BIoloGICAl–EPISTEmoloGICAl ConCEPTS In ThE ThEory of AuToPoIESIS
Terms related to an observational domain
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Corresponding terms related to an abstract explanatory domain
Dynamic object is an observable entity existing in an observational domain that an observer can interact with and associate to a set of well-defined state variables with values that can change in time.
multi-dimensional point (abstraction for a dynamic object) is an element of a multi-dimensional space and is defined by an n-tuple (a set of coordinates) corresponding to the instantaneous values of the state variables of a dynamic object.
State of a dynamic object is the set of observable instantaneous values assigned to each variable associated to a dynamic object (an n-tuple of values). A state transition occurs at a given time whenever a value of a state variable changes.
State of a multi-dimensional point (abstraction for the state of an object) is an identifier assigned to a particular n-tuple that defines the state of a corresponding dynamic object. A state transition occurring in the latter is represented by a different identifier. We need only a changing identifier to express that a transition has taken place
Interaction is the cause-effect coupling between dynamic objects described as the occurrence of a state transition on a dynamic object that provokes a state transition on other dynamic objects by means of an unspecified underlying interaction mechanism.
oriented relation (abstraction for an interaction) is defined as an ordered pair of multi-dimensional points; the order of the pair is established by the corresponding cause-effect timed sequence of triggering and caused state transitions observed in the corresponding interacting dynamic objects.
observational domain is any domain of perceived phenomena occurring in time in which we, as human observers, can perform sensorial and operational experiences through interactions with dynamic objects. Within an observational domain, observed dynamic objects may enter into observable interactions with each other and constitute groups of interacting objects (for us, as observers). An observational domain is delimited by the actual observational capabilities of the community of observers, but it can also expand as new observational means become available (tools and methods), enlarging thus the intersection with the domain of existence of the observed dynamical entities.
multi-dimensional relational space (abstraction for a general domain containing the observational domain) is the space of all possible oriented relations linking pairs of multidimensional points together: within this abstract space, any set of topologically connected oriented relations may be represented by a graph in which the relations are represented as edges (arrows) and the connecting multi-dimensional points as nodes (circles). These graphs are abstractions that represent groups of interacting dynamic objects, at a given time, in the corresponding observational domain. Its mathematical definition as the power set of an n-dimensional space entails that any pair of n-dimensional points would be a member. Among these, I consider only one-way related points (oriented relations) at a given time, and among the latter, only those oriented relations that correspond to observable interactions.
Interaction network is an observed set of dynamic objects acting as agents of interaction propagation within a dynamic system, where
network of oriented relations (abstraction for interaction network) is a graph made of nodes and edges: it is the isomorphic representation of an observed interaction network at a given time.
Dynamic system is the set of dynamic objects observed as a composite unity of mutually interacting dynamic objects. Component is a dynamic object pertaining to an interaction network; it is seen as an observable totality that participates in the constitution of a dynamic system by acting as source and receptor of causation flow.
node (abstraction of component) is a multi-dimensional point defined by the starting or arrival point of a relational arrow in a graph and is in isomorphic correspondence with a component of the interaction network represented by the graph.
Global state is the set of all values assigned to the variables of all components of a dynamic system at a given time.
Instantaneous configuration of oriented relations is the topological arrangement of the graph of a network of oriented relations at a given time depending on the state of each node at that time.
Table 1: Correspondence between terms of the observational domain and terms of the abstract explanatory domain.
CoNSTruCTIVIST FouNdATIoNs
vol. 6, N°3