My Arm is Wet
I stand in the shower as I’ve done on the order of $10^4$ times in my life. I see the beads of water accumulating on my arm. I stare at the water droplets for an unimportant length of time.
It’s interesting that I can see these droplets, yet I would describe their color as clear. The full spectrum of transparent to translucent to opaque is visible on each droplet. I think I even see a shadow underneath some of them. I think about the fact that light travels slower in water than in air, which causes the light to refract, so instead of seeing what’s directly on the other side of the water droplet, I see a distorted version of it. I recall dipping a straw in a clear glass, or trying to pick something up at the bottom of a shallow pool. One interpretation for why light refracts through water is called the principle of least action, which says the light will take the “most efficient” route (with respect to time) through the water droplet, so it does this zig-zag causing the distortion. How a light particle is able to compute “all possible paths” through a medium and pick the “most efficient” one is something I’ll let Feynman, Fermat, and Snell argue about. All I know is quantum mechanics is weird.
The water droplets surround the entirety of my arm. They are a peculiar oblong shape due to the ferocious battle between gravity and surface tension. The hydrogen in the water molecule ($H_2O$) carries a partial positive charge which is attracted by some partial negatively charged molecules on my skin (probably proteins). The fancy word for this is cohesion. However, skin also has natural oils which the water cannot stick to (a property aptly called hydrophobic). Hence, the many individual beads. Water is also able to stick to itself (adhesion as the nerds say). One of the many unique features of water is how strong both the cohesion and adhesion effects are, which is why the beads can get so large.
As the water droplets shift around on my arm, two small ones will combine to create a medium-sized one, which may also combine with others. It reminds me of that game Agar.io (which was popular for like 2 weeks in high school). Alas, as is the fate of all the droplets, they get so large that cohesion surrenders to gravity and that collection of water molecules return to their previous state of fungibility and high entropy.
As surface tension breaks, the water droplets fall differently depending on their location. The droplets on the under-side of my arm slide off in an unimpeded, continuous fashion which I find satisfying. The droplets on the upper part of my arm must maneuver around my arm hair. They sort of puddle in-between sections of the hair, causing this discrete jolting motion. It sort of reminds me of how squirrels move. “Never mess with squirrels” I think to myself.
I then thought about the sizes of the water droplets. There are the obvious large beads. If I inch closer I can see that there are actually many very very small beads as well. My first instinct is to think that the sizes of the water droplets must be described by a Gaussian Curve as there were so many of them, so law of large numbers must apply. However, upon reflection I thought that actually they are probably described by the power law distribution ($1/x^2$ give or take the value of the exponent). We have a system where “the rich get richer” since large beads combine to create even larger beads. So there will tend to be many small beads and a few large beads. However, once surface tension gives up, the largest beads drop off my arm, which will give a truncated power law distribution.
In other words, my arm is wet.