The SI System of Units
The SI System of Units, commonly known as the metric system, is the international standard for measurement. It is based on the concept that there are seven fundamental dimensions that can be measured, everything else being a combination of those seven. For example, length is fundamental and cannot be derived from anything else, whereas area is simply length squared, volume is length cubed, etc. Mass and time are also fundamental, speed and density are derived from them, and so on.
As a result, any physical quantity can be represented by the combination of one real number (the magnitude of the quantity) together with one integer (an exponent) for each dimension. For example, the acceleration “32 meters per second squared” has a magnitude of 32.0, a length exponent of 1 (“meters”), a mass exponent of 0 (there is no mass involved), and a time exponent of -2 (“2” because second is “squared,” but negative because “per” means “divide by”). The tuple representing that acceleration is therefore ( 32.0, 1, 0, -2 ). This is reflected in the standard notation for this quantity: 32.0 m s-2.
The seven dimensions (and the base units used to measure them) are: length (meter), mass (kilogram), time (second), electric current (ampere), thermodynamic temperature (kelvin), amount of substance (mole), and luminous intensity (candela). In the case of length, it’s clear that you are measuring an interval rather than a position. Although it’s not quite so obvious, the same is true of time; the time dimension is intended to measure things like “30 seconds,” not things like “3:00 O’Clock.” The existence of an absolute zero with physical meaning makes things a bit more subtle in the case of temperature, but it’s simplest to think of that in the same way, especially if you need to convert between kelvin and degrees Celsius or degrees Fahrenheit.
For more information on units, dimensions, and the use of SI, see [6].
