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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?

#141

Post by nnq »

ashark wrote: post #53
noir_lord wrote: post #39

Earlier quoted context omitted.

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.

> Code's easy for me (unless "mathy" in appearance like Haskell)

Haskell is not hard to read/understand because it's mathy. It's because of type inference combined with laziness - this leads people to do incredible fits of intellectual masturbation...

Like "hey, the compiler can handle types for us, so lets type the shit out of things, let's even use them to mark side effects, types are fee" ...doesn't matter that types are mainly documentation and by not writing them or making astronaut types you're loosing the main benefit. And "hey, the language is lazy, that extra code containing an infinite loop but so mathy elegant, will never be fully executed so we can have it, it's free, doesn't impact performance"... doesn't matter you need to use 80% of your brainpower better spent otherwise to grok it.

If it would be eager and without type inference it would've evolved into a much more readable and popular language and with a larger community.

Re: How Did Anyone Do Math in Roman Numerals?

#142

Post by gozur88 »

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'd think you could just collect all the numbers and then translate, i.e. if I add some things and get XXVVVVVIIIIIIIIIII, I know that's XXVVVVVVVI = XXXXXVI = LVI.

The problem is IV isn't 6, it's 4.

Re: How Did Anyone Do Math in Roman Numerals?

#143

Post by jacobolus »

Spivak wrote: post #88
dllthomas wrote: post #85

Earlier quoted context omitted.

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.

Personally I wish we had a good notation and separate single-syllable pronunciation for negative digits –1 through –9, and were willing as a society to accept numbers written with a mix of positive and negative digits.

Decimal arithmetic becomes quite a bit easier if you normalize your numbers to the digits from –5 to 5, and it would help prepare students for algebra.

Re: How Did Anyone Do Math in Roman Numerals?

#144

Post by tree_of_item »

rtpg wrote: post #138
allencoin wrote: post #133

Earlier quoted context omitted.

I remember learning Roman numerals in 1st or 2nd grade and finding them to be a lot easier for basic arithmetic. I mean, all of the examples we used in school to learn basic arithmetic had things like "(picture of 4 apples) + (picture of 2 apples) = (picture of 6 apples)". Roman numerals are kind of a pictograph in a way.

but if you're in first grade then you do IV + II = IVII...?? To each their own, but I'm unsure of the relative ease of roman numerals

One of the points the article made was that IV wasn't really a thing when the Romans were actually using these numerals.

Re: How Did Anyone Do Math in Roman Numerals?

#145

Post by MattLeBlanc001 »

interlocutor wrote: post #137

Fun fact: What is known as "arabic numerals" in the west is known as "indian numerals" in middle-eastern countries. That's because it came from India. https://en.wikipedia.org/wiki/History_of_the_Hindu%E2%80%93A...

I'm arab and never heard that arabic numerals are known as indian numerals in middle eastern countries.

Re: How Did Anyone Do Math in Roman Numerals?

#146

Post by nawgszy »

jacobolus wrote: post #126
nawgszy wrote: post #114

Earlier quoted context omitted.

>1 is one thing, 2 represents 2 things, 3 represents 3 things and so on I follow you thus far. >Then I have to remember that 2 + 2 = 4, and 3 + 2 = 5 No you don't. You have to remember that 1 + 1 = 2; 2 + 1 = 3; ...; 9 + 1 = 10; and then the rules repeat themselves, respecting columns for addition. All mathematics between 1 and 10 like 4 + 5 are already known at this point. Roman numerals, on the other hand, give you…

You’re speaking from a position of bias and ignorance (we all do this sometimes, but it’s important to be aware of), with a lifetime of familiarity with Hindu–Arabic number notation and almost no experience reading/writing Roman notation or translating back and forth between written numbers and pebbles or other tokens on a counting board, which is how most calculations were done in Roman times (persisting to this day…

>You're speaking from a position of bias and ignorance

I made a fairly concise point, but you're right about one thing

>we all do this sometimes

Because you most certainly just did

>As for your specific concerns: the easy pattern is that the letter for a group of five literally looks like half of the letter for a group of ten.

That's not the issue with the "easily repeatable pattern". The issue is this:

>V = X/2, L = C/2, D = ↀ/2, ↁ = ↂ/2, etc.

Do you see that "etc" you post? That's because, to represent 10^n, you need to know 2*n + 1 characters.

This is an obvious downfall that Hindu-Arabic numerals obviously do not have. Even if you ignore the shorthand (which would be foolish, parsing 5-9 characters in a row can take a serious moment of focus), you still need to know an unbounded amount of characters to represent the integers alone, and let's not even discuss the obvious fallacy of fractions etc..

Also,

>Objectively, the Roman system is easier to teach up to a basic level

Even this is an unfounded statement. Make an argument. Prove it. Objectivity of teachability can't possibly be something you just throw out casually in an argument, let alone an argument where you told someone they were biased and ignorant for, as far as I can tell, no reason at all.

Re: How Did Anyone Do Math in Roman Numerals?

#147

Post by Double_Cast »

bonoboTP wrote: post #37
nnq wrote: post #34

Earlier quoted context omitted.

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 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…

Since I learned programming, my personal notes draw a distinction between "=" (defines set of coordinates) and ":=" (assignment).

cf.

  f(x) = x^2 + 1
  x := 2
  f(2) = 5

Re: How Did Anyone Do Math in Roman Numerals?

#148

Post by interlocutor »

MattLeBlanc001 wrote: post #145
interlocutor wrote: post #137

Fun fact: What is known as "arabic numerals" in the west is known as "indian numerals" in middle-eastern countries. That's because it came from India. https://en.wikipedia.org/wiki/History_of_the_Hindu%E2%80%93A...

I'm arab and never heard that arabic numerals are known as indian numerals in middle eastern countries.

Here's an example: http://www.chrono24.ae/ulyssenardin/marine-chronometer-manuf...

The digits are on the watch are standard arabic digits but the description calls it "indian numerals"!

Re: How Did Anyone Do Math in Roman Numerals?

#149

Post by Double_Cast »

marcosdumay wrote: post #62
empath75 wrote: post #25

Earlier quoted context omitted.

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).

According to Wikipedia [0], the most efficient radix is Euler's Number.

But what would it even mean to construct a numeral-system with a non-integral radix?

[0] https://en.wikipedia.org/wiki/Radix_economy

Re: How Did Anyone Do Math in Roman Numerals?

#150

Post by dllthomas »

crowbahr wrote: post #113
dllthomas wrote: post #85

Earlier quoted context omitted.

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

V + I = VI though. You just have to put the larger number first for the addition.

That might be enough to prevent you from getting any well-formed wrong answers.

It's not enough of the story, though - consider:

    VI + V = VIV
    V + IV = VIV
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