"Meaning Finds a Way: Interdisciplinarity and Thermodynamic Equilibrium,or I Want to be A Renaissance Man."

(Presented at the Association For Integrative Studies Conference, Detroit, MI Spring 1998)

Bonnie L. Kyburz and Judith Clayton Van



Bonnie's view: Theory
Exploring important events in our cultural evolution, Ralph Abraham
believes that "the same theme may be traced through time, over space, or
through an evolution of ideas or myths" (xiii). For example, "despite their
seeming differences," argues Abraham, "the discovery of the wheel around
4000 B.C. and the Chaos Revolution that began in the 1970's are related and
significant events in which attractors (representing the stable regimes of
history) appear, disappear, or undergo radical transformation" (14).
As scholars working in Composition, Judy and I applaud Abraham's
Interdisciplinary moves, his willingness and his ability to map scientific
theories so confidently onto cultural "meaning-making" systems.

 Such concepts have brought Judy and I together. Through our talks
and our work together, we  hope to advance our understanding of the ways
which interdisciplinarity may become more boldly manifest in our classrooms
and in our scholarship. And, while we've  come to consider the possibility
that our boldest and most recent thinking on interdisciplinarity may be
contentious, we feel fairly certain that in terms of pedagogy, we're on
solid ground. And we feel relatively safe in assuming that others will share
our confidence in the capacity of a particular discipline-specific
theoretical discourse to speak to phenomenon in other fields, across the
disciplines. Even when we're talking about science.

 Judy and I have talked frequently about interdisciplinarity and the
ways in which the concept is often held suspect within the disciplines,
across the disciplines. Yet, such suspicions are not unfamiliar to us.
Workers in Composition, for example, have had a long a conflicted history
with this kind of "borrowing" from the disciplines.

 During the educational reforms of the 1950's, for example, some
called for a shift in our focus--concern for student needs were in many ways
replaced by a devout interest in the "long term goals and the nature of the
subject" (North 9). Methodological purity and departmental clarity of
identity was the goal. As Stephen North notes, such emphasis was "guided by
the 'tripod' metaphor for English studies, English conceived, that is, as
consisting of three separate components: language, literature, and
composition" (North 10).  For Arthur Applebee, such divisions were to be
upheld and further enumerated; he notes as problematic that notion that
Beyond the cliche that each of these studies deals with language, they have
no real unity as subject matter; attempts to interrelate them have been
artificial and, for the most part, short-lived. . . . Inevitably, the edges
of the subject have blurred and wavered, creating for the teacher of English
a perpetual crisis of identity. (qtd in North 10)

Judy and I believe that the blurring of these edges has been formative for
our discipline, creating a crisis of identity only if we deny
interdisciplinarity as a feature of our work. For most teachers of writing,
Applebee's claim that the construction of the tripod is merely convenient,
that it is a flimsy interrelationship between language, literature and
composition--well, it is simply naive. Most teachers of writing today
consider rhetoric to be imbricated across the disciplines, particularly
across the spectrum of programs that constitute English studies
(Berlin,Harris, Faigley).

 Further enumerating the interdisciplinary conflicts within
Composition, Stephen North suggests that despite the diversity of various
methodological communities--each of which derives knowledge from a variety
of disciplinary practices--a community of inquirers cohered, and a field
emerged. For North, we had created ". . . an accumulated knowledge of
relatively impressive size, but one that lacks any clear coherence or
methodological integrity" (3).  North reflects upon this "problem" by
recalling Paul Deising's Patterns of Discovery in the Social Sciences;
Deising notes that:

A community is located by finding people who interact
regularly with one  another in their work. . . .  Although they do not all use
exactly the same  procedure in their work, there is a great deal of
similarity, and the differences are accepted as variant realizations of the same
values. (qtd inNorth 2) North finds that, with careful consideration, the interdisciplinary
fabric of Composition created a valid, if contested field of inquiry.

Perhaps the most outspoken on the matter of rhetoric as
interdisciplinary was composition scholar James Berlin, who argued that
rhetoric (in large part, the subject matter of Composition programs)
imbricated across the disciplines. For Berlin, rhetoric was constituted by a
series of competing epistemological and ideological orientations that traced
to antiquity, to Platonic and Aristotelean differences regarding Truth and
Knowledge. These differences somehow organized into a coherent
structure--the emerging field of Composition. Our field was (and is)
informed by classical rhetoric, philosophy, ethics, psychology, sociology, and many other disciplines, each somehow competing for prominence as we
struggled to unify for the sake of disciplinary validity. Yet, we have
remained interdisciplinary, and today we are recognizing the value of such
structure. Judy and I have been pleased to explore some particular ways in
which this is so, and our work together has been monumentally refreshing and
revitalizing.

