From I skuggan av framtiden (Modernitetens idéhistoria)
by Sven-Eric Liedman
The multiplication tables
"July 4, 1662. Up at 5 a-clock. By and by comes Mr. Cooper, Mate of the Royall Charles, of whom I intend to learn Mathematiques; and so begin with him today, he being a very able man and no great matter, I suppose, will content him. After an hour's being with him of Arithemtique, my first attempt being to learn the Multiplication Table, then we partied till tomorrow; and so to my business at my office again.
July 9. Up by 4 a-clock and at my multiplication table, which is all the trouble I meet withal in my arithmetique."
These lines are taken from a diary written way back in 1662. The name of the author is Samuel Pepys. At 29 years of age, he had received a solid education at the University of Cambridge and was starting off on a career that would eventually propel him to top positions in British society, among them the task of organizing the modern British navy.
Nowadays Pepys is famous for having written one of the most fascinating and revealing diaries of all time. The diary, recorded from January 1, 1660 to May 1696, discusses the various and sundry things, both big and small, that make up a person's life. Pepys' honesty was unfaltering. However, because he employed a kind of shorthand, his diary remained unread until the early 19th century, when an ambitious clergyman undertook the task of deciphering it.
We will not dwell on the diary as such, but rather what it has to say about the multiplication tables. For the modern reader, it may be surprising to learn that a well-educated man of that time had not mastered them. These days children do so in elementary school, and this has been the case for a number of generations. The multiplication tables are as essential as reading and writing skills. Whenever a study is released showing that such-and-such a percentage of children have not mastered them, an outcry inevitably arises. It is as if the entire foundation of public education had started to crumble.
That was clearly not true of Pepys' time, and it may be worthwhile to ask why. But first we must reflect a little on the nature of knowledge, in particular how both practical and theoretical assumptions, as well as prevailing conventions, determine what is deemed necessary to learn. Few of Pepys' contemporaries attended a regular school. Only a small minority could read or write. You learned what was necessary for your profession and daily chores from your parents, friends or older co-workers. The very hardships of everyday life demanded extensive knowledge. You couldn't even cook dinner unless you were familiar with a host of rather intricate details as to what was edible, how to preserve nutrients for an extended period of time, and how to prepare food. It was most often women who possessed this kind of knowledge, particularly where childbirth was concerned. But even the shepherd boy had to know such things as what pastures to steer his flock away from, how to treat injuries, and what do if a sheep fell sick. Apprentice craftsmen were given a more structured education. Nevertheless, it was not a matter of schooling in the sense of being cut off from the real world of earning a living. Apprentices contributed to the work of their masters and guilds while learning their trade. It may be true that modern trade schools try to simulate working life as much as possible, even manufacturing some products. But production is never the primary goal, and there remain aspects of education that have nothing at all to do with the marketplace. You might say that schools represent models of something else, in particular the various aspects of adult life. Modern schools ultimately aim at inculcating in their students a sense of their civic duties, their responsibilities as rational and emotional being.
It took a long time - in most European countries until the 19th century or later - before the majority of the population received regular schooling. In much of the world, including the Soviet Union and China, the great literacy campaigns did not come until the 20th century. In the poorest countries, general education has still not taken hold and illiteracy is actually on the rise. In Pepys' time only a small minority attended school, the overwhelming percentage of whom were men.
We can trace Pepys' schooling quite accurately. He grew up in London, his father being a respected tailor. Among his relatives was Edward Montague, later Lord Sandwich, one of the great men of his time. This undoubtedly contributed to Pepys receiving such a solid education; a highly-placed protector was required if you were ever to turn your education into a decent career. Pepys attended Huntingdon Elementary School and St. Paul's High School (located in the area of London now watched over by the enormous cathedral, designed by Christopher Wren, later a close friend of Pepys), where he was administered a heavy dose of Latin and Greek, as well as strictly puritanical lessons in Christianity. Pepys was often to express his gratitude for having received a classical education. And it turned out to be extremely useful when, at the age of 18 (older than most of his classmates), he enrolled at the University of Cambridge.
As is still the case, Cambridge (just like its sister university at Oxford) consisted of various colleges. Pepys ended up at Magdalene, one of the less exclusive colleges. We know very little about his years there. In the diary written after the fact, he relates various student antics, as well as a kidney stone attack that required a painful but successful operation. He also speaks of Samuel Morland, his tutor. According to one biography of Pepys, Morland personified the "astounding versatility of his time." The breadth of his knowledge would be inconceivable today: mathematics, the ins and outs of diplomacy, Latin, and technical innovations. It was Morland's fascination with scientific experimentation for which Pepys most remembered him. Though many of Morland's efforts were a flop, his knowledge of hydraulics, i.e. using fluids to direct the flow of energy, won him an appointment to design the royal court's exquisite fountains. He also invented a "talking trumpet." But he did not feel called upon to teach Pepys the multiplication tables. How could this possibly be?
One approach to solving this mystery is to look more closely at what it meant to study at Cambridge back then, what was actually taught. The fact is that we know quite a bit about Cambridge of the time. Nor did the school differ much from Oxford or the majority of other European universities.
A modern time traveler would find much to regard as exotic at 17th century Cambridge. There was no specialization at the introductory level. Instead of choosing a major, the student took each subject with the same degree of seriousness. The were no real exams, only brief tests, nor grades. Exams and grades made their appearance at most European universities in the late 18th century.
But there were plenty of lectures. As at most universities, Cambridge lecturers spoke slowly enough that the students were able to take verbatim notes. Books were prohibitively expensive for the average student, so you had to make your own.
Two skills were cultivated above all else. The most important was the art of disputation or defending a thesis. This art is still practiced in the Nordic countries and France, but not until it is time to receive a degree. England, the U.S. and Germany dropped the idea long ago.
At 17th century Cambridge, disputation was a commonplace activity. Each college scheduled such an event two or three times a week, and they tended to be rather undramatic affairs, with the emphasis on argument and counter-argument. However, there was also such a thing as a public disputation, which was a more serious matter. In this case, the student was to defend two or three theses of his own choice. A specially assigned opponent was charged with refuting the theses as best he could. Logical dexterity was the name of the game. Since Aristotelian logic was the basis of all argument, mastery of deductive reasoning in general and the syllogism in particular was essential. In fact, the syllogism was the opponent's primary tool. The disputant (otherwise known as the respondent) would try to identify the syllogism and find a corresponding one to use against his opponent. Thus, the entire event was like a fencing match that continued until one combatant was able to back the other into a corner, out of which no syllogistic sleight-of-hand could rescue him.
The disputation was a kind of rehearsal for what was regarded as the most important skill an educated person could possess - dialectic, the ability to set one argument against another, to examine their plausibility and ultimately arrive at the truth.
The second essential skill was eloquence or rhetoric. At Cambridge, this art was cultivated with special scrupulousness. In addition to following strict rules, the student was required to both capture his listener's attention and speak in a convincing manner. Though any number of subjects were fair game for rhetorical exercises, those favored by the ancient Greeks tended to dominate. The length of a presentation varied considerably; it was to be written in advance but delivered orally. Despite the lack of an opponent, a panel of judges was always there with a rigorous critique.
The third skill, which had been linked to the other two since ancient times, was the discipline of grammar. Dialectic, rhetoric and grammar comprised the "trivium," i.e. the junction of three roads (thus the source of the word trivial, i.e. that which is to be learned first). Grammar was still primarily a matter of understanding, speaking and writing Latin, something of which most students, including Pepys, had rather extensive knowledge by time they arrived at the university. And there was no letting up there either - Latin was the language used at the university.
In addition to the trivium, there was the quadrivium, i.e. the junction of four roads. While the trivium constituted the core of what later was to become the humanities, the quadrivium formed the embryo of the modern exact sciences. In this case the four roads were arithmetic, geometry, astronomy and music. Way back in ancient Greece, the Pythagoreans had already regarded these disciplines as the four branches of mathematics. Arithmetic and geometry were considered to be manifestations of pure thought, whereas astronomy and music submitted the events of the real world to mathematical description. Looked at from another angle, arithmetic and music could be classified together in that they dealt with discrete units - essentially the realm of whole numbers -while geometry and astronomy looked at continuums. It may be obvious to us that astronomical calculations demand significant knowledge of geometry, but where did music fit in? To answer this question we must look at the discoveries of the Pythagoreans regarding the nature of musical harmony. They were able to demonstrate that high C entails twice as many vibrations as middle C. This discovery, still one of the fundamental principles of acoustics, gave fuel to the idea that the rotation of the heavenly bodies produced divine music, a concept which lived on into early modern times. Using musical notation, Johannes Kepler was even able to convey the beauty of these harmonies.
The trivium and quadrivium were still part of the formal curriculum available to Pepys when he arrived at Cambridge. But they were mixed in with a large number of other disciplines. The notes of John Cole, a Cambridge student of the time, provide a fairly good indication of the multifarious curriculum. Though the subjects were classified in a rather scholastic manner (Thomas Aquinas might have done something similar in the 13th century), the system was much older than that, much of it going back to Aristotle.
