POWER AND PEDAGOGY:

Transforming Education through Information Technology

By Robbie McClintock

Cumulative Curriculum Project Publication #2

Institute for Learning Technologies
New York, 1992

Copyright © 1992 by Robbie McClintock
All rights reserved

This book is produced and distributed in device independent format.

Readers are free to copy the electronic text and to reproduce copies by other means for critical, educational, or scholarly use, provided they do not alter the text or distribute bulk reproductions for profit.

Institute for Learning Technologies
Teachers College, Columbia University
525 West 120th Street
New York, NY 10027-6625

To Moira,
for the example of her growth and maturation,
and to Max,
who has read, encouraged, clarified, and cajoled,
and best of all, who has inspired through her precept and example,
the effort to pack compelling force into a trim form.

Contents

Chapter 1: A Perspective on the Task

Chapter 2: The Computer as a System

Chapter 3: The Educator's Mission

Chapter 4: The Span of Pedagogical Possibility

Chapter 5: Making a New Educational System

Chapter Six - Education and the Civic Agenda

Appendix

Preface

Educators propound reforms, but schools remain the same. Without material agency, new methods fail. A scheme captures the educational imagination -- spokespeople think it out, the daring to try it, researchers document its effects, and the committed demand its adoption. Thus, the idea diffuses from various centers -- but then, sporadically, resistance builds, enthusiasm falters, influence weakens; ineluctably, distinctive practices gravitate back to the norm. Pedagogical weathering soon makes the new shingles indistinguishable from the old.

Without political vision, technological innovation leaves the quality of life unimproved. Anticipations of future technologies depict wondrous tools for living, but then culminate with "a day in the life," usually a banal office routine with little at stake that was different from what would be at stake in the corporate office anywhere today. Such visions do not inspire people to solve human problems old and new, to join together with shared hopes and historic aspirations, enabled now to act on issues hitherto in- accessible to the common weal.

We need to join pedagogy and power. Educators inspired by visions of human potentiality need instruments of action, substantial agents of change, with which to work. Technologists creating new means for bringing intelligence to bear upon the work of the world need a civic agenda, a vision of historic possibility, consciously espoused and responsibly defended. Without power, educators will continue cloaking their delivery of lame services in high-minded impotence. Without pedagogy, technologists, bleating complacent corporate compromise, will recreate the injus- tices of the contemporary world with the new-forged tools that might otherwise transcend it. Educators need power, not purity; technologists need vision, not predictability. Together educators and technologists have the historic opportunity to improve the civic prospect -- that is the message of Power and Pedagogy.

Chapter One - A Perspective on the Task

Let's look ahead. In the twenty-second century, how might an historian of education sum up the major changes in pedagogical practice over the sweep of time? Imagine that we commission Elizabeth Ironstone, leading authority on the computer as an agent of change, to study these changes. She reports, not in the multimedia of her time, but in the prose of ours. This might be her executive summary, introducing Toward the Educative Polity.

###

Through most of history, education was a loose system of ap- prenticeship and indentured service in households, the main loca- tion of productive activity. Those who wanted their children to be- come learned employed tutors to help them out. A few schools ex- isted within specialized institutions, such as cathedral priories and monasteries, but these were not like the schools that eventually proliferated, for students were not divided into classes or grouped according to age.

Around 1500, a major pedagogical transition began as printing with moveable type made an unprecedented era of educational development possible. But the transition was not a quick and simple change: to bring it off, innovators had to develop a complex of different, yet interrelated, educational strategies, which together eventually made mass schooling for all a practical reality. Key steps in this process involved:

These developments were tightly interrelated. The transition required the integration of complex factors into a functional system: the design of educational space and time; a chosen pattern of educational motivation; pedagogical materials suitable for use in such places with such motivations; methods of instruction suited to the organization of the cultural materials, teachers adept at using such tools and strategies; and arguments demonstrating that the substantial costs of it all were worthwhile -- all were simultaneously essential to the historic transition to mass schooling.

Sixteenth-century educational reformers worked out integration of these six, interrelated matters. For five hundred years, educators perfected, expanded, and developed the basic components of the educational system introduced early in the era of print, in due course creating modern systems of universal, compulsory schooling. As the degree of elaboration and penetration of the system into society changed, the specifics justi- fying the effort evolved to stay synchronized with cultural trans- formations. The main features remained stable, however. The design of the classroom and the organization of the school day, the motivational strategies employed, the scope and sequence of textbooks, the definition of good teaching practice, and the rationales for public support remained very stable. The reason for the underlying stability was rather simple: throughout it all, the character and limitations of printed textbooks remained substan- tially fixed, the keystone of the system.

We who inhabit the electronic ethos of the twenty-second cen- tury must remember that early in the twenty-first, the function of printed materials changed rapidly, becoming restricted to their current role of verifying and guaranteeing standard data sets when the electronic versions possibly could be altered. Before then, physically printed materials had a more central intellectual function. For five hundred years, books were the unmatched resources for making ideas, knowledge, and culture available to students, and so long as this role was unquestioned, educators paid little attention to how the characteristics of books shaped the whole instructional enterprise. But during the last half of the twentieth century, diverse innovations in communication and computation occurred, displacing books from their privileged educational position and creating our current, electronic means of access to cultural achievements.

From our vantage point, we can see how the microcomputer, and all its attendant peripherals, quickly matured into powerful multimedia systems. They thereby created a significant historical dilemma for educators at the end of the twentieth century. How were educators to make use of these new resources? Did the existing educational system comprise permanent, necessary arrangements? Should schools remain forever a system of classrooms for twenty-five children, of similar age and talent, overseen by a single teacher, learning set subjects that had been divided into lessons, competing for grades and recognition? Were these arrangements historically relative accidents, sensible in one communication context, but perhaps vestigial survivals in a new context, with distorted functions? In planning computer-based edu- cational efforts, what should educators take as givens that would remain stable, before and after the introduction of powerful infor- mation technologies?

At first, this question was not clear to educators. Early users of computers in education simply assumed that most features of the given system would remain stable, only getting better through judi- cious use of the new technology -- with a good deal of divergence, we might add, over what "better" might mean. There was an initial wave of enthusiasm, and a strong undertow of skepticism, and lots of ingenious, but encapsulated, efforts to incorporate computers into the educational system. Through such efforts to introduce computers into late-twentieth-century schooling, educators became increasingly aware that the then-existing practice was a complex technical system highly adapted over centuries to making use of books as the prime medium of cultural exchange. Encapsulated innovations repeatedly engendered inflated expectations and produced disappointment and disdain.

Unfortunately, the old system had spawned a huge establish- ment of educational research, which functioned to optimize tech- niques and programs within the given system. Almost all its methods for measuring results were system-specific: they assumed that existing divisions of subject matter were the appropriate domains for testing, that standard grade-levels were fit bases for norming results, and that verbalized information was the prime indicator of learning. The bias of such research helped to protect the existing arrangements from systemic changes.

To organize education to exploit the possibilities of an electronic media for cultural exchange, possibilities far more powerful and flexible than the printed media, educators had to rethink the system as a whole. They needed to take none of it as a given that would necessarily persist, unchanged, from before to after the in- troduction of computers. Further, to assess a new system, relative to the old, they had to develop a whole new type of educational research, one that did not presume, in its standards of testing and measurement, that structural accidents of the old system were educational necessities of timeless applicability. The full, fun- damental re-examination of educational options, and the methods for assessing them, began in the 1990s. It initiated the second historic transition in educational practice.

Looking back from the twenty-second century, the results of this re-examination are clear. Educators began to explore new solu- tions to all aspects of the existing system. They stopped applying computers to the educational strategies that had been developed in the early era of print. Instead, they started to search for edu- cational strategies that seemed sensible in an era of digital informa- tion technologies.

These developments took shape in the decade preceding and following the year 2000. Educators gave up trying to introduce new technologies into the established system and they thought out an alternative system, which ineluctably displaced the old one. They came to call it the Cumulative Curriculum, and one of its pioneers, the educator Frank Moretti, described it this way:

We seek to replace the superficial traveler through the sequential school, who collects knowledge trinkets to memorialize each stop on the cultural itinerary, with the philosophical explorer, whose very search for knowledge is a search for self and community. The word cumulative points to the growing personhood of the child. As the Latin indicates, it is a "heaping up" within. Able to instantly access the totality of his work through time, the child has control of his intellectual history as a series of understandings rather than the usual cryptic external judgments symbolized by [grades]. Accordingly, a child need not see each year as a separate beginning but rather as a continuation of a substantially accumulated educational reality, which is his currency entering a new year. The challenge for the child is to understand his rich past and to plan a series of strategies for moving to the next stage. He chooses his educational future in the context of the world within him that he has already shaped and formed. In this context, adults have to give up the security that comes from pretending to know precisely what it is that children ought to learn, by year, by subject. . . . The child begins with his own rich world, which is the starting point of all inquiries. . . . He understands that the art he will master is that of the tentative hypothesis, the value of which is determined by the degree to which it has to the power to explain. What the student of the cumulative curriculum will perceive as "learned" are formulations whose parenthood is not in doubt. Clear about his ownership and authorship, he will perceive all that he knows as the immediate horizon of his all-too-human vision and will seek to extend it, to glimpse a new world and form new understandings that embrace the old.

Once tried, this effort to help student's take possession of their own learning, to "heap it up from within," succeeded rapidly. Old sequential school systems, which had seemed impervious to change, rapidly adopted the cumulative curriculum. Since its initiation at the turn of the twenty-first century, of course, the new system has evolved steadily, more and more thoroughly displacing the vestiges of the print-based educational system. The results have been liberating and profoundly progressive.

Democracy, which had been, for the most part, a predominantly political development through the twentieth century, has gained a substantial cultural import. The persistent tendency of print-based education to reproduce and accentuate differences of power, privilege, and wealth has been decisively reversed. The digitization of the culture has been thorough and with it participation in its full powers has been decisively broadened and tools that strongly amplify human powers of calculation and control have become accessible to nearly all. The great twentieth-century aspiration, verbalized by John Dewey through Democracy and Education, has become substantively fulfilled, although in an environment of pedagogical practice quite different from any he could then imagine.

