A brilliant aid in understanding special relativity is the surveyors' parable introduced by Taylor and Wheeler [ 1, 2 ]. Suppose a town has daytime surveyors, who determine North and East with a compass, and nighttime surveyors, who use the North Star. These notions of course differ, since magnetic north is not the direction to the North Pole. Suppose further that both groups measure north/south distances in miles and east/west distances in meters, with both being measured from the town center. How does one go about comparing the measurements of the two groups?

With our knowledge of Euclidean geometry, we see how to do this: Convert miles to meters (or vice versa). Distances computed with the Pythagorean theorem do not depend on which group does the surveying. Finally, it is easily seen that “daytime coordinates” can be obtained from “nighttime coordinates” by a simple rotation. The geometry of this situation is therefore described by Figure 3.5, where the $x$ and $y$ directions correspond to geographic east and north, respectively, but where the $x'$ and $y'$ directions correspond to magnetic east and north, respectively. If the surveyors measure $x$ and $x'$ in meters, but $y$ and $y'$ in miles, and do not understand how to convert between the two, communication between the two groups will not be easy!

The moral of this parable is therefore:

1. Use the same units.
2. The (squared) distance is invariant.
3. Different frames are related by rotations.

Applying that lesson to special relativity, the first thing to do is to measure both time and space in the same units. How does one measure distance in seconds? that's easy: simply multiply by $c$. Thus, since $c=3\times10^8 \frac{\mathrm m}{\mathrm s}$, 1 second of distance is just $3\times10^8$ m. 1) Note that this has the effect of setting $c=1$, since the number of seconds (of distance) traveled by light in 1 second (of time) is precisely 1.

Of course, it is also possible to measure time in meters: simply divide by $c$. Thus, 1 meter of time is the time it takes for light (in vacuum) to travel 1 meter. Again, this has the effect of setting $c=1$.