Fundamental to the classification reflected in Cole's notes is the distinction between "objective" and "directive" sciences. An objective science deals with how things are (knowledge), an objective science with what to do (action). Although this distinction has long been discarded, there remain traces of it in the demarcation between the arts and sciences. However, for the last century and a half, "science" has referred primarily to the natural sciences; in the mid-17th century, the concept was much broader. The scientiae were comprised of the four traditional university faculties: theology, law, medicine and philosophy. (Cole divides philosophy into the four familiar categories of metaphysics, physics, mathematics and ethics). Of these four faculties, philosophy was the one with which most students came in contact, although there were elements of theology in the basic curriculum. Mathematics was sub-divided into the subjects discussed above: arithmetic, geometry, astronomy and music, plus optics, which attained an equal status with the others. Consistent with the Aristotelian spirit, ethics included economy and politics. Politics covered both military and diplomatic history.
The artes, i.e. instruction in what to do, were broken down into the communicative and the reasoning disciplines. The communicative disciplines involved how to get through to other people, while reasoning focused on the proper use of human rationality. Actually the only reasoning discipline was logic (or dialectic, as Cole would have defined it), the key to the art of disputation. Grammar and rhetoric, the other branches of the trivium, were both considered communicative disciplines (as was poetry).
The most important thing to emphasize here is the difference between theory and practice, insight and action. In his book The Concept of Mind (1949), Oxford philosopher Gilbert Ryle discusses the distinction in the previous British tradition between "knowing that" and "knowing how." Any system of education tries to impart certain concepts of reality; e.g. that the Earth revolves around the sun or that the U.S. Constitution is based on the balance of powers according to Montesquieu's model. In addition, education is aimed at teaching basic skills such as literacy, understanding written Latin, or making an oral presentation following the rules of rhetoric.
By identifying the dividing line between concept and practice in the curriculum offered to Pepys, we can gain some insight into the criteria against which a well-educated person of the time was judged. The scientiae instructed him as to the nature of reality, while the artes imparted essential skills. Just as modern schools provide models of the adult world, the 17th century university prepared the student for a life in which reaching truth in accordance with the rules of logic, as well as speaking with other people in a convincing manner, were the keys to success (and if you threw in a little poetry suitable to the occasion, it might not hurt either). In addition, the student was expected to gain at least passive knowledge of what, from our vantage point, looks like an extraordinarily broad range of subjects.
This dividing line also reveals how the student was to absorb the requisite knowledge Grammar, rhetoric and dialectic provided the reasoning and communicative tools necessary to probe the secrets of physics and mathematics. You reasoned and communicated your way to the mysteries of physics and mathematics.
The goal of the universities was simply to impart existing knowledge, not to perform new research. The prevailing attitude was that all knowledge had already been attained. With the exception of the new truths inherent to Christianity, the great masters of antiquity could never be surpassed.
Nevertheless, a university always provides experiences and opportunities that transcend its own curriculum. Pepys remembered his tutor for his captivating though unsuccessful experiments. Though completely marginal to the institutional setting, these experiments hinted at things to come in the scientific disciplines. At this point, the Scientific Revolution was already far along: Copernicus, Galileo, Kepler and Descartes had publicized their works. Though you would hardly have known that by looking at the Cambridge curriculum, there were a number of books to be bought in town if you were interested in the groundbreaking concepts these men had introduced. One person who took advantage of the books was none other than the young Isaac Newton.
Newton and Pepys eventually got to know each other. Only ten years younger, Newton came to Cambridge in 1660 after having been forced to interrupt his studies and work on his father's farm. Only the intervention of a concerned rector persuaded Newton's mother to change her mind. Newton's previous education had consisted of the usual intellectual fodder, namely "Latin and more Latin, with a bit of Greek toward the end and no arithmetic or mathematics worth mentioning." He succeeded brilliantly in these subjects, while developing an interest in mathematics and mechanics on the side. He made a number of mechanical inventions, picking up some practical math from his brother, who was on his way to a more practical career. But not until Newton entered the university did he have any real contact with theoretical mathematics or the new natural sciences. Even at that point he sought out books on his own. Though a professorial chair in mathematics had just been established, its first holder was unable to help Newton to any significant extent. By time the professor got around to quizzing Newton about what he knew, it turned out that the young student had skipped over Elementa, Euclid's elementary book on geometry, and mastered Descartes' considerably more advanced work. The professor immediately realized his student's genius; and at the tender age of 27, Newton succeeded him. Though Newton had already made some of his historic discoveries and done the spadework for his theory of gravitation, he did not publicize any of his findings until much later. When he finally did so, his work was so important that the professorship receded into the background and he earned his living as an official at the London Mint. The most important channel for his scientific discoveries was not the university but the Royal Society, the new but highly renowned scientific academy in London where original research was highly valued. It was here that Newton and Pepys became colleagues. Pepys was chosen as president of the society in the 1680s, while Newton was accorded the same honor ten years later. During Pepys' tenure, Newton published his most famous work, Principia Mathematica (1687). Thus, Pepys was the one who gave his imprimatur (stamp of approval) to the printing of the book.
Cambridge did contribute to Newton's career, but only marginally. It is quite revealing that his work did not lead to a major upsurge of interest in mathematics or physics at the university. It's true that toward the end of the 17th century, mathematics came to be regarded as an important subject and the core of a unique, well-designed curriculum. But it would be a long time before Cambridge gained a reputation as a center of scientific research. Oxford was even more recalcitrant in this regard; Newton's older colleague, the great physicist and chemist Robert Boyle, was actually turned away. As an experimental alchemist, he was forced to build his own laboratory outside that venerable institution.
So Pepys did not learn the multiplication tables at Cambridge. At this point, we are beginning to suspect why, but perhaps only hazily. To clear things up a little more, we will have to examine the status of mathematics at Cambridge. John Wallis, a former student and eventually a renowned mathematician, wrote that mathematics was simply regarded as a way to pass the time: "Mathematics was not seen as an academic discipline, but rather an occupation for mechanics, merchants, sailors, carpenters, and surveyors; possibly for a few calendar makers in London." This list is interesting in several ways. Calculation was for people who needed to master a type of ars or skill irrelevant to the educated. Remember it was a sailor who finally taught Pepys the multiplication tables.
The same was the case throughout Europe. Descartes relates in his Discours de la méthode that, at the famous Jesuit college of La Flèche in the early 17th century, he was taught that mathematics could only be used within the arts mécaniques, i.e. by certain kinds of artisans.
Thus, mathematics was not one of the skills expected of the educated man. It was assumed that he knew something about the world of numbers, but it never occurred to anyone that he should be able to sit down and carry out a series of calculations. Until the late 17th century there were very few lecture notes that have been preserved and contain any kind of mathematical notation - a further sign of the discipline's obscurity. One set of notes that does so refers to the four basic arithmetic operations, then proceeds quickly to various branches of mathematics, such as music, astronomy and mechanics.
We might add that not even music - either as a theoretical or practical discipline- was accorded prominent status at Cambridge. Nevertheless, students who had some inclination in that direction were able to cultivate it during their university years. Pepys was among these students. He was a dedicated music lover throughout his life, and a fairly decent flutist as well.
It would be interesting to shift our perspective for a while. At first glance we might assume that the multiplication tables were considered to be pretty elementary stuff back in Pepys' time. But is that really true? We should not be misled by the fact that some common artisans had mastered them. By doing so, we would fall for the old prejudice that people without a solid formal education are incapable of carrying out complex tasks. Actually, the sailor who taught Pepys mathematics had overcome the difficulties inherent to mastering recently discovered knowledge. While dialectic and rhetoric followed rules that were thousands of years old, the multiplication tables were virtually fresh headlines, at least by the standards of the time.
Nevertheless, human beings have known how to multiply for a very long time; the Egyptian Papyrus Rhind from around 1600 B.C. testifies to that. And this knowledge was not only a matter of book learning, there were oral traditions as well. The methods could be extremely elegant. One approach was the "Russian Peasant's Algorithm," which some people claim has lived on into modern times in Siberia. Let us take a look at it.
If you want to know how much 47 x 7 is, you can set up two columns as follows:
In the left column, you divide the number in half each time until you get to 1. In the right column you double the number each time. Finally you add up all the numbers in the right column that are opposite odd numbers in the left column. In this case, you add 7 + 14 + 28 + 56 + 224 in the right column. And sure enough, the sum of these numbers is 329, which is exactly 47 x 7!
Neither the author of Papyrus Rhind nor the Russian peasants knew anything about the multiplication tables, which rely on something that arrived rather late in the history of mathematics, namely the equal sign. We tend to take the equal sign for granted, since we are exposed to it in grammar school, or even earlier. We seldom, if ever, think about it; and if we do, we are likely to overlook its real significance, assuming that it points to the result of a mathematical operation. Thus, the equation 9 x 5 = 45 looks perfectly natural to us, whereas the equally correct expression 45 = 9 x 5 appears odd.
We don't really know how Cooper and his initiate Samuel Pepys looked at all this. One thing for certain is that the equal sign was introduced by English mathematician and court physician Robert Recorde in his book The Whetstone of Witte. Published in 1557, the book was totally bypassed at British universities. Nor was it intended for highly-educated people, but rather for the common folk, as demonstrated by the fact that it was written in colloquial English instead of Latin.
