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ABSTRACT
Reality, both material and conceptual,
functions as a complex network of continuous adaptive morphological formation.
The morphological form is a well-formed formula (wff), a Sign, an organized
process of information. The Sign is formed within a triadic set of relations,
which are encoded spatial and temporal measurements. Using a Cartesian
quadrant, the six possible relational modes are examined to show how reality is
moulded within both symmetrical and asymmetrical functions.
1. MORPHOLOGICAL
FORMATION
I am examining reality as a complex network of continuous adaptive
morphological formation. Physical reality whether crisp or vague exists only
within morphological forms, and equally, conceptual reality, whether
experienced as individual information or as shared knowledge, functions only
within morphological forms. I refer to the process of morphological generation
as semiosis. The morphological form in itself, material and conceptual, is a
well-formed formula (wff), termed a Sign. In defining the morphological
entity as a wff, I refer to its development as a coherent form within a
triadic set of relations, which are encoded spatial and temporal measurements.
As a result of this triadic interaction the Sign exists as itself and in
relations with other Signs, a process that permits both the networked continuity
and diversity of reality (Taborsky 2002a, 2002b).
2. The
Cartesian Quadrant
The analytic model used to examine this transformative
morphological process is a two-dimensional Cartesian coordinate quadrant
(Figure 1). The model enables a morphological analysis that acknowledges
differential spatial and temporal parameters of measurement. The ontological
and epistemological ‘cuts’ (Atmanspacher 1994, 1999, Primas 1993), which are modeled
respectively as the vertical Y and horizontal X axes, establish measurement
parameters for six predicative relations. These six relations function as
semiosic codal measurements; when a selection is made from these six and linked
within a triadic functional set, the result is a morphological reality, a sign.
Whether this morphological unit is open or closed, is fuzzy or crisp, is an
atom, a cell, a word, an action – it is a sign, a morphological reality, a wff.
The vertical ontological Y cut, a result of
temperature differentiation, demarcates spatial experience into internal and
external spatial values. The morphologies within each zone are asymmetrical,
internal space provides an insoluble completeness of data and external space provides
a reducible discreteness of information.
The horizontal epistemological X cut differentiates two
further asymmetries; that between the local (individual) spatial values and the
global (communal) spatial values. This is an important differentiation, for a
basic property of a robust wff is its ability to permit the informational
interaction between local non-distributed and communal distributed measurements.
With this cut, which acts as the introduction of the temporal parameters of
present, perfect and progressive time (Matsuno 1998, 1999), we now have an analytic
scheme of four quadrants, I, II, III and IV (Figure 1). I add two further
functions to the quadrant, namely, the aspatial and atemporal universal function,
and the interface function located at the coordinate origin, which brings the
relational functions to six in total (Table 1).
3. Seven
Measurements
The morphological architecture comprises seven basic
measurements: internal and external space; local and global space; and present,
perfect and progressive time.
Internal spatial measurements develop informational morphologies
without a boundary; that is; the function is isolate and cannot ‘see’ or react
to spatial parameters. This type of information is high energy, vague and
therefore not niche-dependent, expansive and rapidly dissipative; and, when
linked to other measurements, promotes ‘roll-over’ transformations of informational
content. External spatial measurements designate the morphological boundary as
definitive of the information content. Local spatial functions establish
morphological forms that are contextual, non-distributed descriptions that
function as discrete informational sets. Global spatial measurements set up general
morphological forms with distributed non-local parameters of informational interaction
that function as symmetry-inducing normative constraints.
Time is not an abstract detached measurement
(Newtonian/Galilean linear time) but is a concrete material measurement
functioning as a compositional property of the morphological reality. There are
three materially different temporal measurements which produce three different
morphological realities (Matsuno 1998, 1999).
Present time measures a reality that
functions within ‘now’ time without links or references, without past or future.
The information provided by the morphological measurement of pure present time
operates only in internal and local, i.e., isolate space. An example is a ‘feeling
of heat’ or the result of the first thermodynamic law of universal energy. Perfect
time moulds experience within distinct asymmetrical parameters, i.e., as ‘this’
instantiation differentiated from ‘that’ instantiation; that is, as operating
with specific properties and enables individual comparisons. It operates in
external and local, i.e., closed space. Progressive time establishes
values within a generalized continuity; it has no capacity to describe an individual
state whether in present or perfect time but can only deal with commonalities
operating as a continuous morphology. It operates within global or open space
and both internally and externally.
