# What base are Roman Numerals considered to have? **URL:** \ **Category:** Factual Questions\ **Created:** [February 3, 2009, 2:21am UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202 "2009-02-03T02:21:17Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![seodoa](https://avatars.discourse-cdn.com/v4/letter/s/4af34b/32.png) [@seodoa](https://boards.straightdope.com/u/seodoa)\ **Post date:** [February 3, 2009, 4:53am UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/21 "2009-02-03T04:53:18Z")
> [@Indistinguishable](#): > > Asking what base Roman numerals have is like asking whether pigeons are upper-case or lower-case; the concept doesn’t apply. Yeah, but, which are they? ---
**Author:** ![Koxinga](https://avatars.discourse-cdn.com/v4/letter/k/4af34b/32.png) [@Koxinga](https://boards.straightdope.com/u/Koxinga)\ **Post date:** [February 3, 2009, 5:20am UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/22 "2009-02-03T05:20:54Z")
But how did the Romans count out loud, and does that have any bearing on the question? Would they use a positional number system when speaking of the number MDCCLXXVI, or would they say the equivalent of “em dee see see ell ex ex vee eye”? ---
**Author:** ![Rigamarole](https://avatars.discourse-cdn.com/v4/letter/r/77aa72/32.png) [@Rigamarole](https://boards.straightdope.com/u/Rigamarole)\ **Post date:** [February 3, 2009, 5:29am UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/23 "2009-02-03T05:29:29Z")
> [@Koxinga](#): > > But how did the Romans count out loud, and does that have any bearing on the question? Would they use a positional number system when speaking of the number MDCCLXXVI, or would they say the equivalent of “em dee see see ell ex ex vee eye”? Reminds me of a stand-up routine I saw once where the comic said, “Man, New Year’s Eve with the Romans must have been a blast. (counting out with methodic slowness) X! I-X! V-I-I-I!” ---
**Author:** ![Svejk\_1](https://avatars.discourse-cdn.com/v4/letter/s/ea666f/32.png) [@Svejk\_1](https://boards.straightdope.com/u/Svejk_1)\ **Post date:** [February 3, 2009, 8:57am UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/24 "2009-02-03T08:57:50Z")
> [@Koxinga](#): > > But how did the Romans count out loud, and does that have any bearing on the question? Would they use a positional number system when speaking of the number MDCCLXXVI, or would they say the equivalent of “em dee see see ell ex ex vee eye”? No, they’d just say the equivalent of [one] thousand seven hundred seventy six. And when you take into account the words Romans used for numerals, than it becomes clear pretty quick that their counting system was base ten; why else would the have simple, non-compound words for ten, a hundred and a thousand, but not for, let’s say, 11, 121 and 1331, or 12, 144 and 1728? ---
**Author:** ![Koxinga](https://avatars.discourse-cdn.com/v4/letter/k/4af34b/32.png) [@Koxinga](https://boards.straightdope.com/u/Koxinga)\ **Post date:** [February 3, 2009, 9:38am UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/25 "2009-02-03T09:38:38Z")
> [@Svejk\_1](#): > > No, they’d just say the equivalent of [one] thousand seven hundred seventy six. And when you take into account the words Romans used for numerals, than it becomes clear pretty quick that their counting system was base ten; why else would the have simple, non-compound words for ten, a hundred and a thousand, but not for, let’s say, 11, 121 and 1331, or 12, 144 and 1728? Yeah, and I think [this bit](http://en.wikipedia.org/wiki/Roman_numerals#XCIX_vs._IC) in the Wikipedia article on Roman numerals makes it clear that multiples of ten was the significant determinant of how numbers were expressed on the page. So why couldn’t this be regarded functionally as base 10? ETA: I know that the Romans themselves didn’t always stick to a uniform standard, using stuff like IIX and IIII and the like. But under _modern_ usage, isn’t it notable that each digit in an Arabic numeral expression transfers directly to a corresponding Roman expression? Eg, in 1776, 1000 = M, 700=DCC, 70=LXX, 6=VI, hence MDCCLXXVI. ---
**Author:** ![sturmhauke](https://avatars.discourse-cdn.com/v4/letter/s/e47c2d/32.png) [@sturmhauke](https://boards.straightdope.com/u/sturmhauke)\ **Post date:** [February 3, 2009, 9:55am UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/26 "2009-02-03T09:55:19Z")
> [@Maastricht](#): > > Does anyone have a cite as to why that theory isn’t factual truth? Think about it for a minute. For this corners thing to hold, you have to write the digits in some pretty strange ways, and then you count some corners one way and some another way, and anyway you admit that the nine is inexplicable. It really doesn’t make any sense. ---
