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A building near my workplace has a very large carved inscription: $MDCDXXXIV$

As it looks like roman numeral, I was trying to see what year it was meant to represent. Logically, I'd think it's 1934, but it should be written $MCMXXXIV$.

Is $MDCD$ a valid replacement for $MCM$, like $IIII$ is a valid one for $IV$ in some circumstances?

SteeveDroz
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  • There are two rules for Roman numerals. (1) Numerals are written in descending order of size and (2) an out-of-place numeral should be understood as subtraction from the next numeral. Many numbers have more than one representation under these rules. Some people prefer the shortest representation - that's just a preference, not a law. For example, the 54th entrance at the Colosseum is numbered LIIII rather than LIV and the 49th is XXXXVIIII rather than IL or XLIX. – in_mathematica_we_trust Sep 20 '13 at 10:04
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    @in_wolfram_we_trust I think you should make your comment an answer, possibly with a link to some source that explains this. – Vedran Šego Sep 20 '13 at 10:23
  • @in_wolfram_we_trust The "subtractive" rule became "official" only during the Middle Ages. Stone carvers in ancient times were not bound to it and something like IIX for VIII can be seen (it requires less space). – egreg Sep 20 '13 at 10:42
  • @egreg: Representations like $iiij$ for $4$ and $\ell xxxxviij$ for $98$ remained very common throughout the Middle Ages. (These are actually quoted from $$x^M;guld; iij^C;guld;\ell xvij;guld;iiij^M;lb;vij^C;lb;\ell;xxxxviij;lb;x;s;ij;d$$ from $1410$: $10367$ gulden, $4798$ pounds, $10$ shillings, $2$ pence. And in the late Middle Ages and Renaissance all sorts of variant notations appeared: $CCCM$ for $300,000$ ($1550$), $M\cdot CCCC\cdot8II$ for $1482$ (~$1600$), $MCCCC4XVII$ for $1447$ ($1447$). – Brian M. Scott Sep 20 '13 at 21:48
  • @BrianM.Scott Perhaps I should have said "widespread" rather than "official". But the idea I wanted to convey is that the Romans didn't really have a precise rule about when using the subtractive rule. – egreg Sep 20 '13 at 21:53
  • @egreg: I agree completely with the spirit of your comment; I’d simply go further and say that the Romans rarely if ever used it, and judging by what I’ve seen of medieval accounts, the additive notation remained more common through the Middle Ages. I’d go so far as to say that the ‘rule’ is largely a modern invention that has never been strictly adhered to in practice (e.g., dates on buildings, some clock faces). – Brian M. Scott Sep 20 '13 at 22:01
  • as far as clock faces are concerned, IIII should be more "correct" than IV. I think that the subtractive rule is not a modern invention, but just a shortcut devised by carvers. By the way, M is a later retroficting: the actual characters used are a C, a I and a backwards C – mau Sep 22 '13 at 10:05

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no. But keep in mind that neither IMM for 1999 is, even if many people use it. The only "official" difference numbers are IV, IX, XL, XC, CD, CM.

mau
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