Illuminating Major Creative Innovators with the
Model of Hierarchical Complexity
Michael Lamport Commons and Linda Marie Bresette[1]
The
development and improvement of a society and its culture depend on major
scientific innovations. Societies with
higher rates of major innovation generally provide better quality of life for
their citizens. Over the long run,
societies with the largest number of innovations will tend to dominate the
world's economic scene. Still it is
only an extremely small number of people who make such innovations. This chapter offers at least four cardinal
reasons for why this is so. The major
reasons posited for the shortage of scientific innovators are as follows: a
lack of development of extremely complex thinking required to identify
phenomenon and create and integrate paradigms, necessary personalities,
sufficient education, and appropriate cultural conditions that support
innovation.
CREATIVE INNOVATIVE CULTURAL CONTRIBUTIONS
Minimally,
creativity must be original action. The methods, theories and techniques do not
have to be original, only the manner in which they are used. In addition, creative acts become social
memes of long standing (Dawkins, 1976,
1981; Feldman,
1980; Feldman,
Csikszentmihalyi & Gardner, 1994). In a metaphorical sense,
memes are to cultural evolution what genes are to evolutionary
biology. Genes are the basic biological
units of information that are transmitted from one individual to another in the
form of DNA. Memes are the basic
cultural units of information that are transmitted to other people in the form
of behavioral patterns. In the course of positive adult development,
major innovations are new memes that are extreme examples of generativity (Erikson,
1959, 1978). Some generative acts are
not only important to ourselves but are useful to society as well. Innovative generative acts can lead to
something new in society.
We approach
this matter of creativity—of creative innovation—from the perspective of the
Model of Hierarchical Complexity (MHC).
The MHC of Commons
and Richards (1984a, 1984b; Commons,
Trudeau, Stein, Richards, & Krause, 1998) is a system that classifies
development in terms of a task-required hierarchical organization of required
response. The model was derived in part
from Piaget's (Inhelder
& Piaget, 1954, 1958) notion that the higher-stage actions coordinate lower
stage actions by organizing them into a new, more hierarchically complex
pattern. The stage of an action is
found by answering the following two questions: a) What are the organizing actions? b) What are the stages of the
elements being organized?
THE MODEL OF HIERARCHICAL COMPLEXITY
The Model of
Hierarchical Complexity
The Model
of Hierarchical Complexity (MHC) (Commons
& Richards, 1984a, 1984b; Commons,
Trudeau et al., 1998) is universal system that classifies the task-required
hierarchical organization of “ideal” responses. Every task contains a multitude of subtasks (Campbell
& Richie, 1983; Overton,
1990). When the subtasks are completed
by the ideal actions in a required order, they complete the task in
question. The classification does not
depend on the content or context, so it is species, domain and cultural
free. Tasks vary in complexity in two
ways, either as horizontal (involving
classical information), or as vertical
(involving hierarchical information).
Horizontal (Classical Information) Complexity
Classical
information describes the number of “yes-no” questions it takes to do a
task. For example, if one asked a
person across the room whether a penny came up heads when they flipped it,
their saying “heads” would transmit one bit of “horizontal” information. If there were two pennies, one would have to
ask at least two questions, one about each penny. Hence, each additional one-bit question would add another
bit. Let us say they had a four-faced
top with the faces numbered one, two, three, or four. Instead of spinning it, they tossed it against a backboard as one
does with dice in a game. Again, there
would be two bits. One could ask them
whether the face had an even number. If
it did, one would then ask if it were a two. Horizontal complexity, then, is the sum of bits required to
complete a such tasks.
Vertical (Hierarchical) Complexity
Specifically,
hierarchical
complexity refers to the number of recursive times that the
co-ordinating actions must perform on a set of primary elements. Actions at a higher order of hierarchical
complexity: a) are defined in terms of actions at the next lower order of hierarchical
complexity; b) organize and transform the lower-order actions; c)
produce organizations of lower-order actions that are new and not arbitrary, and cannot be
accomplished by those lower-order actions alone. Once these conditions have been met, we say the higher-order action
co-ordinates the actions of the next lower
order. Stage of performance is defined as the highest-order of hierarchical complexity of the task solved. Commons (Commons,
Goodheart, and Dawson, 1997, March; Commons,
Richards, Trudeau, Goodheart, & Dawson, 1997, March) found, using Rasch
(1980) analysis, that hierarchical complexity of a given task predicts stage of
a performance, the correlation being r = .92 (hierarchical complexity of the
task that is completed).
