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

Re: How Did Anyone Do Math in Roman Numerals?

#61

Post by nachexnachex » Fri, Jul 21, 2017, 3:16 PM UTC

jessriedel wrote: post #41

amelius wrote: post #13

Earlier quoted context omitted.

I prefer Mathematica's notation over Leibniz's, because it is not as ambiguous (dx can also mean d TIMES x, as a simple example, but also dy^2 can mean d(y^2) and (dy)^2)

I'd go stronger than this and say that Leibniz's notation is actively harmful. It is very useful for quickly doing certain kinds of computations, but at the expense of conceptual understanding for students. Obviously, it's fine to use whatever computational aids you want when you understanding things, but most students are taught nothing but this fragile notation.

It's useful for solving (or partially solving for a set of conditions) linear differential equations, say in the fields of mechanics or electromagnetism. One can work with dx and dt as if they were just factors and move them around quite intuitively.

In the same line, it's great at shining a light on the substitution rule for integration.

Given that your point that it can be obscure at first remains valid, I'd walk the middle line of introducing students to the f'(x) notation first; and after the introduction to integrals introduce this notation to them.

Re: How Did Anyone Do Math in Roman Numerals?

#62

Post by marcosdumay » Fri, Jul 21, 2017, 3:17 PM UTC

empath75 wrote: post #25

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.

The higher the base the more combinations of numbers you have to memorize to do basic arithmetic, and fewer steps you have to take when doing things like addition. I'm sure there's a sweet spot. I don't know that decimal is necessarily it.

The most efficient basis when you take into account both storage and calculation work is binary. That's not exactly the reason our computers use it, but it's one reason why they never moved away from it.

But humans are kinda complex, and don't trade well long term learning for boring tasks. We seem to be great exactly around base 10 (probably 12 would be perfect, like people already said).

Re: How Did Anyone Do Math in Roman Numerals?

#63

Post by flatline » Fri, Jul 21, 2017, 3:19 PM UTC

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??

That's certainly one way to do it...

http://www.youtube.com/watch?v=xnuetbfDLpE&t=1m14s

Re: How Did Anyone Do Math in Roman Numerals?

#64

Post by kbenson » Fri, Jul 21, 2017, 3:19 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…

> 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 some simple arithmetic in our current system.

Re: How Did Anyone Do Math in Roman Numerals?

#65

Post by madcaptenor » Fri, Jul 21, 2017, 3:22 PM UTC

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??

There are words for numbers in Latin. From Wiktionary (https://en.wiktionary.org/wiki/Appendix:Latin_cardinal_numer...): unus, duo, tres, quattuor, quinque, sex...

Just like an English speaker sees "1, 2, 3, 4, 5, 6" and pronounces "one, two, three, four, five, six". Sure, the Roman numerals look like letters, but that doesn't mean you pronounce them that way.

Re: How Did Anyone Do Math in Roman Numerals?

#66

Post by radarsat1 » Fri, Jul 21, 2017, 3:22 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…

In the general case maybe not, but to get by in a marketplace you'd need just those one he listed... like.. 3 or 4 things. 5, 10, 100, 1000. Most people can remember 3 or 4 things. Children can do it, let alone market vendors who are used to considering that 5 chickens = 1 goat. (Inflation these days!)

Re: How Did Anyone Do Math in Roman Numerals?

#67

Post by maxxxxx » Fri, Jul 21, 2017, 3:22 PM UTC

jeffwass wrote: post #35

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 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.

Re: How Did Anyone Do Math in Roman Numerals?

#68

Post by kbenson » Fri, Jul 21, 2017, 3:28 PM UTC

radarsat1 wrote: post #66

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…

In the general case maybe not, but to get by in a marketplace you'd need just those one he listed... like.. 3 or 4 things. 5, 10, 100, 1000. Most people can remember 3 or 4 things. Children can do it, let alone market vendors who are used to considering that 5 chickens = 1 goat. (Inflation these days!)

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.

Re: How Did Anyone Do Math in Roman Numerals?

#69

Post by fela » Fri, Jul 21, 2017, 3:31 PM UTC

madcaptenor wrote: post #65

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??

There are words for numbers in Latin. From Wiktionary ( https://en.wiktionary.org/wiki/Appendix:Latin_cardinal_numer... ): unus, duo, tres, quattuor, quinque, sex... Just like an English speaker sees "1, 2, 3, 4, 5, 6" and pronounces "one, two, three, four, five, six". Sure, the Roman numerals look like letters, but that doesn't mean you pronounce them that way.

But that is very interesting, that means that when saying the numbers they were basically using something similar to Arabic numbers!

Re: How Did Anyone Do Math in Roman Numerals?

#70

Post by malnourish » Fri, Jul 21, 2017, 3:37 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…

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.