The multiplication tables constructed with the use of the equal sign yield exactly the same results as the Russian Peasant's Algorithm. But they have a big advantage once you have learned them: they are much faster. Setting up the two columns above requires a good deal of time, even for a very simple calculation. With the tables already in your head, you have a convenient, if extremely limited, calculator at your disposal.
Speed was not a crucial consideration for a Russian peasant. At most he used the algorithm several times a year, for example when he bought homespun cloth from a merchant or figured out how much seed to sow. The same was true of a Cambridge student; the chief criterion for success was being able to quickly construct a winning argument or an irrefutable syllogism. When Pepys left the university and arrived in London, he encountered an entirely different world. Knowledge was highly valued there as well, but it was the kind of knowledge that could be applied to buying and selling, handicrafts and manufacturing, administration and military might. Latin and syllogistic logic could hardly measure up to arithmetic, the natural sciences, technical advances, even history.
Life in London was bustling. More and more the clock told people when to go to work and hurried them on their way (Pepys' diary is meticulous about the time of day). Quantities were increasingly important in the routine of daily life. What was the quickest way to determine how much food and drinking water the crew of a ship required? Were there any tricks that could speed up a purchase when other customers were waiting in line? There were many people in London who could make use of a revolutionary new approach to performing calculations.
So Pepys was constantly reminded that he lacked certain everyday skills. Though his diary does not tell us why he decided to employ Cooper's services, his devotion to study leaves no doubt that he longed to adjust to his new life. People are often driven by the need to catch up with those around them, particularly when they leave the confines of the university and enter the real world.
Thus, Pepys had taken a giant step away from the Cambridge setting where mathematics was disparagingly regarded as an activity for the common folk. On the contrary, he was fully prepared to learn from the common folk. The multiplication tables boosted him a little further toward prestigious positions, above all Secretary to the Admiralty, the highest civilian officer in the British Navy.
In Pepys' time the multiplication tables were reserved for occupations practiced by a small minority of the population. But it wasn't long before they were adopted by trade schools and other educational institutions with a practical orientation. Finally the grammar schools integrated the tables into their mathematical instruction. The real breakthrough came with the introduction of popular education. This was a radical new concept, that nearly the entire population should be taught the fundamentals of knowledge. In most Christian countries, these fundamentals included the tenets of Christianity. Whereas spelling had previously been considered of little importance - you sort of made it up as you went along - it now became a key skill, along with the multiplication tables. In fact, spelling and the multiplication tables were the minimum skills required of a literate person.
Why were these particular skills considered to be so essential? The Russian peasant could continue to use his algorithm, at least until the sweeping literacy campaigns after the 1917 Revolution. In most European countries at the turn of the 20th century, the majority of people still lived in the countryside and only rarely had the opportunity to use the new skills. So what was the point of teaching them in the schools? In the first place, requiring pupils to learn them was an unparalleled disciplinary tool. In the second place, they offered a simple way of classifying people into the knowledgeable and the ignorant.
Whoever mastered the tables was looked upon as a mature and competent person, while he who insisted on remaining ignorant was viewed with contempt. Parents devoted more time to drilling the multiplication tables into their children's heads than anything else. As Pippi Longstocking, a popular character in Swedish children's literature was well aware, memorizing the tables was the best way to keep teachers off your back.
No doubt the multiplication tables also prepared rural folk for the modern world in which everyone needs to do some basic calculation. But, lo and behold, suddenly the mini-calculator came along and upset the apple cart. It is difficult to know how long the tried and true multiplication tables can hold out. So far grammar school pupils still chant its praises, though perhaps not with the solemnity of previous generations. Nobody has to tell them that there are faster and more foolproof ways of obtaining the answer to an arithmetic problem.
To Pepys the multiplication tables looked like the hardest thing that arithmetic had to offer. But he studied industriously, and by July 11, 1662 - two days after having bemoaned the difficulty of his lessons - he talked about the new method of performing calculations, "which I am now almost master of," so that he could continue on in his mathematical pursuits. In early August, Mr. Cooper introduced him to mechanics. Pepys was now on the road to becoming a distinguished president of the academy that would one day publish Newton's Principia.
Pensum, voluntary path, and complementary studies
Schools have existed since at least as far back as ancient Sumeria. Nevertheless, there are cultures even today in which formal education, in the sense of institutions where knowledge considered essential to leading a productive life is passed on from one generation to the next, is wholly unknown. Instead young people are taught to tread in the footsteps of their parent's generation. The oldest members of the community, regarded as marvels of wisdom and sagacity, form the pillars of this informal educational process.
A key feature of the modern era is the emergence of a host of different kinds of schools. As a result, virtually the entire citizenry receives at least several years of basic education.
Regardless of whether a particular society has a centrally coordinated or more loosely administered educational program, we will refer to it as the school system. This section deals with the role of school systems in modern society and how they have reached this point.
A school is an excellent example of what we ordinarily mean by an institution. It possesses a certain degree of permanence. It is founded in order to attain certain goals, sometimes clearly defined, often diffuse or highly diverse. In addition, a school is mutable. Some of the changes it undergoes are due to consciously implemented reforms, others are unintentional but highly tangible nevertheless.
One important function of a school, as mentioned earlier, is to construct a model of the world beyond its walls. As this world changes, we naturally assume that the school will change as well. In practice, the interplay between the changes that take place in a society and its school system is extremely complex.
Let us leave aside for the time being the unintentional changes in a school system and focus on intentional reforms. There is no guarantee, however, that these reforms will always be in sync with what is going on in the outside world. Quite the contrary, reforms may be aimed at preserving something that is in danger of extinction or reviving something that has already disappeared. This responsibility to conserve and revive tradition will always be seen as one of a school system's obligations.
From the perspective of the modern world, the most radical change has been that schools are now expected not only to reflect current reality, but to prepare its pupils for a changing world. Nevertheless, such reformist ideas immediately face opposition from those who maintain that the primary role of a school is to pass on tradition to coming generations. According to these anti-reformists, an educational institution should emphasize classical thought, the wisdom distilled by centuries of tradition and the experience of generations. For them there is no way to see into the future, given that we know absolutely nothing about it and can only make faulty projections on the basis of the fleeting present.
It is revealing that this conservative tradition did not emerge until it had something to challenge. At Pepys' Cambridge, there wasn't much thought given to what should or should not be taught. The curriculum was taken for granted. Nobody made a big deal about how old or new a doctrine or a work was. The important thing was that it belonged to the "canon." Selecting from this canon was far from a cut-and-dried matter, but the age of the material was irrelevant.
With the emergence of claims that certain ideas were better simply because they were newer, resistance developed to these novitates or "fads." The struggle over Descartes' teachings was largely about whether such novelties were permissible or not.
Although these conflicts, just as subsequent skirmishes over the theories of Newton and others, were short-lived, the issue survived when it came to school curricula. The opponents of reform claimed that schools had an obligation to preserve tradition. The classical heritage must not be allowed to disappear. That's how people had always been taught to think, and that's the way it would always be.
In reality, most actual reforms, be they of a sweeping or relatively undramatic nature, were products of compromise, an amalgam of the sometimes contradictory, sometimes complementary aspirations to preserve and renew. After bitter wrangling, a resolution was reached that could include both Latin and modern science, both classical literature and contemporary social sciences. The final result was often highly paradoxical.
What is particularly "modern" about these reforms is the stark contrast between present/future perspectives and the vigilance with which the classical canon is preserved.
Reformers argued that the purpose of the school system was not limited to preparing the student for society as it is currently constituted, but also to supply him with the wherewithal to participate in societal transformations already underway.
To many citizens, the school was the most promising tool for altering society in the direction they themselves advocated. Political reformers in particular viewed schools in this way. Assuming that revolutions are a risky proposition, leading to chaos and unforeseen consequences, the best way to shape a better world was to start with the younger generation while it was still malleable, affording them the motivation and means to construct a new society. Adults have already settled into things as they are, adopted the world's morés as their own.
But even revolutionaries have placed enormous emphasis on the school, which they regard as the most effective tool for propagating to coming generations both their concrete accomplishments and the spirit of their struggle. Nor does it take long before most revolutionaries arrive at the sober view of reformers that fundamental change is impossible without the fresh insights of youth. During the French Revolution both Robespierre and the leaders of the Thermidore rebellion designed major educational programs aimed at the entire citizenry. Napoleon took up the same tack.
Those who opposed these progressive ideas contended that the role of the school system was to transmit the best that humanity, or at least their particular culture, had achieved. Furthermore, the school should be a bastion of religious belief, established custom and prevailing social norms.
Though the above formulation represents the unadorned conservative position, we should not jump to the conclusion that it has been the rallying cry only of political conservatives. In point of fact, many political radicals have promulgated it as well.
Educational policy is an arena in which ideological differences stand out with an unusual degree of clarity. In addition to the conflict between past and future, other dichotomies become visible, including equality/elitism, freedom/discipline, and liberty/civic spirit.
Despite the swirl of ideology that surrounds educational institutions, it would be difficult to pair up individual schools with particular ideologies. A reform measure may have such-and-such objectives, whereas the institutional arrangements that result from the implementation of the measures may be something else altogether. For example, how do you achieve the goal of inculcating democratic values in your students or affording them the best chance to make a decent career for themselves? One approach is to give them formal training in a particular direction - by setting up a democratically-run discussion group or creating a tough competitive atmosphere. Another approach is to include material in the curriculum that sings the praises of democracy or competition. Between these extremes are a host of other alternatives.
