Yoav Ben-Dov
Cohn Institute for the History of Science
Tel-Aviv University
69978 Tel-Aviv Israel
April 1995
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Conceptual models which aim to reflect the structure and accumulation of knowledge can influence the content and the strategy of education. A most prominent example of such influences can be found in the two classical models of knowledge accumulation, the rationalist and the empiricist. I discuss the relation of these models with traditional methods of school teaching in physics and in history. Then, I claim that the "linearity" of these and similar models, in which knowledge is built in an accumulative procedure, fails to account both for the net-like structure of knowledge, and for the relevant features of the actual learning process. As an alternative, a "fractal growth" metaphor is suggested, as a free exploration of a web of interconnections.
Any teaching program of school studies, in any discipline, is written on the basis of some particular (explicit or implicit) assumptions about the nature and value of knowledge in this discipline. These assumptions influence actual decisions in questions like: what are the important items which must appear in the syllabus? what is the right way to present them? etc. Indeed, while it can perhaps be claimed that active researchers should not think too much on what they are doing but should just do it, one cannot purposely "educate" without thinking what education is. The purpose of this paper is to examine some questions concerning the influence of models of knowledge on the formulation of school teaching programs, especially in view of recent developments in the philosophy of science and in the technology of education.
To illustrate the influence of models of knowledge on the structure of teaching programs, let us consider first the example of physics teaching. The subject matter of physics teaching at school level consists mostly of "classical" physics, as developed from the 17th to the 19th centuries. However, not only the content, but also its presentation in the teaching program may be "classical", in the sense that it can be inspired by models of knowledge which were prevalent during that period.
Two models of knowledge, that to a large extent dominated Western thought from the 17th century onwards, were the rationalist and the empiricist models. According to the rationalist position, stated for example by Descartes in his Discours sur la methode, true knowledge starts from first principles that are simple, clear and evident, and then continues by rigorous derivation, so that the solidity of each step rests upon that of the preceding ones. Accordingly, a physics teaching program inspired by the rationalist model would start by stating, in a mathematical language, the basic assumptions of the physical theory under consideration (e.g. Newton's laws of motion in the case of classical mechanics), and then proceed by mathematically deriving the applications of the theory as special cases. In such a study program, the role of laboratory work would be secondary, and it would serve only as an illustration of the derived results. As a pure rationalist might put it, laboratory experiments should not be trusted too much in physics teaching, because their results, in the best case, only approximate the exact "true" results given by the theory, and even more so when carried out with the means and expertise available in a normal school. Thus, a rationalist teaching program in physics would consecrate much more attention to the mathematical derivation of formulas then to laboratory experiments.
The empiricist view, formulated by Bacon in his Novum Organum, and claimed to be followed by scientists like Newton (1686) and Ampere (1827), proceeds in the opposite way. Instead of trusting reason and suspecting the senses, the empiricist suspects pure reason of being liable to lead to useless sophistries, and regards as a true scientist the one who trusts only the evidence of experiment. In this view, true knowledge is built by acquiring experimental and observational evidence, and then generalizing it into scientific laws. Accordingly, a study program in physics that takes the empiricist view for its inspiration would start at the laboratory, and direct the students to "discover" the laws of physics by generalizing the actual results that they got. The mathematical connections between these laws would appear, in this method, as auxiliary modes of organization of the learned contents, and not as their basis: the student's belief in the validity of the physical theory is not supposed to rely on them, but on what he or she saw with their own eyes [2].
It is not surprising that the rationalist and the empiricist models of knowledge can thus be related to physics teaching, because these models were developed, in the first place, to account for the advancement of physical science. But they can also be extended to other disciplines, for example history. In this domain, a rationalist view would regard human history as the unfolding of unchanging logical principles, at which the historian can arrive by reason alone even before any historical evidence is presented; the most sophisticated expression of such a view is undoubtedly Hegel's historical dialectics. A teaching program of history motivated by this view might start by introducing its basic principles - Hegelian, Marxist, Herderian or other - and then proceed to special historical cases which are supposed to illustrate these principles. An empiricist view of history, on the other hand, would assign to the historian the role of ascertaining the facts from evidence, and not from first principles; and when applied to history teaching, it would make the study of history consist only of the facts so ascertained, without any attempt to show how these facts conform to principles arrived at from another source [3,4].
