2001 Sigma Xi Forum Online Proceedings
A New Trivium and Quadrivium
George Bugliarello, Chancellor, Polytechnic University, and former president of
There can be little question that
today there are tensions and conflicts among the humanities, the arts, science and
are also powerful confluences, such as those of art and engineering in architecture or of
imaging technology and the arts. The conflicts have kept us from fully recognizing their
dangerous implications, and the confluences are still too few. As Sarton put it, focusing
on the conflicts between science and the humanities, the most ominous conflict of
our time is the difference of opinion, of outlook, between men of letters, historians,
philosophers, the so-called humanists, on the one side, and scientists on the other. Today
the gap cannot but increase because of the intolerance of both (Sarton). For sure,
tensions and conflicts in the realm of ideas are the fountainhead of new conceptions and
an unquenchable manifestation of human freedom. But when they are based on prejudice or
reciprocal ignorance, rather than on a clear understanding of the opposing positions, they
put at risk the very survival of our species, now propelled at breakneck speed toward an
unfathomable future by scientific and technological advances. The most recent
manifestation of the conflicts are the current postmodernist science wars and
the reaction they have engendered (Ross, Segerstråle, Koertge, Gross and Levitt).
It is simply too wasteful and risky for our future to perpetuate this
status quo. We need to endeavor to understand
the reasons for the conflicts and the opportunities for new confluences.
The conflicts reasons are complex, but significant among them
is the influence that the medieval trivium and the quadrivium continue to exert. In the
Middle Ages, in the rediscovered tradition from Greek and Roman times, the trivium and
quadrivium embodied what an educated person was expected to know. In the trivium, grammar
was a basic foundation, rhetoric encompassed literature and poetry, and logic was
primarily Aristotelian. The quadrivium encompassed four subjects, all based on
mathematical knowledgearithmetic, geometry, astronomy and music. Geometry had its
origins in Egyptian and Greek thought, and arithmetic in Indian and Arab thought
transmitted to the West. Astronomy dealt with movable objects that were deemed to be
permanent and music with movable phenomena that were impermanent (its purpose was to
understand polyphonic secular music).
The medieval trivium and quadrivium dealt with intellectual issues as
distinguished from emotional or expressive ones like art or religion. Together they were
called the liberal arts because in Roman times they were the arts deemed important to the
formation of the free man. By the thirteenth century, their structure was fairly
standardized, with the trivium the basic foundation of university education, and the
quadrivium leading to a masters degree that could be followed by specialized
professional education, particularly in medicine, but also the law. The purpose of the
medieval trivium and quadrivium was thus to elevate and prepare. In the Renaissance the
focus shifted to erudition, with much greater secularhumanemphasis than in
medieval times, with their pervasive theological context, hence the label humanities.
Today the subjects of the trivium, greatly expanded, remain a
foundation of the humanities curricula. Of the quadrivium, arithmetic and geometry are
embodied in math, an introduction to astronomy is one of the more popular science
offerings in liberal arts education and the teaching of music expanded its scope,
abandoning the mathematical focus it had in the quadrivium.
In the medieval period, the trivium and quadrivium excluded
engineering and other areas of knowledge that came to be grouped, somewhat quixotically to
our minds today, in the seven mechanical arts (once again, the medieval number seven):
weaving, blacksmithing and navigation, war (armatura),
agriculture, medicine and hunting, and the theatrical arts. Only for medicine or the law
were the trivium and quadrivium a preparation. Not so for engineering, the arts and the
other mechanical arts. Engineering arose in the earliest times out of utility and military
necessity but in the eighteenth century became increasingly oriented toward civilian
purposes. Only some one hundred and fifty years ago did engineering education, with a
strong use of science, begin being housed in universities.
