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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?

#81

Post by [deleted] »

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…

[deleted]

Re: How Did Anyone Do Math in Roman Numerals?

#82

Post by jdminhbg »

sanityUnbounded wrote: post #78
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

The equivalent to II + II = IIII isn't 2 + 2 = 4, it's 2 + 2 = 22. Simply jamming the symbols together gives you the right answer.

Re: How Did Anyone Do Math in Roman Numerals?

#83

Post by vidarh »

noir_lord wrote: post #39
bonoboTP wrote: post #37

Earlier 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.

Same for me.

Part of it is the brevity, and part of it is the shortcuts. E.g. when I did my masters, one thing I quickly realised was that papers that expressed an algorithm using mathematical notation almost always lacked essential details.

My impression is that it's too obvious when there are too large leaps in code, whereas in mathematical notation everyone accepts leaps that can obscure that essential details have been left out.

E.g. you'd have papers on thresholding of images for OCR (deciding what is background and what is foreground) where it turned out the results were highly dependent on certain values represented by certain variables that were never defined, for example, putting in a situation of reconstructing parameters by trial and error if you wanted to reproduce the results.

Today I'm immediately suspicious if results are presented as maths outside of fields where the maths is essential (and sometimes even then) as I see it as having a tendency to be used to gloss over sloppy work or save space by leaving out essential details.

I'm sure this is not the case in all fields, and that people with a more extensive maths background will be able to fill in more of those leaps without much effort, and so it might very well be acceptable in some fields. But to me a notation that makes it that easy to hide missing details is a liability.

Re: How Did Anyone Do Math in Roman Numerals?

#84

Post by [deleted] »

sanityUnbounded wrote: post #78
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

[deleted]

Re: How Did Anyone Do Math in Roman Numerals?

#85

Post by dllthomas »

jdminhbg wrote: post #82
sanityUnbounded wrote: post #78

Earlier quoted context omitted.

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

The equivalent to II + II = IIII isn't 2 + 2 = 4, it's 2 + 2 = 22. Simply jamming the symbols together gives you the right answer.

Right, much like I + V is IV.

(There is more help; it's not as simple as people have been portraying, though...)

Re: How Did Anyone Do Math in Roman Numerals?

#86

Post by Spivak »

sanityUnbounded wrote: post #78
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

Because if you don't memorize your 'primitive' algebraic rules you'll end up just doing a pullback with roman numerals in the middle. Integers don't have any values, they're mathematical objects with certain properties. Asking about 'the value of 5' doesn't make sense unless you're trying to convert to another, already known, number system.

What is 2 + 5? Well 2 is II and 5 is V which is IIIII. So then we have IIIIIII which is (IIIII)II or VII which is 7.

Re: How Did Anyone Do Math in Roman Numerals?

#87

Post by mywittyname »

kbenson wrote: post #68
radarsat1 wrote: post #66

Earlier quoted context omitted.

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.

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.

Re: How Did Anyone Do Math in Roman Numerals?

#88

Post by Spivak »

dllthomas wrote: post #85
jdminhbg wrote: post #82

Earlier quoted context omitted.

The equivalent to II + II = IIII isn't 2 + 2 = 4, it's 2 + 2 = 22. Simply jamming the symbols together gives you the right answer.

Right, much like I + V is IV. (There is more help; it's not as simple as people have been portraying, though...)

Sure, but that notation was likely born out of convenience by people who wanted a shorthand for situations where it's easier to represent a number as a subtraction but it does make the number system more complicated.

Re: How Did Anyone Do Math in Roman Numerals?

#89

Post by bluehawk »

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.

They mention this in the article, and say there is very little evidence of this being common in ancient Rome.

Re: How Did Anyone Do Math in Roman Numerals?

#90

Post by mywittyname »

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.

According to the article, that notation didn't come into use until the middle ages. So using IIII instead of IV was almost certainly acceptable in the context of transactions. Even if it wasn't, doing the conversion before addition/subtraction would be trivial (and the first step).
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