## Saturday, August 12, 2023

### Probability Defined Relatively Easily

If you react to stimulus X with response Y, then there is a set of outcomes with well-defined probability.

For example, if you respond to a fire with a fire extinguisher, the fire will go out with some probability.

It's defined by sensation and decision.

Stimulus or a situation is defined by your sensor suite. You get nontrivial probabilities because you can't tell similar situations apart. It's too expensive, so you don't bother or cannot pay for it at all. You probably can't instantly see the exact line between 'large' fire (the extinguisher won't work) and 'small' fire (the extinguisher will work). Thus you simply react to all fire below 'huge' (the extinguisher is laughable) with a person-portable quenching device, and the exact probability of success is defined by where you see the line. And whether you're using an expensive highly-engineered laboratory extinguisher tank or a bucket of water or sand.

The strategy for dealing with the stimulus is a decision. Thus sensation+decision=>probability.

It only seems anything but infinitely precise because the probabilities change over time based on e.g. sensor degradation/upgrades or changes in the environment. E.g. if the proportion of oxygen in the atmosphere goes up, it will get harder to put fires out. Perhaps changes in building materials also lead to more pyrophilic fires, without being visually legible.