These seven measurements operate within the dynamics
of asymmetry and symmetry. Local space and present and perfect time contribute
to asymmetry, i.e., to differentiation of form and unique relations; global
space and progressive time contribute to symmetry, i.e., to communal cohesion
and continuity. These seven measurements function as relations. There are six relations,
defined by Peircean code (see appendix) and differing according to spatial and
temporal modes and functions (Table 1).
Table 1: The Six Relations: defined by code/space/time/function
|
1-1 Firstness as Firstness
|
Internal Local
|
Present Time
|
Possible Information
|
|
2-2 Secondness as Secondness
|
External Local
|
Perfect Time
|
Discrete Actual Information
|
|
2-1 Secondness as Firstness
|
Borderline Interface
|
Perfect-Present Time
|
Attractor Phase
|
|
3-1 Thirdness as Firstness
|
External Global
|
Progressive-present Time
|
Statistical Average
|
|
3-2 Thirdness as Secondness
|
Internal Global
|
Progressive-perfect Time
|
Future Propensity
|
|
3-3 Thirdness as Thirdness
|
Aspatial
|
Atemporal
|
Imaginary Hypotheses
|
4. The
Relations
A relation is a dyadic string, a primitive morphology of
interaction, where two nodes functioning as horizons of influence link up to
provide a configuration of data, information or knowledge functioning within
time and space. Within the Peircean semiosis of relations "these different
modes of relation are different modes of connexion" (Peirce CP. 3:464). A
relational string does not exist on its own. Following the principle of the
superposition of states, any string exists by virtue of a superpositional
bonding with two or more states. The wff or well-formed formula, the Sign, is
the result of a transformation of the informational and energy content of three
relations, set up in a triadic interaction of input/mediation/output (see
Figure 2). These three terms can also be examined within the Peircean
terminology as Object, Representamen and Interpretant. The robust sign, as a wff,
is never a dyad, which would merely be an Interpretant signifying,
metaphorically, an Object, i.e., a mechanical interaction. The dyad, it should also
be noted, is a Saussurian frame, where the Signifier (input data) is related to
the Signified (output meaning) via the mediation of an external operator,
language. The sign as a wff operates as a dynamic triadic transformational
process with the Interpretant relation presenting itself as a transformed
measurement, acting as a representation of its Object relation. This interpretation
requires a reference to a logical continuity of experience, the mediate relation,
the Representamen. The triadic wff emerges as a morphological reality by
a process that selects three of the six possible relations and moulds them
into a coherent function. This choice will determine the nature of the
information carried by that wff, and the nature of the possible
interactions that information can have with other wff’s.
4.1 The most basic and primitive relation is found
in quadrant II. This relation moulds information without boundaries, as an
isolate state, in internal and local space and present time. The nature and
horizons of influence of its informational content is therefore vague and
undifferentiated. As such, the content in this morphological phase should more
accurately be understood, not as information, a term that implies discrete differentiation,
but as vague sensate input, enabling multiple and varied subsequent
interpretations. It thus is a basic agent in promoting the emergence of new
signs, by virtue of the relatively unformed nature of its informational content.
An example would be a sensation of ‘hotness’ which can then be transformed into
the specific information of either a malfunctioning furnace or a fever. It
could be a provision of a chemical while the cell is still developing the
meditative means to use this chemical; the provision might promote the development
of normative tactics in the cell to use that chemical. This measurement
acknowledges only that there is an input of unexamined and therefore unbound data
located internally in local space and present time. This data can be
transformed into discrete usable information by the semiosic act which must measure
and stabilize its content by linking it to two other relations; otherwise, its
data content will rapidly dissipate.
It is an important relation, confirming the veracity
of chance and the openness of outputs in this universe. The relation is coded,
using Peircean terminology, as 1-1 or Firstness as Firstness (see appendix).
Topologically, one can define its information content as ontologically real and
epistemologically imaginary.
4.2 The second relation is found in quadrant I. This
relation uses that input energy from Quadrant II and moulds individual forms
functioning within the closures of external and local space and perfect time.