The rationalist and the empiricist models are not, of course, the only ones that can be relevant to the formulation of teaching programs. However, there is an important feature which is common to both, and shared by a larger class. This is their "linearity", in the sense that they both construct knowledge in a step-by-step manner. With each step, a new item of knowledge is added, but without modifying the previous ones.
In the rationalist model, items of knowledge are logically deduced from previous items, which serve as their premises. But logical deductions affect the status of their conclusions, not of their premises: the mathematical derivation of any particular result from Newton's laws modifies nothing in the laws themselves. In a similar manner, the empiricist model builds knowledge from facts which are experimentally discovered one by one. Each fact, as acquired, is regarded as firmly established, so that it cannot be modified by the acquisition of additional ones. Again, knowledge advances step by step, without ever having to go back.
As mentioned above, these two models are not the only possible ones, and indeed, it is hard to find them today expressed in their pure form. However, the feature of linearity is typical to other models as well. Consider, for example, Popper's (1959) model of scientific knowledge as proceeding by series of conjectures and refutations. In Popper's model, there are two different phases in the advancement of science. One phase is the logical elaboration of a theory in order to arrive at concrete experimentally refutable conclusions. The logical derivation itself is a linear procedure, and the experimental testing of conclusions can be carried out one by one. A second phase is the rejection of a theory once refuted, and the acceptance of a more adequate one. But again, a refuted theory is rejected once and for all: having been proven to be untrue, there is no point in going back to it. Indeed, any scheme which considers knowledge as "converging" towards truth (as is the case with Popper's) is liable to exhibit this feature of linearity, because the mathematical image itself which is borrowed here, namely that of convergence to a limit, is concerned with series of terms which follow each other in a well-defined order.
However, views in the history of science which were developed in the last few decades challenge the concept of a linear construction of knowledge. These views are usually formulated in opposition to a basically empiricist position, as the pure rationalist model has grown unpopular in natural science ever since the notorious failure of Descartes' mechanics. Indeed, it seems that in the view of many scientists today, who express themselves on this issues mainly in popular science books and lectures, science is based on the final "verdict of experiment", that is, on facts which are experimentally established one by one as permanent acquisitions of knowledge. However, 20th century studies in the history and philosophy of science seem to indicate that no such "permanent items of knowledge" actually exist. Consider, for example, Duhem's (1906) criticism of the concept of a "crucial experiment": what is justifiably accepted at a certain moment as an experimentally established fact, can later be re-considered and re-interpreted in a completely new manner. Thus, science does not advance in a linear course, in which facts are "discovered" once and for all: any experimental result can in principle be modified, or even dissolve in the light of new achievements [5].
More recent work in the history and philosophy of science has much strengthened this point. Consider, for example, Kuhn's (1962) influential notion of "paradigm", which is, in his view, the essential ingredient in any mature science. A paradigm is a network of facts, theories, concepts, procedures, criteria of verification and notions of meaning which are all interconnected. It is not possible to speak of a scientific "discovery" outside the context of a specific paradigm, and as paradigms have the habit of replacing each other, any discovery is liable to be re-interpreted, or even to lose its value, in some future.