Nevertheless, a school is in many ways a rigid phenomenon, an institution with all the resistance to change that word suggests. Reforms can alter this institution, but rarely as much as intended and never wholly in the prescribed direction. How reforms are implemented and the extent to which their goals are realized constitute a major field of study today, in terms of both education and other areas.
Educational institutions tend to have long, unbroken traditions to look back on. When altering these institutions, the challenge is to create something new without destroying all signs of their hallowed past. One glance at today's universities will demonstrate the extent to which the past lives on in them. The very institution is of medieval origin, and this long history is evident even in universities founded much later on. The guild tradition has not vanished completely, either when it comes to a motley assortment of rites and rituals or to such established traditions as the Master's Degree, which bestows upon a student, like a medieval aspirant, the mark of proficiency within a particular field. Many universities are still run in line with a decisionmaking process that evolved after the Middle Ages, a process that may favor collegial harmony but often stands in the way of efficiency. The close connection between research and higher education, one fruit of William von Humboldt's sweeping university reform in the early 19th century, has also survived at most institutions. The principles of modern bureaucracy, as identified by Max Weber, have left their mark on university administration, often colliding with the old, more personal approach. The objectives of the large-scale university, so different from those of traditional small universities, have filtered down to nearly all institutions of higher learning. Students and other interested parties have a number of channels through which they can assert their demands. The corporate ideal of the dynamic, unconventional leader able to solve any and all problems has also made itself felt at the contemporary university.
Thus, the university is the bearer of its own history. Its past is not something that is simply dusted off at anniversary celebrations, it lives in the very structures that define what the university is all about. Each and every historical layer represents a once firmly-held conviction concerning the nature of the institution; at the very least it reflects the intellectual and social climate of the times. For the most part, there is little remaining of these convictions, but they live on nonetheless, albeit in petrified forms, which we might call frozen ideologies. A frozen ideology can influence members of the university community without their being aware of it. The processes by which decisions or regulations are reached, assessments made, instruction carried out and research organized bear at least traces of bygone ways of thinking . Since the frozen ideologies are layered one on top of the other, they tend to create friction. The demands of collegial harmony collide with those of bureaucracy, which in turn has difficulty accommodating the democratic aspirations of students. And the new corporate ideology of a strong leader is difficult to reconcile with any of the above.
Of course, the last thing reformers are bent on doing is preserving this history, the source of so much conflict and deadlock. According to the most zealous advocates of reform, everything old should be swept away once and for all. But unless they start up new institutions (the approach of the French revolutionaries, closing down the universities completely and replacing them with a college system), this goal is never fully achievable. Institutions are resistant, that's why we call them institutions. What makes each institution distinct is what is commonly referred to as its "unique spirit," an expression that is just as reveling as it is vague. The unique spirit is a product not only of frozen ideologies, but also of more diffuse, unwritten traditions. Ultimately the frozen ideologies define this spirit more than any other single factor.
Thus, the very way in which a school is structured tends to propagate old patterns of thought. But this attempt to preserve the past may also be intentional and concrete. Even in modern times, schools not only prepare the younger generation for a changing world, they also transmit that which already exists, frequently that which has been around for a long, long time. Students may read the Bible or the Koran, Homer or Plato, Shakespeare or Goethe. More contemporary teachings do not ordinarily make it to the curriculum until they have become respectable and fully accepted. This is particularly the case in the lower grades, for which study materials often reflect outdated knowledge. The universities are somewhat more open to contemporary research and thought.
However you look at it, a school is an institution of learning. What is taught there varies widely, anywhere from preparation for a profession or civic life, to shaping character, to instilling discipline, to some combination of these things. Above all, the school must establish goals for its pupils; these goals may be diffuse in themselves, but they must take concrete form at the point academic requirements are set forth. Until recently, most Western high schools required the study of Latin and Greek. However high-sounding the goals of the institution may be - personality development, civic spirit, insight into the meaning of life - a curriculum needs to establish standards in such specific disciplines as grammar, vocabulary or the interpretation of texts.
This concrete expression of a school's goals is called the pensum. It is an excellent term, originally referring to something that, after having been measured and weighed, is judged to be suitable. The pensum is obligatory in nature. It refers to work, evoking the quality of burden or resistance, its Lastcharakter, to borrow a term coined by the young Herbert Marcuse. Occasionally a pensum is made obligatory for all students at a particular level within the school system; this was often the idea behind the early public schools, the impulse to cast everyone in the same mold. At other times students are given a variety of alternatives; at a modern university, the possible courses of study are legion, and a student often has a great deal of freedom within a particular course of study. Nevertheless, once you have made your choice, you have a pensum to deal with. If it involves subjects that interest you, it will naturally feel less oppressive. But it still offers a certain degree of resistance.
Thus, pensum is a better word than curriculum, the most frequently used term in pedagogic research. A curriculum is simply a plan that enumerates an entire course of study, both voluntary and mandatory. In current English usage the curriculum refers both to the plan and to its implementation. A curriculum is a course or a track. The word also lacks the element of compulsion and burden that the word pensum carries.
The school system in which Pepys learned so much - though not the multiplication tables - offered a basic course of study that was more or less obligatory. On the other hand, at least at the university, the actual demands placed on a student were rather vague. The amount of work required varied from one institution to the other. Cambridge was not particularly known for its rigor. The areas in which students faced somewhat more stringent requirements were related to skills rather than ideas. You had to be able to express yourself in Latin, employ Aristotelian logic in debate and follow the rules of rhetoric. There was fewer requisites when it came to factual knowledge. However, there were very definite notions concerning what a gentleman should know, and they definitely applied to Pepys, who came from a respectable but far from dazzling social background. There was certain literature that every student must be familiar with and were therefore part of the pensum. You read Aristotle either in the original or in subsequent interpretations. The version of Aristotelianism that provided the framework for how the course of instruction was structured was a revision of the original. Classical literature played a key role. Both biblical knowledge and theological exposition were indispensable. The British school system was in no way modern, and it would be a long time before it was.
Few students ever limit themselves to the pensum. They also find things to learn on their own. There is always more to garner than what is absolutely required, and the grass normally looks greener on the other side of the pensum. You cultivate your own interests. Many gifted students who were later to make major contributions to our storehouse of knowledge had a hard time with the pensum but trained themselves in other, more inviting areas. During his short and troubled academic career, Charles Darwin, who despised Latin and struggled his way through theology, often ran up against insurmountable obstacles. But he mastered geology and biology virtually on his own. And he became a fully accomplished natural scientist despite the almost total lack of training in the field.
Isaac Newton may have breezed through what was required of him, but he taught himself much more and was even daring enough to dismiss the pensum when it suited his fancy. He passed over Euclid's' Elementa, obligatory since time immemorial, and chose Descartes instead.
David Hume found his watering hole within the pensum itself - the classical Latin authors in general and Cicero in particular were his favorite - but he went way beyond what was asked of him. When he subsequently decided to study law, he thought the pensum despicable and fled back to his philosophers, eventually becoming one himself.
We will label a non-obligatory course of study, regardless of how it is related to the pensum, the voluntary path. You read more than you are told to, you get in touch with people whose wisdom you are not required to partake of, you make your own observations. This voluntary path may appear to be pure pleasure or play at first, but it often develops its own inner compulsion. An inexorable interest is a demanding master.
It is not always a simple matter to distinguish the voluntary path from complementary studies. Complementary studies include that which is not part of your ordinary course of study but which is necessary to learn in order to reach a particular goal. Though not part of the pensum, complementary studies cannot be avoided if you are to fulfill your obligations or get ahead in life. In one sense the voluntary path becomes a goal in itself, whereas complementary studies are only the means to an end. But even this end may be up to you; in other words, there is an essential element of voluntariness here as well.
All indications are that Pepys regarded the multiplication tables as complementary studies rather than as a voluntary path, in contrast to the university studies he had completed several years earlier. We can be fairly certain that he was not required to learn the new shortcut to perform arithmetic operations. If that had been the case, he would have said so in his diary.
The number of possible voluntary paths and complementary studies is virtually infinite. However, the options open to a student are limited by the knowledge and traditions available to a particular time and place. We will call this wellspring of knowledge the potential repertoire. The breadth of the repertoire varies considerably. When a young Russian by the name of Michail Lomonosov, who had been born in 1711 in a remote fishing village near Archangelsk on the White Sea, began to cultivate an interest in literature and nature, his repertoire was simply that which he could observe with his five senses, the handful of people whose knowledge and experience he could partake of, and the few books that could be found in the village. Being a precocious child, he was hardly in a position to pick and choose, but merely took advantage of everything he could get his hands on. Of course, he soon discovered that there was much more to learn than he had access to, and at the age of 19, he set out on the difficult journey to Moscow, where the repertoire was immeasurably larger and where he could study such subjects as Greek and Latin. From there his path eventually took him to Germany and the Netherlands, where he met the philosopher Christian Wolff and came in contact with the cutting edge of natural science, as well as avant garde literature. Back in Russia, he settled down in the capital and became a noteworthy poet and natural scientist. His most renowned discovery was the principle of the constancy of mass.
