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How did anyone do math in Roman numerals? (2017)

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Re: How did anyone do math in Roman numerals? (2017)

#71

Post by earthboundkid »

zapzupnz wrote: post #70

Not really related to the article per se but I always find it interesting how one may become tempted to say "this alternative to a thing I already know makes so much sense , why don't we always use it?" I felt the same way when encountering Chinese numbers via Japanese. If 二 is two, 十 is ten, 四 is four, and twenty-four is 二十四, that's so clear! Two tens and four! I quickly decided that this number system, though somet…

Living in Japan, I became accustomed to using numbers for up to around 10,000 yen ($100USD) due to interactions at the stores and around town, but when I would hear the price of a car (1,000,000+ yen or 100 myriad yen) or a house, it would just confuse me and not register at all. It’s all just based on your personal experience, I think.

Re: How did anyone do math in Roman numerals? (2017)

#72

Post by blub »

rozgo wrote: post #40
andrewl wrote: post #9

In An Introduction to Mathematics (1911) Alfred North Whitehead wrote: 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. Before the introduction of the Arabic notation, multiplication was difficult, and the division even of integers called into play the highest mathematical faculties. Probably…

This is absolutely the case for programming languages. From Haskell to Rust. Programming languages shape the way we think and reason about the problem. Sometimes it does this so well, it leaves us starring into the abyss. Facing dead on the problem domain—after all sides quests have been removed. Once you can delegate away all the busy work, you can focus on bigger and better abstractions.

Both Haskell and Rust are poor examples because one has to focus more on the notation (i.e. types, declarations, etc).

Python is better.

Re: How did anyone do math in Roman numerals? (2017)

#73

Post by mixmastamyk »

I'd previously read that Fibonacci had helped popularize the hindu-arabic notation in Europe. Wikipedia says "In 1202, he completed the Liber Abaci (Book of Abacus or The Book of Calculation)," which included lessons and examples.

Interestingly, he grew up with a merchant father based in Northern Africa and had internalized it.

Re: How did anyone do math in Roman numerals? (2017)

#74

Post by tkzed49 »

blub wrote: post #72
rozgo wrote: post #40

Earlier quoted context omitted.

This is absolutely the case for programming languages. From Haskell to Rust. Programming languages shape the way we think and reason about the problem. Sometimes it does this so well, it leaves us starring into the abyss. Facing dead on the problem domain—after all sides quests have been removed. Once you can delegate away all the busy work, you can focus on bigger and better abstractions.

Both Haskell and Rust are poor examples because one has to focus more on the notation (i.e. types, declarations, etc). Python is better.

Imagine I'm consuming code written by someone else, without looking deeply into its implementation. Would I now be disadvantaged by careful and explicit typing? How much time is spent consuming code versus writing it, of course, is a bit situational.

Re: How did anyone do math in Roman numerals? (2017)

#75

Post by User23 »

ThrustVectoring wrote: post #66
rland wrote: post #64

Earlier quoted context omitted.

I wonder if arabic numerals really are the best system. Too much inertia is invested in them now but I wonder if a yet easier representation exists. For example, I know that there was a brief push to use quaternions in physics.

Base 12 is likely better than base 10. Twelve is the number of phalanges on your hand that you can touch with your thumb, so if that counting system had caught on and stuck we'd likely have a better base for divisibility.

Incidentally there are 12 inches in a foot.

Re: How did anyone do math in Roman numerals? (2017)

#76

Post by User23 »

philwelch wrote: post #62
andrewl wrote: post #9

In An Introduction to Mathematics (1911) Alfred North Whitehead wrote: 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. Before the introduction of the Arabic notation, multiplication was difficult, and the division even of integers called into play the highest mathematical faculties. Probably…

Adding Roman numerals, at least, isn’t hard. If it was I doubt Roman numerals would have ever lasted. Arabic is still, in my opinion, easier to add—from the perspective of a lifetime spent exclusively doing arithmetic in Arabic numerals—but it’s not much easier until you’ve memorized all 50 unique sums of one-digit numbers. Multiplication, though, that’s the real difference maker.