Shortly before the year 2000, a long era of international tensions and war, in which national defense had been the prime function of the polity, ended. Peoples of the major nations turned their energies more fully to nurturing their human potentials. The relaxation of tensions coincided with the development of the new media of education. Liberal reformers regained a sense of their efficacy and people became increasingly confident that they could at last solve the long-standing human problems of industrial democracy. As the third millennium began, the idealistic conviction of some, that each person has a stake in the welfare and fulfillment of all, deepened into a general common sense. Material conditions and cultural convictions converged to provide the historical grounds for the worldwide educative polity.

###

Our informant from the future depicts an alluring vision, one that we may be tempted to dismiss as too optimistic. But these are times of extraordinary potential and extraordinary change. Educators should not face them blindly, recapitulating past expectations and assumptions. However solid seeming, our educational structures are historical creations subject to thorough transformation through the subsequent dynamics of continuing historical change.

Our informant from the future draws our attention to the need to look at the whole educational system in considering how to introduce information technologies into it. A basic proposition provides the generating principle of this essay: in order to have substantial effect improving education, the digitization of our culture will need to elicit a full systemic innovation in education, one that changes not only the medium of cultural exchange, substituting digital code for print, but the entire educational context for working with that medium.

In the chapters that follow, I advance a case that systemic innovation in education is both desirable and possible. I do so by essaying answers to some large questions:

Chapter Two - The Computer as a System

Computers are like wheeled vehicles: they come in many shapes and sizes, each serving a different purpose. Moreover, the computer has yet to mature. It is an emerging technology. Hence, to determine the potential of computers in education, we need to understand what the computer is. To start, consider two distinctions, one between transitional and mature technology and the other between artifacts and systems.

Complicated technologies take a long time to develop their potentialities. They also take capital. Developers cannot perfect their technology in endless years of laboratory work and then deliver it, refined and complete, to a grateful public. To underwrite the costs of perfecting a technology, developers must bring it to market long before it is mature. Profits from transitional implementations sustain the development work, providing resources and disclosing unexpected opportunities for use. Computers have exemplified this drawn-out development: computers have evolved through several distinct, quite profitable incarnations, yet neither the time-sharing mainframe nor the stand- alone micro indicate fully what the computer will be when the technology matures.

In common speech, we generally do not distinguish between typical technological products and the technical systems that make them usable. For instance, "television" can refer to the TV set, that ubiquitous appliance, or to the whole industry -- the networks, their broadcasting installations, the news teams and production studios, advertisers, and all. Likewise, "automobile" can refer to the car in my driveway or to the vast infrastructure -- the manufacturers here and abroad, with their suppliers, advertisers, and dealers; all the roads and bridges and the builders constructing and maintaining them; the service stations and oil producers, refiners, and marketers; and the myriad of designers, workers, police, and service people who make the system go. The car is both a separate artifact and a complex system.

Currently, "computer" usually calls to mind the artifact, the stand-alone personal computer, like the one on which I am now writing. Most of us do not think much about the complex system of which my PC is a transitory part. Computers as a system are important, however. The significance of computers for education will not be well understood by thinking simply of a lot of separate machines sprinkled through existing schools and colleges. Computers are an emergent infrastructure, a system, fully as complicated as that of the car. We need to think about what that system is and how that infrastructure will work. Computers as a system can be a powerful agent of change in education.

To grasp the computer as a system, particularly as it matures, let us concentrate, on neither hardware nor software, but on an underlying process, the digitization of information. The computer, as a system, introduces a new way of representing information in our culture, a new way of encoding ideas. When complete, it will constitute a deep transition in our history, one equal in importance to the introduction of printing, quite possibly to the development of writing itself. Essentially, the computer as a system will envelop all previous modes of representing information, preserving and empowering them by integrating once separate domains of communication into a unified, "multimedia" system.

Information in Matter and Energy
Think of the ways we commonly represent information -- a scribbled note, a neatly printed page, a reflective sign, a painted picture, a ruler uniformly marked, a measuring cup, or the symbolic forms of church or court. With these, people have encoded ideas and information in material objects, in the ink upon the page or the shape of the sculpted stone. Put most generally, through traditional ways of encoding ideas, people expend energy to transform matter in ways that they will find meaningful, making enduring marks and forms in which ideas inhere. People locate the information in the material object. When they do this according to a defined convention and art, the tangible, palpable results are our major forms of traditional communication -- documents, sculptures, pictures, monuments.

Starting with the telegraph and developing through the telephone, radio, television, and computer, people have begun to put their information into controlled pulses of energy itself. The material object, say the telephone, becomes a kind of transparent medium for an infinity of possible conversations encoded in different electrical waves that the phone will generate, transmit, and receive. Increasingly people are representing information in controlled states of energy, not in matter, as they did traditionally. The new practice requires various material tools, with which people apprehend on their human scale the information located in energy, but the information is not in the material, but in the energy. Thus the TV translates the information bearing energy into a material form that I can watch. The picture hanging on my wall is what it is because the information that it contains is in the material that makes it up. My TV, in contrast, can receive an infinity of images because the information it displays is not in the material of the set, but in the electromagnetic waves that it picks up and decodes for me.

This practice of locating information in energy states is not entirely new in our culture. One can take sound to be a form of energy, not a state of matter, and hold that through speech and song people have long encoded information in energy, using the ear as the naturally developed, material receiving apparatus. Other senses, too, especially sight, kinesthesia, and the ability to feel hot and cold, derive much information from energy states and forms of force. Some traditional tools of communication and control also provided readings of the information in energy states. The clock measures time by controlling the release of energy in uniform units. The compass provides a most informative reading of the orientation at any location of the earth's magnetic field. The governor on a steam engine directly translates a change in its energy state into a controlling action. Like the TV -- but unlike the painting on the wall -- clocks, compasses, and governors all inform their users through their changing readings, not through their static states. More strictly speaking, these instruments display information that is fortuitously located in states of energy, rather than encoding it in those states. Traditionally, only the voice and musical instruments went beyond display to encode.

Up until very recently, information encoded in energy has been, however useful and dynamic, troublesomely transient. Speech is the paradigmatic instance. It is powerful and nuanced, yet fleeting and unstable. For a time memory preserves its residue, and writing fixes a stiff representation of it in stable matter. But much is lost. This transience also characterizes many modern media that encode information in wave forms, substituting electricity for sound as the energy medium. Thus telephone, radio, and television have enabled people to encode sound and gesture in electromagnetic waves, amplifying these vastly, without making them much more enduring. Recording signals on tape and other media makes such material reproducible, and thus enduring. Yet this has been a recent, ancillary development. So far, the power of electromagnetic media has resulted from the breadth of their transient reach, not from the ease with which productions can be reproduced.

This transience of electromagnetically encoded information fundamentally affected the usefulness of broadcast media for education. Entertainment results from encountering cultural experiences for their immediate, present value -- they amuse, inspire, absorb, purge, distract, or release us now. Education involves us with cultural works of enduring importance -- we acquire skills, ideas, beliefs, knowledge, information that will empower us over time in the conduct of life. The things at stake in education are the elements of the culture that are on-going, lasting resources. Consequently, the educationally important media are the ones that represent and make such enduring ideas and skills available to people. For the most part, these have been the media that locate information in material objects, particularly in printed texts and pictures.

Commentators complain that educators have done little with the major communications developments of the twentieth century. Despite high hopes, radio and television have not become important educational resources and some infer therefore that education is resistant to technological change. This inference is wrong. The photograph, which extends the pictorial capacity to locate information on film and paper, has been seamlessly incorporated into education. It improves the capacity to work with lasting ideas and information, and educators have quickly adopted photographs in the processes of research and instruction. As conservative a field as art history took without hesitation to 35mm color slides because they served the intellectual needs of the subject. So too, recorded music has become a natural part of music education, far more so than have broadcast performances, for the recordings are stable, enduring resources that different students at different times can study, each with unique purposes in mind. Recordings suit the needs of education because they are stable, easily stored and retrieved, while broadcasts suit the needs of entertainment, absorbing us in their immediate presence.

Educators cannot resist new technologies, provided those technologies have characteristics suitable to educational purposes, foremost among those being a permanence in time. Stop for a moment to consider film, which encodes information in stable, material form yet has not come into robust use in education. Is it an exception to the rule here propounded? No. With respect to dissemination and retrieval, film is not as stable as it might seem. Film is bulky, hard to store, costly to project, and easily damaged. It can be best disseminated in a quasi-broadcast fashion with prints distributed to numerous theaters more or less at the same time, with the production playing as long as it can command a full audience and then disappearing into an archive, from which films are not easy to retrieve. These distribution constraints have made movies, until very recently, far more effective as media of entertainment than of education.

Computers as a system will change that, and much more. Broadly speaking, the communication innovations since the mid- nineteenth century have created a family of technologies for encoding diverse forms of information in energy. The computer is the most recent in this series of innovations, and it is likely, historically, to incorporate all those leading up to it into itself. What seem to us to be separate industries with separate technologies will become branches of a single comprehensive industry and technology, the computer as a system.

One can now see large corporations jockeying to capitalize on this consolidation of technologies. For instance, the major Japanese electronics firms seem to be calculating that they can best shape this process by combining business communication with the entertainment industries, buying up major entertainment conglomerates while designing ever-more computing power into home entertainment devices. The emerging system, however, may in fact be far more robust if built on a combination of telecommunications and education. Digital technologies enhance the staying power of information in time, expanding its educative power relative to its currency as entertainment. We will be developing the thesis that the computer is rapidly incorporating the modern media in one comprehensive system, a system of knowledge and education.

The Analog and the Digital
We distinguished between technologies that locate information in matter, for instance sculpting and printing, and those that locate it in states of energy, for instance radio and computers. Among the latter, we need to make important further distinctions, which have to do with the techniques people use to encode information in energy. To grasp the cultural import of the computer as a system incorporating all the media of communication, to appreciate its potential power, we need to reflect on the way that it encodes information in energy, seeing how that differs from other techniques.