We might compare Lomonsov's situation to that of a young person today who has the good fortune of having been born of well-off parents in a highly developed part of the world. No doubt he has access to computers and the internet, i.e. what appears to be an unlimited source of information.
With the advent of compact disks, much of the world's music is now at your fingertips. Given all the well-stocked libraries, it would take a lifetime of reading to cover only a tiny fraction of what they have to offer. Films and the media represent another inexhaustible source of information. The major cities, where a growing percentage of mankind lives, offer a myriad of new experiences simply by their very existence.
This rapid expansion of the possible repertoire, a key aspect of the modern age, is closely related to technical and economic development and thus to the tradition of the hard Enlightenment. But the repertoire as such belongs to the soft Enlightenment. It may be true that, in their never-ending path of progress, technology and economy, like the natural sciences, require that some people attain advanced expertise in their fields. But beyond those particular needs, the possibilities are infinite, and it is difficult to know what insights and skills are most urgent in order to promote scientific, technological and economic advances.
Thus, every school and university is confronted with increasingly difficult choices. Whereas the youthful Lomonosov gobbled up everything there was to read in his native village, and whereas the best 17th century universities still aimed at providing fundamental training in all of the basic sciences, the deluge of possible subjects has represented a growing problem ever since. Two plausible but irreconcilable paths have emerged. One path entails allowing or even encouraging young people to specialize in one particular field, striving to obtain the most knowledge possible in that area. The other path, much wider, is the one on which most everyone starts out. Its destination is the ability to participate actively in the community and the larger society. Through gaining access to a general pool of knowledge, people are able to understand and empathize with each other more easily.
The most common compromise between these equally rational paths involves a kind of tree-like formation: the trunk is common, but the branches grow narrower and narrower as the student finds his area of specialty.
The idea of a common trunk became particularly relevant when the grammar school was first conceptualized, the objective being to reach the entire population (although children of the privileged classes continued to attend the private schools that had been built exclusively for them). In countries where grammar schools were linked to the dominant religion, a strictly confessional education was long the order of the day. But such things had earlier been taught to the common folk in other ways. What was new and revolutionary was the commitment of the grammar school to teach everyone reading writing, and arithmetic. Nearly every country adopted a similar approach; English-speaking countries coined the phrase "the three R's," and similar witty abbreviations popped up all over the place. Before the era of public schools, the level of reading ability had varied greatly from country to country, the Protestant countries being the most advanced. But now everyone was to get in on it. The ability to write, even less widespread than reading, would also become everyone's privilege. In terms of arithmetic, it is hard to know how extensive this knowledge was before the advent of the grammar school. Even those who lived in remote rural areas where money was relatively unimportant needed to perform some elementary calculations. But the schools offered, and demanded, a more uniform approach. You might master something along the lines of the Russian Peasant's Algorithm, but they were of no help when you had to rattle off the multiplication tables.
There was also a third area of instruction that became integral to the grammar school, particularly in the decades around the turn of the 20th century, and that was national history. Reading, writing and arithmetic are pure skills; it doesn't matter what you read, write or calculate, as long as you proceed methodically from the basic building blocks. National instruction, like religion, had a defined content. A better way to put it would be that content was created. This was the heyday of the national readers, the time when a canon of national myths and narratives was first compiled. National history was written so that everyone could understand it. So it wasn't a question of simply knowing how to read and write, but rather how to read and write your mother tongue, which was portrayed as unique in various respects. Even in the older schools, the study of language and national literature became essential, even primary, subjects. Furthermore, new subjects were introduced with the aim of strengthening the pupil's sense of national identity.
We have already touched upon the background of this nationalistic upsurge (chapter 4). What is important here is that it helped change concepts about what kind of knowledge was most fundamental. The pensum shifted focus in a nationalistic direction.
In order to accommodate this pensum, new material was created that was not found in the existing repertoire. Fragments were lifted from the past, but the sum total was completely new, and even the fragments had to be reshaped in order to suit the demands of the modern age.
This nationalistic trend fueled the belief that a society would be more coherent if everyone shared a common store of knowledge, from which the special expertise associated with particular professions would be regarded as offshoots. Industrialization and urbanization led to geometric growth in the number of fields for which professional training was offered. The demands of individual professions clearly required that complementary studies be added to the common pensum.
When it came to training for prestigious professions such as doctor, engineer or lawyer, there were recurring debates as to how specialized it should be. Some argued that people with such key roles in society needed to attain a broader perspective than what narrow professional training had to offer. Others maintained that rapid scientific and technological progress, combined with the growing complexity of society, required that these professionals devote their undivided efforts to what they could do best.
Similar conflicts emerged in terms of education at all levels, with the exception of the most elementary. On the one hand, modernity brought with it a dramatic increase in the number of professions. On the other hand, the modern age exposed the average citizen to vast changes in their social, political, economic, environmental, and cultural realities. Thus, both sides in the debate received grist for their mill, and the conflict was increasingly difficult to resolve.
It is not difficult to understand why the school system, more than any other social institution, was continually accosted by demands for reform. In most countries, there was a constant flurry of studies, proposals for change, and new edicts. All kinds of fads came and went. The trajectory of educational reform is unpredictable, and you can never be sure where a school system is heading, in terms of either content or goals. However, there is a long-term trend toward pupils spending longer years in school, where they face a growing myriad of options with regard to what path they wish to pursue.
Before looking at a few cases where the interplay between pensum, voluntary path and complementary studies is rather obvious, we should reflect a bit about the nature of the possible repertoire.
The possible repertoire includes everything that can be taught at a certain time and in a certain milieu. It involves not only written material, but all kinds of experiences - the contemplation of nature, the use of artifacts, intercourse with other people, observations of society. All of these experiences affect what and how a person learns.
This possible repertoire also includes documents from the past, even the distant past. Some of these documents may be discussed when a school system is attempting to define its pensum. It is edifying to examine which kinds of documents are looked at and which are ignored. The rate at which something becomes out of date is an excellent measure of how it fits into the modernization process.
If you go to a major research library, you immediately run into literature that nobody would ever consider using in a contemporary school. For example, there is shelf after shelf of books containing tables that help in carrying out complex multiplication and division, not to mention tables of roots, logarithms, etc. At one time these tables were essential both in everyday life and in school. Today they are completely forgotten by everyone except historians of that kind of literature.
The same thing applies to the older natural sciences, except for the highest and most theoretical levels. Works that until recently were considered essential have been discarded. Those who are familiar with the Science Citation Index and similar keys to scientific literature often borrow an expression from atomic physicists and talk about the fission time within various disciplines. Simply put, fission time is a gauge of how old the sources are that are still considered relevant. The shorter the fission time, the more rapid the aging process. In most of the natural sciences, the fission time is just a few years. After that point, virtually nobody returns to this literature to obtain information of use in current research. The only people who do so are historians and sociologists of science, as well as other scholars whose interest is far afield of the purpose for which the works were written in the first place.
Nor would anyone consider including such outdated material, or an update of it, in encyclopedias or instructional guides. However, when it comes to the highest theoretical levels, it's a different story altogether. Modern physicists may be deeply interested in ancient philosophies or religions, a fact of which those who design curricula are often aware.
In the social sciences and humanities, the aging process is less rapid but nevertheless very palpable. Textbooks from 50 or 100 years ago are unusable, not only because the information they contain is out of date, but also because you would have to be thoroughly schooled in that period of history in order to grasp the concepts on which they are based. In rare cases, these textbooks may be read as literary documents, but that is far from the purpose for which they were originally written.
On the other hand, there are genres that consistently re-emerge in both the pensum and voluntary paths. Ancient religious teachings and commentaries are a prime example. People still read the Bible, the Koran and the Bhagavad-Gita and find immediate relevance to their everyday lives. The same may be said of great literature, which can be just as ageless as music or art. Even philosophy at the most general levels retains its pertinence through the ages. Plato's dialogues and Kant's article on the Enlightenment may be read as if they had been written yesterday.
It is not difficult to see that the aging of texts has to do with their position in relationship to the hard Enlightenment or, if you will, the modernization process. The shorter the lifetime of a text or document, the closer it stands to basal development. Wisdom (to use an old-fashioned word) is not among the things that has been transformed by modernity. It is an area where no discernible development occurs; what Buddha or Plato or Lao Tsu say about the human condition still apply, and we immediately understand the maxim of the Pueblo Indians that "the Earth does not belong to man, but man to the Earth." The alphabet with whose help you can write about life and death, love and hatred, suffering and pleasure, has not changed, regardless of how much everything else has done so. Life seemed short for the Egyptians as it does for us, and death was just as inevitable.
This doesn't mean that the experiences of these phenomena have remained the same. Conceptions of death and love are just as mutable as technology or economic fundamentals. But the documents that deal with death or love can constantly be read and reinterpreted and remain unsurpassed. In that sense they are ageless.
There is a kind of spectrum from that which is intensely short-lived to the essentially immortal. It is analogous to the spectrum that distinguishes basal from variable development. Given sufficient resources, physicists will be far beyond today's knowledge within a year or two. But nobody can claim to have created something that makes the Song of Songs hopelessly antiquated.