Kuhn's notion of paradigm has been criticized as ambiguous. It is not clear where to put the limits of one paradigm, so that what lies beyond them counts as a different one. For example, are Newtonian mechanics in the 17th and in the 19th centuries two different paradigms, or a single one? It seems that the problem here comes from Kuhn's too rigid notion, which allows either the development of a single paradigm without changing its basic features (what Kuhn calls "normal science"), or the total replacement of one paradigm by another (what he calls "a revolution"). A more refined view can be found in Fleck's (1935) book, which served as an important source for Kuhn. Fleck uses the term "thought style" in a sense close to Kuhn's notion of paradigm. Like the paradigm, a thought style is a network of concepts, facts, techniques etc., which constitute an indivisible whole through which the scientists find sense in the world. However, the thought style is conceived as a structure which is constantly evolving and modifying itself, so that the distinction between "normal science" and "revolution" is becoming much less sharp: in some cases it might be a projection of the historian's particular point of view, and in others a distinction of quantity (rapidity of change) and not of quality. As for the identification of a particular thought style, Fleck defines it as a system (of concepts, facts etc.) shared by what he calls "a thought collective", which is a scientific community whose members are involved in an actual exchange of information, and who share a common "language of the trade". This community is a network of individuals, whose relation to the network of the thought style might be compared in some sense to the relation between the hardware and the software of an artificial data processing system [6]. However, as Fleck notes, the limits of a thought collective are never sharply defined, and it may have a quite complex structure (for example, different sub-communities within a larger community etc.). This structure corresponds to similar complexities in the structure of the thought style.
Fleck's view of science does not share the linearity of "classical" models of knowledge. The thought style is a network, which is modified in its totality with the acquisition of each new item. Even an initial discovery which leads to the formation of a new thought style (something that Kuhn sees as the defining feature of a paradigm) can become inaccessible to scientists working in the same thought style once that it reaches a more mature stage: in the accomplished network of concepts and techniques, the original results can be meaningless and irreproducible. And exactly as a scientific fact can have its genesis and development, it can also have its decline and demise [7]. Thus, scientific knowledge is not acquired in a linear manner, step by step: at any stage, scientists can go back, and re-interpret previous achievements in the light of new knowledge.
It is not the purpose of this paper to argue in detail for the particular views of Duhem, Kuhn or Fleck, but only to note their general tendency. As it seems, at least an important part of the philosophers and historians of science move today from a linear view of scientific knowledge to a more complex one. Knowledge is no longer conceived as a list of separate items, which can be discovered and enumerated each in its turn. Instead, a body of knowledge appears as a multiply-connected network, in which each element influences and modifies all the other ones. It can therefore be compared not to the structure of a man-made machine, which is assembled part by part and performs its functions step by step (this was Descartes' image, which had a powerful spell over many generations of scientists), but rather to a living organism [8].
This tendency to move from linear views of knowledge to more "organic" conceptions affects not only science, but also other fields, for example history. Pure rationalistic accounts of history seem today to be no more popular than their counterparts in science. However, the temptation is great to see history as a series of events which follow each other in a linear order, to be discovered and ascertained by the historian applying a more or less empiricist method. This image of a line of events marching to the view of the historian was held by many historians in the previous century. But it has been much criticized since, for example in Collingwood's (1946) very influential book. For Collingwood, the linear list of dates, names and events which many view as the solid body of history is not history at all, but "chronicle" [9]. History is not the passive enumeration of events which really happened "out there", in well-defined dates and places. It rather consists of the re-enactment of the events in the historian's mind. The historian brings his own experience to this re-enactment, and the experience of his time (for the historian is himself within history, being its product, and influencing it by shaping the historical consciousness of society), and of periods previously studied, enters into this re-enactment. In this way, the historian's knowledge of the past event (and this is the only way in which this event "exists") is influenced and modified by other events, which can be chronologically more recent. Thus, in Collingwood's view, historical knowledge cannot be reduced to a linear list of isolated facts: historical time is multiply-connected.
Similar considerations apply in other disciplines. It is not clear what exactly "knowledge of literature" consists of, but surely it must include the capacity to be impressed, to appreciate and to enjoy the literary text, and, of course, an acquaintance with the texts themselves. However, a text cannot be "learned" once and for all: the impression it gives is modified by the reader's life experience and by other reading, so that another reading of the same text reveals in it qualities different then before. Similarly, the geographical knowledge of (say) India is influenced and modified by geographical changes in, and knowledge of, the geography of America [10], etc. In all these domains, knowledge appears not as an accumulative series of isolated items, but as a multiply-connected network, which, like Whitehead's (1929) picture, is modified in its totality with the addition of each new element. Thus, it seems that in more than one domain, the metaphor of knowledge as a serial machine can profitably be replaced by the image of the interconnected organism [11].
