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How Did Anyone Do Math in Roman Numerals?
- thunderbong 9y agoI had, for some reason, never thought of that directly. Although I do remember some joke on arithmetics in one of the Asterix comic books. But reading this article and trying out a few things, I found it was great fun!
- sideshowb 9y ago...which is funny (the Asterix thing), because spoken French isn't exactly brilliant with numbers either: 99 for example is expressed as "eighty nineteen", 70 as "sixty ten". My friends lived in France a while and said their landlady could never count their rent (paid in cash) correctly first time. Always stumbled somewhere between 100x+60 and 100x+100 for integer values of x. The Swiss have corrected this in Swiss French.
- mseebach 9y ago> 99 for example is expressed as "eighty nineteen" Actually it's four-twenty-ten-nine (quatre vingt dix neuf) -- -- which is perfectly logical on a twenty-based numbering system. Of course it's not very helpful that they switched to ten-based, but only up to 60. http://www.woodwardfrench.com/lesson/numbers-from-1-to-100-in-french/ http://www.woodwardfrench.com/lesson/numbers-from-1-to-100-i...
- sk0g 9y agoSame thing with Belgian French, much to my dismay. I speak a language that does this as well (Georgian), where say 54 is ormotsdatotxmeti (two times twenty and fourteen.) I didn't find maths particularly different difficulty wise, when thinking about it in Georgian or not. What did trip me up, was the times! Up to x:29 it's 29 minutes past x, but at x:30 it is 30 minutes to ++x. Weird.
- vidarh 9y agoIt survives in part in quite a few other languages as well. E.g. Danish ("fjerds" is a contraction of "four into 20" = 80). Most other European languages at least (I'm sure it's present elsewhere too, but I don't know enough non-European languages to say) have some remnants of more widespread counting in 12's or 20's or both (e.g. in English a "dozen" is 12, a "gross" is a dozen dozen (144), and a "score" is 20, hence "four score and seven years ago" in Lincolns Gettysburg Address - 87 years).
- BrandoElFollito 9y ago73 is soixante treize and is just this : a word (ok, two) one learns by heart. No French think that this is 60+13, but just 73. I understand the point about logics in counting, but this is just a new word to learn, like déposition or balafré. One can analyze these words from an ethymology perspective but normally you just learn them by heart. At least this is what I do in English when I need to remember went or throughout .
- ewanm89 9y agoOkay so the article is wrong about some points. We have evidence for both IIII and IV notation in classic roman archeological finds. The obvious example is the entrance fee doors around the colliseum in Rome, they're are engraved with numbers, in both forms of notation. Seriously I figured they used abacus for everything they just figured out the notation to write it down in at the end some would convert to the if notation while others would not.
- wklauss 9y ago> We have evidence for both IIII and IV notation in classic roman archeological finds. The article doesn't say subtractive notation was not used in classic roman times, it says only that it was rare.
- Emilee999 9y agoLove my job, since I've been bringing in $82h… I sit at home, music playing while I work in front of my new iMac that I got now that I'm making it online… •••••••••>>http://ow.ly/iBXm30dNtIZ http://ow.ly/iBXm30dNtIZ
- TorKlingberg 9y agoIt seems the subtractive notation was used for engravings, where keeping it short was important and nobody was going to do calculations with the numbers anyway.
- jacobolus 9y ago> Seriously I figured they used abacus for everything they just figured out the notation to write it down in at the end some would convert to the if notation while others would not. Yes, this is exactly right, and should be at the top of this discussion thread. Romans (like the Greeks, the Babylonians, and others in the ancient world) did their calculations using a counting board. Roman numerals were only used for recording the final answers. “When a Roman wished to settle accounts with someone, he would use the expression vocare aliquem ad calculos - ‘to call them to the pebbles.’” http://mathforum.org/library/drmath/view/57572.html http://mathforum.org/library/drmath/view/57572.html Our words calculate, calculus, calculator, etc. all come from the Latin word for the pebbles they used as counting-board tokens.
- MichaelBurge 9y agoIn 2017 we just do: $ perl6 -e 'say Ⅻ / Ⅲ' 4
- fahadkhan 9y agocare to explain why this works?
