero is equivalent of an L, one + zero + zero is C, etc (through to 10,000,000 being equivalent of an overlined |M|... after which RNs either run out of levels, or have to start adding multiple over- and side-lines to signify higher magnitudes). The changing letter was the Roman substitute for adding zeroes; without doing that, you can still only count up to nine (or if you cut short - ninety, or nine hundred... or maybe just four, 44/49, or 444/449). Both are essentially decimal because the magnitude shift kicks in at ten, but one lacks zeroes so has to make do with a different way of signifying that shift. (or... would RNs be better described as duopental, seeing as it's actually broken into paired blocks of five?) 146.199.60.87 (talk) 18:00, 22 August 2019 (UTC)

See the section 'A "base 10" system' below. In my experience "bi-quinary" is the more common term. Martin of Sheffield (talk) 20:44, 22 August 2019 (UTC)

• 2. It is NOT a good idea to make too much of "non-subtractive" notation (e.g. IIII, VIIII etc.). In fact perehps we already do, it these needs to be cut down. Interest in it is really only historical, and it has little or no direct relevance to RNs "as we use them nowadays" (what we need to convey to our reader before we go on to other aspects). The little bow to the way the underlying tally is built up right at the beginning is best isolated (in fact it might even be best to remove it altogether? - unfortunately this leaves a gap) rather than hammered again and again right through multiple paragraphs. --Soundofmusicals (talk) 11:45, 18 April 2019 (UTC)

I agree that everyone should know the modern system, not just the original one. However, I think that starting with the original one makes the idea much easier to understand. It makes it easy to see the most important concept: that a roman numeral consists of four parts, for the four powers of ten, and each part is encoded in a similar way but with a different pair of symbols.
Once that idea is explained, the subtractive notation is easily understood as being simply a hack that lets one write only two letters instead of four for "4", and instead of five for "9". Then the use of "X" in the units part is not confusing: "IX" is still one of the units digits (but "X" without a preceding "I" is not).
It is like the "don't" in English: while that word is essential, the best way to master its meaning and use is to learn the grammar of "do not", and then learn that "don't" is just a shorthand for it. It would be very confusing to try to teach students the use of "don't" from the start, as if it were a verb. ("Why can't I say 'He is not don'ting that'?"). --Jorge Stolfi (talk) 23:55, 18 April 2019 (UTC)

The old Romans themselves already used subtractive numbers from an early date - at least they used them (except, for some reason, for "IV") for the numbers of the gates on the Colosseum - these inscriptions were for daily use by ordinary Romans, so they must have already been pretty standard by then. In any case it is simply incorrect to imagine that they are "post-classical". In this context, the idea of a "pre-subtractive" convention as the "original", while plausible, is essentially hypothetical - and does not (or doesn't) warrant a full exposition. --Soundofmusicals (talk) 07:43, 19 April 2019 (UTC)

The Colosseum was built between 72 and 80 AD, so it is not quite "early date". It was the apogee of the Roman Empire, more than 900 years after the Romans began to use those numerals (to say nothing of the Etruscans before them). Things can change a lot in 900 years...
So, the implicit assumption that the subtractive notation was "original" or "used since the earliest times", besides being logically problematic, is speculation too. We sorely need some reliable source WITH PHOTOS of dated inscriptions from the early period.
(Speaking of which, it would be nice to have a gallery or montage with photos of all 32 extant Colosseum gate numbers. A pity that I did not think of that when I was in Rome a few years ago...)
But, fortunately, since the point of that section is to teach readers how to read Roman numerals, it does not matter when the subtractive notation came into use. And it does not matter whether the Romans thought of "X" as "ten units" or "one tenful". For the modern reader, the latter is definitely the right way to read it. It makes the parsing of Roman numerals much easier and unambiguous, and makes the rules for the four groups exactly the same, except with different symbols.
That is, just as there are nine possible values for the units group, starting with "I" and ending with "IX" or "VIIII", there are nine possible values for the tens group, starting with "X" ("one tenful") and ending with "XC" or "LXXXX" ("nine tenfuls"). With your proposed reading, there would be ten values for the units group, from "I" to "X", but only nine for the tens group, from "XX" ("two tenfuls") to "C" ("ten tenfuls"); since "XIII" would be "10 units plus 3 units", not "1 tenful plus 3 units".
Said another way, the simplest algorithm for reading a Roman numeral (subtractive, non-subtractive, or mixed) is

1. Break the numeral into four successive sections, from left to right: thousands (any "M" letters in front), hundreds (the part consisting of "C" and "D" letters), tens ("X" and "L" letters) and units ("I" and "V" letters); except that any "CM" belongs to the hundreds section, any "XC" belongs to the tens, and any "IX" goes with the units. Some sections may be missing.

2. Translate the units section into a decimal digit from 1 to 9, according to the table "I" = 1, "II" = 2, "III" = 3, "IV" or "IIII" = 4, "V" = 5, "VI" = 6, "VII" = 7, "IIX" or "VIII" = 8, and "VIIII" or "IX" = 9. If that section is missing, write a digit "0" instead.