It is interesting to note that tendencies of a shift in a similar direction - from linear constructions to interconnected networks - appear not only in the conception of knowledge, but also in its organization. Today, a great bulk of information passes through the electronic mail network, and it is only expected to grow in the next years. Subsequently, access to knowledge can now find many alternative routes besides the traditional hierarchies of knowledge like universities and libraries, in which particular pieces of information are accessed by the outsider through a linear series of well-defined steps [12]. These developments affect more than just the rapidity and the efficiency of the exchange of information: the network seems to have acquired a life of its own, with new thought collectives (in Fleck's sense) appearing and disappearing rapidly in its virtual, self-organizing landscape. Knowledge can now be made available to any individual in large quantities all at once, and through many alternative routes. Pieces of knowledge, formely catalogued into distinct disciplines in which they can be reached through a linear procedure, become junctions in a multiply-conected network of cross-references.
Curiously enough, within the content of knowledge, interest seems to be shifting as well in the direction of networks and interconnectedness. Multiply-connected dynamical systems, and their typical behavior of self-organization and self-definition, have become a common theme in many areas of research, which until now appeared as disparate: evolution of the species, immunity in the body, urban geography, ecology, economics, the weather system and many others [13]. It is too early to judge the lasting scientific value of the study of "complexity", as this type of research is sometimes called, but it is undoubtedly a focus of much interest today, and the graphics generated by its computer simulations have already had some impression on the aesthetic imagination of our time.
Of particular interest is the fact that these new methods of research can be applied to the brain. "Neural network" simulations appear to imitate interesting features in the electrochemical activity of actual brain tissues, and they can be claimed to based on similar (although, of course, much simplified) structural principles (see Freeman 1991). Although again, it is perhaps too early to judge the lasting scientific value of this line of research [14], at least it has the merit of enabling us to speak in similar terms on the structure of the brain itself, and of the knowledge carried by it [15]. This feature was not shared by previous models of knowledge, which either ignored completely the question of brain structure, or suggested brain structures that have no relation with the actual findings of brain physiology [16]. If so, it can perhaps be expected that the learning process should also be subject to a description in the same terms.
This brings us back to our central issue. Suppose we accept the claim that the organic, inter-connected network image is a better guide to the understanding of at least some important features of the growth and the structure of knowledge - in the scientific community, and perhaps also in the learning individual's brain - than the linear metaphors which previously seem to have prevailed. What consequences, if any, can this acceptance have in the field of education?
A linear model of education would try to make the student follow, step by step, the line of knowledge in the relevant discipline. At each step, a new item is to be taught and learned, and the acquisition of previous items is in general necessary for the understanding of new ones. The teaching program is the expression of this line of items, that the student is supposed to absorb until he or she possesses the complete list required for answering correctly the exam questions. The teacher's role is to ensure this transfer of knowledge from program to student, so that each item is learned in its turn: that is, to lead the student in a well-trodden and secure road, postmarked in advance by the education authorities. At any moment, the school studies consist of several such lines, each corresponding to a different discipline, and usually taught by a different teacher. The lines never cross, as any item is neatly classified into its proper place in a specific discipline: two teachers are not suppose to teach the same thing at the same time.
In opposition to this mode of teaching, in which advancement is made in a well-defined order which can be assimilated to a straight line, one can perhaps propose a simile which is also taken from geometry. Suppose one wishes to cover a multi-dimensional surface with a one-dimensional line. With the tools of geometry available in the previous century, this cannot be done. However, a class of geometrical objects which appeared in the recent decades can do the trick, at least in some sense. These objects are called "fractals" [17], and they seem to play a prominent role in the field of research which studies complex dynamical systems and their behavior [18]. A fractal is a self-similar figure, in the sense that when observed on a finer and finer scale, it appears to turn and split as much as it did when viewed in the original, low-resolution scale: the more you look in, the more you see. A line fractal thus turns and splits enough to be be designated by a mathematical dimension higher that one. That is, it covers much less than the complete multi-dimensional surface, but still passes in the vicinity of much more of it than the smooth one-dimensional line of classical geometry.