**Author:** ![Cider\_Depot](https://avatars.discourse-cdn.com/v4/letter/c/e274bd/32.png) [@Cider\_Depot](https://boards.straightdope.com/u/Cider_Depot)\ **Post date:** [February 3, 2009, 10:38am UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/27 "2009-02-03T10:38:09Z")
> [@Rigamarole](#): > > “All your base are belong to us.” - Julius Caesar “All your ears are belong to us.” - Mark Antony ---
**Author:** ![Cider\_Depot](https://avatars.discourse-cdn.com/v4/letter/c/e274bd/32.png) [@Cider\_Depot](https://boards.straightdope.com/u/Cider_Depot)\ **Post date:** [February 3, 2009, 10:47am UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/28 "2009-02-03T10:47:17Z")
… ---
**Author:** ![Koxinga](https://avatars.discourse-cdn.com/v4/letter/k/4af34b/32.png) [@Koxinga](https://boards.straightdope.com/u/Koxinga)\ **Post date:** [February 3, 2009, 10:47am UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/29 "2009-02-03T10:47:28Z")
> [@Cider\_Depot](#): > > “All your ears are belong to us.” - Mark Antony “I burning your domus” – Nero ---
**Author:** ![Alessan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/alessan/32/465_2.png) [@Alessan](https://boards.straightdope.com/u/Alessan)\ **Post date:** [February 3, 2009, 10:57am UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/30 "2009-02-03T10:57:01Z")
> [@Exapno\_Mapcase](#): > > Although that Wiki article attributes the modern usage to CNN, I always understood that it started with USA Today and the colorful and stylized graphs of odd, unusual, or trivial facts that became their shorthand identity (and putdown) by the staider press even though today every outlet copies them. They were always referred to as factoids, even though USA Today called them snapshots. 3-2-1 Contact Magazine\* - which started running in 1980 - had a regular section called “Factoids” featuring fun (and true) scientific facts. I don’t know if the usage of the word started there, but that’s where I learned it. \*III-II-I Contact? ---
**Author:** ![chrisk](https://avatars.discourse-cdn.com/v4/letter/c/6de8d8/32.png) [@chrisk](https://boards.straightdope.com/u/chrisk)\ **Post date:** [February 3, 2009, 10:59am UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/31 "2009-02-03T10:59:09Z")
> [@Indistinguishable](#): > > Glossing over irrelevant details, there’s precisely one system of base 10, one system of base 9, one system of base 67, etc… Just wanted to return to this point, and put in - I don’t think I’d say that the detail of ‘which symbol do you use to indicate each digit’ is irrelevant generally, though I think I understand what you mean, that considering each encoding so does make all base 10 systems identical. That got me thinking about possible variations, though. The only one I could think of was from a modified base 3 system I read about in a book of Martin Gardner’s scientific american math column, where the three digits stand for, 0, 1, and… wait for it: -1 And this does do surprisingly well for representing integers and even doing basic arithmetic. ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [February 3, 2009, 11:04am UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/32 "2009-02-03T11:04:38Z")
We just did the thing about numbers and corners a month ago. Doesn’t anyone even remember this thread?: > **[Origin of arabic numbers?](https://boards.straightdope.com/sdmb/showthread.php?t=501855)** > > A friend just emailed me this: http://www.orthohelp.com/numbers.htm Which tripped my bullshitemeter and sent me googling for truth. I found this: http://www.geocities.com/rmlyra/Numbers.html Wiki didn’t break the tie, so I come to ask. Is there... ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [February 3, 2009, 11:10am UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/33 "2009-02-03T11:10:52Z")
chrisk, it’s also possible to have a number system with a negative base: > **[Negative base](https://en.wikipedia.org/wiki/Negative_base)** > > A negative base (or negative radix) may be used to construct a non-standard positional numeral system. Like other place-value systems, each position holds multiples of the appropriate power of the system's base; but that base is negative—that is to say, the base b is equal to −r for some natural number r (r ≥ 2). > Negative-base systems can accommodate all the same numbers as standard place-value systems, but both positive and negative numbers are represented without the use of a minus sign (or, i... ---
