Adaptive system

The law of adaptation can be stated informally as:

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

Formally, the law can be defined 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:

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

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 “adaptation 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] Physicists have shown that adaptation to the edge of chaos occurs in almost all systems with feedback.^[3]

Practopoiesis, a term due to its originator Danko Nikolić, is a reference to a kind of adaptive or self-adjusting system in which autopoiesis of an organism or a cell occurs through allopoietic interactions among its components.^[4] The components are organized into a poietic hierarchy: one component creates another. The theory proposes that living systems exhibit a hierarchy of four such poietic operations in total:

   evolution (i) → gene expression (ii) → non gene-involving homeostatic mechanisms (anapoiesis) (iii) → cell function (iv)

Practopoiesis challenges current neuroscience doctrine by asserting that mental operations primarily occur at the anapoietic level (iii) — i.e., that minds emerge from fast homeostatic (adaptive) mechanisms. This contrasts the widespread belief that thinking is synonymous with neural activity ('cell function' at level iv).

Each lower level contains knowledge that is more general than the higher level; for example, genes contain more general knowledge than anapoietic mechanisms, which in turn contain more general knowledge than cell functions. This hierarchy of knowledge enables the anapoietic level to directly store concepts, which are necessary for the emegence of mind.

• Martin H., Jose Antonio.; Javier de Lope; Darío Maravall (2009). "Adaptation, Anticipation and Rationality in Natural and Artificial Systems: Computational Paradigms Mimicking Nature". Natural Computing. 8 (4). Springer: 757–775. doi:10.1007/s11047-008-9096-6.{{cite journal}}: CS1 maint: multiple names: authors list (link)

 

Look up anapoiesis in Wiktionary, the free dictionary.

 

Look up practopoiesis in Wiktionary, the free dictionary.

• Funny animated video explaining the theory of practopiesis, made by Mind & Brain.
• Practopoiesis offers solutions to nine long-standing problems in neuroscience and philosophy of mind