12.

Very, Very Big and Very, Very Small

For the ancient Greeks, a myriad was as big as it got. The word is used today to mean a large, undefined (and quite possibly uncountable) quantity of something—but in ancient Greece it referred precisely to the number 10,000 and was the largest single name for a number that existed.

You could multiply myriads, of course, and Archimedes referred to a “myriad myriad” (100,000,000) as part of a work called The Sand Reckoner, in which he set out systematically to calculate how many grains of sand it would be possible to fit into the entire universe.

Archimedes was testing the number system of his era to its breaking point. The figure he eventually came up with for the size of the universe—which reckoned it as around two light years across, in modern measurements—was itself many billions of times too small. Even today, however, technology and human knowledge continue to push at the boundaries of numbers and language.

One recent word is the prefix exa: an addition to the official International System of Units for naming large quantities.16 Most people are aware that megabytes are units of computer storage on a scale of one followed by six zeros (millions), while gigabytes are a scale of one followed by nine zeros (billions) and terabytes are a scale of one followed by twelve zeros (trillions). Beyond this, however, the terms become increasingly obscure—and recent.

One followed by fifteen zeros has since 1975 had the official prefix peta, while in the same year the prefix exa was established for a one followed by eighteen zeros—the largest officially named international number at that point in history. Both exa and peta are terms adapted from ancient Greek, in each case by removing a letter from one of the numbers between one and ten. Peta is a shortened form of the Greek penta, meaning five, because it denotes five times as many zeros as the basic unit for large numbers, one thousand; exa is a shortened form of the Greek hexa, meaning six, because it denotes six times as many zeros as one thousand.

Exa numbers exist on a scale so huge that the mere stuff of the world around us rarely comes close. Just one exasecond is around 32 billion years, more than double the age of the universe. Yet by 1991, it was decided that new terms needed to be brought into use for still larger numbers: zetta (a one followed by twenty-one zeros, based on the Greek for seven, hepta—because it has seven times as many zeros as one thousand—with the deliberate addition of a z to avoid duplicating s as the first letter of a prefix) and yotta (a one followed by twenty-four zeros, based on the Greek okta, eight, with the use of y to avoid the potential confusion of using the letter o—which could be read as a zero—to begin a prefix).

Vast though they may be, these scales are already starting to come into play thanks to both the level of our increasing knowledge about the universe and the sheer quantities of data we ourselves are generating through faster and more numerous computers. We don’t yet measure our hard drives in yottabytes—that is, 1,000,000,000,000,000,000,000,000 bytes of information—but it’s not outlandish, if present trends continue, to think that someday we eventually may. We have already started to speak increasingly casually of storing terabytes (1,000,000,000,000 bytes) worth of information within home computers.

The future, of course, isn’t just big—it’s also incredibly small, not least in the scale of the technologies required to store all this information, and in the extremely small other things these technologies allow us to see. Yocto (a one preceded by twenty-four decimal places of zeros) is currently as small as it officially gets. In the years to come, though, things are only going to get more extreme in both directions.