Sunday, October 7, 2007
Units: teras, centis and nanos
Inches? Feet? Miles? No: scientists and mathematicians don't use these units. There's nothing morally wrong with them, it's just that people who do technical work need to speak the same language in order to avoid misunderstanding. The metric system is the internationally agreed upon system of units, based on the meter, the gram and the second and powers of 10. However, the most common units of physics are the meter, kilogram (thousand grams) and second (the "mks" system) or the centimeter (1 hundredth of a meter), gram and second (the "cgs" system). Since scientists study quantities varying over a very wide spectrum of sizes, they often use the following Greek prefixes to express units most appropriate to their work:
For example, for your doctor, the distance from your elbow to the beginning of your fingers is probably best expressed as about 30 centimeters. The meter is too large a unit. On the other hand, distances between cities are best expressed in kilometers.
The diameter of an atom is somewhere around 1/10 of a nanometer, while the diameter of a carbon nanotube (see previous blog) is about a nanometer --- not too surprising.
Distances and times are sometimes used interchangeably. A "light year" is the distance light travels in 1 year: approximately 9500 terameters or 9.5 petameters.
In one second, light travels 3 x 1010 centimeters, so in 1 nanosecond (10-9 or 1 billionth of a second), light travels about 30 cm, or about the distance from your elbow to the base of your fingers. If someone asks you how long your arm is, you could say: "a couple of nanoseconds." (See joke at the end of this blog.)
A decimal calculation like multiplication or division is called a floating point operation or a flop. A modern supercomputer can do a trillion of these in a second: a teraflop. For this many operations per second, keeping the distance that light (or an electric field) must travel to a minimum is significant. That's one reason why chip manufacturers keep striving for ever smaller sizes: the bigger the chip, the greater the distances that have to be covered by its electrical signals, so the slower it runs.
Joke
A do-it-yourselfer goes into a lumberyard to buy some wooden studs for building a toolshed. The proprietor asks "How long you want 'em?" The purchaser says "Oh, at least 50 years."
tera = 1 trillion = 1012
giga = 1 billion = 109
mega = 1 million = 106
kilo = 1 thousand = 103
hecto = 1 hundred = 102
deca = ten = 101
deci = tenth = 10-1
centi = hundredth = 10-2
milli = thousandth = 10-3
micro = millionth = 10-6
nano = billionth = 10-9
pico = trillionth = 10-12
For example, for your doctor, the distance from your elbow to the beginning of your fingers is probably best expressed as about 30 centimeters. The meter is too large a unit. On the other hand, distances between cities are best expressed in kilometers.
The diameter of an atom is somewhere around 1/10 of a nanometer, while the diameter of a carbon nanotube (see previous blog) is about a nanometer --- not too surprising.
Distances and times are sometimes used interchangeably. A "light year" is the distance light travels in 1 year: approximately 9500 terameters or 9.5 petameters.
In one second, light travels 3 x 1010 centimeters, so in 1 nanosecond (10-9 or 1 billionth of a second), light travels about 30 cm, or about the distance from your elbow to the base of your fingers. If someone asks you how long your arm is, you could say: "a couple of nanoseconds." (See joke at the end of this blog.)
A decimal calculation like multiplication or division is called a floating point operation or a flop. A modern supercomputer can do a trillion of these in a second: a teraflop. For this many operations per second, keeping the distance that light (or an electric field) must travel to a minimum is significant. That's one reason why chip manufacturers keep striving for ever smaller sizes: the bigger the chip, the greater the distances that have to be covered by its electrical signals, so the slower it runs.
Joke
A do-it-yourselfer goes into a lumberyard to buy some wooden studs for building a toolshed. The proprietor asks "How long you want 'em?" The purchaser says "Oh, at least 50 years."
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