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How Did Anyone Do Math in Roman Numerals?

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Re: How Did Anyone Do Math in Roman Numerals?

#91

Post by Too »

Kluny wrote: post #71
gruturo wrote: post #46

Earlier quoted context omitted.

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, th…

Is it some American thing that measuring things as fractions is easier than decimals? To me being used with metric system 1.6L is equally intuitive as 1 2/3, maybe even more intuitive.

It's just hardwired in the brain how much 0.6, or 60%, represents, I think internally my brain finds the closest easy references like 10%, 25%, 33%, 50% or 75% and then interpolates or adds or removes chunks of 10%, the rest is rounding errors. I mean, i dont have to think consciously if 0.69 is more or less than 75% and i know exactly where both 66.66% and 75% is and can place it somewhere in between.

Re: How Did Anyone Do Math in Roman Numerals?

#93

Post by Spivak »

maxxxxx wrote: post #67
jeffwass wrote: post #35

Earlier quoted context omitted.

I was about to post that in my opinion base-12 is superior to base-10. But someone beat me to it. In a six-fi novel I'm writing, an advanced alien civilisation uses base-12. As to your question specifically regarding base-16 instead of base-12, it depends. Decimal itself is just a bizarre choice, most likely due to humans having literally ten digits. In decimal we can represent exact fractions of 1/2, 1/5, and 1/10 (…

It seems the consensus is that base like base 7 or base 11 definitely would a bad idea.

Unless you believe in the consistency of inconsistency prime bases would be annoying to work with.

Re: How Did Anyone Do Math in Roman Numerals?

#94

Post by SAI_Peregrinus »

oaktowner wrote: post #54

You 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??

Arabic numeral: Cardinal number name | Ordinal number name, with conjugation information

  1: Unus -a -um     | primus -a -um
  2: duo, duae, duo  | secundus -a -um
  3: tres, tria      | tertius -a -um
  4: quattuor        | quartus -a -um
  5: quinque         | quintus -a -um
  6: sex             | sextus -a -um
  7: septem          | septimus -a -um
  8: octo            | octavus -a -um
  9: novem           | nonus -a -um
  10: decem          | decimus -a -um
  11: undecim        | undecimus -a -um
  12: duodecim       | duodecimus -a -um
  13: tredecim       | tertius decimus -a -um
  14: quattuordecim  | quartus decimus -a -um
  15: quindecim      | quintus decimus -a -um
  16: sedecim        | sextus decimus -a -um
  17: septendecim    | septimus decimus -a -um
  18: duodeviginti   | duodevice(n)simus -a -um
  19: undeviginti    | undevice(n)simus -a -um
  20: viginti        | vice(n)simus -a -um
  30: triginta       | trice(n)simus -a -um
  40: quadraginta    | quadrage(n)simus -a -um
  50: quinquaginta   | quinquage(n)simus -a -um
  60: sexaginta      | sexage(n)simus -a -um
  70: septuaginta    | septuage(n)simus -a -um
  80: octoginta      | octoge(n)simus -a -um
  90: nonaginta      | nonage(n)simus -a -um
  100: centum        | cente(n)simus -a -um
  500: quingenti     | quingente(n)simus -a -um
  1000: mille        | mille(n)simus -a -um
From Cassell's Latin English Dictionary, second edition.

Re: How Did Anyone Do Math in Roman Numerals?

#95

Post by criddell »

jaymzcampbell wrote: post #11
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

Another excellent example of the power of good notation to aid understanding and increase efficiency is Dirac, or Bra-Ket notation[1] used in Quantum Mechanics. This allows you to do all sort of calculations with wave functions without constantly grinding to a halt bogged down by integrals and conjugates all over the place. The ladder operators (aka raising & lowering), really put this notation to good use[2]. It wou…

Would you say the same is true for Feynman diagrams in QED?

Re: How Did Anyone Do Math in Roman Numerals?

#96

Post by kbenson »

mywittyname wrote: post #87
kbenson wrote: post #68

Earlier quoted context omitted.

That's just addition. Do you only need addition in a marketplace? Subtraction requires you convert to another form prior to actually subtracting, so you have to know what form you want. Multiplication and division? Harder.

You'd use the take-away method. XX - III = XVIIIII - III = XVII It's literally just addition in reverse. Instead of having reduction passes where you convert IIIII to V, etc., you'd have an expansion passes to convert V to IIIII.

Yes, that's what I said. But you chose a simple case. Try subtracting more complex numbers, specifically something more complex for the subtrahend. E,g, 42 - 13, which is XLII - XIII. Not only to you have to convert, but you have to convert both sides, and to either a similar format that can be subtracted, or to a lowest common format as suggested above (which is not roman numerals, BTW, so you need to know two systems, Roman numerals, and the alternate format with no prefixes to use to arithmetic).

And that still isn't event touching multiplication or division, which are very common in simple commerce. 100 coins for 8 chickens, or 60 coins for 5 chicken. What's the better deal? I want 7 of these 3 coin breads. You say that's 30 coins? Guess I should check that...

Re: How Did Anyone Do Math in Roman Numerals?

#97

Post by yorwba »

wambotron wrote: post #60
yorwba wrote: post #21

Earlier quoted context omitted.

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

I used the version from the Ubuntu Xenial package repositories, and that perl was apparently from November 2015. I guess such is life when you go with long-term support and stable packages.

Re: How Did Anyone Do Math in Roman Numerals?

#98

Post by Sprocklem »

Edmond wrote: post #26
maxxxxx wrote: post #24

Since we have a lot of math experts here I thought I'd ask a question I was always wondering about: Is there an inherent advantage or disadvantage to using the decimal system as we do? Somehow I think octal or hexadecimal would be easier but I am not sure.

I am going to guess base 10 is prevalent because we have 10 fingers ? :) I speak a language (Mende) that has no formal mathematics but counting is done in base 10; there are 10 individual words for 1 to 10 , the word for one is "yaella", the word for 10 is "poo", the word (really expression) for 11 is "poo mahun yaella", which literally translates to 10 on top of 1 ie 10+1...I can only think they stopped at 10 words…

> I am going to guess base 10 is prevalent because we have 10 fingers ? :)

Yeah, basically. There are other ways to count on your hands though. I seem to recall there are places that count on their hands using the 12 finger joints (or segments), and it works just as well.

Edit: To clarify, they use their thumb to point to the joints or segments on each of their fingers, in turn.

Re: How Did Anyone Do Math in Roman Numerals?

#99

Post by maxxxxx »

Too wrote: post #91
Kluny wrote: post #71

Earlier quoted context omitted.

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, th…

Is it some American thing that measuring things as fractions is easier than decimals? To me being used with metric system 1.6L is equally intuitive as 1 2/3, maybe even more intuitive. It's just hardwired in the brain how much 0.6, or 60%, represents, I think internally my brain finds the closest easy references like 10%, 25%, 33%, 50% or 75% and then interpolates or adds or removes chunks of 10%, the rest is roundin…

I agree that fractions are a very American thing. A lot of stuff is expressed as fractions here. But I bet a lot of people couldn't tell you whether 5/16 is more then 1/3 or not.

Re: How Did Anyone Do Math in Roman Numerals?

#100

Post by bdamm »

hinkley wrote: post #80
kbenson wrote: post #64

Earlier quoted context omitted.

> 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 an…

And I'm betting that the 5n-1 behavior was probably only used by those with education, and may have even been a class distinguishing numeric feature, with the benefit of making numerals slightly impenetrable to those who didn't know the trick.
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