For Judy and I, as for Abraham, scientific discourses involving
chaos, thermodynamics, and entropy are capable of imbricating across a
variety of systems, including the disciplines. We find such discourses
relevant for our work with language systems and their uses in Composition.
And while our interdisciplinary moves may as yet feel awkward, we recognize
that they are not made in isolation but as moves that respond to the
epistemological orientations of academic culture. And such moves are
certainly not new.

 In a 1977 essay entitled "The Interdisicplinary Dilemma: A Case for
Flexibility in Academic Thought," Associate Professor of Anthropology at
Washington State U (Pullman), Roald Fryxell argues that this shift is a
natural progression. Fryxell suggests that a
                . . . concentration of intellectual and economic resources of
compartmentalized knowledge has, however, expanded the
limits of the various fields until, as noted, their respective boundaries
have ceased to be significant; and the farther that divergent specialized
studies have progressed, the more stimulating and the more valuable has become the
exploration of the unknown interfaces. Thus, once again we have the
opportunity--in fact, the necessity--for synthetic studies. (9)

Judy and I find that we have been talking of such "unknown interfaces" ever
since we met. Here's what we've been talking about . . .

   In our continuing talks about various scientific discourses and
their value for our work as teachers of writing, we've come to recognize a
general epistemological shift within our field; interdisciplinary methods
and methodologies are on the rise, due to the increasing complexity of our
field, which is both apparently expanding and contracting at the same time,
all in service to the making of meaning. We believe that such large-scale
effects are, in part related to various local interdisciplinary moves that
have always occurred in our increasingly complex classrooms, and that such
moves revitalize rather than fragment or neutralize us. But the work is
ongoing, the rewards are elusive, and our classrooms grow ever-more complex.

In our classrooms today, workers in Composition are involved in far
more than "teaching English" via the canon, far more than teaching
Aristotelean modes of discourse. Instead, we are concerned with liberatory
pedagogy, deconstructing the traditional teacher's role, and effecting small
and large-scale changes in students' lives. Pedagogically, we strive to be
effective, equitable, and revolutionary, following the call of Paolo Freire;
yet, we are ultimately responsible for teaching classical rhetoric often in
reductive, regularized forums. In addition to such competing bouts of
pedagogical singularity and diversity, our field is complexified by cultural
trends which threaten our sense of stability, purpose, and meaning:
Affirmative Action is currently threatened, tuitions continue to rise, and
corporate thinking proceeds to influence educational missions. Moreover, the
diversity of our workplace creates a multi-tiered hierarchy which promotes
our feelings of anxiety and instability; leading to both individual and disciplinary
fragmentation and uncertainty.

        We are no simple academic department; Applebee would have been
disappointed. We have strayed far from his notion of English as a pure
subject. We are complex, diverse, and conflicted. We are increasingly
constrained by our duel desires to maintain some coherent structure for our
field and our classrooms and to find ways of negotiating the constant
changes and conflicts that mark our discipline. Now, thanks to Elaine
Showalter and others, we understand that we have to look good doing it, as
well. What does this increasing complexity mean for our field? We have some
ideas . . .

ENTROPY AND EQUILIBRIUM
Our discipline has emerged in conflict, not unlike others.  Yet we are
strangely regimented in many ways--same syllabi, same textbooks, same
overarching ideology. And today, workers in Composition refer to "our"
epistemological orientation as "social-constructionist," indicating a sense
of coherence. Yet, we think of our academic climate as "postmodern," a
coherent rubric which ironically bespeaks fragmentation and disorder. If we
are working in a postmodern academe, we find that the terms used to describe
that state of affairs-fragmentation, exhaustion, and disorder--are similar   to those used,
within various sciences, to describe systems high in entropy,
which is defined as "a thermodynamic property of a macroscopic body which
corresponds intuitively to the degree of disorder" (Davies 496).

