We tend to think of random phenomena as the purview of probability — situations in which an element of chance is involved, such as flipping coins, rolling dice, or dealing cards. This has the unfortunate effect of obscuring a much broader view of the subject, as the study of uncertainty.
This view encompasses the usual one: when we flip a coin or deal a poker hand, we are uncertain about the outcome. But it's also much richer. For instance, we might not know some quantity precisely, such as the temperature outside or the mass of a planet, but that shouldn't stop us from performing calculations with it. Probability provides a frame of mind and tools for computing in the face of uncertainty.
We tend to think of randomness as an inherent quality in certain objects: dice and coins are random, billiard balls are not. A philosopher would call it "ontological". This leads to a lot of confusion! I remember scratching my head as an undergraduate, wondering "where" the randomness was. Uncertainty, on the other hand, is in our minds; it is "epistemological". So uncertainty isn't simply a more general topic, it has quite a different, and richer, flavor.
In this sequence of posts we approach various topics in probability and statistics from this point of view.
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