Wednesday, December 9, 2009

Wednesday Math, Vol. 100: The victory of Hindu-Arabic numerals.

Welcome to my 100th Wednesday math post. I've missed a few Wednesdays over the past two years and had some weeks when I decided to write about something else on a Wednesday, but this does mean about two straight years of yapping about numbers at least once a week. Usually, I talk about a mathematical concept, but this week, it's more about language and symbols.

The whole world uses the Hindu-Arabic number system these days. It has only ten symbols for numbers and a symbol for the decimal point, which is a period in English, though some languages use the comma instead. Other systems like Roman numerals are just quaint throwbacks now, used sparingly in odd places like the faces of clocks and watches or numbering Super Bowls or sections in an outline. If you want to write a number in any language, our old friends 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 can help you be understood even if you can't even say "thank you" or "Where is the bathroom?" in the language of the person you are trying to communicate with.

Like Roman numerals, Chinese numerals used to be used when people were doing actual calculations, but according to several native Chinese speakers I consulted, for the most part, the use of Chinese numerals today is on writing checks, just like we write the number $437 and write out "four hundred thirty seven dollars" to make sure there is no misunderstanding.

A feature of the Chinese number system and their language that seems odd to Westerners is actually more consistent than what European languages do, and therefore more like math. All the European languages I know, which includes Spanish, Italian and French and all the ones I checked before writing this post, like German and Russian, have special words for the most of the numbers between 11 and 19, and all have special names for the multiples of ten less than 100. Not Chinese. 30 is "three ten" and 13 is "ten three" and 47 is "four ten seven". It sounds a little funny to our ears, and the way we do numbers is so ingrained in us that it's natural to think any other way must be wrong, but their way is more consistent and uses less words. After all, in the European languages, there is no special single word for 200 or 5000. We say and write "two hundred" and "five thousand". The Chinese just start this natural pattern as soon as there are two places in a number. Some have speculated that this consistent use of language may be part of why cultures who use the Chinese system, and that includes the Koreans and Japanese, are considered "good at math".

Another difference from the Chinese and European systems is that 10,000 has its own character, and instead of having a new special name for every number that is a power of 1,000 or 10^3, the Chinese has a special name change at powers of 10^4. In archaic English, we had a single word for 10,000, myriad, which now just means some indefinite large number. This means a translation of Chinese numbers for the different places would go something like this.

1's place - one
10's place - ten
100's place - hundred
1000's place - thousand
10000's place - myriad (we call it ten thousand)
100000's place - ten myriad (we call it hundred thousand)
1000000's place - hundred myriad (we call it million, a name change from thousand)
10000000's place - thousand myriad (we call it ten million)
100000000's place - new special word for myriad myriad (we call it hundred million)

I know some people dislike math, but numbers are a universal language. Without any dark, one world, socialistic conspiracy, every culture that is part of the modern world is using the Hindu-Arabic number system to express number concepts, even the rightfully proud East Asian cultures throwing over their systems to use a superior product. There are documented accounts of tribes in parts of the world that do not have words for any number greater than three, but it isn't mere chauvinism to call those tribes primitive. Having a good number system is powerful technology, and understanding more about math than a neighboring culture is an advantage often exploited on the battlefield.

The ancient Hebrews blame an angry God for their time spent in slavery in Egypt and Persia, but another less mystical explanation is that the ancient Hebrews sucked at math and the Egyptians and Persians didn't. At a time when the Bible has the approximation of pi at 3, the Egyptians had an approximation good to the sixth decimal place. That's not just just showing off, that translates into rounder wheels, and it turns out rounder wheels are a good thing.

Who knew?

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