- yorwba 9y agoUnicode has codepoints for roman numerals 1 through 12 and then the base symbols up to one hundred thousand (ↈ) which I just saw for the first time. That Perl allows them in integer literals is strange, but also logical in a weird way. (Now I wonder what other number systems it supports.) EDIT: Ok, so I installed perl6 (rakudo) just to test this out, and it apparently doesn't work out of the box. Pity.
- deleted 9y ago[deleted]
- MichaelBurge 9y agoI'm not a compiler dev, but it looks fairly new and appears to have many other special Unicode ranges too, including camels and beer mugs??? https://github.com/rakudo/rakudo/blob/beec02a6fa69e3ac290b4dd24c07d87a9f248b13/tools/build/makeMAGIC_INC_DEC.pl6 https://github.com/rakudo/rakudo/blob/beec02a6fa69e3ac290b4d...
- zoffix222 9y agoThat's just a helper script to generate tables for for .succ/.pred string increment/decrement methods. Nd and No chars as numeric literals were available since first stable release in December 2015
- wambotron 9y agoWeird, I just installed it (via homebrew) and it's working for me
- WalterBright 9y agoIt'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 https://en.wikipedia.org/wiki/Leibniz%27s_notation
- CogitoCogito 9y agoNotation is extremely important. It's basically a way to organize how you abstract a problem. If your abstraction is "bad" it will be harder to solve certain problems. It's really not much different everywhere else in society. Different programming languages/frameworks/etc. are doing essentially the same thing (if you ignore the speed of execution). All the languages are Turing complete and can do more or less the same IO. But it's still much easier for people to use certain tools for certain problems than others. The right notation allows you to focus on what's important and forget what is not.
- dmreedy 9y agoThis couldn't really be stated any more clearly[1]; well put. I'll only add that this is true for any variety of abstraction, natural language included. Abstractions encode the biases of their creators[2]. The 'power' of an abstraction comes from the set of things that are easily and concisely expressible; its primitives. However, this is balanced by the truths that are no longer easily expressible, because the encoding doesn't allow for it. There's a certain intuition that semantics and abstraction are tied tightly in this sense; you don't can't really convey what something means unless it's concisely expressible in the abstraction you're using. Slang, idioms, calculus, etc. --- [1] and yet, I guess I'll just babble on adding more words anyway... [2] be they mathematical concepts, programming paradigms, or cultural norms and quirks.
- WalterBright 9y agoI learned this in designing the D programming language. The original syntax for lambdas seemed natural from a compiler point of view, but from a user point of view it was awkward and pretty much unusable. Changing the syntax was a complete transformation in its usage.
- squid_ca 9y agoHere's the article on its own site: http://www.straightdope.com/columns/read/3330/how-did-anyone-do-math-in-roman-numerals http://www.straightdope.com/columns/read/3330/how-did-anyone...
- MayeulC 9y agoThe article is wrong on a couple of counts (for multiplication and division). Here is a more complete one: https://thonyc.wordpress.com/2017/02/10/the-widespread-and-persistent-myth-that-it-is-easier-to-multiply-and-divide-with-hindu-arabic-numerals-than-with-roman-ones/ https://thonyc.wordpress.com/2017/02/10/the-widespread-and-p... (Surfaced on HN with https://news.ycombinator.com/item?id=13636277 https://news.ycombinator.com/item?id=13636277 )
- IshKebab 9y agoHuh so I've wondered how the Babylonian "base 60" system worked. Looking at the image in that article it's not base 60 at all! It's more like a mix of base 6 and base 10. The factor increase for the columns are not: 60x 60x 60x 60 The are 6x 10x 6x 10 Much simpler than it sounds from "base 60".
- flipp3r 9y ago> the Romans greatly preferred the simpler IIII to IV, XXXX to XL, and so on. (The IIII-for-4 notation survives today on the faces of clocks.) looks at watch Well, damn, it's IIII. However my watch does use IX over VIIII, what's up with that?
