The message that windows gives when you are copying a large number of files gives a good example of an uncertain environment. That process recently took over 30 minutes and over the course of that time, the message box was constantly flashing completely different information about the time remaining. Over the course of one minute in the middle of that process the readings were:
8 minutes remaining
53 minutes remaining
45 minutes remaining
3 minutes remaining
11 minutes remaining
It is not true that the answer is random. But with the process that Microsoft has chosen to apply to the problem, the answer is certainly unknowable. For an expected value to vary over a very short period of time by such a range – that is what I would think that a model reflecting uncertainty would look like.
An uncertain situation could be one where you cannot tell the mean or the standard deviation because there does not seem to be any repeatable pattern to the experience.
Those uncertain times are when the regular model – the one with the steady mean and variance – does not seem to give any useful information.
The flip side of the uncertain times and the model with unsteady mean and variance that represents those times is the person who expects that things will be unpredictable. That person will be surprised if there is an extended period of time when experience follows a stable pattern, either good or bad or even a stable pattern centered around zero with gains and losses. In any of those situations, the competitors of that uncertain expecting person will be able to use their models to run their businesses and to reap profits from things that their models tell them about the world and their risks.
The uncertainty expecting person is not likely to trust a model to give them any advice about the world. Their model would not have cycles of predictable length. They would not expect the world to even conform to a model with the volatile mean and variance of their expectation, because they expect that they would probably get the volatility of the mean and variance wrong.
That is just the way that they expect it will happen. A new Black Swan every morning.
Correction, not every morning, that would be regular. Some mornings.