The concept of entropy is related to the Second Law of
Thermodynamics.  "The second law embodies what Lord Kelvin, the
distinguished nineteenth-century thermodynamicist, called a "universal
tendency toward dissipation" (Hayles 13) -essentially, death. Closed systems
high in entropy are considered vulnerable to thermodynamic equilibrium, "the
state reached ultimately by an isolated system." (Davies 496) Entropy, as a
model for the behavior of closed systems, may suggest for our disciplinary
systems that interdisciplinarity is essential if disciplines themselves are
to cohere and have meaning.
 For Judy and I, keeping tabs on how we perceive our field's measure
of entropy relates to our ability to think, teach, and work effectively
within it. We find comfort in various discourses on chaos theory, within
which the concept of entropy has been reconsidered in terms of any final
state of "heat death" or sameness.

STRANGE ATTRACTORS
 For chaos theorist Robert Shaw, "any isolated system" which is bound to
slide toward a state of increasing disorder" (or entropy) may be
mitigated by "strange attractors," which exist in dynamical systems and are
related to scaling effects that allow recurring events to produce
unpredictable pockets of order or meaning. For Shaw, strange attractors
conflate order and disorder, giving "a challenging twist to the question of
measuring a system's entropy" (Gleick 258). Strange attractors serve as
"efficient mixers. They create[d] unpredictability. They raise[d] entropy. .
. , and they create[d] information where none exist[s]" (Gleick 258).  Judy
and I consider our  interdisciplinary moves as strange attractors,
conflating order and disorder and making new kinds of meaning within our
classrooms, our thinking, our scholarship, and perhaps within the field.

DISSIPATION AND BIFURCATION
In addition to Shaw's hopeful ideas, we find refreshing David Porush's and
Katherine Hayles' descriptions of how certain chaotic systems (such as
composing processes) may bypass the second law. Porush  notes that
"dissipative structures [such as composing processes] seem to have a mind of
their own.  They are self-organizing systems that locally contradict the
second law of Thermodynamics" ( C & O 57).  Hayles notes that, according to
Ilya Prigogine and Isabel Stengers (Order Out of Chaos, 1977) entropy is
envisioned "as an engine driving the world toward increasing complexity
rather than toward death" ( C & O 13).  Such increasing complexity can lead
to
 . . . a bifurcation point [which is] the origin of a dissipative
structure--a system-shattering moment when the previous, simpler
organization can no longer support the intensity or frequency of its own
fluctuations, and either disintegrates or jumps to a new level of order and
integration. . . .  .  ( C & O 68)

We believe that there is an interesting trend currently characterizing our
work in  Composition; we are found internalizing our work
as "interdisciplinary' and articulating it similarly in our scholarship.

INTERDISCIPLINARITY AND INTERVENTION
We believe that such interventions-strange attractors, perhaps--may provide
an escape route from the entropic nature of our complex yet paradigmatically
similar academic systems of thought and work. Perhaps such intervention will
provide spaces within which we may circumvent the 2nd law of Thermodynamics
which would lead us to disciplinary exhaustion or death.

For Judy and I, Interdisciplinarity represents a bifurcation in Composition which generates  newer and higher degrees of order from the chaos of our work. For Judy, these new orders of meaning emerged in the classroom, in complex, dynamic interaction with her students (and with herself). The seemingly spontaneous emergence of certain syntheses of ideas were, for Judy, (re)generative. Her interdisciplinary moves salvaged and revitalized her teaching. Later, it seemed as though these engaging moments of insight also rekindled her relationship to the field of Composition. In conversation, we came to understand that we'd both experienced such moments of insight. We've come to believe that our shared experiences may be indebted to our commitment to exploring interdisciplinary knowledges in the classroom and beyond; in fact, that such explorations have been necessarily transformative.

Judy's view:  Praxis

While Bonnie is more theoretical and precise in her scholarship, I came to similar conclusions by a different route:

On first hearing the phrase, when I was eleven years old, and asking
what it meant, I have wanted to be a Renaissance man--a man of universal
genius.  I didn't particularly want to become a man, but I did want to
possess the qualities personified by Leonardo DaVinci.   Later I was
relieved  to find a definition of a Renaissance woman. It's a noun,
denoting,  "A woman who has broad intellectual interests and is accomplished
in areas of both the arts and the sciences."   I intuited that this would
require a broad education because according to my definition of a
Renaissance person--a well rounded, balanced  genius--I recognized that
synthesis was the key.

And yet, early, I rebelled against the biases and restrictions of a regimented education.
I struggled, bored, through school, and after a while, did not go back.
I became an artist  more engaged in the art of the streets, than with fine arts, and barely
educated in the sciences at all. I became a painter, a dancer, a horse trainer, a mother,
an occasional creator of  fictions.

