How Did Anyone Do Math in Roman Numerals? • Hacker News Board

Re: How Did Anyone Do Math in Roman Numerals?

#71

Post by Kluny » Fri, Jul 21, 2017, 3:40 PM UTC

gruturo wrote: post #46

sbuttgereit wrote: post #27

Earlier quoted context omitted.

I apologize for not being one of the experts you speak of, but I do know of others that say there are superior number bases to use for everyday counting. http://www.dozenal.org/drupal/content/brief-introduction-doz... These people believe that base 12 would be superior to base 10. And they do make good points, expressing fractions like those in 3rds become easier. Is it superior in the grand scheme? I'll leave that d…

Maybe this is just me being very naive, but how does it help? It doesn't actually change the properties of the underlying numbers. 10 (decimal) is not divisible by 3, and rewriting it in base 12 as A won't change that. You simply get 29.4 instead of 33.3...

If a kilo, for example, was made of 12 x 12 x 12 (1728) grams instead of 1000 grams, then you could sell stuff by the half-kilo, third-kilo, and 1/12 kilo without going into decimals. The number 1728 would still be written as 1000 in base 12, but 1/3 kilo would be 400 grams instead of 333.3333... as it is now. Useful if you're a grocer.

Other applications, like documenting how much oil to put in a car or whatever, there would be more options for picking memorable numbers. Like, my motorcycle takes 1.6L of oil. It could be 1 represented as 1 2/3 L, which is more visually intuitive. Not sure if I explained that well enough, maybe someone else has got a better metaphor handy...

Re: How Did Anyone Do Math in Roman Numerals?

#72

Post by tathougies » Fri, Jul 21, 2017, 3:47 PM UTC

malnourish wrote: post #70

zw123456 wrote: post #55

I 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 numb…

I'm not 100% sure, but through anecdotal experience and from what I've read (although haven't vetted), we lose track of counters at ~8 of them. That is, III is easily discernable as 3 'I's, but take IIIIIIIII, and try to recognize how many 'I's are there immediately.

That's why you group five I's into a V?

Re: How Did Anyone Do Math in Roman Numerals?

#73

Post by Maken » Fri, Jul 21, 2017, 4:02 PM UTC

nnq wrote: post #34

WalterBright wrote: post #6

It'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…

What I can't understand is why anybody still used Newton's notation. Also, at least for me Leibniz notation tends to make pen-and-paper symbol manipulation simpler.

Re: How Did Anyone Do Math in Roman Numerals?

#74

Post by ufo » Fri, Jul 21, 2017, 4:04 PM UTC

gruturo wrote: post #46

sbuttgereit wrote: post #27

Earlier quoted context omitted.

I apologize for not being one of the experts you speak of, but I do know of others that say there are superior number bases to use for everyday counting. http://www.dozenal.org/drupal/content/brief-introduction-doz... These people believe that base 12 would be superior to base 10. And they do make good points, expressing fractions like those in 3rds become easier. Is it superior in the grand scheme? I'll leave that d…

Maybe this is just me being very naive, but how does it help? It doesn't actually change the properties of the underlying numbers. 10 (decimal) is not divisible by 3, and rewriting it in base 12 as A won't change that. You simply get 29.4 instead of 33.3...

Another thing is that multiplying and dividing by 2 and 5 is easier in base-10. For example, to divide by 5 you multiply the number by 2 (just add it to itself) and then divide by 10 (a right shift).

On the other hand, to divide by 3 you basically need to do long division.

Re: How Did Anyone Do Math in Roman Numerals?

#75

Post by [deleted] » Fri, Jul 21, 2017, 4:05 PM UTC

zw123456 wrote: post #55

I 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 numb…

[deleted]

Re: How Did Anyone Do Math in Roman Numerals?

#76

Post by riffraff » Fri, Jul 21, 2017, 4:07 PM UTC

zw123456 wrote: post #55

I 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 numb…

you skipped over III + I = IV, and VI+III = IX.

Subtractive notation is confusing.

Re: How Did Anyone Do Math in Roman Numerals?

#77

Post by tnecniv » Fri, Jul 21, 2017, 4:08 PM UTC

WalterBright wrote: post #6

It'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

"By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race."

-- Whitehead

Re: How Did Anyone Do Math in Roman Numerals?

#78

Post by sanityUnbounded » Fri, Jul 21, 2017, 4:11 PM UTC

zw123456 wrote: post #55

I 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 numb…

Curious, why do you have to remember that 2 + 2 = 4 & 3 + 2 = 5? Once you know the values the symbols represent, at that point isn't it similar in simplicity to roman numerals?

II + II = IIII

2 + 2 = 4

Don't see how the latter problem lends itself to any more memorization beyond symbols

Re: How Did Anyone Do Math in Roman Numerals?

#79

Post by bllguo » Fri, Jul 21, 2017, 4:13 PM UTC

riffraff wrote: post #76

zw123456 wrote: post #55

I 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 numb…

you skipped over III + I = IV, and VI+III = IX. Subtractive notation is confusing.

I believe some Roman inscriptions were found to use additive, i.e. III + I = IIII, VI + III = VIIII. Certainly I feel that nobody would look at IIII and be confused as to what it represents.

Re: How Did Anyone Do Math in Roman Numerals?

#80

Post by hinkley » Fri, Jul 21, 2017, 4:16 PM UTC

kbenson wrote: post #64

zw123456 wrote: post #55

I 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 numb…

> 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. I'm not sure having to look at all the possible conversions of a context free grammar to reduce the state to its minimum is actually easier than…

Just thinking about how they work here, it looks like Roman numerals are effectively a base 5 notation, with a special behavior for 5n - 1.

In base 10 math there are 18 outcomes for adding two digits, and you have to do carry operations for 9 of them. With carries there are 20 and you have special cases for 10. In Roman numerals there are 10 outcomes, you have to do carries for 5 of them, special casing for two (4 and 9), the numbers are at least one digit longer and non uniform, so it's harder to line up the columns to do an addition in the first place.

No wonder algebra was invented in Arabic.