This brings a new understanding to scale and to measurement. The easiest way to understand this is to examine a fairly simple problem. Benoit Mandelbrot proposed this question to demonstrate the complexity of measurement and scale. There are a number of almanacs that provide this information. However, if one examines the measuring techniques used to determine the length of Britian's coastline, it becomes obvious that this measurement is only an estimate based on the accuracy of the measuring device.
Smaller units mean greater accuracy.
But we can continue that line of thinking indefinitely. There are always smaller fractions, an infinite number. Therefore, the coastline of Britain is an infinite length, however, it is confined within a finite space. We can begin to understand then that perimeter can have an infinite length confined within a finite area. Focusing on quantity will continue to prove frustrating since there are always smaller scales.