[My Computational Complexity Web Log] An Unnatural Post
When we see "natural" in a computer science papers it usually reflects an informal idea of realism, i.e., Clique is a natural NP-complete problem while 1-in-3 SAT is not. Sometimes though researchers use "natural" in a defined term. Generally this should be avoided--no definition can prevent artificial examples but more importantly perfectly reasonable notions that do not fit the rule are, by definition, not natural.
I work with bits and usually take my logarithms base 2, an unnatural logarithm. I use diagonalization to prove lower bounds on Turing machines, an unnatural proof technique applied to an unnatural computing model. I have even been known to use unnatural numbers, like 1/2.