The form in this quadrant has achieved differentiation, it is closed and
establishes a factual or ‘reasonably’ crisp identity in local space and perfect
time. Any discrete entity, from a rock to a word, can be considered an example
of this ‘definitive definitiveness’ and it is the basis of most of our daily
experiences; it is facticity, it is information. Modernism, nominalism and
mechanism have all focused on the morphologies within this relation. The
relation is 2-2, or Secondness as Secondness. Its information can be understood
as both ontologically and epistemologically real.
4.3. The two quadrants produced by the horizontal
epistemological cut, the X cut, introduce non-local or global space and temporal
continuity; in particular, this cut permits open — as differentiated from isolate
and closed— systems and a progressive and continuous time measurement. What we
now have is a bileveled architecture, permitting both asymmetrical and
symmetrical interactions, enabling both metabolic individual processes in
quadrants I and II, and reproductive or causal processes in quadrants III and
IV. The measurements in quadrants III and IV provide distributed values that
ensure temporal continuity and the development of a future-oriented causality
produced within the codes of communal habits, of general laws, of regularities
of morphological forms. These values act as symmetry-inducing constraints to
guide and inhibit the emergent local, individual instantiations developing in
the local level (quadrants I and II) in perfect or present time. Our world
cannot function within only the top level quadrants of undifferentiated isolate
energy and discrete closed instances, for this would reduce reality to
randomness. There must be a function that enables symmetry and reproductive
continuity. The X-cut provides these functions by adding two relations and ensures
an open, symmetry-restoring and therefore complex system.
4.3.1. Quadrant III functions in internal and global
space and progressive time. It operates as a ‘virtual memory processor’. As a
global relation, its measurements are distributed in space; it ‘cancels’
spatial distances; as internal, these measurements and the information they
carry are inclusive rather than exclusionary; as progressive, the relation
links past to future morphologies and provides not only continuity but also
evolutionary and adaptively innovative capacities. If we use an example of this
relation, the internet search engine, we find that “search engines entertain a
model of the Internet that evolves with the Internet” and “continuously
reconstruct the past by updating their indices” (Wouters, Helsten and
Leydesdorff 2004, emphasis added). Mathematically, we can refer to the virtual
mode as a complex negotiator of information, in that it includes both real
propensities or real numbers, which we can understand as actual memories, and
imaginary propensities or imaginary numbers, which we can understand as
vectoral propensities with other morphologies both unformed and formed. This
relation is a major influence in the development of complex morphologies, for
it uses imaginary measurements both ontologically and epistemologically. It
acts as an open non-linear non-historical catalogue of solution concepts, and
can be understood as a networked evolving ‘search engine’ of any and all links
within the past and current, direct and indirect, experience of the community.
These links might not develop into stable common rules of morphological
formation (i.e., functioning in quadrant IV); however, their virtual
existentiality remains extant, in both weak and strong form, and they are
available for potential selection by an emerging instantiation. Additionally, this
relation is functionally ‘in tune’ with the realities of the current
environment for “the past in the Internet is constantly overwritten by the
search engines” [and] “the present, from where the data is collected, affects search
results considerably” (Wouters, Helsten and Leydesdorff 2004). This measurement
enables a system to reason about input signals based on information that is both
currently received and information that was received in the past or is
accessible via other networked links. The time required for this ‘reasoning’
can be examined within Benjamin Libet’s ‘temporal factor’ in cognition of 0.50
second (2004). This ergodic inclusiveness of unformed and non-habitualized
propensities permits an emergent instantiation to bring with itself multiple
alternative models of itself as a measurement proposal to the development of a
new instantiation. This relation is essential in providing hypothetical
morphologies that can introduce robust adaptive values and is an overlooked and
vital mode of measurement. The relation is 3-2 or Thirdness as Secondness. It
is both ontologically and epistemologically imaginary.
4.3.2. Quadrant IV functions in external and global
space and progressive time. It is, like 3-2, a communal measurement but,
functioning in external or actualized space, it lacks the epistemological imaginary
propensities of the internal mode. It functions as a bell curve statistical
average, basing its measurement value on a symmetry-inducing model of the
statistical average of the already-actualized individual morphological forms and
acts to constrain the nature of emerging forms by the pressures of its majority
identity.