Because I valued and questioned my own creativity, my interests were
the creator, creation myths, religion and philosophy.  Reading in religion,
lead me to anthropology, myth, astronomy and science, to physics, various
cosmological theories, astrophysics, quantum theory, and chaos theory.
My search and my synthesis were intuitive.

 After years of painting and learning on my own, I returned to college.
There,  a professor of Art History taught me to write, and to understand writing as art.
After earning a B.F.A. in studio art,  I applied and was accepted as a Master of Fine Arts
candidate in Fiction Writing at Arizona State University.

Ten years ago, when  as a T.A in the English Department, I entered a first year
composition classroom to teach, I thought I was in prison, and the good times
were over. The curriculum committee gave me a syllabus, told what me to teach,
and how to teach it. I was petrified because many tenured English  professors felt
that M.F.A. candidates should not be in the composition classroom at all. Yet, I
completed the T.A. training, received the M.F.A. and the school re-hired me as
untenured faculty.  I was in the classroom again not necessarily because they wanted
me, but because of escalating enrollment, they needed me. I felt enormous pressure
to prove myself and keep my job in an increasingly competitive field where I wasn't
sure I belonged.

I began graduate classes in rhetoric and composition and was
fortunate to have Frank D'Angelo, as my professor.   He
taught the value of a broad general education. He illustrated the
adaptability of Classical Rhetoric, drawing on all four boards of the room
a huge heuristic that writers can use to discuss any topic from Art to
Science, no matter how complex.

 He explained how this heuristic  expanded to include all that people can write or
speak about.  Dr. D'Angelo discussed scientific and social science theories,
and how they apply to writing. He engendered hope that there might be a place for
 me in the composition classroom after all.

Unfortunately, Dr. D'Angelo was soon to retire, and the new rhet/comp folks,
seemed a different breed, responding to a changing academic environment, and the
increasing pressures of Arizona State's booming enrollment.

STRUCTURE:
Dr. D'angelo inspired me to bring all I knew to my teaching, yet I taught for several
more years without referring to my art background because I didn't want these new
rhet/comp  people  to see me as flaky, and I didn't know how to integrate my
own knowledge with the subjects I was supposed to be teaching. However,
meaning did find  a way.

I was losing steam, losing passion for writing, and for teaching. Pressure was
building within me, seeking escape from the codified, highly ordered, closed system
exemplified by the lock-step syllabi, the same book for all, the many meetings to insure the administration that we were all "literally" on the same page.

One day in my classroom while  giving a lecture  on paragraphing to a group of
uninspired first year students, I said the word structure . . . and the sentence trailed away. Turning to the board, I outlined a rock hut, a shepard's hut in the Pyrenees Mountains. Then, I drew a log cabin, and discussed the pioneers in the American west.  Next,  a suburban house, and how they sprang up after the second world war, and why.  Next I outline a castle, then the Pyramids.

I talked about the people, the purpose, the situation, and occasion of the
constructions.  I'm sure the students  thought I'd lost it, but they waited
politely for me to put an extra defense opening in the castle.
 I asked what the drawings had in common.   A student immediately
suggested that everything had a structure, not just buildings  and essays.
How and why things fit together whether it be essay or building, now seemed
more interesting.

We discussed organic structure, formal structure, postmodern structure, and why
some teachers taught the five paragraph essay. A boy said, "that's easy, for the same
reason they built all those little houses in the suburbs. It's easier, more efficient, and
probably cheaper."  But not, we acknowledged very expressive or creative. It was more
utilitarian, and designed to be a quick fix for a problem.

I walked from class with a group of  happy students and I was happy
too, because I'd shared in a way I didn't usually share. I was also a little
anxious because I had the feeling that if one of the "rhetoric people" had
been observing,  I'd be out on my ear. It was kind of thrilling, though,
because I felt I'd gotten away with something.

STYLE
        Later, talking with another class about style, I found they had
little conception of the possibilities of style beyond a vague sense that it
related to fashion.  The next day, while preparing for class, I thought
about that discussion, and my eye happened on my Jansen
History of World Art.

 I remembered a favorite art teacher's lecture on drapery in art through the ages.
In the darkened auditorium, she had shown us the history of a form; its evolution
from the stiffly creased  fabric in early Egyptian Art, to the relaxation of form  in
classical Greek painting, the undulating movement of drapery in Hellenistic
Sculpture, the changes through the Renaissance,  then the return to the
modern geometric forms of  Picasso. By isolating the drapery, we could see a
particular thread, one interpretation of form winding its way throughout the
history of art.

