In a previous post I tried to explain that mathematics is simply another language, and that is very likely why so many people dislike it, because they find it is foreign and can’t read it. It would be akin to me attempting to read a newspaper written in Russian or Chinese. Sure I know a few words, but nowhere near enough to understand even a paragraph let along an entire article. So by and large people try and circumvent learning the language of mathematics by converting it into words. An oddity given the almost universal animosity toward “story problems.”

Unfortunately, this doesn’t work well with large numbers. For the vast majority of people passing through the rigors of their day to day business this doesn’t present much of a problem. Even if one is buying or selling a house or business, typically the largest transaction the average person makes in their lifetime, the numbers can be expressed in universally understandable terms. Then they sit down in their new home, turn on the news, and have no way of conceptualizing what the national debt, the Gross Domestic Product, or the population of the world is!

This difficulty is not entirely because the numbers are large, but also because even in a given language, which is English in this case, the numbers have different names depending on their point of origin. The phenomenon is called “false friends” in linguistics: a condition where a word is spelled, and even pronounced, exactly the same way in different places but with completely different meanings. This ambiguity was recently brought to my attention by my colleagues (they don’t know me from Adam) at Cambridge University in the UK.

When explaining large numbers, typical of areas such as finance, economics and population, a Billion means one thing in the US, may or may not mean something different in the UK, and does mean something completely different in France and very probably in China. It is considered bad form to begin a sentence with numerals, so we resort to a word representing the numeral, and while 1,000,000,000 is a Billion here in the US, it might be a Billion in the UK (legally it is supposed to be) but for some it might be a Milliard, and in France it is a Milliard. It becomes even more confusing at 1,000,000,000,000, which is a Trillion in the US, maybe a Trillion or maybe a Billion in the UK, or Canada, and definitely a Billion in France.

So let’s say I’m reading about a financial crisis in *Le Monde*, or from *Agence France-Presse* that says something about an amount of seven-trillion euros. Does it really mean my US interpretation of seven-trillion, or does it mean I should mentally convert that number to the US meaning of the word, which would be seven-quintillion euros! It is obvious that there is an inherent and gigantic difference depending on one’s interpretation of exactly the same word. The same *English* word.

There are some very cool explanations why the difference in the interpretation of the words, but that involves explaining the mathematics, which would sort of defeat the purpose of trying to get you to read this blog. For those that want the in-depth explanation it is available on Long and short scales on Wikipedia, or you can just watch the short video at Numberphile – How big is a billion? (Hopefully you understand the rules of exponents.)

The solution of course to avoid this ambiguity is to simply write the number out in Arabic numerals (yes, they are called Arabic numerals, not to be confused with Eastern Arabic Numerals). They will remove the ambiguity, but not make the numbers any less confusing due to their large size. And herein lies the reason for learning the language of mathematics, because with very little effort one can easily learn to understand, interpret, add, subtract, multiply and divide gigantic financial and population numbers using scientific notation. And you can learn it for free in about an hour or two at Khan Academy under Basic Exponents or more completely under Exponents and Radicals. Then you’ll be on your way to reading the universal language of mathematics.