A-B-C-D – Is That Really Your Sample Space?

In realty, events are unique kinds of changes in objects or time-reversal properties in definite objects. On some theories, only discrete changes in the shape of an object can constitute events, such as the drying of the lawn. However, the theory of events may also be used to distinguish discrete changes in events that affect one person (e.g., a baseball player’s success in hitting a home run) from those that affect another (e.g., the owner’s decision to sell the team).

To be able to describe an event in terms of its frequency, we must combine the notions of event may be combined. A simple event is an occurrence that repeats itself without an antecedent, such as a thunderstorm or rainfall. The word “occurrence” in this sense would correspond to “repetition” in the scientific community. A compound event on the other hand is any event that changes as a result of something else.

Let’s use the baseball example noted above to illustrate the distinction between event and simple event. An event occurs when something happens, and then it happens again, or it repeats itself. For instance, rain falls on your house twice, and then it happens again. You notice this happening, but it’s not an event. Now, if you substitute the word rain for the word event, you have an empty set, meaning there are no events preceding or following the rain, and there are therefore no events.

An experiment, on the other hand, involves taking a set of possible outcomes, observing them, recording their results, then drawing general conclusions from the recorded data. The hypothesis of the experimenter concerning the possible outcomes is true or false. In the case of a simple event, it’s not necessary to prove anything to be an event, so all events are classified in that category. It’s necessary, however, to provide sufficient evidence to persuade a reasonable person that an event occurred. (The same is true in science experiments.

If we use the baseball example again, we note that (a) there is a single event, and (b) the event happened twice: once when the rain fell on the house, and once when the house was dry. Therefore, we have two events – the first event happened twice, and the second event did not. This is a compound event. So we must now consider all the possible outcomes of these two events in order to decide which one produced the most reasonable answer. Obviously, the first event produced the most reasonable answer, because it happened twice; and the second event produced the second most reasonable answer, because it did not. Clearly, these two events do not coincide with the real world.

How can this be known? We must suppose that a scientist collects two sample spaces, A and B, and then repeats the experiment: once, he finds the event that does not obey the law of physics, and once he finds the event that does obey the law of physics, he adds another sample space, C, containing another event that also obeys the physics law. If he repeats this process nine times, then he will have nine different events that obey different laws from A to C. Nine separate occasions from A to C that obey different laws from A to C, which clearly contradicts our initial example of A-B-C-D, where there is only one event. Clearly, nine separate events produces a much more reasonable result.