The term adaptation is used in biology in relation to how living beings adapt to their environments, but with two different meanings. First, the continuous adaptation of an organism to its environment, so as to maintain itself in a viable state, through sensory feedback mechanisms. Second, the development (through evolutionary steps) of an adaptation (an anatomic structure, physiological process or behavior characteristic) that increases the probability of an organism reproducing itself (although sometimes not directly).[citation needed]

Generally speaking, an adaptive system is a set of interacting or interdependent entities, real or abstract, forming an integrated whole that together are able to respond to environmental changes or changes in the interacting parts. Feedback loops represent a key feature of adaptive systems, allowing the response to changes; examples of adaptive systems include: natural ecosystems, individual organisms, human communities, human organizations, and human families.

Some artificial systems can be adaptive as well; for instance, robots employ control systems that utilize feedback loops to sense new conditions in their environment and adapt accordingly.

Every adaptive system converges to a state in which all kind of stimulation ceases.[1]

A formal definition of the Law of Adaptation is as follows:

Given a system ${\displaystyle S}$, we say that a physical event ${\displaystyle E}$ is a stimulus for the system ${\displaystyle S}$ if and only if the probability ${\displaystyle P(S\rightarrow S'|E)}$ that the system suffers a change or be perturbed (in its elements or in its processes) when the event ${\displaystyle E}$ occurs is strictly greater than the prior probability that ${\displaystyle S}$ suffers a change independently of ${\displaystyle E}$:

${\displaystyle P(S\rightarrow S'|E)>P(S\rightarrow S')}$

Let ${\displaystyle S}$ be an arbitrary system subject to changes in time ${\displaystyle t}$ and let ${\displaystyle E}$ be an arbitrary event that is a stimulus for the system ${\displaystyle S}$: we say that ${\displaystyle S}$ is an adaptive system if and only if when t tends to infinity ${\displaystyle (t\rightarrow \infty )}$ the probability that the system ${\displaystyle S}$ change its behavior ${\displaystyle (S\rightarrow S')}$ in a time step ${\displaystyle t_{0}}$ given the event ${\displaystyle E}$ is equal to the probability that the system change its behavior independently of the occurrence of the event ${\displaystyle E}$. In mathematical terms:

1. - ${\displaystyle P_{t_{0}}(S\rightarrow S'|E)>P_{t_{0}}(S\rightarrow S')>0}$
2. - ${\displaystyle \lim _{t\rightarrow \infty }P_{t}(S\rightarrow S'|E)=P_{t}(S\rightarrow S')}$

Thus, for each instant ${\displaystyle t}$ will exist a temporal interval ${\displaystyle h}$ such that:

${\displaystyle P_{t+h}(S\rightarrow S'|E)-P_{t+h}(S\rightarrow S')

In an adaptive system, a parameter changes slowly and has no preferred value. In a self-adjusting system though, the parameter value “depends on the history of the system dynamics”. One of the most important qualities of self-adjusting systems is its “adaption to the edge of chaos” or ability to avoid chaos. Practically speaking, by heading to the edge of chaos without going further, a leader may act spontaneously yet without disaster. A March/April 2009 Complexity article further explains the self-adjusting systems used and the realistic implications.[2]

## Practopoiesis: Adaptation across different levels of organization

Practopoietic cycle of causation

A theory of how systems adapt across different levels of organisation is called practopoiesis.[3] The question is how a mechanism that enables adaptation gets adapted itself. According to the theory, adaptations are organised in a hierarchy; the purpose of an adaptation processes at a lower level of organisation is creation of the adaptation mechanism at the next higher level of organisation.

For a living system such as an animal or a person, a total of three such hierarchical steps of adaptation are needed—and such systems are denoted as T3. At the lowest level of a T3-system lay gene expression mechanisms, which, when activated, produce machinery that can adapt the system at higher levels of organization. The next higher level corresponds to various physiological structures other than gene expression mechanisms. In the nervous system, these higher mechanisms adjust the properties of the neural circuitry such that they operate with the pace much faster than the gene expression mechanisms. These faster adaptive mechanisms are responsible for e.g., neural adaptation. Finally, at the top of that adaptive hierarchy lies the electrochemical activity of neuronal networks together with the contractions of the muscles. At this level the behavior of the organism is generated.

Tri-taversal theory of mind

When an entire species is considered as an adaptive system, one more level of organization must be included: the evolution by natural selection—making a total of four adaptive levels, or a T4-system. In contrast, artificial systems such as machine learning algorithms or neural networks are adaptive only at two levels or organizations (T2). According to practopoiesis, this lack of a deeper adaptive hierarchy of machines is the main limitation factor for their capability to achieve intelligence.