Notes on randomness and probability
06/26/2023
- Randomness refers to a situation where repeating the same conditions that produce a possible outcome can result in a different outcome, where the only noticeable, perceivable, or measurable distinction between repetitions is time itself.
- True, or absolute, randomness implies that there is no distinction between repetitions except for time. Approximate randomness implies there is no perceivable or noticeable difference - though there could be.
- Because knowing whether a situation is absolutely random requires measurement, and an appromixately random situation is one in which there is no real measurable distinction, it is impossible to know whether a situation is absolutely random. Said another way, it is always possible to wrongly assume one is dealing with an absolutely random situation.
- Likelihood refers to the number of times a specific outcome would occur in a scenario where the random situation is repeated indefinitely, given the number of possible outcomes that could occur from that scenario.
- Probability is a method for calculating likelihood that assumes absolute randomness.
- Because it is impossible to know whether a situation is absolutely random, there is always a possibility that a probability will be wrong. Not simply that the prediction is wrong, but that its application is inappropriate.