Analog coding serves effectively for some specialized computational purposes, but almost all computers, from tiny palm- tops to huge supercomputers, work with information stored in digital code. Such digital code differs profoundly from the analog codes used typically in radio and television. In the paragraphs that follow, we will reflect on how digital code differs from analog and then consider five matters that determine the value of information for human activity -- production and reproduction, storage, transmission, selective retrieval, and intelligent processing. Through these considerations, we will form a sense of why the computer, as it matures, will be a very significant step in our history.

Note at the outset that we could apply this distinction between analog and digital coding to the media that use matter to carry information. For instance, painting and sculpture are highly analog media, whereas alphabetic writing is interestingly ambiguous. It is analog insofar as it is phonetic and digital insofar as it is a prescriptive set of legible conventions. But it would take us afield to pursue these distinctions with respect to media that locate information in matter, for our concerns here are primarily with the media that carry information in energy. How does the digital coding of information in energy differ from the analog?

Analog systems encode information in energy by using the properties of continuous waves so that each successive change in the amplitude of the wave will be analogous to a change in sound or appearance in the human world. Lets construct an example. Take a dishtowel. Holding each corner of one end in each hand, flap it rhythmically in front of you, making it undulate up and down. It is not hard to control the beat of the flapping, making each flap identical in duration, perhaps slow and long or quick and short. That beat is like the frequency of an analog signal. Usually it does not carry the information, but when we are surrounded by many different signals, each with a different frequency, it allows us to find the one signal we want. Observe the flapping towel, however. From beat to beat, it will have all sorts of variations, curving this way then that, depending on subtle changes in the orientation of your hands to each other and the tension they put on the cloth. If you could control the flapping skillfully enough, you could make each change in the way the towel undulated match some other, analogous change in a completely different wave, say the ever changing sounds of a symphony or rock concert. At that point, you would have encoded the concert in the flapping towel rather like the way radio encodes a concert in an electromagnetic amplitude or frequency.

Like the sound itself, the flapping is transient. Analog encoding depends on making significant changes in the energy state of the wave, a most unstable phenomena. Digital encoding is much more stable. Put down the towel and flip the light switch on the wall. The switch has gone from "on" to "off;" it was stable in its former state and is stable in its latter. The light switch is a digital device, although one that does not accomplish much in the way of communication and control. To see simple signals controlling more complicated processes occurring around you, look at another digital switch, the stoplight at the corner. It has two basic states, red or green -- amber is not really a state, but a cue that a change of state is about to happen. There are two unambiguous states, green-go, red-stop. These are easily standardized, stable, and remarkably effective in controlling complex flows of matter and energy. The stoplight is very much like the small charge in a transistor in that one state allows traffic to move and the other calls it to a halt.

Our basic red-green stoplight is a binary digital system -- binary because there are two alternatives and digital because those consist of discrete, unambiguously different states. The typical electric stove, with options on each burner running from warm to high, has a quinary digital control on its coils -- quinary because there are five alternatives and digital because each of these is distinct from the others. Thus, digital systems can in principle have different numbers of basic alternatives, but computers almost always use a binary system, building many subtle variations from a multiplicity of either-ors.

A digital state is what it is, discrete, unambiguous, disjunctive. Digital code does not capture changes similar to other changes, it presents a set of values that are what they are. Digital coding follows a principle akin to encrypting -- there is only one message, which, when encrypted, is put in a way that makes it look indecipherable. With the appropriate key, however, the cryptographer finds the message, not something like the original, but the original itself. For instance, the apparatus for recording music digitally measures sound frequencies at successive instances and records the numeric value of the frequencies. These are samples of the actual sound, not likenesses to it. Digital coding samples a phenomenon, registers the sample, and then reproduces the phenomenon from the sample. If the sampling technique and the technique of reproducing from the sample are very good, it can be extremely hard to distinguish the original from the reproduction. What is coded is an exact value, precisely what it is and nothing else.

What is encoded digitally, therefore, is actually very different from what is encoded in an analog system. The digital system encodes a sample of the thing whereas the analog system encodes an analogy to it. Again, let us construct an example. Consider a full wheel of cheddar cheese. Describing the cheese by analogy can be difficult. I might say it is about the size and shape of an old-time hatbox and that it is heavy, as if the hatbox were filled with water. Its color is like custard and it tastes -- this is the important, difficult part -- somewhat like grapefruit, although its texture in the mouth is very different, a bit like a firm fudge that crumbles and then softens into a paste as one chews it. Describing the cheddar by a sample of it is much simpler. I cut you a little piece, perhaps several from different places in the wheel. The sample is the cheese and you can sniff it or taste it directly from the sample.

When we digitally code the sample, we register what the sample is on an appropriate scale and we code that value, not some approximate likeness to it. Consider recording a singer's voice digitally. At numerous intervals the recording samples the exact sound frequency of the voice, registering in a matrix of precise values what, at each sampling instant, the frequency was. The digital recording carries no information about the voice during the intervals between the sampling instants, but it carries the exact frequency of it at those instants. If the sampling frequency is sufficiently rapid, the sound of the reproduced voice will be essentially identical to the original. Digital code allows the playback to reconstruct the voice. Thus, digital coding registers sampled values, not approximate similarities. That is its first point of difference with analog coding.

Secondly digital code differs from analog because it resists degradation far more effectively. Electrical systems, like everything else, are subject to entropy. Every circuit has in it random fluctuations. Computers are not wondrously free of such static. Minor fluxes are a big problem in analog coding because the locus of information is in tiny incremental differences in the amplitude of waves, which the random fluxes in circuits can easily affect. In the absolute, digital systems are equally subject to noise, but the locus of information is in the basic energy state, not in small changes of that state. When the significant point is simply whether a circuit is on or off, it allows for a huge threshold before an intrusive fluctuation will become significant, making a circuit that is "on" appear to be "off" or vice versa.

To construct an example, consider a binary test for whether or not it is raining: looking out my apartment window to see if the sidewalk is wet or dry. This test is subject to noise -- perhaps in this case we should call it "splash." During the summer window air-conditioners in the building adjacent condense water on hot, humid days, splotching the sidewalk. Also on the road on the other side there is a low spot where water collects from a leaky hydrant and occasionally passing cars splash it onto the sidewalk. Like the noise in the electrical system, extraneous wetness sometimes partially covers a dry pavement. This rarely confuses my binary test, however, because I establish a threshold -- it is raining if the sidewalk is fully, uniformly wet and it is not raining if the sidewalk is dry, or partially splotched from random sources of water. Given the substantial threshold possible in a binary system, very, very rarely will electrical noise cause the misreading of a bit of information.

In sum, in comparison to analog coding, digital code registers values that are attributes of the thing being coded, not likenesses to it, and those values, once coded, will be remarkably resistant to error or degradation. These characteristics make digital code immensely useful in processes of communication and control.

Digitization and Communication
Digital code records samples of phenomena, not analogies to them, and it does so by techniques that are remarkably stable and accurate. By themselves, these characteristics may not seem so extraordinary. But put in context, the context of human use, they have very significant effects on the computer as a communication system. Whatever the medium, in order to communicate people need to be able to produce and reproduce information, to store it, to transmit it, to select among it, and to process it intelligently in the course of action. These five areas determine the relative historic value of different communication techniques. Reproduction, storage, transmission, selection, intelligent action: communication techniques that perform these functions well serve human needs well. Because digital coding registers samples of things and because it resists error and degradation, it has interesting effects in each of these five areas. These effects will determine how the computer as a system can contribute to our unfolding cultural history.

We begin with the problem of producing and reproducing information. What sort of information can one produce with a typical analog medium, audio tape, for instance? The answer defines a wide range of matters -- anything that can be recorded through an electromagnetic analog to sound within certain frequency ranges -- an aria but not a painting, a speech but not a balance sheet. The analog techniques used in the audio system must be closely coupled to the phenomena they record so that the way they modulate electromagnetic waves is precisely analogous to the particular wave patterns they are recording. To use the audio system to record images or the financial transactions of a bank, complex and careful adjustments need to be made in it, radical adjustments that convert the audio system into something quite different. Here the constraints of the analog medium limit the sort of information the system can record. With the digital system, we can produce a much more flexible range of information. As a result, digital coding can absorb both the analog media for carrying information in energy and many of the more traditional media that carry information in matter. For instance, the most familiar digital application now is word processing, enabling people to manipulate electronically the material system of writing with far greater flexibility, precision, and ease that traditional means have availed. In due course, anything that we can represent with a symbolically coded sample, we can record in a digital system.

It is not a trivial task to implement this potentiality. But it is inexorably happening. The first wave of computer uses involved diverse numerical applications. The microcomputer extended these and added extensive textual applications. Recently software designers have incorporated two-dimensional graphics into many programs for general use and three-dimensional imaging for special needs. Supercomputers have begun to record vast samplings of extremely complex phenomena that were simply beyond the ken of analog media -- climate change and molecular structures, for instance. With compact discs, the audio industries have developed and marketed the digital recording of sound, which is fast being incorporated into computing systems. The television and computing industries together are rapidly generating digital systems for producing and recording moving images. Techniques for sampling nearly all the forms of information and capturing them in digital code are quickly developing. In its basic sense, the concept of "multimedia" is this practice of integrating in one system all forms of producible information. When we speak of the computer enveloping other media and incorporating them into itself, we mean the capacity, unique to digital coding, to produce and reproduce many different forms of recordable information. Multimedia implements this capacity.

The difficulties in implementing multimedia are not primarily "technical," in the layman's sense of the term. Ordinarily we think that the technical problem lies in designing an apparatus to accomplish a novel purpose. In many areas, making the apparatus is relatively simple, and it can be done in numerous different ways. What is difficult is setting a controlling standard that will establish agreement on which one of the possible ways to design the apparatus will be the one put into common use. This is in part a question of technical standards -- for instance, what sampling rates will be standard for digitally encoded sound or what screen resolution will be standard for digital high-definition television (HDTV)? But the problems of controlling standards goes far beyond the domain of technical standards -- long established branches of law and language are at stake as well.

