As shown here:
Roman Numerals - The Frantics
And 11 was what?
That’s probably it. You can’t have a positional numbering system without the zero, and the Greeks and Romans never developed that concept.
On the number of our fingers as the origin of the decimal system: There’s an insinuation in the Hitchhiker’s Guide to the Galaxy novels that the big question about life, the universe and everything (the answer to which is, as we all know, 42, but we don’t know the question) might be “What is six multiplied by nine?”. Of course, 6 by 9 is 54, not 42, and that’s part of the joke. But some committed Douglas Adams fans pointed out that in a base thirteen system, 54 (decimal) would be written as 42, and speculated whether Douglas Adams wanted to imply here that God had thirteen fingers on His hands. Adams’ response to this, in the foreword of a later Hitchhiker edition, was simply: “I might be a very sad person, but I don’t make jokes in base thirteen.”
Maybe we moderns are graphic chauvinists.
Nowadays paper is ubiquitous and practically free. I don’t think that was the case 2000 years ago. So even if they had our system back then, how would they use it? What would they write with and on what? A wax tablet? Well, the hand abacus in dtilque’s seems to be about the same size but seems to me, at first blush, to be at least quicker for the types of calculations difficult to to in your head. That is to say, those involving large numbers. The abacus can represent large numbers in a more compact and easy to parse form than written Arabic numerals on paper.
Maybe it says something that the only Romans using a written positional system were what today we would call academics.
Steve?
Wax tablets were in use (they had the advantage of being erasable), but not exclusively. The classic writing material of antiquity was papyrus, made from the fibers of a swamp plant. The Romans produced and traded it in large quantities. Of course it was much more expensive than paper is today, so its use was restricted to the wealthy - but those had access to it, and Rome had a flourishing book trade with texts hand copied onto papyrus scrolls (the Romans measured the length of a text by the number of scrolls it took to write it down, and the Latin word volumen, origin of our modern word “volume”, originally meant a scroll). It’s not as if they didn’t have anything they could have written numbers on.
Parchment, made from animal skin, was also used, but it was much more expensive than papyrus.
I don’t know about more compact— are the columns on your paper really wider than the columns of an abacus?
An abacus is a practical and efficient mechanical calculator, though, and you do not need to waste a bunch of paper on intermediate sums that need not be recorded.
Thank you!
Although I studied Latin in school for two years (as well as some time on my own), I have to admit that I never saw a table of number names that went beyond ten or so.
What interests me about that table is that some numbers definitely follow the “logic” or pattern of Roman numerals – “nineteen” is “undevginti”, which I can rea as “one from twenty”, corresponding to the Roman numeral XIX, with one subtracted from twenty. But “eighteen” is “duodeviginti”, o “two from twenty”, yet the symbol is XVIII, which doesn’t follow that logic at all.
It shows that the Romans had two different ways of thinking about the numbers – the logic of written Roman numerals and the logic of those written out in text, both of which differ from our english-language way of simply adding units to the last number of groups of ten. I wonder if the spoken numbers differed from any of these, but suspect it was the same as the written-out version.
There are other ways of counting, too. The French fashion of calling the number “70” as “soixante dix” (“sixty and ten”) doesn’t correlate with either the english or any of the Roman styles. Then “80” is “quatre vingts” (“four twenties”)
The “quatre-vingts” style stuff is Celtic, not Latin.
Seems like the Arabic system is not only simpler to calculate and compute in, but certainly simpler to pronounce. 48 was duodēquīnquāgintā quadrāgintā octō ? Yikes.
CENTURION: ‘Um’. Understand?
BRIAN: Yes, sir.
CENTURION: Now, write it out a hundred times
Isn’t it either duodēquīnquāgintā or quadrāgintā octō? I think you have a choice, like saying forty-eight or four dozen.
Danish uses the same logic, albeit a bit differently:
Tres = 60 and is a shorter form of tresindstyve where tres is three and tyve is 20
Fjärs = 80; fjärsindstyve: fjär is four
Fems = 100; femsindstyve, fems is five (however, this is archaic, but fems is still used to construct 90: Halvfems.)
Because wheras French adds for the uneven intervals (50, 70, 90) Danish subtracts. French 75 is 60+15 (soixante-quinze) and Danish Fem og Halvfjers. Halvfjers is short for halvfjersindstyve or Half four by twenty. So 75 in Danish is five and half four.
Oh and Danes uses the German style: en og tyve (German ein und zwanzig) i.e. one and twenty.
If you made it this far, you have read more about numbers in Danish than you ever wished for. You’re welcome.
I was pointing out that it’s a different way of conceiving of the numbers. That itis of Celtic origin would explain why.
That XIX seems to follow the “logic” of the written out name is something of a coincidence. The prefix-subtraction form of Roman numerals is not the original form. Originally, 19 was written XVIIII. I’m not sure when the prefix-subtraction form was adopted, but it was fairly late.
As did old English and middle English. Which leads one to wonder if the adoption of Arabic numerals led to the shift to the modern english form.
I know that older clocks wrote “4” as “IIII” and “9” as “VIII”, rather than “IV” and “IX”. I got the impression (which haven’t verified) that the “subtractive” form might have been tken up to make clock numerals less cumbersome and easier to read.
This is correct. III and IV look too much alike on a small watch face. Obviously it should be clear from the position. It’s an aesthetics thing.
The just so story I heard was that III and IIII were difficult to tell apart from a low point of view standing on the ground near a tall clock tower.