Figure 1 - The Cartesian Quadrant
As Kauffman said, “in sufficiently complex systems,
selection cannot avoid the order exhibited by most members of the ensemble”
(1993:16). This referential model functions as a kind of ‘attractor-glue’
(Paton and Matsuno 1998) to which the emerging nascent instantiations are
attracted, and which they then take as their guide for development. The
relation is 3-1 or Thirdness as Firstness. It is epistemologically real and ontologically
imaginary, and produces an abstract model of the record of instantiated
actualities.
5. There are two relations ‘outside’ of this quadrant.
5.1. The full imagination can be understood as the
universal rationality of pure mind, affirming that the universe, while not
designed or in any way a priori does organize energy within evolving
complex and logical networks. This relation is aspatial and atemporal. The relation
is 3-3 or Thirdness as Thirdness and is, I maintain, a property of all informational
and morphological realms, the physico-chemical, the biological and the
socioconceptual.
5.2 The other relation is the Interface, a borderline
relation, which functions as an initial condition (origin) at the point of
intersection of the Y and X cuts of differentiation. It acts as an intervening
random-phase pointer to promote the coupling of relations; if it does not
accomplish these links its information and energy content will dissipate.
Within Peircean terms, it can be understood as an act of ‘prescission’, which “is
always accomplished by imagining ourselves in situations in which certain
elements of fact cannot be ascertained" (CP 2:428). It is a highly charged
anticipatory relation that focuses “attention to one element and neglect of the
other” (CP 1.549). Its two different modes of codification are continuously entwined
in their attempt to link relations; therefore, external actuality is always
exploring the new informational potentialities within internal vagueness and
vice versa, and symmetry is always exploring asymmetry and vice versa.
The relation is 2-1 or Secondness as Firstness,
operating in local space – both isolate and closed - and both present and
perfect time. There are six interface typologies characterized by the dyadic
bond of the interface relation with another relation. We will not go into any
depth at this time in examining these typologies and will only point out the
crucial importance of this relation. The Interface can function alone (see
5.2.1) or will be linked with any of the other five relations. The Interface,
acting as this coupling function is a ‘pointer function’, and enables a complex
superposition of these six relations.
5.2.1 The chaotic or strange attractor is the relation
of 2-1 alone. It operates without links in which case the measurement acts as
an initial condition of differentiation in a state of high excitation. It is
highly volatile and expansive (its internal spatial and present temporal nature)
and ‘confrontational’ (its disconnected external spatial and perfect temporal
nature). If it does not find/attract symmetry inducing measurements its
informational content will dissipate. It can be understood as a relation of
anticipatory exploratory freedom and is more frequent in complex systems.
6. Morphological
Formation
We now examine
the semiosic process of morphological formation. The morphological architecture
of a wff/sign is triadic in the shape of a non-linear windmill - not a linear triangle
as often envisaged.
It is made up of three relations, whose integration
enables morphological realities to exist and interact [Figure 2]. The three
relations can be defined as Input Relation, Mediation Relation, and Output
Relation. Peircean terminology is Object-Relation, Representamen-Relation and
Interpretant-Relation. The Input relation can also be understood as a signal,
as data, as a minor premiss. The Mediation relation can be understood as
knowledge, memory, universal or major premiss. The Output can be understood as
information, conclusion, interpretation.
6.1 Dependent on the measurements of the relations
involved, the sign can function in different geometric forms, as a point, as a
linear line, as a nonlinear parabola. The most robust morphology is a parabola,
for here, the apex or mediate relation functions as the compressed measurement
of the symmetry-inducing global space/progressive time measurements, with the
other two lines understood as the asymmetrical differential values of local
input and output. What we find is a superposition of states, where some
measurements will dominate and others will become peripheral or will
operationally dissipate. What drives the different results? The triadic
morphology is not a self-organized autocatalytic or autopoietic reality (Maturana
& Varela 1980) but is a result of complex networked interactions with other
morphological measurements, both internal and external, both local and global.
That is, the sign as a wff is not isolate but open; its so-called
‘self-organization’ is not that of an isolate self-defined assertion but a
networked collaboration.
