Ivars Peterson's MathTrek

July 27, 1998

Beyond Extra Large (and Ultra Small)

Metric prefixes come in handy for expressing both large and small quantities. So we have megawatt power systems and gigabyte hard drives at the high end, and we have nanoscale electronics and femtosecond lasers at the low end.

Advances in scientific research and technology keep pushing us to new frontiers in the domain of metric prefixes.

In the July Scientific American, Philip and Phylis Morrison describe the escalation in the amount of stored knowledge since the days of the famed library in ancient Alexandria. The library probably shelved the equivalent of 50,000 books today. Counting the literature of China, India, Iraq, and Iran, the total of number of books available at that time might have numbered approximately 100,000.

About 1,500 years later, a librarian at Harvard estimated that, in 1945, "worthwhile" printed material amounted to about 10 million books. With one byte as a unit of information representing roughly the equivalent of a single character of English text, it's possible to store that text as 10 trillion bytes, or 10 terabytes, of data. Images, drawings, photographs, audio and video recordings, and huge databases, however, require enormous amounts of additional storage space.

The U.S. Library of Congress now holds about twice the postwar book count. Because it also has 3.5 million sound recordings and other byte-hungry material, however, the total store comes to a couple of petabytes (a million billion bytes).

One can plausibly estimate that fresh text, including newspapers, amounts to less then 100 terabytes annually. Recorded music, films, photographs (including family snapshots), and other materials add considerably to that accumulation. "The biggest byte makers are the television stations of the world," the Morrisons say. "Although it is hard to correct for innumerable repeats, our best source puts their originality at one tenth of all they send out and so allots them under 100 petabytes annually."

To assess the totality of information production, one can also try to include ephemeral signals conveyed from one person to another. The sounds of telephone calls add up to some 1,000 petabytes worldwide, or a few exabytes. Face-to-face speech provides several more exabytes of data.

At this stage, the summing gets trickier. The Morrisons simply conclude, "No estimate of the eventual human store seems quite credible as yet."

There's one other problem. Few people know what metric prefix comes after "exa."

The Conf&eacuterence G&eacuten&eacuterale des Poids et Mesures (CGPM), however, has already come to the rescue. In 1991, this international body adopted new prefixes representing 1021, 1024, 10-21, and 10-24. This means that 1,000 exabytes equals 1 zettabyte (ZB), and 1,000 zettabytes equals 1 yottabyte (YB).

I first encountered the new prefixes in 1993 when researchers measured voltages in a superconducting circuit so small that they had to use the term milliattovolt, where "atto" stands for 10-18. The proper term is zeptovolt.

Here's the complete table of official metric prefixes:

Power of 10 Prefix Symbol Power of 10 Prefix Symbol
24 yotta Y -1 deci d
21 zetta Z -2 centi c
18 exa E -3 milli m
15 peta P -6 micro m
12 tera T -9 nano n
9 giga G -12 pico p
6 mega M -15 femto f
3 kilo k -18 atto a
2 hecto h -21 zepto z
1 deka da -24 yocto y

Many of the prefixes come from Greek and Latin words, often via French. "Zepto" is derived from the Latin septem, meaning 7, because this is the seventh prefix in the system of metric prefixes. The s was replaced by z to avoid confusion with the abbreviation for the second. The prefix "zetta" was coined to parallel "zepto." Similarly, "yocto" is derived from the Latin octo, meaning 8, and "yotta" parallels that term. (See A Dictionary of Units of Measurement at http://www.unc.edu/~rowlett/units/.)

You might be interested to know that an attoparsec is a distance of about one inch (3.1 centimeters). The distance of the most remote object yet observed is about 125 yottameters (13.2 billion light-years). The diameter of the largest known galaxy is approximately 53 zettameters. At the other end, an atomic mass unit equals 1.66 yoctograms. (See http://www.newscientist.com/lastword/answers/lwa078.html.)

Now you can really start talking extra large and ultra small.

Copyright 1998 by Ivars Peterson

References:

Morrison, P., and P. Morrison. 1998. The sum of human knowledge? Scientific American 279(July):115.

Taylor, B.N., ed. 1991. The International System of Units (SI). NIST Special Publication 330. Washington, D.C.: U.S. Government Printing Office.

Peterson, I. 1993. Measuring superconductor magnetic noise. Science News 143(Jan. 16):37.

You can check out A Dictionary of Units of Measurementat http://www.unc.edu/~rowlett/units/.

Comments are welcome. Please send messages to Ivars Peterson at ipeterson@maa.org.