Formulating
the Postformal Orders of Hierarchical Complexity
Commons (Commons
& Richards, 1978; Commons,
Richards & Kuhn, 1982; (Commons,
Trudeau, et al, 1998) showed that the postformal stages were true hard stages
in the Kohlberg
and Armon (1984) sense, but with some small modification. As Marchand (2001) summarizes, Kohlberg and
Armon distinguish "hard" stages (in which development occurs in an
invariant and universal sequence, e.g., the Piagetian stages) from "soft"
stages (in which development is conditioned by particular experiences arising
from differences in personality, upbringing, social class, and age). Commons (Commons, Trudeau, et al, 1998) used
a mathematical system derived from Luce’s (e.g.
Krantz,
Atkinson, Luce, & Suppes, 1974; Krantz,
Luce, Suppes, & Tversky, 1971) work on measurement. Each proposed stage was checked with the
main three axioms. Again, these
assumptions state that any given higher-stage action has to be defined in terms
of an associated lower one and organize those lower-stage actions in an
non-arbitrary way.
Commons’
and Richards' concerns lay with the general specification of any empirical task
that possibly could be used to demonstrate either the presence of, or the
development into, a postformal stage.
They de-emphasize the reconstruction of the "reality" of a
person "at a given stage."
Instead, they attempt to develop a general way to specify the
organization of tasks in any domain that a person "at a given stage"
can do. Other attempts to specify what
it means to be at a postformal stage can be found throughout the work reviewed
here (e. g. See Table 2).
Postformal
Orders of Complexity
We assert
that highly creative innovations require postformal thought. Four postformal orders of hierarchical
complexity have been proposed (Commons
& Richards, 1984a, 1984b, Commons,
Trudeau et al., 1998), beginning with systematic thinking and developing
through metasystematic to paradigmatic and cross-paradigmatic thinking. The four postformal orders, according to the
MHC, are displayed in Table 1.11. There
is a growing consensus that these are the postformal stages as shown in Table
2.
Place Table 1 about
here
Table 1.11 Postformal Stages, as described in the
General Model of Hierarchical Complexity
|
|
What is done |
How this is done |
The end result |
|
11
Systematic operations |
Constructs multivariate systems and matrices |
Coordinates more than one variable as input. |
Events and ideas can be situated in a larger
context. Systems are formed out of
formal-operational relations. |
|
12
Metasystematic operations |
Constructs multi-systems and metasystems out of
disparate systems. |
Compares and analyzes systems in a systematic way. Reflects on systems. Creates metasystems of systems. |
Metasystems are formed out of multiple systems |
|
13 Paradigmatic operation |
Fits metasystems together to form new paradigms. |
Synthesizes metasystems |
Paradigms are formed out of multiple metasystems |
|
14 Cross-paradigmatic operation |
Fits paradigms together to form new fields. |
Forms new fields by crossing paradigms. |
Fields are formed out of multiple paradigms. |
Innovators functioning at each of the four
stages do tasks of different hierarchical complexity that do not overlap with
one another. They do the different
tasks using skills that are increasingly rare.
The end results are entirely different for society. People have been
known to accept the expertise of people functioning at the systematic and
metasystematic stage. The results of
innovation become much more expensive at the paradigmatic and
cross-paradigmatic stages. The results
change the world culture and our very view of the world. In fact, at the cross-paradigmatic stage,
so few people exist that societies have no mechanisms to encourage such
activity, as far as we know. Yet it is
the that change the course of civilization.
For example, Copernicus changed our view of our place in the universe,
making the earth just another planet revolving around the sun. Darwin changed our view on our origins and
place within the world of animals make us one more animal. Copernicus lead to modern physics and
astronomy, Darwin to modern genetically based medicine evolutionary biology and
psychology, palenotology, and behavioral psychology.
Systematic
Stage
This stage was introduced by Herb Koplowitz
(personal communication, 1982).[2] Kohlberg
(1990) referred to this stage as consolidated formal operations and only much
later saw his moral stage 4 as being the same.
