How did anyone do math in Roman numerals? (2017) • Hacker News Board

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

#121

Post by madcaptenor » Tue, Jul 28, 2020, 1:27 PM UTC

earthboundkid wrote: post #71

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.

Similarly, Indians express large numbers in terms of lakh (10^5) or crore (10^7) which is confusing to people using the thousands-based system.

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

#122

Post by Jedd » Tue, Jul 28, 2020, 2:00 PM UTC

philwelch wrote: post #100

Jedd wrote: post #67

Earlier quoted context omitted.

> Adding Roman numerals, at least, isn’t hard. I find it insanely difficult - but as you note, a lifetime of arabic numerals, and a lack of skill in appropriate tools (eg. an abacus) will skew that comparison. > ... but it’s not much easier until you’ve memorized all 50 unique sums of one-digit numbers. This doesn't feel right. I don't think I have memorised the sum of all pairs of 1-digit numbers - but contemplating…

I was going off the rough estimate that 0-9 is 10 digits and 10x10 is 100 but that reduces to 50 thanks to commutativity. I think 45 if you don’t count zeroes—I don’t know where you get 36 from. I also use the term “memorize” pretty loosely—I remember that memorizing times tables was a thing but not so much for plus—but addition is simple enough that most people can kind of intuit what 7+4 heuristically if they’re sa…

I think I'd calculated combinations, but dubiously ignored where both were identical - that's where I ended up with 36.

OTOH do we memorise any of the x+1 combinations? I hope we don't, but perhaps we do. I genuinely can't say at this point. I was trying to work out how I processed sums such as 8+7 earlier, and concluded that so far I can tell, I work out the difference of one of those numbers from 10, subtract it from the other, then it's a very simple addition - ie that becomes 10+5. But I'm now unsure if that's what I do as a general rule, and am even less sure what other people may do.

Times table I vaguely recall learning by rote in formative school, but that's an awfully long time ago, and trying to self-analyse my mechanisms for multiplications is highly challenging. It feels like I try to move those back to multiples of 10 or 100, again, too.

I recall reading aeons ago that the only intuitive interface is the nipple - beyond that, everything is learned. So what makes for an intuitive or sensible mathematical representation of things is probably so arbitrary as to be pointless arguing about. It feels that the kinds of things we do, day to day, with numbers, that base-10 arabic number system is optimum, but that may simply be the lack of exposure to a better system.

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

#123

Post by shultays » Tue, Jul 28, 2020, 2:24 PM UTC

Grustaf wrote: post #106

shultays wrote: post #27

Earlier quoted context omitted.

They probably had algorithms for it, but even then it sounds challenging. Addition sounds easy and works mostly like how we do base 10 addition. I imagine they would first go for sub 5 part which is a bit exceptional and had to be manually. And then start grouping letters together like we do and create carries if they reach the next letter. Subtraction sounds harder. It sounds close enough to our base 10 system but b…

How numbers are written down does not necessarily correspond to how you do calculations. Given that 499 was called 499 I’m pretty sure they thought in base 10, so subtracting 1 from 500 would be trivial. Writing it down took a few more symbols but so what?

Hmm, I was assuming they didn't have a concept of base 10. If they do have it I wonder how they couldn't make the connection and write stuff in base 10 as well instead of a mixed base with weird rules

Then I guess the real challenge is converting numbers around?

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

#124

Post by dhosek » Tue, Jul 28, 2020, 2:54 PM UTC

Jedd wrote: post #122

philwelch wrote: post #100

Earlier quoted context omitted.

I was going off the rough estimate that 0-9 is 10 digits and 10x10 is 100 but that reduces to 50 thanks to commutativity. I think 45 if you don’t count zeroes—I don’t know where you get 36 from. I also use the term “memorize” pretty loosely—I remember that memorizing times tables was a thing but not so much for plus—but addition is simple enough that most people can kind of intuit what 7+4 heuristically if they’re sa…

I think I'd calculated combinations, but dubiously ignored where both were identical - that's where I ended up with 36. OTOH do we memorise any of the x+1 combinations? I hope we don't, but perhaps we do. I genuinely can't say at this point. I was trying to work out how I processed sums such as 8+7 earlier, and concluded that so far I can tell, I work out the difference of one of those numbers from 10, subtract it fr…

As a parent of young children and former math teacher, yes, we do absolutely memorize those sums. It usually happens at an early enough age that the process of doing so evaporates early in life and becomes part of your base mental code. I spent a significant part of my teaching life teaching high school math for college students (and occasionally grade school math for college students) and there are very much people who never managed to get that memorization step completed. What's really fascinating is that it's an orthogonal skill to higher mathematics. I've seen students who needed to use a calculator to do 6+5 and yet managed to be able to solve algebraic problems. This is, I must add, uncommon, but it's less because one skill depends on the other but rather because the failure to gain the basic math skill leads to an unwillingness to try to gain the more abstract math skill.

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

#125

Post by ahazred8ta » Tue, Jul 28, 2020, 3:13 PM UTC

mdiesel wrote: post #39

AnimalMuppet wrote: post #35

Earlier quoted context omitted.