The often passionate conflicts we perceive today among the humanities, the
sciences, engineering and the artsthat is, between and among the descendants of the
medieval liberal arts and mechanical artsarise not only out of their different
origins, but also out of their different purposes and methods. These differences, in turn,
are at the root of conflicts in the realm of values. Not to be overlooked as a source of
conflicts are differences in social status, particularly in the United States, where the
liberal arts and law are the predominant background embodied in elective government and
Wall Street, while engineering, and to some extent the sciences, embrace far more the less
advantaged and the immigrant. Differences in origins actually predate those stemming from
the idea of the trivium and quadrivium that crystallized them. For instance, one could say
that the task of engineeringthe creation of functional artifactspredates
science, art and the humanities, since it is carried out, albeit instinctively, also by
other, older species (suffice it to think of beehives or birds nests). Science has
what we believe to be a religious origin. It became largely independent of religion in
Greek and Roman times, then subservient to it in medieval times in Europe, and divorced
from it in the conflicts of the Renaissance. As to art, we do not quite know what impulse
led to the Lescaut or the Sahara cave paintings, but we know that for most of time its
motivation was religious, from the Egyptian monuments and hieroglyphics to the Parthenon,
Borabodur, the Sistine Chapel, or the artistic calligraphy of the Koran. The origins of
the immense field we call the humanities, from philosophy to poetry to mythology, are as
diverse as the field itself. Today, sciencefor sure in the Westremains
divorced from religion, and the humanities have expanded into myriads of rivulets.
The purpose of the humanities is to understand and civilize man; that
of science is to understand naturea domain vaster than man, but that includes him.
The arts complement the humanities by being the sensory inspirers of reflections and
emotions. The goal of engineering is to extend through artifacts, that is, machines,2 the capabilities of our body and in order to do so to modify
nature, e.g., the course of a river so that we can navigate it.
The methods of the humanities are based on literacy. Science is
meta-literate and progresses through the strictures of verifiable truths that require
precision and objectivity. It is a cumulative enterprise, built on previous discoveries
and knowledge. Engineering is cumulative also and requires utility. So does that cognate
modification of nature, medicine, guided in its purpose of healing by Hippocratic
principles starting with the imperative of not harming the patient (akin to but more
easily articulated than the engineering one of exercising due care). Art,
after its long history of having been descriptive, or inspirational or reflective, has now
become mainly reflective. Like engineering, it creates artifacts, but is no longer
constrained by rules as it was in the Renaissance, in Classical Greece and in some other
cultures. And it is not cumulative.
The Question of Culture
That there are these differences does not mean, however, that there are different
cultures, as in the concept of two cultures (Snow). We live in a world in which we all use
pills, cars, running water and computers, wear the same kind of clothes, eat more or less
the same kind of food, and behave more or less in the same way. It is a world in which
science and engineering have enormous influence on our language,3
thoughts and lives. Thus if we subscribe to a broad view of culture as embracing the total
pattern of human behavior and its products, embodied in thoughts, speech, action and
artifacts, it is obvious that we are all living under a common culture, albeit with
different and very powerful subcultures, such as those of the humanities, the arts,
science and engineering. (If any, the dichotomy is between life in the developed and in
the poorer parts of the world.) But we are at great risk when, within this common culture,
we indulge in internecine cultural warfare, rather than reasoned and knowledgeable
A consequence of todays cultural disarray are multiple crises.
In the humanities, far more serious than a crisis in taste, which no one can agree on
today how to define, is the loss of the ability to illuminate and guide society. That
original intent of the liberal arts is defeated by the exclusion of science and of the
modification of nature, even though they are a defining part of our culture. All society
and civilization presupposes language, but a culture based only on literacy is not
co-extensive with all human civilization (Plumb).
Multiple smoldering crises in science and engineering stemming from
questions of purpose and social control have contributed to societys ambivalent
views of science and technology, manifest, e.g., in the controversies around
sustainable development or genetic engineering. The question of science for sciences
sake, or for social purposes is parallel to that of art for arts sake, or for a
purpose that transcends it. And in engineering, just as our own fist can be used for good
or for bad, should machines be created regardless of consequences, even if they can be
used to enhance our negative drives, as in the case of weapons, or should they be created
only if they reinforce our ability to survive in a civilized way? The conflicts in science
and engineering are heightened by dilemmas of independence versus power, or of an unfettered sense of duty versus the attraction of material rewards, and
uncritical adherence to corporate discipline.