Thus, the production and reproduction of information is not simply a technical process. It is a process controlled by law and driven by incentives. Digital coding of information will affect these domains as well. For instance, copyright makes sense in a system in which people locate information in material objects -- copying consists in expending the energy to implant the information in matter, preeminently by putting ink on a page. Copying information that is located in matter is a laborious, error-prone process, subject to legal processes. Recording and reproducing information that is located in energy has very different characteristics. It becomes extremely inexpensive, with the result that it can be done ad hoc by anyone who possesses easily available, inexpensive tools. Already, spontaneous reproduction through analog means, such as photocopying and audio and video tape, has put considerable stress on laws pertaining to the right to copy. The broadcast industries have had to develop novel ways to realize economic benefit from cultural works, ways that turn less on the right to copy and more on the right to use a work.

With digital coding the reproduction of material becomes even faster, cheaper, and vastly more accurate than it does with analog electronic media. Once something has been sampled and captured in digital code, the idea of a copy of that sample ceases to make much sense. The copy is not really a copy, but a second instance of the original. The computer radically changes the conditions bearing on the reproduction of information and ideas. Once the infrastructure is in place, the reproduction of materials has a negligible cost with respect to materials, work, or quality. In principle, in a digitally encoded culture, anyone can have instances of anything they wish without added cost to the system. It will require an elaborate process of technical, social, and legal development to achieve actualize such potentialities.

Digital coding will also transform the problem of storing information. Librarians concerned with the preservation of materials traditionally attend closely to the durability of paper and its possible substitutes. The key question they ask is: "How long will it last?" This makes a lot of sense as long as the information is located in matter. If the paper will quickly degrade, the cultural community will soon need to reprint its materials or reproduce them on some alternative material such as microfiche. The shelf-life of all this is important as each cycle of reproduction is very costly, as well as an occasion for material to be lost and errors in reproduction to creep in. With digitally coded materials, shelf-life remains limited, but the costs of reproduction and the likelihood of errors arising from reproduction drastically declines. Hence, the keepers of the heritage need to rethink the standard principles of storage and preservation. Continuous reproduction can make the quest for durability unnecessary. Since reproduction is very cheap and very accurate, the problem is not one of finding the most enduring materials and keeping them as stable as possible. Rather the problem becomes one of regularly refreshing the energy-states in which the information is located and making sure that it is scattered in enough separate instances that a catastrophic failure in one instance would not obliterate the heritage.

Other, more novel problems of storage also arise. With respect to information located in material objects, we naturally store materials in institutions adapted to the attributes of the objects. Thus we use libraries for books and museums for paintings and artifacts. Much intellectual specialization arises because people need specific skills to work effectively in these different collection of material resources. Insofar as we can record all these resources in digital code, we will store them in one, comprehensive system and we will thereby diminish in power many objective goads to intellectual specialization.

As digital coding makes information easier to store with much diminished threat of loss, so too it improves our ability to transmit information. Transportation costs and limitations have long been a significant determinant of communication capacities. Through the twentieth century, techniques of coding information in energy have greatly reduced the costs and limits on its transmission. With the substitution of digital for analog coding, these developments are extending far further as we enter the twenty-first century. Analog systems using energy as the medium have developed two major principles: point-to-point circuit switching, as through the telephone, and the use of wide information channels in broadband transmissions, as through radio and television broadcasting. Digital systems are combining and unifying these two principles, allowing the links between point-to-point switched circuits to be wide information channels, creating a single transmission net of extraordinary flexibility and power.

We are already everyday users of the basic principles essential to these changes. My mother is eighty-eight and legally blind, but she can use a push-button phone with confidence and has a good head for phone numbers and thus she keeps up familial and social connections all over, in Mexico, in Canada, and around the United States. Each time she dials someone's number, she instructs the phone system to establish connections within its circuits to link her phone with that of the person she is calling. Phones code and decode voices from a very simple electrical signal that can be easily transmitted through complex switching systems and has a narrow band for coding information, one just sufficient for the low- fidelity reproduction of ordinary speech. How much traffic the phone system can bear depends on how many separate circuits it can switch together at any time and on how many separate transmissions its trunk lines can aggregate together in simultaneous calls. You'll get a busy signal if the system runs out of switches or transmission room.

Radio and television use much wider bandwidths, and they code them more intensely, with the result that their signals can be much more complex than those of the telephone. Thus radio can reproduce sound with much greater quality that the telephone, and the amount of information transmitted via television far exceeds that used in a phone conversation. The wider bandwidth, however, makes point-to-point switching in such transmissions more complicated to do without introducing noise into the signal, and without overwhelming the capacity of connecting circuits when many parallel transmissions are traveling on them simultaneously. Various properties of digital coding facilitate the combination of circuit switching with the information intensive transmissions that characterize broadband systems.

Both analog and digital systems make use of what we will call micro-time, the actuality of incredibly brief instants. For instance, radio waves fluctuate several million times per second and each fluctuation produces some of the information we hear. The higher the frequency, the more information the signal can contain, provided we can keep the receiver tuned to the proper spot upon the spectrum and provided we can minimize interference between signals and other sources of noise. Because the information bearing medium is a continuous wave, however, we find it much easier to propagate the information onto the medium at the rate it occurs at, and at which it is to be received. In contrast, when the information has been captured in digital code, it becomes much easier to make use of micro-time in more flexible ways: capture, transmission, and delivery can be separated. The pace of capture depends on the pace of the phenomenon, what we call "real time." Transmission of the binary units, the bits encoding the phenomenon, can take place in different time -- it can squeeze into each tenth of a second, or less, the information needed for one second of conversation, giving the circuit to other conversations for the remaining nine-tenths, or more, of each second. By this technique, and others like code compression and error correction, the capacity of a circuit carrying digital data can be greatly expanded.

Further, the transmission of analog data depends very closely on the particular characteristics of the transmitting medium. With the transmission of digital data, it does not matter what the transmitting medium is, provided that medium has been adapted to transmit digital code. Thus all the different electromagnetic transmission media in common use now easily transmit digital data. More importantly, new media, useless for transmitting analog information, for instance, laser light in fiber optic cable, increasingly transmit digitized information with significant gains in speed and volume, at lowered cost, and with increased dependability. The frequencies of light waves are much higher than those of electromagnetic waves. Hence, we can pack information far more densely per unit of time into light for transmission over fiberoptic cables than we can with electricity over wires or electromagnetic signals in space. The usable bandwidth is much, much wider. The higher density allows much more intense timesharing of the circuit and the greater bandwidth means that in each instant a much larger load of information will be charging through the circuit. As a result, a system is emerging in which all forms of information -- text, numerics, graphics, audio, video -- can be transmitted, switched from point-to-point, as easily as we can with the phone.

Digital coding, thus, is making possible the use of one system to produce all forms of information, to reproduce anything in the system with low cost and little loss, to provide for its indefinite storage through this process of continuous reproduction, and to transmit any element of it to any user fast and cheaply. By themselves, these developments make oodles of good information easily accessible, threatening to overwhelm the user in a vast babel of bits. These three characteristics are of a piece with each other, setting limits on what intellectual resources a culture can provide its members. But they do not, alone, make for a well developed system of communication.

Selective retrieval, enabling people to get precisely the information they want and when they need it, has always been a key problem of culture and communication. How can you get from the culture the ideas and information that you want and need? And even more perplexing, how can the culture intimate to you and everyone else what possibilities of interest it does and does not offer in the infinity of circumstances surrounding us? Retrieval is a fundamental problem of all cultures, and it is becoming an even more pressing problem with digitally coded information. It is the fourth determinant of communication effectiveness in history and the widespread digitization of information is transforming it as well.

Throughout history, major communication advances have brought with them new ways to retrieve information. The practice of citing books and articles by title and author, edition and page, rose to full significance in the era of print. The printed book, which could be distributed in many locations in identical versions, needed some logically effective technique of reference and recall, one that would work in many different places and many different times. Prior to that people referred far more vaguely to an author and an argument or thesis, and to retrieve the actual text a scholar needed to know where a specific instance was physically located, with diverse works bound together for convenience. Today, people often handle their personal libraries in this pre-print fashion, jumbling certain books together say by size, or just shelving them as they come, able to find any particular one, not by a sense of logical order, but by having a feel for where it is by some sense of spatial juxtaposition. That works for small libraries, but it spells chaos for large collections of printed books. For those, people needed to develop far more systematic techniques of reference and recall.

With digitally coded information, the situation is much the same: people need to master new, more powerful retrieval routines to manage the cornucopia of information. These techniques relate to two different problems in the use of information -- exchanging information and applying ideas. In both exchanging ideas and applying them to problems, people need to retrieve information selectively. Exchanging materials is somewhat similar to the phenomena of point-to-point switched circuits while applying them is related to finding a station or channel in broadcast communication. Exchange requires the precise identification of start and end points and application requires the substantive sifting through extensive materials to select out the precise components pertinent to the problem at hand. Since the problems and prospects in each domain are rather different, let us consider each briefly in turn.

Our means for managing the exchange of information have already been heavily influenced by characteristics of digital coding, at least insofar as digital coding involves discrete units, as distinct from continuous waves. For instance, integer numbers are a system of digital entities: each number is discrete, autonomous, separate from any other. So too is the alphabet, which is a more restricted set of discrete elements, most simplistically twenty-six, but preferably 256, if we take extended ASCII code as the norm. Long before computers, people became adept at using numbers and letters to assign precise locators to all sorts of objects, persons, phones, buildings, accounts, parts, and so on.83 Implementation of these coding principles in digital computers enhances our capacity to manage them greatly, extending the scope, precision, and speed of the process. In substance, the problem of addressing things so that information about them can be exchanged from point-to-point is less technical than socio- political: the problem of privacy, of censorship, of deciding what limits, if any, to place on the reach of possible exchange. Whenever the power to exchange information increases significantly, it brings such problems with it. The abuse of privacy thus seems to be a structural issue, occurring at the margins where new ways to manage exchange are developing. Historically, people seem to opt for accepting the benefits of new systems of information exchange, after instituting measures to ensure that they will not be used to subvert personal security and integrity. Unfortunately, this trade-off has not always been benign as the tragic abuses of totalitarian regimes of right and left repeatedly demonstrate. As computers make it possible to exchange information that was formerly "private," easily kept to oneself, we will need to face up to difficult issues of defining limits and controlling abuses.