**Author:** ![Bytegeist](https://avatars.discourse-cdn.com/v4/letter/b/9dc877/32.png) [@Bytegeist](https://boards.straightdope.com/u/Bytegeist)\ **Post date:** [February 3, 2009, 2:48pm UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/34 "2009-02-03T14:48:25Z")
> [@Wendell\_Wagner](#): > > … it’s also possible to have a number system with a negative base … Also a [complex](http://en.wikipedia.org/wiki/Complex_base_systems) base. Let the Romans chew on that. **Chrisk** , the system you’re describing is the [balanced ternary](http://en.wikipedia.org/wiki/Balanced_ternary) number system. ---
**Author:** ![Cervaise](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cervaise/32/16693_2.png) [@Cervaise](https://boards.straightdope.com/u/Cervaise)\ **Post date:** [February 3, 2009, 3:24pm UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/35 "2009-02-03T15:24:26Z")
> [@Indistinguishable](#): > > Asking what base Roman numerals have is like asking whether pigeons are upper-case or lower-case; the concept doesn’t apply. Considering how much people enjoy pigeons crapping all over their houses, eaves, fences, and so on, I would argue that they are actually cursive. ---
**Author:** ![RedSwinglineOne](https://avatars.discourse-cdn.com/v4/letter/r/a9adbd/32.png) [@RedSwinglineOne](https://boards.straightdope.com/u/RedSwinglineOne)\ **Post date:** [February 3, 2009, 4:40pm UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/36 "2009-02-03T16:40:07Z")
There are 10 kinds of people in the world, those who understand binary and those who don’t. ---
**Author:** ![Maastricht](https://avatars.discourse-cdn.com/v4/letter/m/a88e57/32.png) [@Maastricht](https://boards.straightdope.com/u/Maastricht)\ **Post date:** [February 3, 2009, 4:51pm UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/37 "2009-02-03T16:51:39Z")
> [@sturmhauke](#): > > Think about it for a minute. For this corners thing to hold, you have to write the digits in some pretty strange ways, and then you count some corners one way and some another way, and anyway you admit that the nine is inexplicable. It really doesn’t make any sense. I admit, increasingly shamefully, that my grandfather explained this to me when I was a bright but seven-year old girl, and that, at the time, it made perfect sense. Now tell me about childhood ideas of _your_ own that \*you \*haven’t challenged yet. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [February 3, 2009, 6:28pm UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/38 "2009-02-03T18:28:48Z")
Quoth **Bijou Drains** : > [@](#): > > Base is the number of unique digits a number system has …Depending on how you define “digits”. The Mayans used a place-value number system mathematically very much like ours, except using powers of 20, instead of powers of 10. But they only used three different symbols to do it. The things mathematically analogous to our digits were constructed out of two of those symbols, in a manner reminiscent of Roman numerals, while the zero had a symbol of its own. ---
**Author:** ![panamajack](https://avatars.discourse-cdn.com/v4/letter/p/47e85d/32.png) [@panamajack](https://boards.straightdope.com/u/panamajack)\ **Post date:** [February 3, 2009, 6:53pm UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/39 "2009-02-03T18:53:33Z")
> [@Maastricht](#): > > I admit, increasingly shamefully, that my grandfather explained this to me when I was a bright but seven-year old girl, and that, at the time, it made perfect sense. I was around the same age when someone showed something similar to me as a method for doing addition. Each numeral has a specific pattern of points on it equal to its number. When adding several numbers at once, you just count up instead of adding the numbers individually. At that age, it was just as fast and even today I use it to check my work. ---
**Author:** ![garygnu](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/garygnu/32/2924_2.png) [@garygnu](https://boards.straightdope.com/u/garygnu)\ **Post date:** [February 3, 2009, 7:42pm UTC](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202/40 "2009-02-03T19:42:38Z")
> [@Chronos](#): > > …The Mayans used… It’s simply “the Maya.” No “ns” at the end. [Previous page](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202.md?page=1) [Next page](https://boards.straightdope.com/t/what-base-are-roman-numerals-considered-to-have/484202.md?page=3)