For 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...
How Did Anyone Do Math in Roman Numerals?
161–163 of 163 posts
Re: How Did Anyone Do Math in Roman Numerals?
#162Earlier quoted context omitted.
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.
An ugly thing about using negative digits with base ten (or any even base) is that you either have ambiguity on how to write numbers, or you have a different number of positive and negative digits. For example, if you do base ten with digits EDCBA012345 (E=-5, D=-4, etc.) -- that's 11 digits -- then five can be written as 5 or 1E; fifteen is 15 or 2E, etc. So you either: - Accept that some numbers can be written in m…
That numbers have interesting relationships to each-other is not an “ugly thing”, but rather a beautiful thing. The relationships exist whether we pay attention to them or not, so giving people a way to write and pronounce those relationships is a nice way to improve numeracy.
Writing numbers in multiple possible ways is really not that big a problem for most uses (for record-keeping in business transactions maybe). Personally I recommend becoming familiar with two different normalizations: all same-signed digits (the form we use now) or [–5, 5] with digits before a terminal 5 rounded away from zero. But in general for personal scratch work numbers don’t need to be normalized unless you feel like it. As long as you understand that 20–3 is the same as 10+7, it doesn’t really matter which one you think of as primary.
We use multiple number representations all the time, with e.g. the vulgar fraction 11/8 alternately representable as the “mixed number” 1 + 3/8, or as the decimal fraction 1.375, the simple continued fraction [1; 2, 1, 2], the percentage 137.5%, or the common logarithm ~10^(0.1383). Figuring out that 1.375, 1.385̅, 1.42̅5̅, 1.43̅5, and 2.6̅2̅5̅ are the same number isn’t that hard, with some practice.
Re: How Did Anyone Do Math in Roman Numerals?
#163Earlier quoted context omitted.
I'm not 100% sure, but through anecdotal experience and from what I've read (although haven't vetted), we lose track of counters at ~8 of them. That is, III is easily discernable as 3 'I's, but take IIIIIIIII, and try to recognize how many 'I's are there immediately.
That's why you group five I's into a V?
This, and another theory states that V is kind of similar to an open hand, i.e. five fingers, making it a convenient abbreviation. Consequently, X is just two V's joined at the vertex.