In the arts, the crises are epitomized by the polemics surrounding
the new historicisman art for arts sake attempting to aestheticize the whole
culture (Benjamin, Gallagher and Greenblatt). The arts have become more esoteric, speaking
more and more to themselves, and relinquishing, by and large, the ability to inspire or to
convey a clear sense of beauty. In architecture, the crises are manifest in many stylistic
inventions for the sake of invention, and in urban planning, in the inability to cope with
the phenomenon of rapid urbanization and the dysfunctional mega-city.
To overcome these crises of todays increasingly atomized
subcultures, it is useful to consider in further detail some collisions and potential
Science, Engineering and the Humanities
The purpose of humanities is the cultured man; that of science the
knowledgeable man. The language of the humanities is ordinary language; that of most
science and engineering is mathematics. Literature has room for emotions, but the
strictures of the discipline of verifiable truth that governs science in its quest for
knowledge cannot be influenced by them. Ultimately, however, one set of endeavors implies
the other. Scientific knowledge impinges on views of the world, such as those of human
origins and race. For instance, archeology or restoration and analysis of ancient texts
depend ever more on science, as does an understanding of the reasons behind turning points
in history, such as those caused by different susceptibility to disease or by the mastery
of a new technology. Conversely, science is powerfully influenced by the culture in which
it is embedded, as dramatically evidenced by the contrast between science in the Middle
Ages and in the European Renaissance, or between science in the West and in the former
Soviet Union. One cannot overlook the influence in the development of science of the four
subjects of the quadrivium, with their mathematical leitmotif. But, eventually, with the Renaissance,
science took off on its own, leaving the quadrivium behind. Biology, physics, chemistry
and the transformation of matter are all beyond the quadrivium (and so is art represented
in the quadrivium only, in a narrow way, by music). This widening gap between science and
the humanities cannot be overcome if scientists fail to understand and appreciate the raison dêtre of the humanities: what they
are about, what are their fundamental tenets, and how they can be judged and appreciated.
In turn, those who cultivate the humanities, if they are to regain their ability to
inspire and guide society, need to understand what science is about, its foundations,
processes and validity criteria. They also need to understand the activities that modify
The conflicts between humanities and engineering, the mother lode of
todays technology, are even more accentuated and evident than those between
humanities and science. For one, the engineering ethos of utility is perceived to clash
with the ethos of the humanities. The conflicts are extreme and asymmetrical. In most
liberal arts curricula there is no single course on engineeringon its role in the
scheme of things and on the nature of its methods. Hence there is little fundamental
understanding by the humanities of what engineering, this continuation of biology by other
means, is about, and of the purpose, impacts, processes, dilemmas and high dramas of
technology. This severely limits the ability of the liberally educated when confronted
with an engineering project, to address questions that are crucial to the avoidance of
technological determinismof the if it can be done it will be done, of a
world ever more technological regardless of consequences. Yet questions such as the
probability, nature and severity of the side effects of technology cannot be addressed
without the involvement of the humanities. Most engineers recognize the need for a
presence of the humanities in their college education (with some twenty percent of the
engineering curriculum in the United States devoted to them, in part also because of the
weakness of high school curricula) yet this does not seem to produce a true reciprocal
understanding. Clearly, this requires a far better integration.
An area where the humanities, science and engineering need urgently
to come together is the environment. If we are to be successful in reducing our mounting
environmental problems, science must continue to provide the knowledge, and engineering
the designs and artifacts for reducing environmental damage and ensuring the long-term
sustainability of our species. This cannot occur without the involvement of the humanities
in understanding what the environment means in our lives and of how it is affected not
only by technology, but also by human drives, emotions and ethical credos.