Fractals seem to appear in the growth of systems like body tissues, microbe populations, and even crystals, for example a snowflake. The unique form of each snowflake comes about from the random choice of each water molecule whether or not to join its crystallizing fellows at a given moment. However, from this multitude of random processes, all highly interconnected, arises the visible order of the six-fold symmetry. As a fractal, the snowflake shows more and more splits on smaller and smaller scales. In this way, a relatively small quantity of water can give rise to a snowflake covering a relatively large volume, which is what makes snow much lighter than solid ice [19].
The fractal can perhaps be adopted as a new image for the process of learning: not an advancement in a pre-determined straight line, but rather a voyage which turns and splits between the multiple connections of the network of knowledge. Suppose one wished to encourage learning in this way. Let the students explore the network by following items as they lead to each other through their multiple interconnections. Let them start somewhere in the network, for example with a preliminary question, and proceed as their needs arise, as the answers that they arrive at give rise to new questions, as their interaction with the physical, the virtual and the social environment push them, and as their inclinations and curiosity lead them. The point here should be that they explore the network through their own efforts, turning and splitting as they find necessary, and not that they absorb a list of pre-determined items. Is there a reason to believe that such a way of learning by free exploration might be more effective than the linear line of conducted accumulation?
First, learning by free exploration sounds more fun, as it resembles play activity. We shall return to this point later. But there are other reasons to be unsatisfied with a linear conducted method. For one thing, as noted in the previous section, linear teaching programs do not allow for the interconnectedness of knowledge. Suppose, for example, that one wishes Dante's Divine Comedy to be learned at school. Is it more appropriate to assign it to the domain of poetry, of history, of philosophy, or even of physics - each taught by its own teacher? Any decision in such a question would be to a large extent arbitrary, and imply the neglect of important elements of the learned material. A free exploration is not hindered by such constraints, which come from the need to classify each item of knowledge into its proper place in a well-defined list.
Another kind of problems with the linear and fixed teaching programs comes from the fact that each one of them tells a particular story about the world. What are the items that are important to know, and how are they related to each other? Through choices in such issues, a world-image is implicitly projected to the students. To borrow a term from present-day historical studies, a teaching program expresses a "narrative", a linear story which is told through the choice and arrangement of what is represented as "the facts", and this is true not only in history, but in other disciplines as well: a teaching program in physics tells the story of what physics is about, etc. But whose story is it? In a democratic society, the majority groups have a priviledged access to the public educational system. In extreme cases, rigid study programs can thus become a tool by which children of minority groups are pressured into accepting the majority world-view [20]. Hopefully this does not happen often, but in a general manner, schools and school programs always push to the center: the answer that corresponds to the common consensus necessarily passes the exam. Thus, rigid teaching programs lead to a standardization of the student population, as they disfavor the original and the uncommon, including the original and the uncommon which might give rise to a new future consensus. In a free exploration, it is the student's choices which determine what is studied, so that this push towards standardization is much weakened.
Is the present application of the linear teaching method a success? It is known that most of the particular items "learned" at school fade from memory soon afterwards. Was there any sense in teaching them in the first place? It can be claimed that a lot has to be learned for a little to be retained, and children do learn a lot, as through their school years most of them get to answer the questions in many exams. But the assessment of this fact is problematic. Suppose the students have correctly answered the questions. Does it mean that they "know the subject" (whatever that means), or rather that they have mastered the techniques of arriving at "correct" answers to exam questions? This is surely not the same thing, as the second includes, for example, the art of getting tips from the teacher. If the second is the case, then how did they arrive at this mastery? The teaching program and the textbook teach the subject matter, not the practical methods of exam-passing. To a large extent, the students might have learned exam-passing by trial and error (that is, an exploration as free as allowed by the circumstance), preparing their homework or studying to exams, either alone or in groups. This learning activity is free inasmuch that each particular choice is made by the student, within the network of the relations between himself and the subject matter, the teacher, the school authorities, parents, friends etc. This network is heavily constrained by the demands of the school teaching programs. But from the student's point of view, the programs only set the context for the process of learning; they are not the lists of items actually learned at each moment.
