Friday, July 10, 2009

The big and the small

Scientists have long studied extremes. Astronomers have long studied objects that are very large, such as galaxies and universes, whereas chemists and biologists have studied things that are very small, including atoms, molecules and microscopic organisms. The book "powers of ten" by Philip and Phylis Morrison gives an excellent visual demonstration of things at various scales.
It is no wonder that when marketers need superlatives to describe their products, they look toward scientific jargon. Apple has an mp3 player called the Nano, my son has a robot called Megatron, and there is a lottery in the USA called Mega Millions, even though as far as I know the prize money is much less than a trillion (or a billion for those of you in long scale countries).

Nano and Mega are part of a class of prefixes that are used to modify units in powers of ten. For instance a kilo-meter is 1000 meters, and a centimeter is 1/100th of a meter. According to the international systems of units (SI), the following prefixes are defined:

yocto, zepto, atto, femto, pico, nano, micro, milli, centi, deci, deca, hecto, kilo, mega, giga, tera, peta, exa, zetta and yotta.

It is interesting to note that as technology evolves, more and more of these prefixes become commonplace. Most of us are familiar with kilo as used in kilogram. Radio waves provides us familiarity with mega as the FM stations operate in the megahertz range. As computer processors increase in speed, we have for the last decade or so been working on computers with gigahertz processors. Memory density has also increased dramatically with personal computer memory, both volatile and nonvolatile, routinely in the gigabytes range today. The world's fastest computers have recently broken the petaflop (1015 flops) barrier and business and scientific computers routinely deal with terabytes and petabytes of data and will need to access exabytes in the not too distant futures. Sometimes the prefix is omitted; for instance the calorie unit we see on food packaging should more accurately be called a kilocalorie since it is the energy needed to raise the temperature of 1 kilogram of water by 1 degree Celsius.

One interesting note about measuring computer memory using the SI prefixes. Modern computer memory locations are indexed using a binary address, i.e. a series of binary digits (or bit). For instance, 1 bit can denote two locations, since it can have the value 0 or 1. On the other hand, 2 bits can denote four locations, i.e 00, 01, 10 and 11. In particular, n bits can denote 2n locations. This is why computer memory is generally arranged in chunks whose size is a power of 2. Ten bits can address 210 = 1024 locations. If each location contains one byte of memory, then 1024 bytes is referred to a kilobyte. 16 bits can address 216 = 64* 210 = 64 kilobytes even though 216 is really 65,536. This deviation from the SI usage of the prefixes can cause confusion and thus in 1998 prefixes were introduced which are powers of 2:

kibi, mebi, gibi, tebi, pebi, exbi, zebi, yobi.

For example, 1024 bytes is referred to as a kilobinarybytes or a kibibyte whereas 280 = 1208925819614629174706176
bytes is called a yobibyte. As of this writing, these binary prefixes are still not commonly used in the scientific literature (although I did use it here). I wonder when we will start seeing products named after these prefixes?

A related note on the subject of very small and the very big, the word quantum in common usage means a significant or sudden amount as in "a quantum leap". On the other hand, its usage in physics is almost the opposite; a quantum is the smallest indivisible unit of a physical property.

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