Fischer (1980) listed it as the third level in the fourth tier. At the systematic order, ideal task
completers discriminate the frameworks for relationships between variables
within an integrated system of tendencies and relationships. The objects of the systematic actions are
formal-operational relationships between variables. The actions include determining possible multivariate
causes—outcomes that may be determined by many causes, the building of matrix
representations of information in the form of tables or matrices, and the
multidimensional ordering of possibilities, including the acts of preference
and prioritization. These actions
generate systems. Views of systems
generated have a single “true” unifying structure. Other systems of
explanation, or even other sets of data collected by adherents of other
explanatory systems, tend to be rejected.
Most standard science operates at this order. At this order, science is seen as an interlocking set of
relationships, with the truth of each relationship in interaction with
embedded, testable relationships. Most
standard science operates at this order.
Researchers carry out variations of previous experiments. Behavior of events is seen as governed by
multivariate causality. Our estimates
are that only 20% of the US population now functions at the systematic
stage. Our guess is based upon data
that about 20% of the population are in professions requiring systematic stage
action. These professions require
graduate degrees. Hence, the percentage
of graduate students and professionals are good examples. For example, in Plano Texas 2000 census,
17.6% of the population had graduate or professional degrees In Geneva New York, it was 19.5%.
Metasystematic
Stage
At the
metasystematic order, ideal task completers act on systems; that is, systems
are the objects of metasystematic actions.
The systems in turn are made up of formal-operational
relationships. Metasystematic actions
analyze, compare, contrast, transform, and synthesize systems. The products of metasystematic actions are
metasystems or supersystems. For
example, consider treating systems of causal relations as the objects. This allows one to compare and contrast
systems in terms of their properties.
The focus is placed on the similarities and differences in each system's
form, as on well as constituent causal relations and actors within them. Philosophers, mathematicians, scientists,
and critics examine the logical consistency of sets of rules in their
respective disciplines. Doctrinal lines
are replaced by a more formal understanding of assumptions and methods used by
investigators.
As an
example, we would suggest that almost all professors at top research
universities function at this stage in their line of work. We posit that a person must function in the
area of innovation at least at the metasystematic order of hierarchal
complexity to produce truly creative innovations. By definition of the metasystematic stage, it means that they
have to coordinate at least two multivariate systems. We find that true adult creativity depends on an adequate
performance on other related tasks.
This is because the solution to tasks the society deems creative quite
often requires a new synthesis of systems of thought (the metasystematic stage)
or even a new paradigm (the paradigmatic order) or a field (the
cross-paradigmatic order).
Paradigmatic
Stage
At the
paradigmatic stage, actions create new fields out of multiple metasystems. The objects of paradigmatic acts are
metasystems. When there are metasystems
that are incomplete, and adding to them would create inconsistences, quite
often a new paradigm is developed. Usually,
the paradigm develops out of a recognition of a poorly understood phenomenon. The actions in paradigmatic thought form new
paradigms from metasystems.
Paradigmatic
actions often affect fields of knowledge that appear unrelated to the original
field of the thinkers. To coordinate
the metasystems, people reasoning at the paradigmatic order must see the
relationship between very large and often disparate bodies of knowledge. Paradigmatic action requires a tremendous
degree of decentration. One has to
transcend tradition and recognize one's actions as distinct and possibly troubling
to those in one's environment. But at
the same time, one has to understand that the laws of nature operate both on
oneself and on one’s environment—a unity.
This suggests that learning in one realm can be generalized to others.
Examples of
paradigmatic order thinkers are perhaps best drawn from the history of
science. For example, the
nineteenth-century physicist, Clark
Maxwell (1873), constructed the paradigm of electromagnetic fields from the
existing metasystems of electricity and magnetism of Faraday
(2000), Ohm, (1927), Volta
(1800), Ampere
(1926), and Ørsted
(1820). Maxwell’s equations for fields
and waves, showed that electricity and magnetism could be united, thus forming
the new paradigm. The wave fields can
be easily seen as the rings that form when a rock is dropped in the water or a
magnet is placed under paper that holds iron filings. This paradigm made it possible for Einstein to use notions of
curved space to describe space-time to replace Euclidean geometry. The waves were bent by the mass of objects
so that the rings no longer fit in a flat plane. From there modern particle theory has been able to add two more
forces to the electromagnetic forces giving us the standard
electromagnetic-weak force.
Cross-paradigmatic
Stage
The fourth
postformal order is the cross-paradigmatic.
