A friend’s wife is an astrophysicist, and so one day I found myself chatting with one of her astrophysicist friends, and the subject of what counts as a planet came up… I said something like “So, there’s basically a whole lot of junk floating around out there, and the planet size cutoff is kind of arbitrary, right?” He said “Well, it follows a power law….”
So what he meant was that there’s a whole lot of junk out there, and that the size distribution of that junk is such that, say, objects that are twice as large might be twice as uncommon. (Or ten times as uncommon – but whatever the proportion is, it persists over a range of sizes). Distributions like that look like straight lines when you plot them on exponential scales, like this:
So, although there are other reasonable definitions of where to make the planet size cutoff (like: large enough to have become spherical due to its own gravity), there’s no natural size gap that separates planets from smaller things.
My manager was trained as a condensed matter physicist before moving over to web search, and he said he was stunned when he first saw one of the graphs showing how some host attribute or another (like number of pages on a host) varied with number of hosts. It was a perfect power-law line, spanning almost ten orders of magnitude (like from 0 to 1000000000). He says that there is no way to get a power law like that in condensed matter physics – it’s basically the study of crystals, and crystals aren’t available in such a wide range of sizes. He wasn’t trained in cosmology, but guessed that cosmology probably does have power laws over that range.
So for ten-orders-of-magnitude-power-law-phenomena our candidates are: cosmology and the web. Are there any others?