Science, Engineering and the Arts
It is almost inevitable that art as a great conveyor of myths (Campbell) and
science and engineering as great untanglers of mythsbut also the creators of new
onesoften would find themselves in conflict. However, the conflict should not be
irreducible, as history and a broader view of human evolution suggest. In the Renaissance,
art, science and engineering could still be combined in a figure like Leonardo, but they
eventually diverged and with that diversion came a mutual lack of comprehension. Today,
the aesthetic aspects of science again are being underscored by the new views of nature
made possible by scientific discoveries, as articulately expressed by Roald Hoffmann
(Hoffmann). On the other hand, the aesthetic impacts of technology, unlike those of
science, have always been evident, given the presence that
artifactsmachineshave in our life. But with the exasperating functionality of
mass production, an engineering appreciation of the aesthetic qualities of artifacts has
often come to be neglected. Recently, with structural arte.g., the view of a
bridge also as a work of art (Billington)and with the growing commercial importance
of aesthetics in automobiles and other functional artifacts, the time is ripe in
engineering for a renewed appreciation of aesthetics. Unfortunately, in the required
curriculum of our engineering schools, not a single course deals with taste, aesthetics or
style. Neither, for that matter, do arts curricula focus on the kinship of art and
engineering as modifiers of nature. The consequence is, much too often, human-made
environments with no emotional impact, that can benumb, rather than inspire.
Both artists and engineers create artifacts, that is, something that
did not exist before. In the history of modern man, artistic artifacts and fairly
sophisticated functional artifacts seem to have appeared in appreciable numbers at about
the same time, some forty thousand years ago. In spite of this connection, there are many
profound reciprocal misunderstandings. For one, the creativity of the modern artist is
unfettered, but that of the engineer is, by necessity, controlled. Art expresses emotions.
The supreme rule of engineering is rationality. This is not to say, however, that there is
no emotion in engineering and no rationality in art. It would be a terrible world if the
one were to prevail at the exclusion of the other. What we have rarely achieved is the
blending of the two, something that occurs today mostly in architecturebut even
there constantly pushed in one direction or the otheror in the design of automobiles
and some other artifacts.
A further source of conflict is the individuality of a work of art versus the potentially endless replicability of
many products of technology. Here again, a blending of individuality and productive
capacity could make for a less alienating world. For instance, new materials, the
incorporation of electronics, and the use of sounds to complement aesthetically the
functionality of structures, offer engineering a vast domain of possibilities. At the same
time, new art forms are being stimulated and made possible by scientific and technological
developments, as in computer art. This makes it possible to think of a new convergence of
art, science and engineering in a fusion of these three powerful mythmakers of our time.
An art that was freed from representational demands and given the possibility of
unconstrained creativity by the advent of imaging technologies like photography can now
converge again with science and technology. In turn, science and technology offer art new
creative possibilities enhanced by combining the functional with the expressive and the
Science and Engineering
That science and engineering are quite different was understood by Galileo but not by
Francis Bacon (Wolpert), a confusion probably stemming from the ignorance of the
mechanical arts in the medieval trivium and quadrivium.4
The connections between science and engineering are, of course,
obvious. The language of modern engineering is primarily math and science. In turn,
science not only uses the inventions and the instruments of engineering and
technologymetals, paper or the computerbut at times has been inspired by them,
as in the clocks influence on planetary theories, or of artillery on the development
of ballistics, or of the invention of the radio on the development of radio astronomy.
Thus science and engineering benefit each other and have complemented each other in
extending the human reach. But, as discussed, they have a different purpose, different
methods and different places in education. The touchstone of science is verifiable truth,
that of technologythe process in which engineering is
embeddedcost-effectiveness. Science literacy has often ignored technology literacy,
viewed erroneously as simply the application of science. The conflicts arising out of a
different purpose are evident in issues such as the drilling for oil in Alaska, or the
direction of our space endeavors.
What Should An Educated Person Know?
