A Different Kind of Multiplication

Post by teilo » Tue, Jun 08, 2010, 11:39 PM UTC

gjm11 wrote: post #3

The author claims, apparently confidently, that the Romans used this method but had no idea why it worked. It's not clear how he knows this. I dare say most people who used it didn't know why it works, but then probably most people today don't know why long multiplication works. Barring good evidence to the contrary, I bet that whoever thought the method up had a pretty good idea of why it worked. Of course it's poss…

Agreed. I have often noticed a tendency among professionals who should know better, to presume that ancient peoples were somehow less intelligent than we are, and less capable of applying their minds to complicated and even abstract problems. It is just plain not true, and there is so much anthropological evidence to demonstrate this fallacy that it is idiotic that it is still repeated.

In this case, it is an especially bad assumption, given that he is talking about a system of mathematics that significantly post-dates the great Greek mathematicians. If Archimedes could invent a method to solve problems today solved by integral calculus, 2000 years before Newton, and implemented Riemann sums in his methods, I hardly think that this little trick confounded explanation at the time it was used, particularly since it works with ANY system of notation.

Post by koeselitz » Wed, Jun 09, 2010, 12:47 AM UTC

This article is flatly wrong. Some early Romans may well have used so-called 'Roman numbers,' which retained some common use among the masses throughout the years; but any Roman of real education, particularly a Roman geometer or mathematician, of an era after around 100 BC would've used the more convenient and refined Greek numerals, which were base-10 just like our own, and which were in fact a bit more complex than our numbers in that they used separate characters for the tens and hundreds slots. In fact, the Greek system of numerals predates the Roman by hundreds of years. [See here: http://en.wikipedia.org/wiki/Greek_numerals]

This belief that Arabic numerals were the first base-ten system of numbers, that our own modern methods are vastly superior to the methods of the past, or that, as the author of this article puts it, "the Romans did not know anything about the binary system," is silly misinformation. And for what it's worth, Apollonius of Perga's treatise "On Conic Sections" is probably the most complex and beautiful mathematical treatise I know of before or since - and yes, that's counting everything from the modern era.

Re: A Different Kind of Multiplication

Re: A Different Kind of Multiplication