Retrieval that involves sifting, selecting, and applying ideas presents different problems and opportunities. Our existing techniques for doing this involve time-consuming secondary processing of materials -- indexing books, abstracting articles, cataloguing things under key words and subject headings, adding captions to pictures and tables, annotating works with cross- references and footnotes. Digital coding makes these practices more effective in three significant ways. First it facilitates the processing by creating tools to help people to index, abstract, caption, and catalogue their culture. This presents us incremental gains. Second, it makes many traditional references, which had been unidirectional from one work to another, usefully bi- directional. Only where very special indexes have been laboriously developed can I go into a library and ask for a list of works that cite a passage that specially interests me. In a digital environment, the electronic reference that implements a note will point both ways, something that will make traditional references useful in powerful new ways. Third, traditional references implemented digitally will save users much time and energy, for following out a reference will be nearly instantaneous. Currently it is often hard to maintain a train of thought in following a reference as one needs to go off to the library or bookstore, perhaps having to wait weeks for a work to arrive from a distance. Digitally coded links will be fast and transparent. Together, these three changes will significantly enhance traditional resources for the reflective retrieval of ideas and the application of them to our controlling purposes.

In addition, new retrieval resources are under development. These require no intelligent pre-processing of materials aside from the capture of them in digital code. Instead, the end-user of the material specifies criteria of interest, and the system matches materials in it against these criteria, showing the resultant possibilities and allowing the user to further winnow the results, should that be necessary. These principles have been most fully developed with respect to the retrieval of textual materials. Their novelty still engenders some confusion, and many people, among them even professional librarians, misuse the concept of "full-text retrieval." Thus some think it simply means retrieving for an inquirer the full text of a document, rather than an abstract of it. More properly it means conducting the search for matches to an inquirer's criteria of interest against the full-text of everything in a collection, rather than against a list of keywords. Techniques for such full-text retrieval are becoming both sophisticated and fast, and users can apply them to both the flow of current information generated through correspondence, calls, and news, as well as to libraries of accumulated information.

Techniques of search and retrieval have historically developed far more fully with respect to text than with other forms of information. Up to now, we use text to catalogue most other forms -- maps, pictures, numeric tables, films, recordings, and so on. Yet text processing is not the only form of intelligent recall and retrieval that we can do. We can often find our way to places with a visual- spatial memory that is much more effective that verbally forming a set of directions for ourselves. We associate both moods and ideas with various sounds and melodies and even colors and places. All this suggests that beyond full-text retrieval, there lies the domain of "non-text retrieval." In non-text retrieval we might point to a geometric relationship and request the computer to search a graphic database for other instances of the similar relation or play a chord and have the system call up musical compositions in which it occurs. Non-text retrieval should in principle be possible with digitally coded information, but for the most part it is a possibility that awaits development.

One area in which non-text retrieval has been underway for some time, however, gives an idea of its potential power -- statistical processing. Statistics can be thought of as a numeric system for selecting and retrieving information that allows for judgments of significance and relevance that are very hard by textual means alone. Also, the ability to zoom-in and zoom-out to different levels of detail on graphical materials such as maps, diagrams, and photos provides substantial non-text retrieval capacities. In general, digital code enables us to capture and link different kinds of information pertinent to complex phenomena and to represent their interactions in ways that we can see or hear, using those senses to select directly between combinations. All sorts of complex controls work this way, especially in simulation systems and innumerable computer games.

These variations on non-text retrieval really carry us into consideration of the fifth area in which digital coding is deeply influencing our culture -- the intelligent processing of information. For the most part, up to the twentieth century, communication tools used external artifacts to extend the memory, while leaving the intelligent processing of ideas to take place almost exclusively inside the human body and brain. Through cultural history, people have accumulated vast stores of memory projected outside themselves into man-made objects. Despite all that externalization of memory, the possible agents for the key verbs describing intelligent operations on information and ideas are still almost exclusively human person -- perceiving, sensing, thinking, correlating, inferring, deducing, concluding, and so on. With the computer, man-made objects are becoming useful in performing these intelligent operations.

Memory, to be meaningful, must ultimately return to a sentient human mind -- a library unread is not a culture preserved. In externalizing memory into material objects, humans have not alienated memory from ourselves, but enhanced our capacity to remember by transferring parts of the task to objects that we make and manage. So too, in externalizing intellectual activity, we do not entirely alienate it from ourselves. Instead we compensate for limitations, strengthen capacities for demanding operations, and enhance attention, precision, finesse, or speed.

To understand how the computer is accelerating the transfer of intelligence to external tools, it is important to realize that this is not a sudden novelty in our culture. We perceive the world with our senses and prepare it for thought: through most of history, people did this without the aid of instruments. That began to change some centuries ago. We can interpret the rise of modern science as the intellectual fruits of externalizing capacities for perception into instruments of observation. Clocks and chronometers permitted people to perceive time with ever greater precision. The telescope and microscope enhanced the human capacity to see distances and details. The thermometer lent accuracy to our capacity to perceive differences of hot and cold. Exact scales and rules and other measures, tuning forks, prisms, filters, balances, samples, gages, a wondrous panoply of instruments, allowed inquiring minds to develop the empirical base of observation upon which they built our stock of scientific understanding.

By working with digitally coded information, instrument designers are extending the power of perception greatly. The unmanned space-probes reporting on the solar system have perhaps been the most dramatic of these extensions, with wondrous photographs and other readings radioed back as masses of digital code. Not since the invention of the telescope has our ability to perceive the universe around us so leaped forward. But digital read-outs are all around us with the computer creeping into all sorts of mundane tools, enhancing our capacity to track and control their use. For many decades car instrumentation, for instance, was very stable, consisting of a few analog gages that indicated the car's speed and possibly the RPM's of the engine, while additionally giving key hints about the state of the car's fuel, coolant, engine oil, and electrical system. That's fast changing now with digital sensors in new and old places giving a much more exact picture of the car's condition of operation, with an onboard computer relating readings to one another -- "it's getting pretty close to empty" gives way to "range remaining fifteen miles." The computer will greatly extend the reach and accuracy of instrumentation as people apply it with increasing effects to small matters and large.

With the computer, people can externalize into their instruments more than their powers of perception. When Edison claimed that "genius is one percent inspiration and ninety-nine percent perspiration," he probably thought that the human capacity for both inspiration and perspiration were basically fixed, and by perspiration he had in mind the laborious calculations needed to test speculative insight, separating good from bad. Digital systems do not do away with the need for perspiration, but they extend what we can accomplish with a given amount of it. Most forms of calculation, correlation, combination, and connection that people can make, computers can help them make better. They can expand our abilities to sort, order, rank, and select. Even this process of externalizing powers of calculation is not entirely new historically, as one who has worked with a slide rule will realize, but it is being vastly increased. The consequences are likely to be very great.

Many people think that numeric calculation is the peculiar domain for computers, but their reach goes far beyond numbers. The computer can operate on anything that in some meaningful way can be represented in digital code through an organized data structure. And any operation that can be accurately described within the compass of binary logic -- AND, OR, NOT -- the computer can perform. Let us leave as moot whether people can, or should, or ever will, externalize into tools that one percent of their genius -- inspiration. They are externalizing in all sorts of ways that other ninety-nine percent, amplifying greatly their powers to calculate and control objects of their attention. Even if artificial intelligence, in the sense of the computer being an autonomous rational agent, is not soon coming to pass, if ever, AI, in the sense of amplified intelligence, is rapidly emerging all about us. We need to come to terms with its implications.

This, then, is the computer. It is the representation of our culture in digital code and the development of all the cultural possibilities that result. The computer makes cultural work easier to produce and reproduce, to preserve, to transmit, potentially accelerating intellectual attainment and opening cultural access in unprecedented ways. The computer greatly augments human powers of selection, memory, perception, and calculation, potentially amplifying the intelligence that each and all can bring to bear upon the panoply of questions that life puts to them. We turn to the implications of this computer for the activity of education.

Chapter Three - The Educator's Mission

Digitizing our culture will occasion significant historical change. It will not do so overnight, but in a matter of decades as we round one of history's majestic promontories. Should we go by adrift, blown this way, then that, in mindless disarray? Or should we sail confidently around the cape, adventuring hope and considering intent?

Only a catastrophe will stop us from rounding this historic point, driven by a powerful means of communication. This assertion does not propound a technological determinism, wrought as if technology were some suprahuman force, determining our lives apart from us. Technology is one human, all-too-human, means that people have always used to make their history. We, like they, will live with the consequences, and we need to take responsibility for how we shape our lives with our historic innovations, the computer among them. In saying that we are rounding an historic bend created by our inventing new communications technologies, we propound no determinism; we simply characterize the effect of human initiatives on the human destiny.

Thus Norbert Wiener, one of the key innovators in the development of automatic control systems, called his reflections on the social implications of cybernetics, The Human Use of Human Beings. One might think this title strange, if one thinks of the computer as something separate and apart from human beings. But it makes good sense, if one recognizes that the computer simply helps to enlarge our human abilities. The computer is extending human capacities to remember, to perceive, to think. It neither displaces these powers nor obviates our needs for them. Through technology, humanity augments itself, and humans are as responsible for their conduct with their powers augmented as they were without. As we extend our intellectual faculties with the computer, what human use of human beings should we fashion with them, particularly as educators?

The Reciprocity of Equity and Excellence
Equity and excellence: these aspirations have drawn Western culture into modernity, and for better and for worse they are pulling the other cultures of the world along. Both equity and excellence are many-sided aspirations and they have long stood in a creative tension with each other. Historically, educational effort has been one of the means for cultivating both equity and excellence in productive, potent ways.

Let us survey the historical significance of equity and excellence, the mission these qualities perform in life. In doing that, we do not intend to define them philosophically. We will neither argue normatively that here is the one correct conception of equity or excellence, nor pick analytically, exposing flaws in this or that version. Instead, we inquire why representatives of our tradition have taken equity and excellence seriously, seeing important matters to be at stake through them. What has been the use and disadvantage of equity and excellence in cultural experience?

Equity generates historical vigor. Where there is no equity, the favored become arrogant while the deprived become despairing. With an approximate equity, all persons and groups engage fully, from within, in the realization of their unique potentialities. Equity is to the polity what good conditioning is to the athlete.