Thus, neither the pensum nor the voluntary path are by any means inured against old works. They can be said to radiate wisdom, but they also contain something else. Such works disclose a world and way of thinking that once was as real as what we experience today. In that sense, they carry the past with them. Education, both compulsory and voluntary, bears traces of distant and not so distant times. Even educational reforms are linked to the frozen ideologies that render institutions what they are. All institutions conserve. However progressive a school aims to be, it shares this trait of all institutions.
You might think that the modern university would develop a fixed classical repertoire to counterbalance the restlessness of contemporary society. But that is rarely the case. The greater the possible repertoire, the more difficult the selection process. Since the classical, though defined as that which is ageless, is subject to the ebb and flow of opinion, any particular pensum will be heavily criticized. Why is one thing included and something else not? Why only the Western tradition at the expense of the Islamic, the Chinese, the Indian? Why so many men and so few women? Why Marcel Proust and not Herman Hesse? Why the Beatles and not the Rolling Stones?
Thus, the classical becomes the subject of inevitable controversy. Any pensum in this area will meet resistance and awaken the desire of pupils to pursue voluntary paths. What is considered classical is a matter of fashion. In recent decades it has seemed that the past has been the primary object of fashion shifts and controversies (this may be one area where the word "postmodernism" assumes concrete meaning: a stage where you don't strive after anything totally new outside the natural sciences, technology and economics, but rather look back to past ideas and values). Only in a platonic, static world does the classical represent a fixed canon. In reality, it has always been the subject of controversy. Today we normally refer to several simultaneously existing classical traditions, largely due to the fact that so much is available all at once. A Vivaldi renaissance can occur while Schönberg experiences a new spring.
When it comes to a discipline belonging to the hard Enlightenment, it goes without saying that its practitioners will share many insights and skills. Physicists who specialize in a certain field are able to communicate with colleagues around the world and feel confident that they have a similar background (although when it comes to abstract theory, both their ideas and their intuitive approaches may vary more). On the other hand, an historian of science may listen to the lecture of a colleague and remain totally in the dark. Thus, it is important that he find colleagues who understand what he is doing. An essential trait of knowledge is that it can be shared, talked about and experienced with others. The fact that no two people ever have identical views makes shared knowledge that much more enticing. The similarities may be great, but the differences are inescapable. And those very differences give rise to unforeseen nuances in the knowledge itself. A work of art is far more than what its creator envisages, not only because his intention cannot never be fully manifested, but also because the work lives a life of its own in the eyes of its audience. Those who view it bring their own histories to bear, thereby transforming the work of art itself. This in turn paves the way for recurring attempts to rediscover the creator's original attempt. This process highlights the fascination of shared knowledge, in whatever field it may appear.
On being your own teacher
In the summer of 1809, Wilhelm von Humboldt, the Prussian Minister of Culture and Education, released guidelines for the examination of prospective government officials. Much of what Humboldt had to say was new and revolutionary. In the first place, he recommended a kind of grading system, whereby the applicant would be judged as to his natural gifts, as well as his educational accomplishments. Nevertheless, the examination was not to focus on the sheer multitude of facts that he had managed to assemble. Much more important was whether the learning process had left its mark on the way he thought and acted. According to Humboldt, you can be an excellent economist without carrying around a bunch of statistics in your head, or a good diplomat despite a degree of ignorance about history.
On the other hand, the examiner was to place special emphasis on two criteria that were impossible to evaluate according to any rule of thumb. The first criterion involved knowledge of "the realm of practical philosophy that constitutes the basis of the law, in that it reveals the goals of humanity - which, though they may not determine the goals of the state, nevertheless influence them - and generate the ideas that articulate the strivings of the individual, as well as the interplay of faith and intuition." For Humboldt the most important consideration was the applicant's attitude toward humanity, the intellectual clarity with which he advanced his ideas, and the warmth with which he embraced them. How he looked at people in his everyday life was also of great concern. In particular, it was incumbent upon him to respect the lower social classes. By applying these criteria to a prospective official, you could judge whether he would be a typical reformer or a loyal official, consistent or inconsistent, noble or petty, "narrow-minded or liberal, one-sided or many-sided."
The other criterion was the prospective official's general intellectual capacity, his powers of perception, his manner of reasoning and drawing inferences, his common sense, his ability to observe and imagine.
Such an examination could also provide some sense of the "degree of general academic knowledge" possessed by the examinee.
Humboldt's guidelines, only a few pages long, constitute an excellent summary of the grandiose program for intellectual and academic renewal of Prussia advocated by many German philosophers and scholars of the time. Thanks to his official position, Humboldt was able to back up his words with deeds, not to mention the fact that he was one of the clearest thinkers in this area. The idea of radically renewing both the university and the public school system had already been formulated by many others - just think of Kant, Fichte, Schleiermacher and Schelling. Humboldt differed from them in that his aristocratic background allowed him to obtain a prominent political position. But he was also a philosopher and linguist of rank, a leader of his generation.
Humboldt became one of Prussia's great reform ministers, despite the fact that his tenure in office wasn't very long. His most important achievement was the new university at Berlin, founded in 1809-10. This was an entirely new kind of institution; directly or indirectly, it was to become a precedent for much of the world. However, Humboldt wasn't content with remolding higher institution, but rather sought to reform the entire school system from the bottom up.
However, before venturing off any further, we should take a closer look at some the remarkable features of the statute on examination of prospective officials. Humboldt was not out to change testing procedures for their own sake. Rather he wanted to forge a new type of official. He was not interested in encouraging petty scrupulousness, detailed knowledge of the law and the regulations or unconditional loyalty. Instead he stressed a liberal attitude, noble ideals, respect for people's humanity, and the willingness to dare new approaches. You might say that he had a philosopher's mindset, or at least an awareness that laws and regulations are based on ethics and rights. Thus, it was important to be familiar with the fundamental concepts of practical philosophy.
In Humboldt's description of the human condition, it is easy to see the influence of Kant and Kantian philosophy. But the fact that ethics and the philosophy of rights were in vogue in many countries was not only due to Kant. As a result of revolutions and the emergence of totally new political systems, it was more difficult for rulers to defend their legitimacy with reference to tradition, and ultimately to God. The king of France was forced to abandon his claim to be carrying out God's mandate and received the people's instead. Even Napoleon called himself "empereur de tous les français." But on what were the rights of human beings based? Reference was made to basic equality and the common faculty of reason. This was clearly a philosophical response.
Though the Prussia of 1809 had not undergone a revolution, zealous reformers like Humboldt wanted to base its claims of legitimacy on rationality. There was major resistance to such concepts, and in the post-Napoleonic period it was particularly relentless. Once more tradition was the foundation of legitimacy. The kings, Prussia's as well, claimed whenever possible that they were fulfilling God's special edict in exercising their power. Nevertheless, practical philosophy defended the territory it had gained, surviving the Holy Alliance of reaction.
A key word in Humboldt's statute is Bildung (education). The prospective official's was to be tested both for his natural abilities and his educational achievements. Bildung was not only a matter of understanding the rational pillars of the law, but also developing a person's native abilities. We will take a look at the word, given that it had such a powerful impact on the German language in the decades around the turn of the 19th century.
Bildung involves more than the narrow learning process. Bildung as a concept is closely related to the evolutionary thinking of the late 18th and 19th centuries. In terms of pedagogy, the learning process of individuals was linked to other developments in a person's immediate world, and sometimes beyond it as well.
The pedagogic concept of Bildung can be traced back rather directly to the Greeks' paidei'a (pedagogic program). When the word Bildung began to be used in the schools, it often served as a translation of Latin's educatio or formatio, or of their French and English counterparts. Formatio (a person's formation in childhood and during his school years) comes close to the general Aristotelian (and Platonic) concept, which held an undisputed place in the pensum of educational philosophers, and which - with or against their will - influenced their theories. But Bildung was to become something more specific, related to the particular concepts of human beings that emerged in Herder's and Humboldt's time.
There were consequences -certainly not wholly unintentional or unwished-for - of the fact that Bildung became the catchword for a whole philosophy of pedagogy. That becomes obvious if you take a look at Herder, its apparent originator, who speaks of a "Universalgeschichte der Welt," i.e. a universal history of the world's evolution. And Herder really means it when he says "universal" - he unites geological, biological, historical and personal perspectives. The process is similar in all areas.
Coming from that perspective, Herder outlined a broad program for the education of the individual. He opposed all types of compulsory learning, the prototype of which he found in Latin studies. Like nearly all Romantics after him, he was highly skeptical of Latin's educational value.
With Herder, the concept of Bildung, particular in the area of pedagogy, became popular, spreading from German-speaking cultural circles to the Nordic countries and Russia. The concept never really made it to England, France or Italy, and it remains impossible to translate Bildung to any of those languages. What is normally suggested are words like education, formation, culture, or cultivation, but none of them quite makes the grade. The best translation, self-cultivation, was proposed by Fritz K. Ringer's in his book Fields of Knowledge (1992).
