Comment by nawgszy | Hacker News Reader

Comment by nawgszy | Hacker News Reader

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>You're speaking from a position of bias and ignorance

I made a fairly concise point, but you're right about one thing

>we all do this sometimes

Because you most certainly just did

>As for your specific concerns: the easy pattern is that the letter for a group of five literally looks like half of the letter for a group of ten.

That's not the issue with the "easily repeatable pattern". The issue is this:

>V = X/2, L = C/2, D = ↀ/2, ↁ = ↂ/2, etc.

Do you see that "etc" you post? That's because, to represent 10^n, you need to know 2*n + 1 characters.

This is an obvious downfall that Hindu-Arabic numerals obviously do not have. Even if you ignore the shorthand (which would be foolish, parsing 5-9 characters in a row can take a serious moment of focus), you still need to know an unbounded amount of characters to represent the integers alone, and let's not even discuss the obvious fallacy of fractions etc..

Also,

>Objectively, the Roman system is easier to teach up to a basic level

Even this is an unfounded statement. Make an argument. Prove it. Objectivity of teachability can't possibly be something you just throw out casually in an argument, let alone an argument where you told someone they were biased and ignorant for, as far as I can tell, no reason at all.

That was not a personal judgment, just a straight-forward factual assertion. (Unless you have spent a decade doing calculations on a counting board...?) Pretty well everyone, including myself, is speaking from a position of bias and ignorance when discussing Roman numerals and counting boards, because these are not pervasively used for basic calculation in our society. We should bear that in mind and try to get outside of our preconceptions before making off-hand judgments.

It’s very seldom that anyone in the Roman empire – or medieval Europe – would need bigger numbers than, say, one million, especially for writing final answers down. But at least one counting board we know about from 300 BCE probably had lines for 10 orders of magnitude, and it’s not like more couldn’t easily be added if necessary. http://www.akg-images.fr/archive/-2UMDHU23V18G.html

As for fractions: Roman fractions were mostly twelfths (think inches and ounces).

Roman numerals and counting boards are obviously not an ideal system for writing down very large or very precise numbers, as I said. I’m not here claiming that they are a better basis for society’s numeration than more strictly positional Hindu–Arabic numerals.

My point is that we shouldn’t be so hasty to dismiss them out of hand or exaggerate their flaws. They were a highly effective system for doing complex calculations: precisely estimating the positions of stars and planets centuries into the past/future, running a bureaucracy overlooking an empire of 60+ million people, building large-scale engineering projects, and so on.

When it comes to teaching, I can only go by my own anecdotal experience trying to teach young children about numbers, the writings of various elementary math teachers, and the fragmentary remnants of debates in medieval Europe. I don’t know of any modern peer-reviewed research about Roman or medieval European counting boards, sorry.

(There is lots of evidence that learning place value using Hindu–Arabic numerals is very difficult for children, compared to other concepts and skills, requiring several years of study before primary school students really figure it out.)

Seems like counting boards might make a partial comeback sometime though: https://vimeo.com/204368634

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