Billions and Billions

In case you never watched the famous PBS prgram Cosmos, the above title was an expression used Carl Sagan to approximate the countless stars, planets, and galaxies found in the universe. It became Sagan's catch phrase.

The term "Billion" has been turning up in the news a few times, lately. Back in September, the world population eclipsed 6 billion. In November, for the first time a billion web pages were downloaded from the Internet in a single week. Then, just recently it was reported by the BBC that there are now over one billion "unique and indexable" web pages on the Internet.

For comparison, there are currently about 300 million people with access to the Internet world wide. Approximately three million new computers are being sold monthly worldwide, at least half are to new users.

If every web page was printed on a single sheet of paper, the Internet would fill about three or four million books, making it one of the 100 largest libraries in the world. One college library I know with about 4 million books (University of Arizona) uses two three story buildings and portions of five other buildings to house all their books. Of course, most web pages are more than a single sheet big (this one may be, but most are not), and for every unique and indexable "page" there are probably dozens of files. The Internet is quickly becoming the largest depository of information, if it isn't already. It is already, at least, the most used.

A few other interesting statistics: The same survey indicated that there are about 4.2 million reachable web sites. I do not know if that is domain "named" sites or if it includes personal web sites. (I assume the latter). Also it was found that 86.5% of web documents are in English. As the web continues to grow in non-english speaking countries, I suspect that the percentage will fall. The survey also searched web links. There were 750,000 links pointing to www.yahoo.com, 260,000 links pointing to www.mp3.com, and 4,000 links pointing to www.pokemon.com. This survey is at the very least an interesting snapshot of the web as it exists today. I would be interested to see how fast all of these numbers grow.

A billion is a big number. To visit every web page on the internet would require a page a second for thirty two years with no time to eat or sleep(1). I suspect that in thirty two years, the Internet may be up to 20-50 billion pages by then.

A billion dollar bills laid end to end would circle the globe at the equator four times.

This is assuming we are talking English or French billions. In many languages, a billion is not 109, but 1012 or a million million. Such is the case with Spain. I got an E-Mail from a reader to this site who pointed out that Spanish newspapers occasionally mistranslate the English "billion" as the same as a Spanish "billion". For you Spanish readers, a "billion" is translated "mil million". A Spanish "billion" is in English a "trillion".

A trillion dollar bills laid end to end would stretch from the Earth to the Sun.

Update (March 2000): Apparently North America, France, and the Netherlands are the only place where a billion is a billion. I got a few notes saying that most of Europe counts differently. The best explanation came from Johannes Spielman of Germany who wrote:

Just a little addition to your explanations about language and billions.
Actually, and you can see it for yourself when you open your Dictionary,
the word 'billion' in English (US) is the same as 'milliard' in English
(GB)! So not only Spanish and German do have that problem.
And if you want to know it really well:
The counting in German is:
Million 10^6
Milliarde 10^9
Billion 10^12
Billiarde 10^15
Trillion 10^18
Trilliarde 10^21

I decided to look up more info on this topic and found a few paragraphs from The History of Mathematics Volume II by D. E. Smith. Basically, the term "million" was not invented until the thirteenth century, and not universally adapted by Europe until the sixteenth century when it became standardized in most every language. Then according to Smith:

The Billion. Until the World War of 1914-1918 taught the world to think in billions there was not much need for number names beyond millions. Numbers could be expressed in figures, and an astronomer could write a number like 9.15 x 107, or 2.5 x 1020, without caring anything about the name. Because of this fact there was no uniformity in the use of the word "billion." It meant a thousand million (109) in the United States and a million million (1012) in England, while France commonly used milliard for 109, with billion as an alternative term.

Historically the billion first appears as 1012, as the English use the term. It is found in this sense in Chuquet's number scheme (1484), and this scheme was used by De la Roche (1520), who simply copied parts of Chuquet's unpublished manuscript, but it was not common in France at this time, and it was not until the latter part of the 17th century that it found place in Germany. Although Italy had been the first country to make use of the word "million," it was slow in adopting the word "billion." Even in the 15th edition of Tartaglia's arithmetic the word does not appear. Cataldi (1602) was the first Italian writer of any prominence to use the term, but he suggested it as a curiosity rather than a word of practical value. About the same time the term appeared in Holland, but it was not often recognized by writers there or elsewhere until the 18th century, and even then it was not used outside the schools. Even as good an arithmetician as Guido Grandi (1671-1742) preferred to speak of a million million rather than use the shorter term.

The French use of milliard, for 109, with billion as an alternative, is relatively late. The word appears at least as early as the beginning of the 16th century as the equivalent both of 109 and of 1012, the latter being the billion of England today. By the 17th century, however, it was used in Holland to mean 109, and no doubt it was about this time that the usage began to change in France.

As to the American usage, taking a billion to mean a thousand million and running the subsequent names by thousands, it should be said that this is due in part to French influence after the Revolutionary War, although our earliest native American arithmetic, the Greenwood book of 1729, gave the billion as 109, the trillion as 1012, and so on. (Op Cit pg. 84-86)


1. While no one could visit every web page in their life times (the vast majority I would never want to visit. pokemon.com tops the list). Though I suspect many of the people who make it to this site are giving it a good try. How many of you out there have made a hard copy of a web page just so you can finish reading it in the bathroom?

Back to the Glossary
Back to Archives