Rarely has anyone argued that equity should produce universal sameness, entailing precise equality with everyone getting the same measure of goods, neither a jot more nor less, than anyone else. Human beings and their circumstances vary too much in real ways for mathematical identity to be the norm of equity. The norm of equity, however, cannot tolerate differences that are too extreme, so extreme that one person cannot recognize commonalty with another. Whether the cleavage be between rich or poor, townsfolk or peasant, minority or majority, domiciled or homeless, or any other distinguishing mark, it cannot be so great as to define separate orders of being that have no mutuality, one with the other. When that happens, equity disappears.

Equity involves respect for differences within a broad ambit of commonalty. This general principle links the main practical expressions of the drive to equity in our tradition -- equality before the law; the guarantee of minority rights; and maintenance of equal opportunity. Without equality before the law, commonalty breaks down and the community shatters between those who bear the burden of onerous laws and those who enjoy exemption. Without the guarantee of minority rights, respect for differences evaporates, suppressed at one or another difficult juncture by a tyrannous majority. Without efforts to preserve equal opportunity, separations in status and differences in condition build until neither haves nor have-nots can preserve a pretense to commonalty with their counterparts. Equity is unity in diversity, e pluribus unum.

What good arises historically when equity pertains? Were humans and their conditions all identical, equity would simply describe a condition, not an achievement, wrought for a purpose. But people all differ, and we can all mutually benefit from our differences when we arrange them well. Civilization, community, and polity all serve to enable people to arrange their differences in constructive ways: equity is the governing principle of these arrangements. Thus the fruits of equity seem somewhat paradoxical -- they arise, not from making everyone more alike, but in enabling people to share maximum benefit from their differences.

Plato began the Western discussion of justice by recognizing that human civilizations were complicated groupings of different people, each with different conditions, interests, and skills. Civilized people had a stake, he observed, in their not being all alike, but in their benefiting from their differences through a division of activity, with each person perfecting special interests and gifts. Justice was a peculiarly civilized problem, a problem of equity, one of harmonizing the fruitful differences among people so that the variety of capacities served the good of all. The virtue of each deserved nurture and respect. Equity allows each to realize unique potentials and to participate actively in the shared effort of civilization.

A society that does not maintain equity will include many who accommodate to misfortune through despair and passivity. They will not make the most of their possibilities and will drag as a weight on the resources of the whole. Others will experience their inequitable privilege as a dimension of their being, something not achieved but given in the apparent order of the world. They will fail to nurture acquired strengths, confusing such accomplishments with gifts of nature. Increasingly they will enjoy the forms of power, without its substance, lordly buffoons. Even between those extremes, where people would seem to enjoy a bracing modesty, they will deflect their energies in behaviors of avoidance and emulation, shunning the needy and aping empty privilege. Thus even the middle class can become at once anxious and over- reaching.

Equity improves the chances that a people will achieve a collective vigor in the face of history. Rarely does a single group by itself ensure the greatness of the whole. For the quality of life to flourish, a wide range of people must have a sweep of skills, each exerting effort, doing well what each does best. Equity makes it possible for each to feel that he can become somebody of worth and that he can do it best by respecting his condition, skills, and interests, making the most of what these are. Equity makes diversity beneficial. It leavens the energies of a people. Equity energizes: that is its historic value to the conduct of life.

We have been reflecting on what equity, as a condition, does for people in history. This question differs from the problem of how a people can achieve or maintain a condition of equity in their history. What food does for me is not the same as what I do to get food -- one has to do with nutrition, the other economics. How equity benefits civilization is not the same as how a civilization becomes equitable. Failure to note this distinction often confuses discussions of equity, especially as it relates to excellence.

Historically, where life is equitable, people will display more cultural vigor. People maintain equity through their history, however, by treating it as a difficult balance that they need to maintain and keep, a dynamic tension between commonalty and difference, unity and plurality, identity and multiplicity. Recognizing this tension, people can then use opportunities for change to move first toward one pole and then toward the other, whichever is deficient, continually channeling effort toward the side of the balance that seems then insufficient. Achieving and maintaining equity is thus like riding a bicycle -- the rider subtlety steers and sways against the direction of fall, turning away from a tumble, crossing the balance point, and then turning back the other way as the imbalance reverses. Should she lean exclusively to this side or to the other, the rider will flop to the ground. The rider keeps the bike upright, continually steering it away from the side to which it is falling, bringing it upright, then starting a fall in the other direction, all as a simple expression of her kinesthetic sense -- she acts and does not find it easy to be consciously articulate about riding a bike. So too, people maintain equity, moving back and forth between commonalty and difference, as a simple expression of their sense of justice, sometimes nurturing distinctions and sometimes leveling differences in ways that they sense to be fit even though they may find them hard to plan or explain.

As movement enables the rider to steer the bike against the direction of fall, so historical development allows people to maintain equity by swaying between commonalty and difference. In a static society, people cannot shift their direction between solidarity and variation, and an imbalance toward one or the other cannot be righted. Perceiving this link between social rigidity and the loss of equity, ancient Greek historians argued that a breakdown in equity caused stasis, the paralysis of a society riven by excessive differences. They had cause and effect reversed, and Machiavelli in his Discourses explained most clearly that the problem really worked the other way around: when dynamic development petered out, people became frozen in their oppositions, unable to shift against their fall. Then their differences inexorably widened, equity decayed, and the creative components of society turned to internal strife, one with the other, leaving the culture in a prolonged, irreversible decadence. In contrast, in a continually developing society, dynamic circumstances enable groups to change their direction of movement with respect to difference and commonalty, shifting from leveling to differentiating and then in time back to leveling and on, thus permitting the preservation of equity over time.

Expansion, change, dynamism: these enable people to sustain equity over time. One cannot balance the stationary bicycle. In the same way, a quiescent society, one that lacks historical movement, cannot maintain equity. Thus, looking at what equity does for people in history, we have observed that the condition of equity maintains the vigor of a society. But looking at what people must do in history to get and preserve equity, we find that their capacity to change, to develop, to move dynamically in history enables them to approximate and maintain equity over time by employing their sense of justice to shift between cultivating commonalty and then difference, difference and then commonalty, thus keeping the dynamic balance, riding the bicycle of time.

What drives this capacity to develop, to change? What pedals the historical bike? Here excellence enters the equations of history. Historic development flows from the ability to break through the molds of the moment. A person who excels at something penetrates beyond given levels of achievement. Historical dynamism arises from this drive to excel. Conservative excellence is an oxymoron, and its proponents confuse real excellence with conventional achievements. In actuality, equity is the much more conservative virtue, for it enables each, in a fit way, to contribute to the common enterprise. In contrast, excellence does not conserve; it forces change. To excel is to shatter molds, exceed norms, to better the existing standards. An ever flowing excellence preserves the dynamism, the historical movement, that permits people to maintain equity. Excellence drives change so that people can accentuate commonalty when differences begin to become extreme and they can nurture differences when commonalty begins to cloy and suffocate the spirit. Excellence, by breaking beyond the given, turns the wheels of change.

Many who write in praise of excellence attribute to it the fruits of equity. Excellence does not necessarily guarantee a high level of competence across all the walks that contribute to the common weal. General levels of competence are the work of equity: with equity, each person feels that she has a fair shake and will, therefore, live her life, integrally, to the hilt, proud and engaged. To attain a high level of general competence, each and all must exert themselves, and equity promotes such universal exertion. Historical change, however, does not come from diffused competence, but from localized, unexpected innovations that alter existing balances between groups and functions, unexpectedly forcing readjustments among all components of society. These innovations take place when someone, in one or another walk, comes to excel all expectations, to surpass existing norms and eclipse familiar patterns.

An historic flow of excellence keeps a civilization in dynamic development, allowing it to maintain equity over time. Thus we can say that the historical function of excellence is to be the historical source of the condition of equity. What, however, is the historical source of excellence? If excellence produces equity, what produces excellence? To a certain extent, excellence is an indelible expression of the human spirit, what Nietzsche called the will to power, an aspiration to find and fulfill one's possibilities. In this sense, excellence happens anywhere, often under the least propitious circumstances. Thus change has eventually, surprisingly, welled up throughout all societies, even the most static and regressive. Yet however inexorable, excellence as a driving dynamism has been more prevalent in some societies than in others and it is for this source of relative prevalence that we search.

With respect to the maintenance of equity, significant excellence can originate from any sector of society. In that sense, excellence is intrinsically egalitarian. What is important in excellence for keeping equity is not that excellence occur regularly at the leading edge, whatever that may be, but that it occur with sufficient dynamism that it forces readjustments among all the parts, allowing them to shift orientation, like the cyclist, between the poles of equity. Such excellence can sometimes occur in a society that arbitrarily channels all advantage to limited groups, but it does so very rarely as the indelible spirit rises up from within one or another dispossessed group. Thus redeeming religions arose from decadent cultures. But societies that provide all their participants with opportunities to develop, to generate a compelling excellence, will more continuously undergo the dynamic readjustment of their parts.

Increasingly in modern societies, people have been using the intrinsic egalitarianism of excellence to maximize the likelihood of its occurrence and to keep social relations in continual movement. Since excellence can occur unexpectedly in any and all walks of life, a society that approximates equity, and provides all walks with nurturing opportunities, will be the most dynamic, the one continually forced to undergo change and innovation. The frequency with which an energizing excellence wells up will be improved by ensuring that each and all have opportunities for self- development. Here is the wager of participatory polities: equity is the historical condition that increases the frequency that excellence will emerge in one or another sector, forcing realignment throughout the culture.

Excellence sustains equity; equity occasions excellence. Excellence drives historical development; equity spreads human competence. The two together foster progress, an improving quality of life for a growing number of persons. The great achievement of modernity -- roughly the half millennium from 1500 to 2000 -- has been to harness equity and excellence together and to use them to transform both the material and cultural conditions of life, extending unprecedented opportunities to a multitude of peoples.