- ldjb 9y agoThere's a theory[0][1] that it's mostly down to aesthetics. It looks visually more pleasing that way when split into three groups of four numbers: I, II, III, IIII (consisting of I only) V, VI, VII, VIII (consisting of I and V) IX, X, XI, XII (consisting of I and X) [0] http://mathtourist.blogspot.co.uk/2010/08/iiii-versus-iv-on-clocks.html http://mathtourist.blogspot.co.uk/2010/08/iiii-versus-iv-on-... [1] https://www.hautehorlogerie.org/en/encyclopaedia/glossary-of-watchmaking/s/roman-numeral-iiii-on-dials-1/ https://www.hautehorlogerie.org/en/encyclopaedia/glossary-of...
- sharpercoder 9y agoPersonally, I find distinguishing III and IIII quite hard in several fonts. However, the difference between [II and III] and [III and IV] is easier to read.
- genmon 9y agoThere are a few theories detailed here: http://mentalfloss.com/article/24578/why-do-some-clocks-use-roman-numeral-iiii http://mentalfloss.com/article/24578/why-do-some-clocks-use-... The reason I always heard is about ease of casting: it requires a more complex mold if 4 is written as IV instead of IIII.
- maxxxxx 9y agoSince 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.
- empath75 9y agoThe 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.
- marcosdumay 9y agoThe 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).
- Double_Cast 9y agoAccording 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 https://en.wikipedia.org/wiki/Radix_economy
- Edmond 9y agoI am going to guess base 10 is prevalent because we have 10 fingers ? :) I speak a language (Mende) that has no formal mathematics but counting is done in base 10; there are 10 individual words for 1 to 10 , the word for one is "yaella", the word for 10 is "poo", the word (really expression) for 11 is "poo mahun yaella", which literally translates to 10 on top of 1 ie 10+1...I can only think they stopped at 10 words because there are ten fingers to do elementary arithmetic?? granted there are other words for high magnitudes...there are apparently other languages with other bases besides 10 so who knows...possibly due to using other cultural artifacts to serve as digits.
- barking 9y agoThe greeks used the method on this page (http://www.trottermath.net/algebra/multsqs.html http://www.trottermath.net/algebra/multsqs.html) to do multiplication so I suppose the romans did too.
- deleted 9y ago[deleted]
- oaktowner 9y agoYou 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??
- flatline 9y agoThat's certainly one way to do it... http://www.youtube.com/watch?v=xnuetbfDLpE&t=1m14s http://www.youtube.com/watch?v=xnuetbfDLpE&t=1m14s
- madcaptenor 9y agoThere are words for numbers in Latin. From Wiktionary (https://en.wiktionary.org/wiki/Appendix:Latin_cardinal_numerals 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.
- fela 9y agoBut that is very interesting, that means that when saying the numbers they were basically using something similar to Arabic numbers!
- jacobolus 9y agoIn my opinion the important innovation of Hindu–Arabic numbers is not having different symbols for each digit, but rather using the same ten symbols (and no others!) for representing larger groups, which gives the system a lovely uniformity across numbers of different scales. There aren’t many (if any?) human languages that duplicate this feature of being a purely positional system.
- SAI_Peregrinus 9y agoArabic numeral: Cardinal number name | Ordinal number name, with conjugation information 1: Unus -a -um | primus -a -um 2: duo, duae, duo | secundus -a -um 3: tres, tria | tertius -a -um 4: quattuor | quartus -a -um 5: quinque | quintus -a -um 6: sex | sextus -a -um 7: septem | septimus -a -um 8: octo | octavus -a -um 9: novem | nonus -a -um 10: decem | decimus -a -um 11: undecim | undecimus -a -um 12: duodecim | duodecimus -a -um 13: tredecim | tertius decimus -a -um 14: quattuordecim | quartus decimus -a -um 15: quindecim | quintus decimus -a -um 16: sedecim | sextus decimus -a -um 17: septendecim | septimus decimus -a -um 18: duodeviginti | duodevice(n)simus -a -um 19: undeviginti | undevice(n)simus -a -um 20: viginti | vice(n)simus -a -um 30: triginta | trice(n)simus -a -um 40: quadraginta | quadrage(n)simus -a -um 50: quinquaginta | quinquage(n)simus -a -um 60: sexaginta | sexage(n)simus -a -um 70: septuaginta | septuage(n)simus -a -um 80: octoginta | octoge(n)simus -a -um 90: nonaginta | nonage(n)simus -a -um 100: centum | cente(n)simus -a -um 500: quingenti | quingente(n)simus -a -um 1000: mille | mille(n)simus -a -um From Cassell's Latin English Dictionary, second edition.
