# Pattern

A pattern is a repeating set of events or objects that is identifiable and to some degree predictable. The repetition can be exact or approximate. Some common examples include repeating wallpaper designs (typically exact) and the seasons of the year (approximate). Patterns can also be more abstract or conceptual, in which case they may be called heuristics; one example might be the idea that "history repeats itself". In fact, one might consider any explanation of a phenomenon to involve identifying patterns that match past experiences.

Humans are exceptionally good at detecting patterns, leading to a common description of our species as "pattern-seeking animals". It is this tendency that underlies almost every special ability humans possess: symbolic thought, pervasive tool use, complex language and mathematics, detailed "theories of the world" (including, for example, scientific knowledge), and so forth.

Pattern identification is also closely related to another human tendency, that of "making up stories" to explain poorly understood phenomena (see also Mythology).

Some potential problems that arise in pattern identification include:

## Meaningful patterns

Whether a particular pattern is "significant" or "meaningful" in some sense is a complicated issue.

Consider a very simple setting: toss a coin ten times and record the sequence of "heads" (H) and "tails" (T). Here are some possible outcomes of this "experiment":

1. H, H, H, H, H, T, T, T, T, T
2. H, T, H, T, H, T, H, T, H, T
3. H, T, T, H, T, H, T, H, H, T
4. H, T, H, H, T, H, H, T, T, T

All of these outcomes have equal numbers of heads and tails. This is not required, of course; sequences of all heads or all tails are possible, or indeed any number of heads and tails, so long as they add up to 10.

In any case, for a "fair coin" (heads and tails equally likely), all 4 sequences under consideration have the same probability of occurring — namely, a 1 in 1,024 chance. However, most people would be surprised if either of the first two sequences actually occurred in practice, and wouldn't be at all surprised if either of the last two occurred. Why? Because the first two have easily discernible patterns: in the first, obviously the heads and tails are "bunched" together" while in the second, they alternate (each head followed by a tail and vice-versa). We don't expect real coins to behave this way.

Interestingly, though, sequence number 3 also has a pattern to it that we wouldn't necessarily expect to see in practice: the sequence is "anti-symmetric", meaning that if the order of the 10 outcomes were reversed and the heads and tails switched (each H is replaced by a T, and vice-versa), the resulting sequence would match the original. (Sequences 1 and 2 have the same property, by the way.)

So, if you were looking for such anti-symmetric sequences, the third outcome would be significant to you; if you weren't, it wouldn't be.

Does the fourth sequence have any meaningful pattern? That is left as an exercise for the reader...