This law is a component of the unicist logic developed in 1986 by Peter Belohlavek, which has been incorporated into the suite of laws that govern the operation of artificial intelligence in managing adaptive systems.

Adaptive systems became understandable after the discovery that only supplementation and complementation relationships exist in nature. The triadic structure of entities, defined by a purpose, an active function, and an energy conservation function, is governed by the laws of supplementation and complementation. Here, the active function promotes growth by supplementation, whereas the energy conservation function ensures survival through complementation.

The Law of Complementation

The law of complementation asserts that the functionality of an entity’s purpose is achieved through the active function of another entity, and vice versa, while a shared energy conservation function establishes a unified field. Complementation occurs only when the purpose is also part of a supplementation process that threatens its stability.

To put it simply, complementation between two entities means that one entity has what the other lacks, and they share a common goal. This commonality is the basis for meeting each other’s needs.

Examples of Complementarity:

• Couple: The members of a couple complement each other because one has what the other lacks and vice versa. However, they are only truly complementary if they share a common project.
• Brick and Mortar: Brick and mortar are complementary in building a wall, covering each other’s needs. This complementarity applies only if there is a shared wall to be built. If they are part of different construction projects, they are merely hypothetically complementary.

The Functionality of Complementation

Complements reinforce the purpose by mitigating the entropy generated by the active function. Complementation balances the disequilibrium caused by supplementation and augments the purpose’s reliability and functionality, ensuring operational and functional cooperation.

• Operational Complementation: Enhances reliability and operational cooperation.
• Functional Complementation: Increases functionality and functional cooperation.

For complementation to be effective, it must surpass a minimum energy threshold. It can be asymmetric or symmetric and becomes functional when it contributes necessary added value, not merely convenience. True essential complementation is realized at this level.

In the evolutionary context, complementation involves the amalgamation of asymmetric complementation with a declining slope and symmetric complementation. Parasitic complementation naturally generates the involution of the unified field where it is installed.

At an operational level, the laws of supplementation and complementation define the unicist binary actions that enable adaptive systems to function. The binary actions initiated by the active functions are termed UBA type A, and those based on the energy conservation function are called UBA type B. Binary action type A creates opportunities by generating value, whereas binary action type B secures results.

The Unicist Research Institute