The exclusion of the medieval mechanical arts from the university education based
on the trivium and quadrivium has roots that go back to classical Greece. When Plato
identified three ascending stages of human development through education, he missed
technology, that is, the power to modify the physical and biological world. (One might
speculate whether, because of the absence of the archeological and anthropological
knowledge we possess today, he could not possibly have had a sense of the crucial role
technology had played in the emergence of humans and in making life in Greece what it was
at the time). Plato considered only the perception of beauty and good, that is mainly the
humanities, the power to reflect, that is the foundation of philosophy and of what today
we would call science, and the elements necessary to make rational decisions, that is,
again, in his time, mainly philosophy. The absence of an explicit sense of the importance
of machines and technology is manifest even today in the architecture of
E.O. Wilsons consilience (Wilson).
The crucial questions for our culture are, what is it, indeed, to be human,
and how can we maintain and enhance our humanity as we develop ever more revolutionary
scientific advances and our ever more powerful and pervasive societal organizations and
processes and machines? To answer, we need to understand the indissoluble complex formed
by us as biological organisms, by the society around us, and by the machines we have
createda complex that, in short, could be called the biosoma (Bugliarello). Although there have been
countless attempts to differentially characterize the three biosoma entities, we still do
not quite understand their interactions and we are still confused as to the essence of the
most recent of the three components, the machine. Recognition of the nature, potential and
pathologies of the biosoma as a whole and of its components remains, by and large, terra incognita and will continue to be so until we
come to face the possibilities of human cloning, self-reproducing machines, or
irreversible loss of privacy.
The different characteristic of the performance of biological
organisms, society and machines further illuminate the basis of the conflicts between
liberal arts and science or technology, as well as between art and engineering. Biological
organisms, as well as society, are of a semi-definite nature, in the sense that, in spite
of all the advances of our biological and social sciences, their behavior or performance
cannot be exactly predicted, at least for the foreseeable future. Functional machines, on
the other hand, have a definite performance; they can be trusted to respond exactly, if
well designed, to the intent of their creator. Artistic machines, such as a painting or a
sculpture, could be called artifacts of indefinite performance, because their creator can
never really know how they will be perceived by those who view them.
In their long existence on Earth, living organisms have had the
benefit of the crucible of evolution, unlike the machines we humans are creating, as their
emergence has been simply too rapid. Thus, if developed with inadequate social controls,
machines could threaten our survival through their power and ubiquity, the very qualities
that make them so useful to us. In this terribly complicated world we have created, we can
remain in control only through the development of a moral sense based on three solid
understandings: what science can tell us, what rules and instruments our society needs in
order to guide wisely the modifications of nature and the creation of machines and what
engineering can and cannot do. The sum of these three developments is exquisitely human
and should be a cornerstone of a truly liberal education. Other animals may only know,
instinctively, without reflection, what is strictly necessary to their survival and obey
some social rules. They may also, instinctively, modify nature, as when they build a nest
or use a sticksimple machinesbut they cannot build on the immense scale we
humans can, as they lack the rational method of science and the complex machines of
engineering. And they have no conception of spiritual and aesthetic canons and of a
A New Trivium and Quadrivium
An education cannot be called truly humanistic if it fails to look at humans in
the context of the evolutionary history of the biosoma and its projections into the
future. The heritage of the medieval trivium and quadrivium that remains at the core of
our humanities education is simply inadequate to do so. To be sure, to pose and attempt to
answer questions such as what role art, literature or history play, or should play in our
lives, is essential, but it is not enough. There are other questions, from the nature and
the implications of an explosively urbanizing world to cloning, that are equally essential
to the future of our civilization but demand a cultural
understanding of science and engineering, that is, of how and why we go about learning
about nature and modifying it. The consequences of that dearth of understanding are quite
evident in the long sweep of time from Roman times to the Middle Ages. In that period the
lack of focus, for instance, on remedies to adverse manifestations of nature, and on
infrastructures for public health, contributed to the lethality of the pandemics that
arose repeatedly with terrifying impact. Today, with over six billion people crowding the
globe, with the accelerated alterations of our environment, and with the creation of
weapons of mass destruction, those consequences can be far more serious. In dealing with
the human-made world around us created by science and technology, it may be charming, but
terribly confining and crippling, to have to say, like Rebecca West,
always troubles me because it reminds me that in this mechanized
age I am as little able to understand my environment as any primitive woman who thinks
that a waterfall is inhabited by a spirit, and indeed less so, for her opinion might from
a poetical point of view be correct. I know enough to be aware that this bridge cannot
have been spun by a vast steel spider out of its entrails, but no other explanation seems
to me as plausible, and I have not the faintest notion of its use. But the man that comes
down the gangway of the ship
him I can understand, for he is something that is not
But if education in the humanities needs to be greatly broadened, for
the same reasons education in the intellectual and moral faculties must be required of
those who endeavor to understand and modify nature. The medieval doctor was steeped in
both sets of faculties, but his goal (there were no women doctors at the time) was
primarily to influence the course of a disease, that is, to modify naturethe only
facet of the physical modification of nature that was included in the universities at the
time. Today, given our enormous scientific and technological powers, the potential
consequences of not having a clear and widely agreed upon sense of the ethical and
humanistic imperatives that must guide those powers are, again, enormous.