If we look for examples in which actual learning is undoubtedly taking place, we can find free exploration in many of them. Consider, for instance, the mastery of computer applications. Children are notoriously good at it, and clearly, a lot of learning is taking place here. But this learning usually owes nothing to the school system, or to fixed teaching programs. Most children seem to learn the secrets of the computer world by freely exploring any software that they can lay their hands on, and this, again, either alone, or in groups which are themselves free to set their course.
Another example is the study of language. A lot of work through many years in the school study of a foreign language does not make the average student a fluent speaker, while a relatively short stay in a country where this language is spoken can do much better. In the first case, a fixed linear teaching is followed, while in the second, the individual explores the network of terms and constructions of the foreign language through interaction with its speakers, an exploration which is not purposely aimed at the acquisition of vocabulary and grammar. And of course, a similar free exploration is taking place along with the very effective learning of a first language.
Learning by free exploration can perhaps be regarded as the most primitive mode of learning. The young infant moves about in the world, touches and tastes, and sometimes falls or bumps. In this way, he acquires much knowledge about his physical and social multiply-connected environment [21]. He may be guided by a parent, but the momentary decisions of his conduct are mostly his own. Neither are his actions directed to a conscious goal. The baby throwing, again an again, toys from his bed might be studying his body movements, the fall of objects, or the limits of patience in his social surroundings. He surely acquires useful knowledge in all three domains, but for him, this does not appear as a conscious goal. His activity is playing, not conscious learning. The natural urge for play may perhaps thus have, as one of its major functions, the study of the world through free exploration [22].
As we saw, learning by free exploration can be claimed to be more adequate to the view of knowledge as an interconnected net, and if the studies of the brain structure as a neural network are to be trusted, it might also correspond more closely to the structure of the learning individual's cognitive system. This does not necessarily mean that school teaching should stop altogether from being linear, and commit itself exclusively to the enhancement of free exploration. Still, for some purposes it might be useful to accept as a working hypothesis the idea that actual learning is brought about by the free exploration of a multiply-connected environment. This environment consists not only of the physical (or virtual [23]) settings, but also of the social connections of interaction, imitation and guidance. The learning individual's choices and actions are internally free, but within the constraints imposed, with varying degrees of rigidity, by the environment. And in their turn, these actions influence and modify the environment in which they are taking place.
Education through free exploration is in some sense what was going on in the institute of private tutoring: before the installation of the modern public educational system, the tutor and the student were free to steer their way in the fields of knowledge, as needs arose from their common interaction. This manner of education, which took place in priviledged social circumstances, is not applicable on a large scale. Today, the public educational system must define the goals and means of the education of groups of students, which are prepared for the mass selection procedures after their graduation [24]. This makes compulsory teaching programs almost inevitable, so that the possibility of learning by free exploration is much restrained.
However, recent developments in the technology of education can perhaps be used to compensate for some of the undesirable effects of this situation. As mentioned in the previous section, computerized means of information transfer can now be applied to give each student his or her own access to the network of knowledge. The very nature of information retrieval through the computer system invites one to apply a method of free exploration, as the items of knowledge are not arranged for it in a pre-determined order. Each particular piece of information can be accessed in several ways and from several directions, through a multitude of interconnections and interreferences. The items so arranged cannot be totally "covered" in any single journey, but they can be explored to any desired depth by a single individual, or by a small group.
There is, however, a common feature in all the examples of learning by free exploration that we discussed, that some may find disquieting. In none of these instances does the assimilation of moral values seem to be involved. The sense of orientation in physical space is value-free. The study of language is disconnected from moral considerations, as one can learn "the language of the enemy", who is often regarded as evil. Computer mastery by youngsters is in many cases accompanied by sophisticated sabotage. And on the ethics of methods of exam passing in today's highly competitive society, it is perhaps better not to speak.