This approach to understanding form made a huge impression on me, but
I had been  an art student. I wondered if my students would find it as interesting,
but I figured, what the heck, at least I'd be sharing something that had intrigued me.
I hoped that they might grasp the concept, and then be able to pick out threads of
similarity in our readings. I didn't know how the knowledge would translate.
Nevertheless, through visual images, I had understood  the concept of style as
culturally influenced and hoped they might too.

Being in a computer classroom that semester allowed me to put the
images on my web page and show them to the class. My students were intrigued,
but they wanted to know why we were looking at these pictures and how they related to
writing. Trying to answer, I remembered WinstonWeathers',discussion of style.
 I took the book  to the next class.  Weathers says style is "proof of a human being's
[or a culture's] individuality, . . .a gesture of personal freedom against inflexible states
of mind . . . in a very real way has something to do with freedom . . ." and
through which . . . we can reveal to students the connection between
democracy and style." He asserted that through the study of style, "the
student is equipping himself for a more adaptive way of life with a society
increasingly complex and multifaceted."

My student's liked this idea of personal expression and freedom, but didn't know how
it related to the drapery . . . and I wasn't sure either.  Trying to make the connection, I said,
"While each of you  are responsible for a persuasive essay, there are many ways,
or styles available to write it. Think of the different geometric styles--Egyptian,  undulating Hellenistic Drapery, modern geometrics of Picasso–yet still the same form,
drapery.

I  related the drapery styles to the writing styles of  famous authors we
had read, including Henry James, Hemingway, and the present day Thomas Wolf.
Then I explained  Weathers' idea of multiple grammars, that writers use different
grammatical structures for different rhetorical purposes. We discussed alternative
ways of saying the same thing. Henry James had his way, Hemingway his, and you
have yours, I said.

 I  asked students to write a persuasive essay about style,
including descriptions of the art we had viewed and the authors we had read.
I gave no other parameters regarding content or form.   We read these essays
aloud. All good, all different, all fulfilled the writing assignment, yet
each student displayed  their own style. It was empowering because although
quite different, just as the styles of drapery had been,  each was clearly
valid.   It was an "aha" moment for them. By bringing an outside element
(drapery),  to the assignment we had escaped its traditionally static nature.

ELEMENTS OF PERSUASION

        The next major shift in my teaching  came like a visitation. I was
in the computer classroom, at the new, white  board, discussing the
Rhetorical Triangle that shows the relationships of three elements of
argument, speaker, audience, and message. I said, "arguments occur within a social context, and they are produced by writers or speakers who are addressing an audience."  I drew a
triangle.  We discussed the mathematical implications of triangles in terms
of origins, foundations, and structures of order.

Attempting to move from an abstract visual representation of rhetoric to an explanation of how writers enact these principles by deploying the artistic proofs, or appeals, I explained "logos," that in Greek means "word," and  refers to the internal consistency of the message--it's logical appeal--and wrote it at the top of the triangle.   Next, I explained "ethos," that in Greek means
"character,"and I wrote it on one corner of the triangle. "Ethos" refers to the credibility, manner
and reputation, of the writer or speaker. Then, I explained "pathos," Greek for emotion, which I wrote on the other corner. "Pathos"refers to the impact of the message on the audience, with appeals to the emotions of the audience, and its power to cause the audience to act.
I concluded with an example, then said "Logos, Ethos, Pathos,  three elements necessary to a
balanced  argument" . . . and thought I had completed the lesson.

 Nevertheless, I was drawn back to the top of the triangle. Beside
"logos," I wrote "idea." Next to "ethos," I wrote form. And beside "pathos," I wrote
"force."
        "Idea, Force and Form," I said, "the Kabbalistic formula the
ancients posited for creation. A balanced triangle is the formula for an
essay, for a life, for any creation.  With no idea, the  force and form can
be powerful and elegant, but you cannot create. If one employs all force and
idea with no form, the same result occurs, no creation.  It takes the
balance of three." I felt like I'd said something inappropriate-burped in
church or something.

 I had never put this together for my self, and here, impromptu, I
had shared a connection of seemingly disparate ideas with impressionable
first year students.  What if I were all wet? Curiosity caused me to
persist, collecting information about triads that I shared with my class. I
came up with quite a list, some obvious, others more buried in  myth and
subsumed  in our unconscious: From western religion, Father, Son, and Holy
spirit, from early Cretan origin myth, Gaia--the body of earth. Chaos--the
gap between heaven and earth, a state of disorder, a system in movement.
Eros--desire, the creative principle connecting Chaos and Gaia. Other
triads, too numerous to list, come from many disciplines.