Please explain the easy method for adding, for example MCMLXVII and LXV. I mean that seriously, I'm curious what the trick is.

Re: How did anyone do math in Roman numerals? (2017)

#78

Post by d2v »

philwelch wrote: post #62
andrewl wrote: post #9

In An Introduction to Mathematics (1911) Alfred North Whitehead wrote: 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. Before the introduction of the Arabic notation, multiplication was difficult, and the division even of integers called into play the highest mathematical faculties. Probably…

Adding Roman numerals, at least, isn’t hard. If it was I doubt Roman numerals would have ever lasted. Arabic is still, in my opinion, easier to add—from the perspective of a lifetime spent exclusively doing arithmetic in Arabic numerals—but it’s not much easier until you’ve memorized all 50 unique sums of one-digit numbers. Multiplication, though, that’s the real difference maker.

This is only tangentially related, but until now I never really thought about how I sum single digit numbers, but it's not by having memorized all combinations. I'd say I have all combinations that sum to 10 or less memorized, which adds up to 25 unique combos (plus the rule that number + 0 = number).

If I can tell it sums to more than 10, I break it up mentally into [larger number] + [smaller number] = [larger number] + ([smaller number] - remainder) + remainder, where [larger number] + ([smaller number] - remainder) = 10

You could break it down further by just memorizing what each digit less than 10 is when you add 1. Then you can do addition like 5 + 4 = 1 + 1 + 1 + ... = 2 + 1 + ... = 8 + 1 = 9. Then you'd only have to memorize 9 things (10 if you include 0). I guess this assumes that you know the order numbers go in though, whereas memorizing all of the combinations doesn't require that.

Re: How did anyone do math in Roman numerals? (2017)

#79

Post by eholk »

User23 wrote: post #76
philwelch wrote: post #62

Earlier quoted context omitted.

Adding Roman numerals, at least, isn’t hard. If it was I doubt Roman numerals would have ever lasted. Arabic is still, in my opinion, easier to add—from the perspective of a lifetime spent exclusively doing arithmetic in Arabic numerals—but it’s not much easier until you’ve memorized all 50 unique sums of one-digit numbers. Multiplication, though, that’s the real difference maker.

Please explain the easy method for adding, for example MCMLXVII and LXV. I mean that seriously, I'm curious what the trick is.

I think originally Roman numerals didn't have shorthands like IV instead of IIII. In that case, to add Roman numerals, you just write the letters all together, sort them, and combine smaller digits into larger digits as necessary.

Re: How did anyone do math in Roman numerals? (2017)

#80

Post by jeffcoat »

User23 wrote: post #76
philwelch wrote: post #62

Earlier quoted context omitted.

Adding Roman numerals, at least, isn’t hard. If it was I doubt Roman numerals would have ever lasted. Arabic is still, in my opinion, easier to add—from the perspective of a lifetime spent exclusively doing arithmetic in Arabic numerals—but it’s not much easier until you’ve memorized all 50 unique sums of one-digit numbers. Multiplication, though, that’s the real difference maker.

Please explain the easy method for adding, for example MCMLXVII and LXV. I mean that seriously, I'm curious what the trick is.

  MCMLXVII + LXV
   = MCCCCCCCCCLXVII + LXV (canonicalize)
   = MCCCCCCCCCLXVIILXV    (concatenate)
   = MCCCCCCCCCLLXXVVII    (sort)
   = MCCCCCCCCCLLXXXII     (combine, VV => X)
   = MCCCCCCCCCCXXXII      (... keep combining, LL => C)
   = MMXXXII               (... C{10} => M, nothing left to combine)
   = MMXXXII               (optionally, look for ways to re-write with the subtraction rule)
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