Throughout history, we have come up with better and more accurate ways to measure physical quantities like time, length, mass, and temperature. This has been crucial for our scientific and technological development. Each of these quantities has a precise definition and is informative about some aspect of the current state of the physical world. For example, the mass of an object can tell you how much work is necessary to lift it at a certain height. The outside air temperature determines the kind of clothes you would wear when you go out. And so on.
Probabilities are also quantities that measure something — they have a very precise and unambiguous mathematical definition. But still, they don’t relate to things in the physical world as straightforwardly and as intuitively as measures like mass and length. What does it mean to say that there is a probability of 47% that it will rain during a particular day? Or that the probability of winning the lottery is 0.00000032%? How would knowing the probability of an event be useful to you in your decisions that depend on that event?
This post’s aim is to explore the meaning of probabilities. More precisely, I’m going to focus on the question: how do probabilities, as a mathematical concept, relate to the physical world?