Sunday, December 18, 2011

Billions and trillions

One of Carl Sagan’s books that I really like is “Billions and Billions”, where he wrote about the importance of exponentials, the connection between hunting and football, the true size of the universe, the decline of our planet, government and even abortion. Though I read it in English, I once, in a friend’s house, found a Spanish translation of the book and I was surprised when I realized the translated title: “Miles de Millones”, which means “Thousands of Millions”. If you are a native English speaker you might be thinking “Why were you surprised? A billion is a thousand millions, in other words it is 109”, and that is the main reason I decided to write about this because in most Spanish speaking countries the term “Billion” means a million of millions, i.e. 1012, and probably now you understand my surprise.
Historically, the term billion in English was first used to design 1012 following the French numbering system and it was introduced in the 15th century[1]. Now that meaning is part of the denominated long-scale system where a trillion is 1018, meanwhile in the short-scale system, used in most of the English speaking countries, a billion is 109 and a trillion is 1012. Surprisingly, the short-scale meaning was introduced also by France in the late 17th century even though they officially use the long-scale system nowadays. In the past, England used the long-scale system for a long time but they changed to the short-scale one, meaning that when reading old documents from England you must be careful about the meaning of billion and trillion.
If you are used to the exponential notation, then this whole discussion might be pointless since you use an unambiguous way to describe large quantities that doesn’t need the confusing terms billion and trillion. In that sense, the International Bureau of Weights and Measures (BIPM) suggests to avoid the use of billion or trillion since their meaning is language dependent and I think that scientists that publish or communicate their work should be aware of this language ambiguity and avoid it or at least be clear about the scale they use. As a recent example, we have the news about the MIT camera that is able to capture video at the speed of light, where they use in the title the sentence “one trillion frames per second” and they even use the word trillion over all the official website of the project, I couldn’t find a footnote or an explanation of the scale they are using and, therefore, after my first excitement about having a camera capturing data at 1018 frames per second I had to use my common sense to realize that they are talking of 1012 frames per second since their results have time lengths of nanoseconds (10-9 seconds) and hundreds of picoseconds (100 times 10-12 seconds). I’m not saying that their results lost importance because the camera works just at 1012 fps, that’s still very impressive if we take into account that most of the video cameras we had commercially don’t go further than 30 or 60 fps and that the fastest video camera I have worked with has a maximum frame rate of 1000 fps. I’m just saying that at first I imagined the amount of data captured and the transfer and storage capacities needed to work with it but later everything looked a little bit smaller because my reference frame was using the large-scale system.
In a globalized world, where communication between people from different countries and languages is a common thing, we need to have standards to communicate our ideas unambiguously and we must try to allow everyone to fully understand the information we are sharing with them, even though their common sense should be enough for them to understand us. Since there is not a chance that we have an standard meaning for billion and trillion in the world, I invite everyone to avoid their use or at least to give an explanation of the meaning of those words in their work.

[1] Smith, David Eugene. History of Mathematics. Courier Dover Publications. pp. 84–86. ISBN 978-0486204307.

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