6.1.1 As an example, we posit a triad of three
relations: 1-1, 2-1 and 2-2. These three relations are both internal and
external but they are all local; there is no symmetry-induction or global
measurement of Thirdness. Link them and a resultant form can be either: 1-1-1,
a short-term internal feeling; or 1-1-2, a brief consciousness of that feeling;
or 1-2-2, a spontaneous cry as a reaction to that internal feeling. In the
first case, energy within the discrete morphology of 2-1 and 2-2 must be
dissipated to reduce the final form to that vague internal feeling. In the
second and third cases, energy must be dissipated but it will not be as much as
in the first example. In all cases, no memory is involved. What causes the
emergence of a particular morphology? The particular morphology functions
within a larger morphological domain, that of its current environmental network
and its historical network and therefore, is linked, informationally, with this
larger domain.
6.1.2 Another example could be: 2-2, 2-1, 3-2. These
relations are both internal and external, but more external than internal, in
local and global space. Link them and you could get, dependent on the nature of
the morphological or semiosic act within the larger morphological domain:
2-2-3, which is a normative mechanical act, such as a heart beating according
to its internal typological symmetry-inducing memory encoded within Thirdness.
Or the morphological form might be encoded as 2-2-2, where it loses the
forward-focused aim-direction of symmetry and provides a strictly mechanical
entity, without an internalized set of rules, such as a weathervane which can
only react to an external causality. Or, you could get 1-2-3, which is the
robust ‘normative’ sign, acting within relations that provide both phenotype
(local) and genotype (global) results, as well as within relations that provide
both freedom (local internal) and individual boundaries (local external).
7. Conclusion
The production of morphological signs, understood as
measurable variables of information functioning in modes of space and time, operates
within a complex semiosic architecture (Figure 1). This architecture sets up
the sign as a wff, a mediated and coordinated triad of relations (Figure
2). The relations are chosen from a set of six possible relations, defined by
different spatial, temporal and functional properties (Table 1). The triadic
morphology operates within three of these six. These three relations may differ
from each other or the triad may use three similar relations; e.g., three
relations in the mode of Firstness as Firstness (1-1) will produce an expansive
explosion of unfocused data. This architecture enables a complex and dynamic
information generation in all realms of reality.
First, the system permits a continuous flexibility
of morphological formation, for the open and vague nature of the internal data functioning
in the relation within the second quadrant (1-1) means that the use of its
informational input supplies an important element of freedom of interpretation.
The Interface relation (2-1) with its capacity to pick up this input
information, define it as origin (i.e., without the constraints of memory) and
link it to any of the other relations, provides the system with a tremendous evolutionary
adaptability and a capacity to promote diversity of individual instantiations.
A morphological instance can emerge that is strictly local and without memory;
this random information can be picked up by another measurement with global
properties and incorporated into its memory base to guide future
instantiations. Other forms are possible; a morphological reality can emerge
that is both local and global; i.e., it has the capacity for both irreversible metabolism
and a reproduction of type. A morphological reality can emerge which computes
its next instantiation referenced only to the attributes of its present state
(mimetic iconicity); this would provide for an expansionist spatial breadth of
this form. A morphological reality can emerge which computes its next
instantiation referenced to an historical connection (indexicality); this would
provide for increased depth and longevity of this new specific type.
Importantly, a morphological semiosis using the six
relations has the capacity for, not one, but three types of memory and symmetric
continuity. There is the historical memory of accumulated values of the successfully
articulated collective (3-1, the statistical average); an example is natural
selection. There is the memory of virtual propensity (3-2), which permits tacit
links which may never be articulated but which remain available for future
morphological attempts at formation. Finally, there is the memory of
rationality (3-3), which lies, I maintain, at the basis of life, understood as the
increasingly complex yet pragmatic logical ordering of energy/matter.
This morphological architecture, made up of six
relations integrating different modes of space and time and a triadic
morphological process integrating symmetry and asymmetry, provides our universe
with a system that permits specificity and uniqueness, while enabling the
instantiation to promote the robust capacities of a continuity of type. These
properties enable typological control over the environment, as well as providing
the freedom to develop new knowledge and new interactions with the
environment.
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Appendix
The three Peircean modal categories refer to the quality
of information provided by the system. Firstness, symbolized as “1’, is defined
as a mode of potentiality. It is an internal and local mode. Information in
this mode is potential but not actual. Secondness (2) is defined as a mode of
individual actuality. Information in this mode exists ‘as it is’. It is an
external and local mode. Thirdness (3) is defined as a mode of generality, of
necessity, of rules and laws. Information in this mode exists as knowledge,
understood as a substratum of normative conventions. It is a non-local mode and
functions within both the internal and external zones.