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

A theory that life can be understood as a hierarchy of adaptive processes. Adapative processes at lower levels of organization (such as evolution by natural selection) create properties of the adaptive mechanisms at higher levels of adaptive organization (such as genes). The theory of practopoiesis states that life can be explained by a total of four such levels of organization.

These levels are (from lowest to highest):

Evolution -> Gene expression -> Cell anapoiesis -> Cell function


Notably, the theory introduced the level of anapoiesis, an adaptive process not previously formulated as a general concept underlying biological processes, although much evidence existed pointing towards such mechanisms. This evidence was usually classified under the general umbrella of homeostatic mechanisms.

Practopoiesis was initially developed the explain the functioning of brain and the emergence of mental phenomena. The main tenet is that the adaptive capabilities of the brain are organized into a hierarchy of learning/adaptive mechanisms. As a result, the system learns how to learn, or adapts its adaptation capabilities.[3] The theory proposes that all our semantic knowledge and our procedural knowledge (skills) are stored in a form of the "fast learning" mechanisms at the level of anapoiesis, and that these fast adaptive mechanisms have been acquired (or poietically created) over individual's lifetime through interaction with the environment and expression of genes, i.e., by neural plasticity. It is the anapoietic processes of "fast learning" that are responsible for implementing mental operations such as perception, attention, recall from memory and decision-making. Importantly, it follows that neural spiking activity operates at a level higher than anapoiesis (cell function) and thus, is not directly responsible for mental operations. Spiking activity is necessary for closing sensory-motor loops and thus for creating behavior. Anapoietic mechanisms dynamically reorganize these loops and that way form a mind.The theory offers a set of empirically testable predictions.[4]

Practopoietic cycle of causation

For a living individual 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.