It is not difficult to visualize uncertainty. Just think of flipping a series of coins where each toss is independent. The probability of tossing a head is 0.5, and -log(0.5) is 1 for base 2 logarithms. The probability of tossing h heads in a row is as follows:
Solving for h produces the following:
Almost everything we do statistically has uncertainty, -logp, at the core. Statistical literature refers to uncertainty as negative log-likelihood.