During this period, technologies for the mechanical reproduction of information, particularly printing, greatly facilitated efforts to promote both equity and excellence. Printing expanded access to the defining documents of law and religion. It empowered vernacular cultures to address all the complexities of civilization and it evinced the creation of a community of scientific discourse. Printing altered numerous arenas of activity, giving people the opportunity to achieve unprecedented excellences in them. Printing also enhanced equity by nurturing both commonalty and diversity, helping to provide general access to cultural assets and to preserve the distinctive resources of numerous groups and specialists. Consciously and unconsciously, people made printing a powerful leaven in modern culture by discovering ways to use it as a means promoting both equity and excellence.

No less needs to be done with the computer as a system. We are rounding a bend of history that will express our culture in digital code. We should do so aware of the importance of equity and excellence for the enduring quality of historic life. During the rise of modernity, education has been a domain that helped to link equity and excellence constructively, making use of the pedagogical possibilities of print. The task before us now, as the era of print gives way to that of the computer, is to find ways to renew the pedagogical link between equity and excellence, which has been strained of late. Educators have a mission to nurture our historic capacity for equity and excellence. To do that, they need to use advanced technologies to create an education that will be both integral and liberal, both meaningful relative to each person and worthy of each person's autonomy.

Education, Liberal and Integral
It is one thing to say that education should promote equity and excellence. It is another to explain what kind of education can best do that. Links between educational activities and their results, both biographical and historical, are not direct. People believe that the extent and quality of education makes a difference in the experience of individuals and groups, but the results unfold slowly over time and many other contingencies affect the outcome.

Most tests of educational outcomes cravenly duck this difficulty. Evaluators assume that all results empirically evident at the conclusion of an educational activity will endure, relatively unchanged, for as long as they may be significant. Thus they measure the quality of education by the grades a person earned in a sequence of courses and they estimate the quality of schools, teachers, and programs by measuring how well children perform under their influence at one or another instant of time. It is a testament to our tolerance for absurdity that the educational research establishment allows such a methodology to stand.

Think of investment theories. With respect to education, researchers and the public obsessively look only at the rate of current return. Which method, they ask, yields the highest immediate gain? Economists long ago realized that this was a poor way to ascertain the value of an investment, for every investment has a useful life, which may be long or short, and a pattern of payoff across that life, which will vary, instance to instance. By measuring only the immediate current return, investment in growth industries would make little sense at their start, for at the start growth industries often lose money and usually require plowing back whatever profit they generate into development and expansion. Often the time to invest in growth industries is when they have negative current returns. In general, if people judged only by current returns, practices of deferred gratification would seem merely masochistic, yet these have been among the historically most productive economic strategies. Like economic investments, the benefits of education accrue over long periods and they accumulate in many forms. Our educational measures provide very weak resources for investigating these cumulative benefits and educators consequently have trouble making good sense of the relative value of the various means they might adopt.

If the computer as a system has fundamental significance in education, it will be as a long-term transformative agent. Experimental measures of how effective one technique is relative to another rarely measure long-term secular effects, showing how a systemic innovation, operating from kindergarten through graduate school, performs, across the full span of people's lives, relative to other system options. In education we have not yet invented the techniques of integration for calculating the full values of the whole education, leaving claims of measured worth partial and deceptive. Hence, little will be gained by culling the literature to show that a selected method, used in this subject through that grade, will accelerate performance by some fractional current return. We should legitimate experiments in a different way.

Let us try a different method; let us attend to intuited preferences, especially to those that recur frequently in different times and places, trying to reason out why those intuitions may have a vital truth to them. Over and over again, people in many times and many settings have had strong, intuited preferences for and against particular types of education. Neither they nor we can rigorously measure out quantitative grounds for these preferences, taking the full span of education from infancy through maturity into account, but we can thoughtfully understand them and perhaps see how they connect to the imperatives of equity and excellence. Such reasoning may help us understand how to use digital technologies as historically constructive agents in education. Here we will concentrate on two such recurrently intuited preferences, a persistent quest for an integral education and for a liberal education, which we will see, as our reflections unfold, link pedagogically to the more general aspirations of equity and excellence.

Commentators often resort to the term "liberal" in discussing education. They rarely agree precisely on what it means. I will return to the topic and give a version of it. But first, let us consider the other recurring preference, that for an integral education. Commentators rarely use the term "integral" in discussing education. Yet they almost always agree about the matters that we can describe with this term. An integral education is one that the student integrates and makes her own. Educators analyze the functions that lead to an integral education when they study the processes of assimilation and stress the importance of intellectual synthesis. Likewise, they have often decried education that fails to be integral, objecting over and over to rote learning, empty mimicry, and taking on airs. If the term is a bit novel, the phenomenon is not -- it simply has not been definitively named in educational discourse.

Education should be integral, it should consist of things that a student integrates into a set of skills, understandings, preferences, and beliefs that comprise a whole, one that integrally characterizes the person. A person who has achieved an integral education would be likely to have what psychologists once called "an integrated personality," and would be, in an even more traditional terminology, "a person of integrity." Integral education need not lead to bland sameness in all; rather, as we will see, it should take into account the differences that characterize each. Cultures are collective human works of such complexity that no person can integrate into his character all that is of value in one of them. Were a culture so simple, or the human character so all encompassing, history would freeze in a repetitive classicism, which is probably why so many primitive cultures persist unchanging. In a single, complex, culture, many, many different integral educations are possible and desirable.

People do not easily achieve an integral education. The world of education has many stock nincompoops -- pedants, bores, pettifoggers, humbugs, fakers, dreamers, incompetents, sticklers, marionettes, drones, bombasts, drudges, and charlatans. All exhibit a failure to integrate acquirements fully. In a more positive vein, the great studies of education in our tradition have put the problem of integral education central. Plato's Republic, turns on the question of how the person can integrate appetite, emotions, and reason in a harmonious unity in which each part, keeping to its proper business, contributes constructively in coping with the claims of experience. Rousseau's Emile, turns on the issue of how the wise educator can hearken to the unfolding readiness of the maturing child so that her development is neither forced nor stunted, keeping instead to a regimen of challenges that strengthen her as she rises to each. Dewey's Democracy and Education turns on the problem of situating the child's growth in his reflective experience, nurturing and sustaining it, from the world of play outwards into that of science, work, social bonding, and politics. Throughout these, and many other works of our educational tradition, the pedagogical problem centers on the importance of integrating the particulars of education into an integral whole for the person and the group.

How does a person integrate cultural acquirements into his character? Consider some hypotheses responsive to this question, a question that is far too complicated ever to receive a conclusive answer. The generalizations that follow here have their roots, not primarily in psychology, but in history and other cultural studies, along with simple introspective reflection. We should entertain them, not as claims to achieved knowledge, but as design heuristics that may enable us to create more effective modes of practice. Too often, educational researchers adopt methods that exemplify the old saw, "penny wise, pound foolish." Let us reach, as widely as we can, for knowledge tested in the crucible of controlled observation. But when, owing to the complexity of the activities at issue, we cannot subject the full spectrum of relevant variables to sound experimental study, let us not truncate our thinking about them to deal only with those few variables that we can grasp through controlled observation. Where the phenomena are many-sided, as in understanding how a person integrates cultural acquirements, we should turn to philosophy, anthropology, history, literature, to all the human studies, to advance our reflections.

In integrating learning, it does not suffice to learn to recognize something or even to repeat it on cue, or to know a lot about it. A person who thoroughly assimilates a language may know far less about it than someone who has been taught it extensively without integrating it into his living or his work. An integral education challenges a student with things that are new to him, but it also allows him to select, to incorporate, to synthesize the new into what he knows, thinks, and believes. Sometimes, something new will not simply integrate with what came before, but will force him to reintegrate many of his ideas, and he will call that a transformative educational experience. Traditionally, formative education, which accentuated the ardor of thoroughly assimilating one's learning into one's life and work, often called for long apprenticeships capped with production of a difficult, unexpected masterwork.

An integral education will usually be a student-centered, active education. Teachers cannot integrate material for their students. This problem is quite evident for anyone who tries teaching skills that depend on a person's kinesthetic senses -- just about any sport that turns on one's sense of balance and coordination. Take, for instance, water-skiing. You can explain to someone what to do over and over. He won't get it until he gets in the water and feels the pull of the boat, the resistance of the water on his skis, and then, quickly or laboriously as the case may be, he gets the knack of letting complex forces intersect through his legs, arms, and torso. At that point he has integrated instruction and experience, using his kinesthetic senses to get up on the skis, and a whole new discourse can start between teacher and student, a discourse based on a shared understanding of the essential experience. The same holds for cycling, dance, gymnastics, diving, the use of tools: "let me show you" can at best inspire the student to trials in which he gets the feel for it himself and then a new exchange can begin between two people, who both know how to do it, in which they exchange the fruits of their complementary experiences.

As learning to manage one's body in complex ways requires that the student use her kinesthetic senses to integrate precept and example into her set of abilities, so too does integrating intellectual and emotional acquirements. Here the essential resource is the sense of judgment. Do not understand by "the sense of judgment" a quasi legal process of applying rules to instances, handing down a judgment about how a rule applies to a case. Rather the sense of judgment is a philosophic term for the process by which a person forms likes and dislikes, commitments, and rejections, in the full flux of experience. The sense of judgment generates selections. It is a biological, characterological, esthetic sensibility, and a teacher must appeal to a student's sense of judgment -- her sense of the interlocked importance and significance of things in the world she experiences that she uses to make choices, to allocate attention, to discern differences, to perceive possibilities, to respect limits, to sense dangers, to define aspirations, to obey precepts, to form intentions, to act for herself in her world. An educational system that does not effectively engage and make use of the sense of judgment that its students possess will be futile and dysfunctional.

Educators do not find it easy, however, to work with and through their students' sense of judgment. The system often functions as if students neither can nor should form likes and aversions according to their inner light, whatever that may be. "Eppur si muove. But still it moves," Galileo muttered, and so they do. Hence, the ineluctable working of each student's judgment, affirming this and rejecting that, makes it necessary that the design of formal education pay careful attention to the diversity of cultural and social conditions. Anyone can have transformative experiences, for better and for worse, and with only a few constructive (however painful) transformative encounters, the anonymous child of poverty and cultural marginality can rise to great achievements. But such metamorphoses will not occur without recognizing the child's sense of judgment as it stands, from the beginning. Hence, the refined preferences of bourgeois civility cannot be the presumed sense of judgment in an education for someone for whom street-smarts are a condition of survival. Instead, the starting points for integral education need to be numerous, diverse, and many-sided.

