Tonight I've been writing a paper for my linguistics class on the historical development of Hawaiian Pidgin English into Hawaiian Creole English as it exists in the present day. This is an important, if subtle, distinction: a pidgin is a simplified language that is used as a second-language lingua franca between two or more groups of people who cannot otherwise communicate with each other, while a creole is an actual language used by a group of people as their primary language. Pidgins can be created between any two (or more) languages, and oftentimes throughout history have developed into full-fledged creole languages. The “Pidgin” spoken in Hawai‘i is a true creole, no longer a pidgin (and hasn't been for quite a few decades). (It draws mainly upon English and Hawaiian, but also upon languages such as Japanese, Chinese, Tagalog, and Portuguese, from the various people groups that were brought in to work on the plantations after the overthrow of the monarchy in 1893.)
The interesting part in this is that, while pidgins are simplified forms of language used only for specific purposes (such as business transactions) and not spoken otherwise, the creoles they develop into are complex languages capable of dealing with all aspects of life that their speakers encounter. This flies in the face of the established linguistic wisdom that languages tend to simplify over time, which is why it got me interested. For instance, in the Middle Ages English used to have special verb forms for present singular verbs, namely -e for first person (“I speake”), -(e)st for second person (“thou speakest”), and -eth for third (“he speaketh”). These have now been dropped completely, and first, second, and third all use the same form of the verb now (the bare verb stem itself, “speak” in this example). Middle English itself is a simplification of Old English, for instance having dropped the nearly one dozen forms of the word “the” that used to exist. Many other examples from other languages could be given as well.
Given this general trend, what are we to make of the fact that a full-fledged creole language seemingly arises from a simplified pidgin? There are several things to keep in mind. First, we must remember where this complexity comes from: it does not arise from nowhere, but rather comes from the languages that originally combined to create the pidgin. Speakers of a pidgin borrow syntax, grammar, and vocabulary from their native tongue and weave it into the collective pidgin language, increasing its complexity. Second, we must remember that there are intelligent agents at work. The observation that languages tend to decrease in complexity is a result of the fact that people like ease and simplicity. If everyone understands you when you take shortcuts in your speech, leave out a conjugation here, a declension there, pretty soon everyone's doing it and shortly thereafter those conjugational and declinational forms no longer exist. However, if people can't understand what you're saying, or you can't figure out a way to say what you want to in the pidgin you're using, you will add (or more likely borrow from your native tongue) ways of speaking that will allow you to express what you want.
In a way, it's similar to the loophole in the Second Law of Thermodynamics that allows life to exist. Technically, it's not quite as iron-clad as that law, because people could, if we chose, increase the complexity of our language; however, it's overwhelmingly unlikely. Also, the decrease of entropy in one portion of a system requires an equal or larger increase in another, while the increase in complexity of a pidgin turning into a creole requires no such corresponding simplification in the parent languages, but the general idea is similar. It's possible to mathematically quantify the entropy of a particular message in information theory, and it would be interesting to see how the entropy of a language changes as it develops from a pidgin into a creole.
(There are slight differences between how languages and physical systems change. Physical systems tend towards states of high entropy, because those are more likely, and thus simpler. Think of the number of ways in which the parts of a clock can be assembled such that the clock will work. Now compare that with the enormous number of ways that you could arrange those same parts without the clock working, and you'll see why over time, without repair, the clock would tend toward one of those numerous simpler states [since a non-working clock is simpler than a working one]. Languages, on the other hand, tend towards states of low entropy, because for languages those are simpler. Think about having 12 different ways to say “the” compared to one. One way is simpler in this case, which is one of the reasons English no longer has 11 other ways. This apparent inversion [physical states tend towards high entropy, languages towards low] comes about because of the way entropy is defined in information theory, but regardless of the semantics, the basic idea is that both physical systems and languages tend to change into less complex forms, even if the way of measuring such complexity is different.)