The word Bildung comes from Bild (picture). Herder and some of the other pioneers in this field were ultimately inspired by a recurrent idea in Christian mysticism to the effect that the goal of the human being is to become an imago dei, the image of God. In that sense, the educational process is goal-oriented: it aims at attaining an ideal. Thus, it is possible to establish criteria for who is and is not educated.
But Bildung is also an unlimited process - guided from within, spontaneous, creative. In that sense, it shies away from objective yardsticks and approves only that which is subjective.
The internal tension between these two aspects of Bildung reveals an opposition that re-emerges in everyday pedagogical questions, i.e. the opposition between the subjective and objective ideals of knowledge. Subjectivism claims that knowledge is valuable only in relation to the particular student. The learning process entails establishing a link between knowledge as yet unknown to the individual and his own experiential world. In other words, every learning process is unique. Objectivism, on the other hand, regards knowledge as unchanging from one person to the next. To know something is like having money in the bank; you can compare figures with another person if you want to know who is the wealthier.
It doesn't take a lot of insight to see that neither pure subjectivism nor pure objectivism is sustainable. Knowledge, as opposed to information, is always related to me, my experience, and where I am in life. But knowledge is also communicable; there must be a common thread between that which I know about Mars and that which you know after having read the same textbook.
The original power of the Bildung concept was that it referred to knowledge's objective, as well as subjective, aspects. On the one hand, the subjective aspect was emphasized more, since the system against which the new concept rebelled was a fortress of objectivism. But Bildung put up a barrier against arbitrariness from the very beginning. If the goal of education was no longer to mold yourself in God's image, it was that much more about re-aligning yourself with the time in which you lived and thus garnering the resources necessary to affect the future. Given the grandiose evolutionary thinking of the early 19th century, it was incumbent on the individual to adopt as his own that which human development had deemed most important. He would become an image of the truly human only so far as he succeeded in that task.
One of the principle advocates of the new concept of Bildung was Johann Heinrich Pestalozzi, a Swiss inspired by the egalitarian thinking of Rousseau and Kant. Pestalozzi was at least partially successful in his attempts to apply his thinking to school curricula; his experiments won a devoted following. He argued that education must be available to everyone. In other words, true popular education was a realistic alternative. Though open to all, the common path must be strictly personal as well.
Pestalozzi had a direct impact on Humboldt's reform plans in terms of Nationalerziehung, the national education of which Fichte spoke so enthusiastically. Pestalozzi's principles would be applied at the elementary school level.
The most important document in which Humboldt puts out his ideas of the Prussian (or rather the Prussian and Lithuanian) school system is "Der Köningsberger und der Litauische Schulplan," written in 1809 as well. In it he outlines a kind of school that brings to mind Plato's dialogue "The State," not to mention numerous 20th century educational experiments. Humboldt wanted to do away with the special educational paths that had been available only to the privileged. The public grammar school, which had already been proclaimed in Prussia, should provide fundamental instruction to all children without exception. In presenting his school, he reasons philosophically to prove that only three educational stages are possible, i.e. elementary, middle and university. Thus, there can be no alternative paths, no emphasis on one discipline or trade. Pupils would not be offered detailed knowledge of society or institutions, but only models of the truly human. It would deal only with "Menschenbildung." If you introduce special educational objectives and try to pass on knowledge necessary for the pupil's future instead for concentrating on "the main intellectual currents," the whole process becomes "impure" and you wind up with neither "complete people" nor "complete citizens in the various social classes." Everything else is Unnütz, useless, Humboldt concludes, appropriating the favorite word of his utilitarian opponents.
In the elementary school, where Pestalozzi's program was to be adopted, only "language, number, and proportion" were to be studied, language being limited to the mother tongue. Other of Humboldt's official writings indicate that it wasn't always so easy to implement Pestalozzi's ideas. Prospective teachers were sent to the master's own school in hopes that they would pass on his wisdom to their colleagues. The program was modified to conform to Prussian conditions. According to Humboldt, the essential principles were: 1) Upbringing and instruction form a unified whole; children are never left to themselves but are kept busy all day; 2) Instruction is to instill in the child love and fear of a higher being. Rewards and punishments are basically unnecessary; whipping is out of the question; 3) Children teach each other, the older pupils guide the younger; 4) The older children serve as guardians of the younger; 5) Seriousness is the order of the day, playing is forbidden.
Secondary education, which was to be available only to those who excelled in elementary school, should afford pupils the skills and knowledge enabling them either to go on to the university or adopt a profession (There is a blind spot in Humboldt's school plan: not once does he touch upon what paths would be open to women. The reader can only conclude that they have been unreasonably excluded). The curriculum would be divided into language, history and mathematics. All are important: Humboldt condemns the narrow focus on language in the older schools. Everyone must be educated in all three areas, he asserts. The classical languages are preferable to the modern, since they are so foreign to the students' experience that their formal structure can be more easily discerned. Hebrew is also useful in that " its construction is closely related to the language of primitive peoples." A typical 18th century thought is enshrined in that expression.
Humboldt's preference of the classical languages provides a key to the pedagogical thinking of his time. If we want to fully understand this way of thinking, we must be cognizant of three concepts cherished by Humboldt and his contemporaries:
1. All languages - as all phenomena that belong to a particular category, e.g. mathematical operations, philosophical systems, plants, animals or countries - represent variations on a common theme or, as Humboldt would prefer to say, various expressions of the same fundamental form. The important thing is to detect and comprehend this form, since it provides the key to all the particular variations on it.
2. Thus, the factual aspects of knowledge are the least important. The drive to understand the phenomenon of language cannot be satisfied by achieving a complete mastery of one language, not even Greek; rather, it is vital to grasp language as a fundamental form. There are many different ways to arrive at concepts about history, and there is no fact or set of facts required to gain insight into the crucial question of how the distinctly human manifests in historical developments. Humboldt looked at mathematics in much the same way. Thus, it was irrelevant whether a prospective official was familiar with one or another fact. What was crucial was that which constituted the basis of all individual facts.
3. Each individual possesses a number of different faculties or abilities, what Humboldt calls his natural propensities. These propensities can be developed and refined through an educational process that sets its sights on the essential or formal aspects of knowledge.
In describing what was later to be referred to as the idea of formal knowledge, the third of these concepts has been emphasized, sometimes exclusively. This concept also provided the framework for the evolution of Humboldt ideal later in the 19th century. But for Humboldt and his contemporaries, the other two concepts (which were intimately connected) were equally important. Even those (like Hegel) who did not subscribe to the concept of distinct faculties or abilities could accept the other concepts and thereby look at educational issues much as Humboldt had done.
It's true that Humboldt, as opposed to many of his younger contemporaries, emphasized individual differences and the importance of empirical investigation. But ultimately he assumed that all languages share a common basis. He ties this idea to one of the Kantian philosophy's most difficult concepts: schemata. According to Kant the categories of the understanding cannot be attributed to the empirically given, but rather to a kind of middleman, namely the power of the imagination. By means of the imagination, these categories are transformed to schemata, which serve as links between what the senses provide and what is thought. Humboldt defines this act of transformation as essentially linguistic in nature. Thus, it is through language that sensory impression and thought first meet. This process is a kind of synthesis, which is more visible and more complete for a language with a rich declension system like Greek. The knowledge of such languages facilitates the identification of the general language form.
Humboldt did not pursue a similar line of argument with respect to mathematics or history. But he obviously believed that they too possessed some kind of fundamental form.
Humboldt's ideas are most thoroughgoing at the university level. Before reaching that level, pupils should have learned not only language, history and mathematics, but also, and above all, how to learn. Mastery of the learning process is the quality necessary for the kind of university studies Humboldt wanted to introduce. The university is the place to attain pure knowledge, "and a person can only find it in and through himself." This process demands freedom and privacy or, in short, that the student essentially be left on his own. No longer can he learn from others. The professors may be there, but from the very first university studies demand an approach to research for which the student cannot simply follow in another person's footsteps. The most a teacher can do is awaken an urge already residing within the pupil. Certainly the teacher's greater experience can make him an effective counselor. But in his heart of hearts, the student must be unshackled. Of course, he may choose his own teachers. But when it comes down to actual research, although he is intertwined with the collective evolution of humanity, he is ultimately alone.
At the university outlined by Humboldt, there is no dividing line between fundamental education and research; on the contrary, a student is bound to carry out research. Nevertheless, Humboldt is using the word "research" in a broad sense, constituting the studies one pursues on one's own with the objective of attaining new insights. At the same time, Humboldt's understanding of research is quite close to our contemporary view: it is a systematic search for knowledge that nobody has possessed earlier. When the university was established in Berlin based on Humboldt's concepts, this was the basic attitude toward research enunciated in the charter. Teachers were required to pursue research and not simply instruct, as had been the case earlier. In addition, students were to do their own work and take their own exams, particularly when it came to writing their doctoral dissertations.
Just on the face of it, these changes were thoroughgoing and of decisive importance for the future. But no more than other similar proposals did they lead to something absolutely new or change the situation all at one time. There had been many professors doing research earlier - Newton and Linnaeus had done their most important research while connected to the university. What was new was that research was regarded as compulsory. When filling academic posts, research merits were of utmost importance. The result was a decided increase in industriousness and productivity.