- zw123456 9y agoI 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 numbers, I have to learn that 1 is one thing, 2 represents 2 things, 3 represents 3 things and so on. Then I have to remember that 2 + 2 = 4, and 3 + 2 = 5, there is more memorization required. Where Roman Numerals for someone with little or no education could get by in the market square with some simple rules and even use twigs as a primitive calculator. It is not until you get to much more complex ideas that the Arabic notation wins out. So perhaps, different notations lend themselves better or worse depending on the application ? Just some random thoughts that this very interesting post brought to mind.
- kbenson 9y ago> 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.
- radarsat1 9y agoIn 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!)
- kbenson 9y agoThat'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.
- vok 9y agoClaude Shannon created the THROBAC I to do this. https://www.flickr.com/photos/synesthete/2591624549 https://www.flickr.com/photos/synesthete/2591624549
- hrehhf 9y agoOff topic rant: It bugs me when people mix our standard numerals with Roman numerals, such as 12MM to mean twelve million. They are different numerals and the meaning is not defined when they are used together. And Roman numerals are not like SI suffixes, meaning they are not multiplicative; Roman numerals are additive, so MM is two thousand, not one million. Also, M is an SI suffix, so 12M means twelve million and 12MM just looks like a typo. Obviously people do not use SI suffixes may not feel the same way, this is just my pet peeve because I use SI suffixes in science.
- deleted 9y ago[deleted]
- Garet_Jax 9y agoSome aspects of 'math' came along with arabic, but Roman Numerals work fine for their situation, at that time. In conversation, it's just the I-M/0-1000 range for instance, learning how to notate that number is a different issue. Notation is somewhat straight-forward: When you get to 4, the number undergoes a state change to 'subtract from the next number, dropping everything behind it, and we're in a new state so "the" number is changed to 5' so III becomes IV. Otherwise, just keep adding 1. That should work, adding to the previous rules as the state changes. Going to X leaves the V rules in place. So it would be a XXXII-bit computer, for example.
- EGreg 9y agoI heard they divided by two on one side and multiplied by the other, adding 1 where they needed. In fact they did this in ancient Egypt too! http://www.mathnstuff.com/math/spoken/here/2class/60/egyptm.htm http://www.mathnstuff.com/math/spoken/here/2class/60/egyptm....
- aphextron 9y agoPerhaps this is why there were really no Roman mathematicians. For how much they admired and emulated the Greeks, they themselves were never really able to contribute to math and science in the same way. Practically everything we think about today in western civilization in terms of Law, Architecture, Engineering, and Urban Planning comes directly from the Romans. Yet they never produced an Archimedes or a Pythagoras. Euclid remained the height of mathematical sophistication in the West through their entire reign until the rise of Arab/Islamic mathematics in the 800s.
- jacobolus 9y agoSeems unlikely. Greeks and Romans probably did calculations in pretty much the same way, using a counting board. The early Greek way of writing numbers (look up Attic numerals) was the direct ancestor of the Roman method. The alternative later way the Greeks (e.g. Euclid, Archimedes) wrote numbers was using their alphabet for 1–9, using separate letters for 10–90 and 100–900, then writing 1000–9000 with a “thousand” symbol plus the letter for 1–9 on top. Overall also a big pain in the butt.
- interlocutor 9y agoFun 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%93Arabic_numeral_system https://en.wikipedia.org/wiki/History_of_the_Hindu%E2%80%93A...
- MattLeBlanc001 9y agoI'm arab and never heard that arabic numerals are known as indian numerals in middle eastern countries.
- interlocutor 9y agoHere's an example: http://www.chrono24.ae/ulyssenardin/marine-chronometer-manufacture-abu-dhabi-edition--id4350609.htm 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"!
- JadeNB 9y agoFor what it's worth, you can find this material on the Straight Dope site itself; no need to go through the WCP site (which doesn't let you read the article without Javascript). http://www.straightdope.com/columns/read/3330/how-did-anyone-do-math-in-roman-numerals http://www.straightdope.com/columns/read/3330/how-did-anyone...