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

Artificial Intelligence Interpretations:

ChatGPT Interpretation

The Law of Complementation and its role in the evolution of adaptive environments, as outlined within the unicist logic framework, presents a sophisticated understanding of how entities interact within systems. Developed in 1986, this concept has become integral to the design and operation of artificial intelligence (AI) in managing adaptive systems. This approach to understanding adaptive systems is rooted in the observation that entities engage in only two types of relationships: supplementation and complementation.

Understanding Supplementation and Complementation

The unicist framework posits that all entities can be understood through a triadic structure consisting of a purpose, an active function, and an energy conservation function. These elements interact through laws of supplementation and complementation:

• Supplementation involves the active function promoting growth by adding value or capabilities that an entity does not possess.
• Complementation, on the other hand, ensures survival by providing what an entity lacks to maintain its stability, facilitated by a shared energy conservation function.

The Law of Complementation

This law emphasizes the interdependence of entities to achieve a common purpose. Complementation occurs when the active function of one entity fulfills the purpose of another, and they share an energy conservation function, thus creating a unified field. This interaction is based on the premise that one entity possesses what the other lacks, underpinned by a shared goal which makes their relationship symbiotic rather than merely additive.

Examples of Complementation

• Couples serve as a classic example of complementation, where partners provide what the other lacks, unified by common goals or projects.
• Building materials, like brick and mortar, complement each other in the construction of a structure, each fulfilling a need that the other cannot, predicated on the goal of building a specific wall or edifice.

The Functionality and Impact of Complementation

Complementation plays a crucial role in balancing and enhancing the functionality of systems by:

• Mitigating entropy generated by the active function, thereby reinforcing the purpose of the entity.
• Enhancing operational and functional cooperation, through both operational complementation (which enhances reliability) and functional complementation (which increases system functionality).

For complementation to be truly effective, it must exceed a certain threshold of energy investment and can manifest as either asymmetric or symmetric. It’s considered functional when it provides necessary added value beyond mere convenience, indicating a level of essential complementation.

Evolutionary Implications

In the context of evolution, complementation encompasses the integration of asymmetric (with a declining slope) and symmetric complementation. It’s important to note that parasitic complementation can lead to the involution of the unified field, highlighting the need for beneficial and synergistic relationships.

At the operational level, the laws of supplementation and complementation underpin the binary actions (UBA type A and B) that enable adaptive systems to function effectively. These actions facilitate the creation of opportunities (type A) and the securing of results (type B), illustrating the fundamental dynamics at play in the evolution of adaptive environments.

This framework provides a deep insight into the interplay between different entities within adaptive systems, emphasizing the importance of complementation and supplementation in fostering evolution and sustainability.