Sure. But they did those things by experience and rules of thumb. They didn't do a real stress analysis on those aqueducts, for instance.

For those interested in reading further, the ideal (unloaded) shape of an arch isn't a semicircle, but a catenary. It sounds so simple: so hangs the chain, stands the arch. Took until Hooke in the 17th century before that was written down, though there are earlier (15th century) examples in architecture. The Romans were still working on the Greek ideology that the circle was the perfect shape. Not to belittle what th…

"Ut pendet continuum flexile, sic stabit contiguum rigidum inversum -- As hangs a flexible cable, so inverted stand the touching pieces of an arch." (although they figured out at some point that this curve was close to being a parabola)

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

#126

Post by gerikson » Tue, Jul 28, 2020, 3:39 PM UTC

frandroid wrote: post #52

> The IIII-for-4 notation survives today on the faces of clocks. What? On which clocks?

On this new Omega Constellation, just as a random example

https://www.omegawatches.com/watch-omega-constellation-omega...

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

#127

Post by tetris11 » Tue, Jul 28, 2020, 4:45 PM UTC

User23 wrote: post #75

ThrustVectoring wrote: post #66

Earlier quoted context omitted.

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.

Don't you mean the other way around

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

#128

Post by philwelch » Tue, Jul 28, 2020, 5:36 PM UTC

Jedd wrote: post #122

philwelch wrote: post #100

Earlier quoted context omitted.

I was going off the rough estimate that 0-9 is 10 digits and 10x10 is 100 but that reduces to 50 thanks to commutativity. I think 45 if you don’t count zeroes—I don’t know where you get 36 from. I also use the term “memorize” pretty loosely—I remember that memorizing times tables was a thing but not so much for plus—but addition is simple enough that most people can kind of intuit what 7+4 heuristically if they’re sa…

I think I'd calculated combinations, but dubiously ignored where both were identical - that's where I ended up with 36. OTOH do we memorise any of the x+1 combinations? I hope we don't, but perhaps we do. I genuinely can't say at this point. I was trying to work out how I processed sums such as 8+7 earlier, and concluded that so far I can tell, I work out the difference of one of those numbers from 10, subtract it fr…

I agree that Arabic numerals are better, but I did want to make the point that Roman numerals aren’t quite as bad as you might think having already learned Arabic numerals.

Your method for summing 8+7 is what I think I do for things like 7+4 (since I can visualize 7 as “three less than 10” and 4 as “one more than three” all in the same thought to reach 11), but for 7+8 my brain noticeably spits out 15 immediately and only a moment later does it actually do the processing you mention.

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

#129

Post by morelisp » Tue, Jul 28, 2020, 5:56 PM UTC

phist_mcgee wrote: post #89

morelisp wrote: post #81

Earlier quoted context omitted.

Whiggish bullshit. Functional code and GC were invented in 1959. Some level of static typing was de rigeur in most application-development languages after assembly and before the scripting boom starting in the late 80s. In Coders At Work Frances Allen bemoaned the effect C's popularity had on automated program analysis since 1970: > C has destroyed our ability to advance the state of the art in automatic optimization…

Woah don't cut yourself on that edge there mister.

Oh sure when Alan Kay says it he gets a lab but when I say it I'm an edgelord.

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

#130

Post by morelisp » Tue, Jul 28, 2020, 6:09 PM UTC

sk0g wrote: post #88

morelisp wrote: post #81

Earlier quoted context omitted.

Whiggish bullshit. Functional code and GC were invented in 1959. Some level of static typing was de rigeur in most application-development languages after assembly and before the scripting boom starting in the late 80s. In Coders At Work Frances Allen bemoaned the effect C's popularity had on automated program analysis since 1970: > C has destroyed our ability to advance the state of the art in automatic optimization…

So Rust, Python, Julia etc are no more productive, safe, or easy to use than programming was in 1959?

The question is not whether any particular language you might pick today is better than any other language you might pick in 1959, but whether there is some kind of teleology or "progress" to which languages are aspiring or at least slouching.

GC (and "memory safety" more generally) was not invented to solve the problems of C after C somehow revealed them solving the problems of e.g. Fortran. C variously sidestepped and ignored the work on program analysis including GC and memory safety for various commercial, aesthetic, and incidental reasons. Similar things are the case for C++ (vs. e.g. Object Pascal / Simula), Objective-C and Swift (vs. Smalltalk and Self), JavaScript and PHP (vs. nearly everything).

Lisp from 1959 stacks up incredibly well against Python today. Fortran still autovectorizes better than most modern languages. Pascal remains better to teach structured programming, we just don't teach that much anymore (and you can tell just by grabbing a half dozen loops at random and trying to figure out how well their conditions capture their invariants). Languages don't get better over time. They do get marketing budgets unimaginable before the 90s ("thanks" largely to Sun and Java for kicking this off), and for the past 20 years or so weird personal identity arguments on top of that (probably somehow Perl's fault).