The objects of cross-paradigmatic actions are paradigms. Cross-paradigmatic actions integrate
paradigms into a new field or profoundly transform an old one. A field contains more than one paradigm and
cannot be reduced to a single paradigm.
One might ask whether all interdisciplinary studies are therefore
cross-paradigmatic? Is psychobiology
cross-paradigmatic? The answer to both
questions is “no.” Such
interdisciplinary studies might create new paradigms, such as psychophysics,
but not new fields.
This fourth
order has not been examined in much detail because there are very few people
who can successfully perform tasks of this order of hierarchical
complexity. It may also take a certain
amount of time and perspective to realize that behavior or findings are
cross-paradigmatic. All that can be
done at this time is to identify and analyze historical examples.
Copernicus
(1543/1992) coordinated geometry of ellipses that represented the geometric
paradigm and the sun-centered perspectives.
This co-ordination formed the new field of celestial mechanics. The creation of this field transformed
society—a scientific revolution that spread throughout world and totally
altered our understanding of people’s place in the cosmos. It directly led to what many would now call
true empirical science with its mathematical exposition. This in turn paved the way for Isaac
Newton (1687/1999) to co-ordinate mathematics and physics forming the new field
of classic mathematical physics. The
field was formed out of the new mathematical paradigm of the calculus
(independent of Leibniz,
1768, 1875) and the paradigm of physics, which consisted of disjointed physical
laws.
René Descartes
(1637/1954) first created the paradigm of analysis and used it to co-ordinate
the paradigms of geometry, proof theory, algebra, and teleology. He thereby created the field of analytical
geometry and analytic proofs. Charles Darwin
(1855, 1877) co-ordinated paleontology,
geology, biology, and ecology to form the field of evolution which, in its
turn, paved the way for chaos theory, evolutionary biology and evolutionary
psychology. Charles Darwin
(1855) noted that finches had diverged into a wide variety of birds. If they had not been isolated in the closed
environment of the Galapagos islands, these finches would have represented a
wide number of species, as was the case of mainland species of birds. Many people had been exposed to just such
novel situations but made nothing of it.
Although Darwin discovered this phenomenon in the early 1800s, it was
not until many years later that he himself made any sense of it when he devised
his theory of evolution. Darwin saw
that evolutionary forces had transformed the birds differently. But, while Darwin’s specific observations of
finches did not have much impact on the direction of science, his evolutionary
theory did. Darwin created a good deal
out of three new interrelated paradigms: paleontology, evolutionary biology,
and ethology.
Darwin’s
theory constituted a radical innovation in the science of his time for three
reasons:
1. He presented
evolutionary evidence establishing the fact that human thought and action are continuous
with animal thought and action;
2. He proposed
an explanation for human evolution that was not teleological, that is one that
did not claim an ultimate purpose; and
3. Darwin's
theory brought together four distinct prior paradigms, those of: biology,
ecology, animal behavior, and geology.
Albert Einstein
(1950) co-ordinated the paradigm of non-Euclidian geometry with the paradigms
of classical physics to form the field of relativity. This gave rise to modern cosmology. He also co-invented quantum mechanics. Max Planck
(1922) co-ordinated the paradigm of wave theory (energy with probability)
forming the field of quantum mechanics.
This has led to modern particle physics. Lastly, Gödel
(1931), co-ordinated epistemology and mathematics into the field of limits on
knowing. Along with Darwin, Einstein,
and Planck, he founded modern science and epistemology.
Table 2 summarizes most proposals for postformal
stages (for a review, see Marchand, 2001).
The columns represent the major adult developmental stages. The rows list the researchers and some key
publications for the names and numbers of the stages.
Table 2
Comparative
Table of Concorded Theories of Formal Stage
|
Researchers |
Abstract |
Formal |
Systematic |
Meta-systematic |
Paradigmatic |
Cross- Paradigmatic |
Transcen-dental |
|
Bowman.
(1996), Commons
& Richards (1984a,b); Commons
(1991); Commons
& Rodriguez (1993); Commons
& Wolfsont (2002); Rodriguez
(1989) |
9 (= 4a) |
10 ( = 4b) |
11 ( = 5a) |
12 ( = 5b) |
13 ( = 6a) |
14 ( = 6b) |
|
|
Sonnert & Commons (1994) |
group |
bureaucratic |
institutional |
universal |