Popular opinions become entrenched in the tissue of society whether it’s valid or not. For people to look at measuring length differently, it took Lewis Fry Richardson noticing discrepancies in the length of borders while investigating the cause for war.
By noticing that as the scale decreased, the size of borders increased, Richardson accidentally discovered a fractal dimension.
The fractal nature of object mean that the rougher an object becomes, the closer it gets to gaining another dimensions. In the example of borders, a single dimension border with a jagged enough coast line gains mathematical properties of a two dimensional object.
Mandelbrot expanded on Richardson’s finding by noticing that the fractal state was the norm in the natural world and not the exception – as many Euclidean idealists would like to believe.
Fractals lead to the unique scaling properties of plants, living organisms, cities, companies, and even markets. The influence of fractals spread to anything that maintains a similar structure at different levels or behaves similarly at different time scales.