I am looking to teach my eldest son arithmetic with Roman numerals (in the genuine sense without conversion to a decimal notation first). Is there scope for a forum on this subject area? It is quite good fun (well, addition is quite straightforward, subtraction is relatively easy multiplication gets more interesting and division is where the fun really starts!) Alex

This is a nice video that explains Roman numerals and at least the addition and multiplication of them.

This is the resource I have used in the past: http://turner.faculty.swau.edu/mathematics/materialslibrary/roman/ "It is important to remember that the Romans did not think in terms of our familiar numbers—they thought only in terms of the Roman Numbers. They were familiar with numbers such as XIII and MCMLXVIII directly without thinking these were 13 and 1968. They had a lifetime of experience with numbers represented only as Roman Numerals."

It's much more difficult to think in different numbers than it is in different words, at least for most people. Most of those I know who are fluent in the language of a place they have lived in for many years do mental arithmetic in their native language, even if they rarely use it otherwise and haven even forgotten large chunks of it. Edited to add: apart from subcontinental shopkeepers, in the UK, who when speaking their own languages to each other, at least in their shops, often revert to English numbers, which is positively bizarre. I don't know any well enough to lead the conversation round to why they do this.

Given that you've said many Georgians prefer anything but their own numerals, I don't think that counts. It's obvious that some older numbering systems are far less efficient than others. But Hindi numbers, as far as I can see by googling, appear boringly normal. I wonder if speakers of languages like Polish hate their numeral system, or just find it fiddly. Also, does Russian do anything like this?

Yep. Adna kniga - one book ( adj. fem. + nominative ) Dve knigi - two books ( noun fem. + genitive ) Tri knigi - three books ( noun + gen. ) Čitîre knigi - four books ( id. ) Pjatj knig - five books ( noun + gen. plural ) etc... Some of the numbers decline, others don't. Sometimes both halves of a number decline, sometimes just one does. Sometimes you use special numbers when you're counting people, but only if there's seven or less of them. The Russian counting system essentially consists of a colossal middle finger pointed toward the West.

I'd recommend trying Egyptian numbers instead. They are quite straightforward, well adapted to the decimal system and in theory require nothing but counting objects. You can multiply using original Egyptian techniques of combining duplications and multiplications by 10. I tried it with my daughter, she liked it. But I've never done fractions and divisions with them. Roman numbers are not so great for the decimal system (because of V, L, D) and the principle of subtraction (IV = IIII) is a mess. Moreover, they look exotic when used for numbers over a few thousands. (Eight Egyptian digits denote numbers up to one million.) I'd suppose they thought of MCMLXVIII as mille nongenti sexaginta octo. The language itself suggests a decimal system and decomposes the number into one thousand, nine times one hundred, something having to do with six and eight. I'd say, the written representation is counterintuitive. Come on, no one knows how to decline them. I think usually I only decline the last component (gen. 52: piisjat dvuh instead of pjatidesjati dvuh).

Heh, true. I'm honestly glad for that as there's no way I'd get them all right if I had to decline them in the middle of saying something.