Even earlier, there were students who had written the dissertations they then defended in public. But more often than not, their professors or even an outsider had done the writing. The point is that it didn't matter, for the simple reason that, according to classical university doctrine, knowledge was eternal and unchanging, the great unsurpassable systems were all constructed in the past. Students were expected to cultivate the art of reasoning on the basis of ageless truths. By the early 19th century, this had long since been regarded as an outmoded concept, and there was hardly anyone who still believed in it. But the university charter still referred to it, i.e. it lived on as frozen ideology. Humboldt aimed to eliminate this concept by requiring that students do their own work. Thus, a new ideology emerged according to which even the shortest academic essay should present some kind of new knowledge. Plagiarism, previously an unknown concept in this context, was considered the most heinous of crimes. Academic independence became an honorable concept, just like artistic originality among the Romantics of Humboldt's era.
Humboldt's argument for the inextricable connection between higher learning and research was that both basically represented infinite processes. A person's educational process was endless. Nor was there such a thing as ultimate human knowledge. Neither on the individual nor collective level did evolution ever reach a final stage. Nor did it have any kind of static goal that could be set in advance. The human drive for knowledge could lead us on and on. Thus, there was a correspondence between the education of the individual and that of humanity as a whole, and it was because of this correspondence that research was so indispensable to the university.
According to Humboldt, the university should demonstrate the commonality of all research and thus of knowledge in general. The responsibility for this was borne primarily by philosophy, which Humboldt regarded as the central discipline. Philosophers were to manifest the spirit that was common to all knowledge seekers and thus prevent individual disciplines from being isolated and linked to a particular type of knowledge or, even worse, a particular practical activity. In general the philosophy faculty - which included philosophy, history, language and mathematics - was regarded as central, while in the old type of university it was considered a lower discipline, representing merely a preparatory stage to the study of theology, law or medicine.
Early on the university at Berlin did all it could to engage the dominant German philosophers of the time. Fichte was the first man to occupy the central teaching chair, Hegel the second. Hegel took his job literally, writing an encyclopedia of the various disciplines once it was clear that we would succeed Fichte. Though he didn't succeed in turning everyone at the university into a disciple, most of them adopted a position either for or against his system. At this time, there was still a kind of discussion fellowship that was never to return. After Hegel's time, philosophy became one subject among many, central but certainly not dominant.
The reason for this shift is not difficult to understand. There was a structural contradiction in Humboldt's university plan, a contradiction that did not become evident until later. If research was to be a compulsory element of all disciplines, special efforts were required. Natural scientists needed laboratories. For humanists, a new type of institution called the seminar was emerging. Humboldt himself had attended one of the first seminars during his student years at Göttingen. From the beginning a seminar was both a method of working and a physical facility with a standing library. The method of working was essentially the same as today's university seminars: students report on the preliminary results of their research, after which a teacher leads a discussion. What distinguished the seminar from a lecture or ordinary class was that everyone present was expected to participate. The teacher and students worked together to achieve sustainable results. The approach conformed well with Humboldt's concept of the essence of research; it is likely that he had his seminar experiences in mind when he publicized his ideas for the new type of university. (The research laboratory is also based on the principle of the common search for truth)
The methods of working recommend by Humboldt were effective. A series of successful research groups gradually emerged at the university in Berlin. Just take Leopold von Ranke's famous history seminar. Ranke began to design the seminar shortly after becoming professor at Berlin in 1825. Many of Germany's best 19th century historians received their education in von Ranke's seminar, or among Johannes Müller's equally well-known research group of young anatomists and physiologists, who made a series of major breakthroughs in the 1830s and 1840s.
As a result of this successful research, Humboldt's concept of the unity of knowledge, a unity of which philosophy was the guardian, became increasingly untenable. Research within the various disciplines led to the emergence of new methods and tools, which were joined to new theories. New experiential worlds opened up, new contexts were revealed. It wasn't a coordinated effort, nor could it ever have been. Different disciplines developed different approaches to research. Specialization grew - the university at Berlin soon became the most specialized research institution yet known, It was increasingly difficult to win any respect for the kind of encyclopedia Hegel had written in the 1810s.
Thus, Humboldt's program contained inner contradictions. In addition, external circumstances prevented his ideas from being fully implemented. For him, the university was a place where total freedom would reign. Nothing but purely intellectual skills would be respected; governmental and other authorities would wield no power inside the walls of the university. In other words, higher institutions of learning were to be oases where young people could pursue truth without limitations other than the those of human understanding and the particular discipline. Ultimately, of course, the student would (unfortunately, Humboldt says) have to make his way out into professional life, where all ordinary restrictions applied.
The research-oriented university that took form in the 19th century enjoyed a special kind of autonomy. Students had a certain degree of freedom when choosing their curriculum and teachers. Within the confines of the university, teachers could develop theories and attain results that could not be propagated freely in a society that was still strictly authoritarian. Nevertheless, this independence was hemmed in on all sides. Professors wielded influence and power way out of proportion to Humboldt's concept of a research fellowship between students and faculty. On the other hand, teachers constantly encountered external obstacles if their theories could in any way be perceived as disruptive of the social order. Hegel experienced this resistance as early as the 1820s. During the rebellious 1840s, the situation became even more oppressive; after the revolutions of 1848-50, any teacher demonstrating the least sympathy for radical ideas was fired on the spot. Promotion policy was increasingly characterized by downright bias; the rise of anti-Semitism toward the end of the 19th century gradually excluded gifted Jews from university positions that had been open to them, at least partially, 50 years earlier.
The university at Berlin, academically speaking superior to all comparable institutions, bore the deepest traces of an authoritarian and biased society. It would have been scant consolation for Humboldt to discover that there was a greater degree of freedom at the university than in the society as a whole and probably most other European universities of the time. He had striven for so much more.
The discrepancy between ideals and the way in which they were ultimately implemented says something important about pedagogical reforms. It is so easy to view the history of learning institutions as the legacy of a unbroken line of pedagogical theories. While it's true that theories have formed the basis of very palpable reforms and thus been a force to reckon with, the step from ideal to institutionalization is precarious. Humboldt's concept that the search for pure knowledge transcends all other learning led him to view philosophy as the central discipline. But why did he even want to preserve the division into various faculties, if not for the overweening force of tradition? His new hierarchy encounter obstacles as soon as it was put into place. The theologians were not about to willingly give up their superior status, and in periods when the official church had the ear of those in power (as after Napoleon's fall), it regained some of its authority. Humboldt's idea of a university, indeed an entire school system, in which comprehension was of the essence and nobody would slide thorough by viture of memorizing facts was difficult to carry out when examination time rolled around. Not only the traditional work ethic, but also the practical need of a quick and efficient method of determining who possessed knowledge and who didn't, favored the teaching and regurgitation of facts at the expense of deeper insight.
Humboldt's program was the offspring of a period that soon would be relegated to the shadows. Two terms are key to understanding his theories: Aufklärung (enlightenment) and Bildung (education). When promoting the new university at Berlin for the first time, he argued that it would win the support of every German " interested in education and enlightenment." This particular juxtaposition of terms keeps recurring in his later writings as well. In any case, it was an unusual approach. Most people of that time who wrote about education were critics of the Enlightenment, perceiving something deeper and more intimate in the concept of education than simple enlightenment. Nevertheless, the juxtaposition had been employed by Moses Mendelssohn, a Jewish philosopher in Berlin,
in an essay aimed at defining the concept of the Enlightenment. The connection is highly revealing: in his younger years, Humboldt had been deeply influenced by the Enlightenment thinking that blossomed in the Prussian capital and for which Mendelssohn was one of the most prominent spokesmen. Humboldt never let go of these early influences, although he was also deeply affected by philosophical idealism (albeit mostly by Kant, an Enlightenment man himself). In his plans for the university, he arrived at essentially the same ideas as Schelling and Schleiermacher, both Romantics.
Both the Enlightenment and Romanticism vanished as leading currents of thought, while the university at Berlin remained. Some of Humboldt's ideas lived on as frozen ideology. But toward the end of the 19th century there were other intellectual trends that captured the imagination of professors and students at institutions of higher learning. Humanists propagated for a type of education in which their own work stood took center stage, and where the demands on education were much more rigid - or at least more defined - than in Humboldt's time. Natural scientists, now the humanists' main competitors, also laid stake to the possession of essential knowledge, as well as the ability to transmit it. In addition, they often saw themselves as bearers of the Enlightenment tradition, the very backbone of which was advances in the natural sciences. Their emphasis on the concepts of Bildung and enlightenment seem to place them near Humboldt's thinking, but they accorded a special significance to these terms. The Enlightenment they had in mind was primarily the hard tradition, the exact sciences above all, and few of them had any sense of the ethical or political aspects of the Enlightenment so vital to Humboldt. They defined education - as did their humanist colleagues - in terms of learning a set of facts and skills. Humboldt's unlimited development was beyond them, as was the subjective dimension of early educational thinking.
The academic natural scientists, and the humanists even more so, were threatened from the outside by the world of practical men, particularly engineers and industrialists, who looked down on purely theoretical knowledge and who wanted to elevate their own educational institutions - technical schools and trade colleges - to the same status as universities. They viewed themselves as the spokesmen of the new industrial society and demanded to be treated as such. University scholars attacked them for materialism and ignorance of higher values.