Fractal Moments

As any crow could tell you, it’s exactly 94.34 miles along the coast of from San Diego to Long Beach, California. Of course, unable to fly that straight, we would need to travel the coast road, I-5 and Route 1 for a total of 102.51 miles.

But that’s not exactly accurate. Route 1 doesn’t quite hug the coast. It skips inland a little at Dana Point and elsewhere. So to get the exact distance along the coast we need to carefully trace along the coastline and include the distance around all the major bays and peninsulas. The distance is actually 113.725 miles.

Are we getting closer? Perhaps. But what if we measure really, really carefully and include all of the small jogs and inlets in the coastline? Then we measure again, including the distance around even the smallest variations; the boulders, the rocks, the pebbles, the grains of sand? Each time we re-measure the coastline at a greater level of detail, the measured distance from San Diego to Long Beach increases.

The Red line travels the coast road. The Black line traces the coastline. The Green line follows every major curve and jut.

Our crow, no doubt, would be unable to understand this, and perhaps neither can we, but the fact is that the closer we look, the larger the distance becomes. If we include the infinitely small in our coastline measurement, the total distance becomes, itself, infinite.

It’s called a ‘fractal’ and no, it doesn’t make sense. But the point is that the measurement of distance is based on our own perception and our decision to ignore details like minor coves.

If we pay attention to every detail, the distance becomes infinite.

So is time very different? How long is an hour if we pay close attention to every single minute? If every single second is tasted, savored, and filled with meaning and substance then how long does that moment become?