What are the forms of integration in education? To develop a sense of their range, reflect briefly on three ideal-type constructs that we can generate intellectually to help organize the wealth of experiential particulars -- combinatorial integration, self-reflective integration, and transformative integration. The first, integrating things by combining them together, seems to start early as the child draws connections wonderingly between different elements of experience. Combinatorial integration is relatively uncritical. It motivates all those childish questions -- what? how? why? where? when? The integration happens by a kind of passive proximity -- things need to stand just beyond the perimeter of the person's understanding so that he can encounter them and spontaneously make a connection between what he knows and these new matters. If he simply stays within his web of existing connections, no new combinations form, and if something is too distant from his current stock of integrated information and ideas, he will just let it pass without forming a lasting anchor in his realm of attention. Although it is most common in childhood, combinatorial integration continues through life and it is the normal way people incorporate new impressions and form new skills. Daily attention to the news probably has the function of exercising and keeping current a person's combinatorial integration of experience.

Self-reflective integration involves bringing to consciousness the unifying interests and capacities that constitute an assertion of unique personhood. Often, this form of integration seems to start in adolescence and to carry through early adulthood with the formation of a conscious vocation. For self-reflective integration to occur, a person needs a sense of multiple options. She exercises a projective imagination, seeing different possibilities unfolding in the foreseeable future. She discovers that her interests are many- sided and cannot all be reconciled together by simple combinatorial judgments. Choice becomes necessary, and with it arises the need for criteria and principles, a conscious sense of self, goals, purposes, tastes, and values. She must form these for herself and in modern Western cultures, at any rate, often she rails at the bland assumption of her elders that of course she will simply take on all the norms and expectations that they model for her. Yet forced into self-reliance in this self-reflective integration, she feels that the stakes are high -- while rebelling against presumptive models, she looks about for inspiration and encouragement, and step-by-step she forms her controlling sense of self.

Transformative integration shatters a person's established sense of self and recombines the parts in a new combination and purposeful orientation. Such a reintegration can occur at any time of life, usually through powerful experiences not under the person's control -- a trauma, disease, or upheaval in circumstances. Some significant challenge upsets a person's existing order of ideas, skills, and convictions, and he must reintegrate them in order to cope with the new circumstances. Sometimes in the course of formal education, one encounters a new perspective on things or new ideas or data that undercut the existing integration of a subject, forcing one to rethink it all. Increasingly, as the normal life span lengthens and people seek to maintain a sense of vital engagement with their circumstances, they subject themselves to transformative challenges, consciously through career changes and unconsciously through mid-life crises.

An integral education will help the person use her judgment to mobilize the fullest range of knowledge and skills in defining and pursuing the vital itinerary of her life. Insofar as her education is not integral, it will consist of acquirements of no vital import for her, of skills that will decay unused, of things learned but soon forgotten, of masks and routines performed with hidden resentment to please the powers-that-be. Through an integral education, a student takes responsibility for being whom she is, for both those things she recognizes as fruits of her conscious will and for those things she knows to have been accidents, whether negative or positive, that befell her arbitrarily, yet befell her, and not someone else, some other onto whom she can pass responsibility.

Integral education involves not a sovereign, all-powerful self, but the ever-varied particularities of personhood. As we shall see, each person's achieving an integral education is a key to promoting equity in our culture, But for now, simply let Michel de Montaigne sum up the ideal of integration in education -- "Bees pillage the flowers here and there, but they then make honey of them which is all their own; it is no longer thyme and marjoram; so the fragments borrowed from others [the student] will transform and blend together to make a work that shall be absolutely his own; that is to say, his judgment. His education, labor, and study aim only at forming that."

As Montaigne perceived, through an integral education a student forms her judgment. In this sense, an integral education is closely allied to that other recurrent educational preference, namely for a liberal education. Let us reflect on the preference for a liberal education and then return to see how integral education and liberal education together help nurture equity and excellence in historical experience.

One can find numerous different descriptions of liberal education. In part, this multiplicity of visions has arisen because commentators treat the term "liberal," not as an adjective, but as part of the noun phrase, "a liberal education." They busily describe the distinctive features of a liberal education and they of course differ about what these are. Let us ask instead, why did people start qualifying education with the adjective "liberal?" They started using this adjective because it meant "appropriate for a free person." They did not mean by this that a certain kind of education would take slavish youths and magically make them free. The autonomy of the person was not the result of the education; the autonomy was the condition occasioning it. Some people were free, as distinct from dependent, and free persons would find a certain type of education particularly appropriate for themselves, which came to be called a liberal education -- an education worthy of the autonomous, self-directing, responsible person.

No studies mysteriously made people free; no subject had a liberating potency. The autonomy of the student, his moral freedom and responsibility, was not the consequence but the condition of a liberal education. Only on recognizing the student's inalienable autonomy did the choice of subjects traditionally represented by the liberal arts make sense. An unfree person lived and worked, bound by a determining status that laid down what skills and knowledge the person would need in order to function effectively within his allotted station. For the unfree, efficient education would impart those predetermined acquirements and nothing else. For the free person, the self-determining person, the problem of education was more complicated. What skills and knowledge the free person would need in the course of his autonomous conduct in the community could not be fully predetermined. Hence, an education worthy of a free person was one that would enable him to learn whatever skills and knowledge he needed as he conducted himself in open-ended self- governance. In order to do that without incurring a crucial dependence, exactly when autonomy was at stake, he needed to be able to learn his ever-changing skills and knowledge without dependence on paternalistic teachers and other authorities. Consequently the liberal arts were those disciplines the mastery of which would enable the free person to grasp any further concept or capacity as the need arose without dependence on teachers.

Note the phrasing, "without dependence on teachers." This stricture does not suggest that the free person will be without teachers. Quite the contrary, the free person will be autonomous with respect to them, taking responsibility for attending to this one and ignoring that one, able to judge the worth of their teaching for herself. What does a youth, aware of her autonomy, want as preparation? She sees life as a continual development throughout which she will always be responsible to herself and others for certain particulars. Owing to these responsibilities, she seeks competence; but having a keen sense of her ever-changing possibilities, she cannot say honestly exactly what competencies she will desire as she unfolds her life, and she is loath to let her pursuit of competence hamper her prospective development. Consequently, she seeks an open preparation that will enable her, in the all-important school of life, to move forward independently into whatever matter she feels drawn. Hence, neither an introduction to the great books nor the beginning of a specialty, the liberal studies were simply a rigorous discipline in the intellectual tools with which one could gain access to any particular matter. Such access might involve intense engagement with teachers -- be they persons, books, or situations. Having had an education worthy of a free person, she would proceed through those engagements without becoming dependent upon them.

In ancient times this discipline in the tools of study came through grammar, rhetoric, logic, arithmetic, geometry, astronomy, and music. But these subjects were not the crux, making the education in them liberal. They empowered people to conduct themselves later in life in ways befitting their freedom. Hence, ancient commentators like Seneca derided people who took pride in being occupied with the liberal studies; he held that one should work instead to be done with them, for no good came of them themselves; rather, they served simply as a preparation for the truly serious matter of self-formation. Can someone, after a suitable preparatory discipline and engagement, acquire new knowledge, skills, and understandings on their own without dependence on teachers and formal instruction? If one can answer in the affirmative, that person has a liberal education, an education worthy of an autonomous person, one who can proceed to acquire needed knowledge without reliance on others.

With the liberal assumption of the student's autonomy, the teacher accepted an important but highly circumscribed function: the self-effacing work of making himself unnecessary. Most pre- modern pedagogy is incomprehensible without realizing that its aim was not to make the teacher more effective, but to make him progressively less important. Traditionally, teachers had the self abnegating responsibility to make their assistance unnecessary by helping students build up their capacities to learn on their own. This is a goal common to most professions. The doctor who healed in such a way that he promoted the permanent dependency of his patient on his prescriptions would be called a pusher, not a physician. The healing arts aim to bring the patient to full strength and vigor, where she is no longer dependent on medical care. So too, the teacher should build up a student's capacity to learn on her own, independent of the teacher's care.

Traditionally, this effort to educate to independence was a controlling goal of educational practice. Formal pedagogy was to help the student arrive as quickly as possible at a point at which he no longer needed instruction in order to continue developing apace. For instance, the medieval scholastic, John of Salisbury, observed, when asked why some arts were called liberal, that "those to whom the system of the Trivium have unveiled the significance of all words, or the rules of the Quadrivium have unveiled the secrets of nature, do not need the help of a teacher in order to understand the meaning of books and to find the solutions of questions." This same desire to end one's dependence on one's teachers was implicit in the way the Renaissance educator, Batista Guarino, recommended his course of studies: "a master who should carry his scholars through the curriculum which I have now laid down may have confidence that he has given them a training which will enable them, not only to carry forward their own reading without assistance, but also to act efficiently as teachers in their turn."

Consider again the question of equity and excellence. We can hypothesize that a liberal education, the capacity to acquire further mastery independently, helps a person to achieve excellence. To excel is to transcend the limits of attained achievement, to pass precisely into those regions where teachers cannot lead. Excellence is a free assertion, a gratuitous quality, something achieved but not mechanistically caused. An education worthy of free persons enables a person to excel, not because it makes her excellent, but because it helps her make herself excel. Educators cannot guarantee that someone in their tutelage will come to excel in a particular walk of life. Such eventualities are beyond the educator's reach and depend on the student's ability to sustain her drive later into the realm of unprecedented achievement. What the educator can do is help the student develop abilities to learn self- sufficiently whatever she later feels she needs. Having become able to learn what she will, without dependence on help from others, the person pursuing excellence can better navigate the realm where she is setting new standards. As an education that enables a person to learn ever more without dependence on teachers and authorities, a liberal education supports people in their drive to excel.

In a similar way, we can hypothesize that an integral education supports the quest for equity. Equity in education entails in large part, that each person, despite differing from others, should attain an integral education. The problem with equity is to resp