See the Wikipedia article on Welsh numerals. Welsh has both a vigesimal form and a decimal form.
Except, of course, for a few echos of a base-12 system; namely, “eleven” (“one left over”) and “twelve” (“two left over”). I mean, they still reference base ten, but I’m referring to how we don’t start our “-teens” until you get to 13.
(Which happens to make “teen” in English a convenient way to express a certain period in life, one that has to have a different association or etymology in other languages, like Spanish adolescente).
Probably one of those 14 century digital clocks where you couldn’t tell the hour based on the position of the little hand.
I heard somewhere that IV in particular was avoided because J hadn’t yet appeared as separate from I, and U hadn’t yet appeared as separate from V; thus, the god JUPITER was also IVPITER. It would have been some sacrilege to start spelling his name to create a number. Anyone ever hear this?
I have my doubts the subtractive method was used originally. When you can have four consecutive numerals the same and divisions of 5, 50, and 500 you don’t need any subtractions. Doesn’t mean they thought about it that way though. The letters we use now for Roman numerals weren’t consistently defined in the past.
It is worth pointing out that the Danes actually adopted a simpler system. When I spent six weeks there in 1971, older folks would say fem og halv tres (five plus halfway to the third 60) for 55, people who had gone through school since about 1950 said femti fem. Since that was over 50 years ago, I imagine every one has adopted the new system of counting by now.
Time for a joke: Why can’t a computer scientist tell Halloween from Christmas? Because Oct 31 = Dec 25
One Louder.
Cf. the Swiss/Belgian system for numbers from 70 to 99 (septante, huitante/octante, nonante).
Which completely ignores the question. How did they say the number? It’s easy enough to point to the word for “three”, but words for large numbers must be constructed in some systematic way. What was that system?
I think CC really was asking if Roman numerals were pronounced like the number they represented or some other way. As far as anyone knows, they really did just say the number.
Yeah, that’s the point I was trying to make (but didn’t). The utility of a positional number system seems to be that you can do complex calculations on paper. Back then only the wealthy could afford paper and some of their astronomers did use a positional number system.
It does make me wonder if the spread of Arabic numerals tracks with the availability of cheap paper.
Weren’t Arabic numerals already in widespread use in Europe by the time small watch faces were even technologically possible?
I have no idea. I’ll take your word for it. Roman numerals were and are still used on clock and watch faces.
I was actually asking. A quick search suggests that, yes, Arabic numerals were already in use by the time watches became a thing. However, the first example given in the Wikipedia article is a 16th century watch with both Arabic and Roman numerals. Why must everything be so complicated?
They say fifty or sixty first then the ones. 62 is Sexaginta duo. Just like we say Sixty two. Ignore the bit with the Roman numbers, the Romans just said the number in latin.
Yes.
The subtractive method was used as early as the first century AD, according to this.
This is a tombstone found in present-day Bulgaria dated to the second half of the first century and you can clearly see fourty-four written as XLIV. That is indeed late, well into the Imperial era. Moreover this is a ceremonial inscription, leaving open the possibility that its use was for aesthetic reasons.
I also found this WaPo story that touches on the raging debate at the turn of the 20th century about how to properly render 1900 in Roman numerals. In it, a classics professors says the Romans were “indifferent” as to which was the proper way.
It occurs to me too that the Roman system then matches the abacus. Four beads and a separate “5” bead. Move each bead in turn to the right as you count. From four to five, move the beads back and the 5-bead to the right.
Beads which are on the right:
I
II
III
IIII
V
VI
VII
VIII
VIIII
now move all to the left, go to the second rown of beads, move 1 to rhe right.
X
At a certain point it became easier (less confusing?) to write as subtract 1 than count 4, hence IV and IX etc.
But (afaik) they did just say the number in some systematic way, not constructed new words. E.g. 1,000,000,000 = decies milies centum milia [or something].
At least, e.g. here is a quote from Suetonius:
professus quadringenties milies opus esse…
Note, he’s talking about money, which is where such big numbers typically naturally came up. Second, speaking of being systematic, note that even though he is talking about $40,000,000,000, he does not say quadringenties milies centenis milibus sestertiorum — that part is understood.
There was not a special word for million or billion, if I understood correctly, certainly not scientific notation or prefixes. As for Roman numerals, a line placed over a figure multiplies it by 1000.
Arabic numbers are all made by addition, not subtraction. Forty-eight is “eight and forty”: thamāniyah wa-arba‘ūn.
But speaking of subtractive numeral systems: Finnish for nine is yhdeksän, eight is kahdeksan. It’s clear that the former is derived from yksi ‘one’ and the latter from kaksi ‘two’. The -eksan suffix may be analyzed etymologically as ‘is not there’, here it means ‘subtract from ten’.
In the related Uralic language Komi, nine is ökmys, eight is kökjamys - derived from the same Uralic roots for ‘one’ and ‘two’ with a suffix that means ‘lacking from ten’.
The Malay word for nine is sembilan, from se- ‘one’ and ambil ‘take’. Eight is delapan, from dua ‘two’ and alap ‘take’.
Yes, I’ve read that. It was compared with 15 written in Hebrew numerals. Ordinarily י yod is 10, and ה heh is 5, so 15 should be yod-heh. But when you put them together it spells the beginning of Yahweh. Yod-heh counts as a divine name on its own: the Rastafari “Jah.” So this one exception uses ט ṭeth (9) and ו vav (6) to write 15. When written together: טו it looks like it should be pronounced “ṭu.” This explains why the Fifteenth of Av is called Ṭu be-Av. (The real word for fifteen is ḥamesh ‘esreh.)
Is there any language that has two different words for a number, one for the number itself and one for the numeral that represents the number? Such a situation seems unusual to say the least.