3. Translate each of the other section into a digit. The same table holds for the tens group, with "X,L,C" instead of "I,V,X"; for the hundreds, with "C,D,M" instead of "I,V,X", and for the thousands, with "M" instead of "I". (The Roman numerals are no longer used for values above 4999, so there cannot be any symbols in the thousands section that would correspond to the "V" and "X" in the units section. Thus that table is only "M" = 1, "MM" = 2, "MMM" = 3, and "MMMM" = 4.)

4. Read the four digits, in the same order as the sections, as a decimal number, in the usual (Arabic) notation

5. Any string of letters that cannot be unambiguously parsed and translated by the above rules is an invalid Roman numeral.

This algorithm seems to be the simplest to learn and execute, both on a computer or in one's head. The table in step 2 could be replaced by an algorithm, like

2a. Translate the units section into a number. Count each "I" as "1", "V" as "5", and "X" as "10"; except that "I" before "V" or "X" counts as "-1", and "II" before "X" counts as -2. Add all these numbers and write the result, which should be a single digit between 1 and 9. If the units section is missing, write a digit "0".

While this variant makes the logic of the system more evident, after a bit of practice people will surely use the table version mentally. (That is how people read written words, especially in English: not letter by letter, but all at once -- as a single "ideogram", or a group of a few ideograms.)
Also, unlike the table version, this variant would also accept "IIIIII", "IIIV", and "IVII" for 6, "IVV", "IIXI" and "VIV" for 9, "IVIIII" and "IVIV" for 8, etc.
All the best, --Jorge Stolfi (talk) 02:34, 20 April 2019 (UTC)

• 3. What we don't want is to picture a complete, but largely hypothetical "additive system" - remembering that (probably) "D" and (certainly) "M" were never part of the "Classical" system at all. Historical concerns need to be kept very much in the background at this stage, of course, we are, as I said concerned first with the system as we use it, BUT we DO need at all costs to avoid incorrect historical information. Your repeated "might be" shows you actually understand this yourself - but we shouldn't talk to our readers in code. "MMMM" - to take the most glaring example - is NOT in any way shape or form "additive" notation for 4,000, and never has been. --Soundofmusicals (talk) 11:45, 18 April 2019 (UTC)

I agree that one must not invent history, not even for pedagogical reasons. So maybe the description of the non-additive system should be limited at "CCCCLXXXXVIIII" or whatever is the largest historically attested value. It would have the benefit of getting to the subtractive system sooner.
On the other hand, since the point of that section would be to teach the how RNs work, not to tell their history, I think that it would be OK to use examples up to "MMMMDCCCCLXXXXVIIII" if SOMEONE has used such numerals at some time for real counting (even in modern times). (As for the history, see the separate thread below.) --Jorge Stolfi (talk) 23:55, 18 April 2019 (UTC)

I think we have already covered this? As often happens, I think we are disagreeing less that we seemed to at first. --Soundofmusicals (talk) 07:43, 19 April 2019 (UTC)

That will have to do for now, as I am very tired and "they" are telling be to go to bed - (I am at the stage of life when I no longer able stay up entirely at my own volition). --Soundofmusicals (talk) 11:45, 18 April 2019 (UTC)

• I restored a few of my edits, and expanded the head section a bit. Please see if those changes are acceptable to you. All the best, --Jorge Stolfi (talk) 04:24, 21 April 2019 (UTC)

Etruscan numerals problem

The Etruscan numerals do not shows properly in my device, do yours?

—Your's sincerely, Soumyabrata 17:17, 17 May 2019 (UTC)

This is a "font" or typeface problem, alas. Although an effort has been made to substitute characters in this article to get as many of them as possible displaying (at least after a fashion) there are a few exceptions. Changing to another default typeface may help - my grat-nephew's computer actually displays more characters (in this article and elsewhere) correctly than mine (they both run Windows 10 on comparable and allegedly compatible machines! Complain to Microsoft (or Apple, if your problem is on a mac). --Soundofmusicals (talk) 13:11, 18 May 2019 (UTC)

Or, yknow... provide them as simple graphics, which will show without issue on any system from the last twenty years (thirty, if they're GIF instead of PNG / SVG), and without need for extra fonts which J. Randomuser may not have the facility to install. You may as well provide images in .PSD format and make the retort that they're perfectly viewable so long as the viewer installs Photoshop or some other advanced image editor. Pages on WP should be built for the LCD. Which in this case doesn't even mean someone browsing with IE6 on their 15 year old eMachines desktop - still-common Win7 and Android Kitkat with reasonably up-to-date versions of Chrome and Webkit are failing to display the characters. At this point in time, proper rendering of those characters is probably no more likely than that of the "aerial tramway" emoji, and as such should be backed up with graphics, rather than expecting exceptional behaviour from a large proportion of the readerbase. 146.199.60.87 (talk) 17:26, 22 August 2019 (UTC)