Ultimately, the most fundamental source of conflicts among the
different domains of knowledge and of our inability to benefit from their potential
confluences is a lack of integration, pragmatically and philosophically. What is called
for is a new conception, a new trivium and quadrivium, propaedeutic to all specializations
and infused with that sense of the future that was absent from the medieval one and
continues, by and large, to be absent today. A new trivium is needed to provide every
educated person with a basic understanding of the endeavors and instruments that help us
address our worldthe humanities, (in the noblest sense of the word) to civilize,
science to understand nature and engineering, broadly defined, to encompass the kindred
activities that modify nature. The interaction of these endeavors and instruments shapes a
new morality, which cannot be defined as the domain of a single discipline or set of
disciplines. And each of these endeavors and instruments involves, in turn, an intimate
interaction of biological organisms, society, machines and the environment. Thus a new
quadrivium is needed to complement the trivium, to provide an understanding of this
biosomic context of our life, starting with the quintessential biosomic nature of the
fountainhead of civilization, the city.
It could be argued that a drastic rearrangement of our education is a
desperate and even counterproductive enterprise (Rosenzweig). Certainly it is an extremely
difficult one, but without a new vision and the will to make it reality, we will
perpetuate divisions and forego opportunities to the ultimate risk of our civilization.
There are obviously many ways to conceive of a new foundation of
education, of a new trivium and quadrivium. However structured and labeled, its essential
feature must be integration, the weaving through each subject the influence of the others.
No domain can any longer be considered in isolation, as it is a piece of a profoundly
interacting whole. As written on the inscription of the National Museum of American
History in Washington, James Smithson was well aware that knowledge should not be
viewed as existing in isolated parts, but as a whole, each portion of which throws light
on the other
narrow minds think nothing of importance but their own favorite pursuit,
but liberal views exclude no branch of science or literature, for they all contribute to
sweeten, to adorn, and embellish life.
- There is still confusion about the terms engineering and
technology. One could say very simply that engineering is related to technology in the
same way that medicine is related to health care. So they are not synonymous, but today
one implies the other.
2. I define here the term machine as synonymous with artifact, a
creation of humans, or more generally, of biological organisms. It is so general that it
encompasses both functional artifacts such as a computer, and artistic ones, such as a
painting. The creation and use of machines by a number of animals (e.g., beehives and
birds nests) predates the machines created by humans, but only with humans it has
reached enormous intensity and sophistication.
- as manifest in myriads of expressions, such as
crystallize, she has good genes, the whole nine yards,
all steamed up, zoom, flying by the seat of your
pants, being on autopilot, carbon copy, full speed
ahead, pedal to the floor, full throttle, xerox
copy, being programmed, coasting, rev up,
straight shooter, cliché, explosive personality.
- However, the terms science and scientist are not synonymous.
Neither are engineering and engineer. In pursuing their goals, scientists may need to do
engineering, e.g., by creating devices, and engineers to do science, e.g., in
endeavoring to understand the dynamics of a river to be bridged.
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