Moral values cannot be "learned" in the usual sense - that is, they cannot be formulated as a list of "correct" answers to an exam. Instead, they have to be assimilated as modes of action. If this assimilation also comes about through the exploration of a network, then it cannot be "a network of morality" which exists in its own abstract space. For morality is neither a list, nor a network of abstract rules and precepts: it is a direction imposed by the human on concrete human acts, within the network of human acts in which the individual finds itself. But in the context of assimilation, this network of acts is permeated with the conscious goal of moral education, as parents in most human societies seem inclined to weave into their relations with their children: not a play any more, but a goal-oriented interaction between an adult and a child [25]. Thus, at least in the case of moral education, free exploration by the individual should be subject to the imposition of external standards. It is perhaps along similar lines that the role of "parental guidance" in other domains should be understood.
[2] The inadequacy of both methods can be appreciated from the actual fluctuation between them. Thus, in recent years there appears to be a tendency to shift from a rationalist to an empiricist approach in the study of physics at school. This, however, does not represent a true innovation, as one can find a criticism of similar then-prevalent methods at the beginning of this century, for example in Duhem (1906). [3] An empiricist can also believe in the existence of unchanging laws of history; but in this view, such laws can only be inferred from the evidence.
[4] For our purpose, it suffices that these two approaches are possible. The question to what extent they are actually applied is complex. On one hand, especially since the collapse of Marxist ideology, it is difficult to argue for a rationalist approach in history teaching. On the other hand, history teaching in school is particularly liable to be ideologically influenced, and such ideological views - that human history is the unfolding of God's plan, or that it represents the inevitable progress towards freedom and democracy, or that it reflects the perennial struggle between one good people and all the bad ones - tend to assume the role of first principles, which precede and underlie the concrete historical events. That is, they have an effect similar to pure rationalism, even though they are not necessarily based on the exclusive belief in human reason.
[5] Duhem's example of Foucault's demonstration in 1850 that light is a wave is only strengthened by later developments, as from 1905 Einstein was laying the foundations of quantum mechanics by re-considering the assumption that light comes in particles.
[6] The analogy to the distinction between hardware and software should not be carried too far, because the network of scientists and the network of their beliefs and acts should probably be compared to a natural data processing system, e.g. the human brain, and not to an artificial one. In the brain, hardware and software cannot be completely separated, because what goes on in the brain constantly modifies its structure, and vice versa. Similarly, the structure of scientific institutions, for example, cannot be said to belong exclusively either to the thought style, or to the thought collective: the two influence each other through its intermediacy.
[7] Fleck's central example is the relation between Wasserman's chemical reaction and the disease of syphilis. One cannot suspect Fleck of being uncommitted to this fact, because as a practicing doctor, he used similar procedures to diagnose his patients. However, as he shows, both the concepts of Wasserman's reaction and of syphilis are historical constructs, which can dissolve at some later stage in the development of medicine: it is conceivable, for example, that different current versions of actually carrying out Wasserman's reaction would someday be classified as medical tests for different forms of illness, so that the statement "Wasserman's reaction is a reliable test for syphilis" would cease to be a part of the accepted and applied medical knowledge. [8] Against this view, one may claim that the process of research and discovery possessed the linearity of a time series: do not the chronicles of discoveries enumerate them in a well-defined order? However, as both Kuhn and Fleck point out, the reason why scientific knowledge cannot be constructed in its totality by a single individual is not only the short span of active human life. Scientific knowledge exists in a community of scientists, and not in the mind of a single individual. In such a community, different things are going on all at once, so that they cannot be ordered along a one-dimensional time series. In fact, as Feyerabend (1975) argues, different co-existing efforts can proceed in conflicting directions, and the historical process of science owes much to such conflicts.
[9] It seems that this is the way in which the study of history appears in the minds of some school students - history as annotated chronicle. Perhaps this is one of the reasons why they consider history as a dull subject, although in principle, it consists of stories, and well-presented stories are usually loved by young and old.
[10] Through movements in the population of researchers, and through understanding by comparison.
[11] This shift is not universal, as in some fields it is, if at all, slower than in others. For example, Chomskian linguistics, that assumes that language is generated deductively from a list of first principles which are biologically encoded in the brain, still enjoys some popularity, although the organic-like structure and development of a living language may seem almost evident. One might be inclined to believe that there are no "laws of grammar", but only habitudes of usage. These habitudes arise from the network of interconnections between language, culture, society, life habits etc., and their complex structure of "layers of language", with the conflicting tendencies of uniformity and variation, reflects the complex nature of this network: the fact that two such layers are still "the same language" cannot be separated from the fact that the two social groups employing them are highly interconnected on many levels, etc.