On my quest I found the Sierpinski Triangle, a fractal.  Fractal geometry, from
Mandelbrot's study of complexity and chaos, is concerned with irregular
patterns of parts that are in some ways similar to the whole, for example
twigs and tree branches with properties of self-similarity or self-symmetry.
Fractal geometry has been applied to diverse fields such as the stock
market, meteorology, and computer graphics. My students had seen one
possible connection between their composing process and this new geometry.
They had considered the Rhetorical triangle, the connections between it and
ancient religious and philosophic ideas of creation.

The more I open myself to these serendipitous teaching events, the
less surprised I am to encounter these strange connections. One day,
when discussing transitions in an essay, I flashed on the importance of
transitions in film. Discussing a popular film, I began to talk about the
cuts from one scene to the next: "What takes place in your mind during those
cuts?" I asked. We agreed that cuts can accomplish much work in a short
time: advance the plot, set up relationships, create tone, locate us in
time, create suspense, and at their best make us understand what is never
explicitly revealed, only suggested.  These orders of meaning emerge from
within the cuts, the dark spaces, quick transitions or fades where our mind
synthesizes much of a film's information.

We began to wonder: when we are  engaged in creative, processes such as writing,
 do we perhaps exist in the unknown interfaces Fryxell describes? Or could it resemble
the leap of faith we make when  synthesizing, bringing disparate information/disciplinary discourses together? Maybe it is.

Even  this  particular suggestion is  another of the wild leaps of faith we make, trying
 to find connections in a hierarcichly organized world of knowledge.   Maybe this is chaos,
 the dark space--the complex dynamic space between--where  mind finds new and exciting
possibilities and connections, the vast deep out of which something new takes form.

Whatever these may be, these unknown interfaces, we have come to imagine that
they are manifestations of the ways in which we've internalized interdisciplinarity.
They have saved us, and they have saved our classes from the entropic action of a field apparently bent on regularizing the teaching of writing.  Our interdisciplinary moves have allowed us to create newer and higher degrees of order--allowed us to escape the sameness
that might destroy our classroom experiences.

 Imagine the class, the networked classroom of students, as a complex
system, and apply chaos models to it. The point where our lack of passion
for teaching and our students' boredom   meet  is encouraged by entropy and
heading toward equilibrium. It is when a system is at equilibrium that
nothing further can happen, only random fluctuations. The move from
equilibrium requires  input of energy, or information;  from chaos theory's
butterfly effect we know that this input does not have to be enormous, but
that it can be subtle. We are encouraged by the knowledge-derived through
interdisciplinary and collaborative means (i.e., dialogue and
reflection)-that with minimal but sufficient force, nonlinear rearrangements
occur and systems make quantum leaps, bifurcations which move systems
forward into evolving complexity.

These connections came suddenly, usually in the classroom. They
began  the second semester that I taught with computers, and I consider the
addition of computers to be one bifurcation point in my teaching that
allowed these changes to occur.  Ralph Abrahams contends that the
Renaissance was a bifurcation point in the evolution of knowledge, spurred
by another bifurcation, the printing press. Thus perhaps  my obsession with
the Renaissance becomes more understandable.

For me, Bonnie,  and the scholars of the Renaissance, these new connections were
 made possible by desire, broad knowledge in disparate areas, and new technology.
 For me, and perhaps for them, the current situation was entropic, and by that I mean
that I  and my students were usually in a state of  frustration, seeking to understand and
explain something in a new way.

We have become convinced that by applying the combined lenses of
thermodynamics and chaos theory to the classroom and viewing it as a
complex nonlinear system, we can gain information about teaching and learning that may help students and teachers  take the leap  from a disciplinary to an interdisciplinary model. This model includes increased complexity and freedom, expanded student use of  computers, student-authored curriculum (with teachers as coaches and/or facilitators), creating knowledge
instead of only learning what is "already known," and a continued understanding of our educations as perpetual, as evolving over lifetimes, particularly in an increasingly
complex and technological society.

Fryxell says it wonderfully, capturing the complexity,  unpredictability, and interdisciplinarity of knowledge: "Knowledge is a continuum, like the sphere of the earth but with the uninterrupted
vastness of a universe. Our formal academic categories are as arbitrary and artificial as the lines of latitude and longitude we scribe on a globe despite the continuity of the earth's surface." We find his words compellingly accurate.