I found this comment posted on the Niklas Luhmann Group to be very helpful:
A system can only be less complex than the environment otherwise it couldn’t make a difference between itself and the environment. But by reducing complexity the system can also increases complexity (like the alphabet reduces our vocal complexity to some letters but it offers also nearly unlimited options to combine those letters to build new words)–Bjarne Schreiber
The complexity issue is about media and form. The letters in the alphabet are medial substratum and words are forms. Letters are used to create one word, then decomposed (unlinked, uncoupled) and reused in different sequences to create other words. The media must be reusable; letters, obviously, can’t just be used to make one word and trapped there forever. In this sense, the letters are not “parts” of the word; they aren’t like machine parts. They are a media, like the iron or metal that machine parts might be made of. The machine could be broken down and the parts melted down (returned to material substratum) and new parts could be made for some other machine.
In spoken language, we have phonemes, morphemes, lexemes, and other elements that are combined into meaningful language.
In meaning-based systems (psychic and social systems) the element can also be called a communication event. It consists of three selections–information, utterance, and understanding. The system makes the selections. The synthesis of these three selections produces meaning; it is a non-decomposable unit of meaning, and it vanishes in the same moment that is emerges. As an element, it has no temporal duration. The meaning event (element) must be replaced by a subsequent meaning event in order for the system to reproduce itself.
For psychic systems, the element is a thought. Thought are only meaningful when there are preceding thoughts to link to and the expectation of subsequent thoughts. But the thought itself has no duration. It’s an event. Structure is the linking of the event to a before and after. The meaning event must refer to previous meanings and expected meanings; this is self-referentiality. The systems refers to its own elements, and it makes new elements out of “old” elements. This also is described in terms of redundancy. As King and Thornhill write,
The redundant aspect of communication becomes structure, providing the means for a communication to be recognized as belonging to the system. The event relies on this recognition for its inclusion as communication belonging to the system.
Temporality allows the formation of structure. The temporal dimension allows for before and after. A unit of meaning is only meaningful within this temporal dimension. The element only exists because there was a preceding meaning unit and there is an expectation of subsequent meaning units.
Expectation and memory are structures. Memory is not a storehouse of images or facts; it is a structure that allows meaning to happen–it is the before of the before/after distinction. The after is the expectation.
Structure is established through a re-entry of the system/environment distinction into the prior distinction. That is to say, the distinction of before/after re-enters the system, which allows meaning to be assigned to either before or after–these are the only two options. Since a meaning unit, or elements of communication, vanishes in the same moment that it appears, the system can only observe before and after. As Luhmann writes,
[The] concept of of autopoietic closure makes it possible to understand the function of enforced binary choices. The system can continue its autopoiesis or it can stop it. It can can continue to live, to produce conscious states, to communicate with the alternative to come to an end. There are, with respect to autopoiesis, no third states. (Autopoiesis of Social Systems,” in Essays on Self-Reflection, p. 13)
For a system to increase its complexity it must specialize, or develop an inclusion/exclusion scheme. “The system invents a choice, which did not exist without it.”
For example, through the invention of property, the economic system created a forced choice between ownership and non-ownership. The economy is about having and not-having. Following the law of the excluded middle, or tertium non datur, there is no third option. The having/not-having form can only be crossed by a payment, which is a communication event. This event, like a meaning unit, has no duration. The economy reproduces itself by linking one payment-event to another payment-event. A payment is the non-decomposable unit of the economic system. Is is also called the symbolically generalized communication medium of the economy.
The economy specializes in monetary payments. If the economy observes something as a monetary payment, the system includes it, or treats it as meaningful (the economy, being a social system, is meaning-based). For the economy, complexity is the linkage or payments in all sorts of ways. There are nearly unlimited possibilities for linking payment to payment. So by excluding everything else, such a morality, religion, politics, and love, the economy has been able to establish great complexity. The economy makes itself less complex that its environment (creates a complexity differential) by observing everything as either a payment or not-a-payment. If it’s not a payment, it must remain in the economy’s environment. It’s a strict either/or without a third possibility. This simplicity then allows the economy to create its own complexity through reentry.
The advantage of money over a barter economy is that monetary payments may be very quickly circulated. The money can be immediately reused. But if you give me a chicken in payment for eight hours of work, I cannot easily trade that chicken for fuel to heat my house. Another advantage is that monetary payments have no memory. This means that the economy doesn’t know how I obtain the money I spend. Only the law takes notice of that. By excluding moral considerations, the economy enhances its efficient circulation of payments.
However, there are limits to a system’s complexity, as described in the complexity-sustainability trade-off.