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7Time, Percentages, and Graphs
You can use various linear units to measure height, width, or depth. That is the first
dimension. Area is the second dimension, and volume is the third. And then you have
time! It, too, is a dimension. In this chapter, you’ll see how time relates to the three socalled
spatial dimensions. You’ll also learn how changing quantities, in any dimension,
can be considered as percentages and portrayed as graphs.
TIME AS A DIMENSION
In mathematics, any measurable quantity can be called a dimension. We use a variety
of schemes and devices to measure time. The ancients used sand in an hourglass. Until
recently, we used spring-wound or weight-driven clocks and watches. Quartz-crystal
electronic clocks use alternating-current (ac) signals at precise frequencies to count
“ticks” of time.
According to the above definition, we can call temperature, weight, brightness of light,
loudness of sound, and intensity of taste “dimensions,” although people rarely think of
them that way. Even taste has at least four “dimensions”: sweet, sour, bitter, and salty.
For now, let’s confine ourselves to the traditional four dimensions commonly called
height, width, depth, and time. This gives us a four-dimensional continuum. Albert
Einstein coined a term for this in the early 1900s, and it has been used ever since: spacetime.
Some folks turn this around and call it time-space.
TIME AND SPEED
Combining length one way with length another way defines an area. Similarly, combining
time with length or distance defines speed. Suppose you walk at a steady rate to
travel a distance of 1 mile in 15 minutes. If you don’t change that pace, you will go
another mile in the next 15 minutes. In an hour (60 minutes) you’ll go 4 miles. Your
speed is therefore 4 miles per hour (mph or mi/h).
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