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How Did Anyone Do Math in Roman Numerals?
51–60 of 163 posts
Re: How Did Anyone Do Math in Roman Numerals?
#52Earlier quoted context omitted.
care to explain why this works?
Unicode has codepoints for roman numerals 1 through 12 and then the base symbols up to one hundred thousand (ↈ) which I just saw for the first time. That Perl allows them in integer literals is strange, but also logical in a weird way. (Now I wonder what other number systems it supports.) EDIT: Ok, so I installed perl6 (rakudo) just to test this out, and it apparently doesn't work out of the box. Pity.
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Re: How Did Anyone Do Math in Roman Numerals?
#53Earlier quoted context omitted.
I think a lot of my confusions when I first learned calculus would have been eliminated with a notation that clearly expressed that derivatives operate on whole functions , not on values. So the derivative of f(x) at x=0 is not some function of f(0), but it is derivative(f)(x). Also, even without derivatives, sometimes the expression f(x) refers to the whole function, sometimes just a particular value of it at a spec…
I've noticed that I understand what is going on much more when a function is written in code than in its mathematical form. A lot of that is familiarity but I don't think all of it is.
Code's easy for me (unless "mathy" in appearance like Haskell) but mathematical notation's always made me feel dyslexic.
I'd love to see this beauty or clarity or whatever that people find in mathematics, but I've never caught even a hint of it. Seems like it needs a good IDE to make up for deficiencies in its language.
Re: How Did Anyone Do Math in Roman Numerals?
#54You know what I've always wondered? How did they pronounce each number? I mean, I read it "eye, eye-eye, eye-eye-eye, eye-vee, vee, vee-eye."
But of course, there's no way they actually said it that way.
Right? Right??
Re: How Did Anyone Do Math in Roman Numerals?
#55I always thought that roman numerals would be a simpler way to do basic arithmetic and might lend itself more to simple commerce. For example: III represents 3 things, so III + II = IIIII For simple commerce application that is simpler, I just have to then remember that IIIII = V, and VV = X and XXXXX = L, LL = C. Armed with just those simple rules I could probably get by in the market place in Rome.
With Arabic numbers, I have to learn that 1 is one thing, 2 represents 2 things, 3 represents 3 things and so on. Then I have to remember that 2 + 2 = 4, and 3 + 2 = 5, there is more memorization required.
Where Roman Numerals for someone with little or no education could get by in the market square with some simple rules and even use twigs as a primitive calculator. It is not until you get to much more complex ideas that the Arabic notation wins out.
So perhaps, different notations lend themselves better or worse depending on the application ?
Just some random thoughts that this very interesting post brought to mind.
Re: How Did Anyone Do Math in Roman Numerals?
#56Earlier quoted context omitted.
care to explain why this works?
Unicode has codepoints for roman numerals 1 through 12 and then the base symbols up to one hundred thousand (ↈ) which I just saw for the first time. That Perl allows them in integer literals is strange, but also logical in a weird way. (Now I wonder what other number systems it supports.) EDIT: Ok, so I installed perl6 (rakudo) just to test this out, and it apparently doesn't work out of the box. Pity.
I'm not a compiler dev, but it looks fairly new and appears to have many other special Unicode ranges too, including camels and beer mugs???
https://github.com/rakudo/rakudo/blob/beec02a6fa69e3ac290b4d...
Re: How Did Anyone Do Math in Roman Numerals?
#57It's interesting how the notation used can encourage or retard progress. For example, Leibniz's calculus notation was vastly superior to Newton's, and calculus theory advanced much more quickly where Leibniz's notation was used. https://en.wikipedia.org/wiki/Leibniz%27s_notation
About this particular case: why hasn't Euler's notation ( https://en.wikipedia.org/wiki/Notation_for_differentiation#E... ) become the clear winner? I mean, its the only one that is both not confusing for beginners (because it doesn't trick them into the "cool, let's `simplify` the dx at the denominator with the next one" mindset) and it also translates easily to code (or other 1D encoding), like you can write "secon…
I like that the Euler notation makes it more clear that derivation is a higher order function.
Re: How Did Anyone Do Math in Roman Numerals?
#58I had, for some reason, never thought of that directly. Although I do remember some joke on arithmetics in one of the Asterix comic books. But reading this article and trying out a few things, I found it was great fun!
...which is funny (the Asterix thing), because spoken French isn't exactly brilliant with numbers either: 99 for example is expressed as "eighty nineteen", 70 as "sixty ten". My friends lived in France a while and said their landlady could never count their rent (paid in cash) correctly first time. Always stumbled somewhere between 100x+60 and 100x+100 for integer values of x. The Swiss have corrected this in Swiss F…
73 is soixante treize and is just this : a word (ok, two) one learns by heart. No French think that this is 60+13, but just 73.
I understand the point about logics in counting, but this is just a new word to learn, like déposition or balafré. One can analyze these words from an ethymology perspective but normally you just learn them by heart.
At least this is what I do in English when I need to remember went or throughout .
Re: How Did Anyone Do Math in Roman Numerals?
#59It's interesting how the notation used can encourage or retard progress. For example, Leibniz's calculus notation was vastly superior to Newton's, and calculus theory advanced much more quickly where Leibniz's notation was used. https://en.wikipedia.org/wiki/Leibniz%27s_notation
About this particular case: why hasn't Euler's notation ( https://en.wikipedia.org/wiki/Notation_for_differentiation#E... ) become the clear winner? I mean, its the only one that is both not confusing for beginners (because it doesn't trick them into the "cool, let's `simplify` the dx at the denominator with the next one" mindset) and it also translates easily to code (or other 1D encoding), like you can write "secon…
It's not much more useful than Newton's. The greatest point of Leibniz' notation is that you can do those things such as simplifying dx, or moving dy to the other side of the equality.
It is confusing to beginners, but it's very useful once you understand it.
Re: How Did Anyone Do Math in Roman Numerals?
#60Earlier quoted context omitted.
care to explain why this works?
Unicode has codepoints for roman numerals 1 through 12 and then the base symbols up to one hundred thousand (ↈ) which I just saw for the first time. That Perl allows them in integer literals is strange, but also logical in a weird way. (Now I wonder what other number systems it supports.) EDIT: Ok, so I installed perl6 (rakudo) just to test this out, and it apparently doesn't work out of the box. Pity.
Weird, I just installed it (via homebrew) and it's working for me