[12] An large measure of "networking" has always been typical of science: scientists communicate not only "up" and "down" within the hierarchies of their research institutes, but also through exchange of letters, conferences etc. However, the electronic mail system does not only much amplify the degree of interconnectedness of the network, but also opens it to the access of non-scientists.
[13] For popular reviews with select bibliography, see Gleick (1987), Lewin (1993). See also Prigogine and Stengers (1979), Atlan (1986).
[14] Still, it is interesting to note the similarity between these developments and James' (1890) introspective observations on the non-linear nature of the process of thinking.
[15] See for example Maturana and Varela (1992).
[16] Consider, for example, the image of a "reasoning agent" located at some definite point inside the brain, with the neuronal system's being just an instrument of communication between this point and the body, much like a spider's net which transmits information to the spider. In the 17th century, such an image, which made one of its first appearance in d'Allamber's dream (Didero 1769), was shared by both rationalists (Descartes' "pineal gland") and by empiricists (Newton's "sensorium"; see Alexander 1956). Another example is the empiricist view that experiences are registered each in its turn, which could lead us to expect the existence of well-defined "memory registers" in the brain; such registers are known to be non-existent, as the removal of specific brain tissues is not accompanied by the disappearence of specific memories.
[17] This term was coined by Mandelbrot (1975). Since then, much literature has been published on the subject. See for example Lauwerier (1991).
[18] The exact relations between terms like "fractals", "complexity", "chaos" (which is a type of behavior typical to complex dynamical systems), "self-organization" and the like are not altogether clear, as no fundamental theory of this field currently exists. But to the extent that this field has any real content, they all seem to be somehow related to it.
[19] A snowflake is certainly not "organic", but it can be said to have something organic-like about it: tree leaves, each one different and still all the same, have a similar multi-branches structure. [20] For example, in pluri-ethnic countries, minority children can be forced to follow a teaching aimed at denying their separate ethnic identity, and this by a majority vote. Autonomy in education can indeed be one of the central issues in an ethnic conflict. [21] The important role of active exploration in the process of learning of the features of physical environment was demonstrated, for example, in an experiment in which two new-born kitten were tied to a mechanism, which ensured that their movements are determined by only one of them, while they both have a similar visual input. The "active" cat developed a normal sense of visual space, while the "passive" cat didn't. Similar results were obtained in studies of sensory-motoric adaptation in human adults (Held 1965).
[22] Thus, there might be a relation between the decline, with age, of the tendency to play, and the decline in some learning capacities, for example the capacity to learn language, or the capacity to learn the structure of the physical environment, as shown, for example, in cases of blind-born people who regained their eyesight at an advanced age. This does not exclude psychoanalytical explanations of play activity (see for example Winnicott 1971), as in any actual play activity, many functions may interlace: it is only in linear models that an effect has to have a single original cause. However, The assumption of a basically psychoanalytical function for play would have difficulties in accounting for what looks like obvious play activity in animals like cats, dogs and dolphins. The holders of such an assumption would either have to claim that animals share the same psychological structures that they ascribe to man, a claim which is difficult to substantiate, or assume that what looks like play activity in animals is in fact something else, thus introducing an arbitrary barrier between us and our animal friends. It seems more reasonable to believe that psychoanalytical considerations apply, if at all, only to the actual choice of the particular form in which the natural urge for play finds its expression.
[23] "Virtual" here may mean many things - hordes of computer space invaders, for example, but also the abstract contents of learning, like the two-body system of the Kepler problem in mechanics. In both cases, it is an imaginary world, which is for the moment perceived as real, if only in the sense that is presents the individual with real challenges.
[24] This may sound somewhat dire. However, it is not the role of the public educational system to promote originality. Almost by definition, originality grows against the education received. In this sense, education should not aim to be perfect: it must allow for the student's later rebellion against it.
[25] Although the same actual interaction can be perceived as moral education by the adult, and as play by the child, like when a child is "playing naughty".
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