Ignorance, Error, and Chaos:Local Learning/Global Research

Published as "Muchi, shippai soshite konton" inGendai shisou

"Japanese Journal of Contemporary Philosophy or Modern Thought"

Volume 24 (11): 363-376 (1996)

Permission granted to publish in English on the WWW by

Professor Koichiro Matsuno, Editor of the issue

John R. Jungck

Department of Biology

Beloit College

700 College Street

Beloit, Wisconsin 53511 USA

1. Introduction

Japanese and American science education and science are frequently compared in U.S. newspapers and popular magazines as two quite different systems. In these reports, Japanese students are described as better scientifically and mathematically on all comparative quantitative measurements. American students and their parents express more emotional affirmation of what their children are learning even though what they are learning may be significantly less by other referents than their Japanese counterparts. In other similar comparative reports, American science is supposedly highly generative of creative ideas and Japanese science enormously productive of pragmatic technological applications. Since I work in two scientific areas that are well represented by major Japanese scientists (computational biology, molecular evolution), I personally have not been able to see any such clear divisions amongst my binational colleagues. Both of these public perceptions or constructed stereotypes, however, mistake, I believe, our science and science education at an even deeper level: namely, at the epistemological foundations of our scientific investigations and learning. In addition, the above examples of strident nationalism are frequently uncomfortable to most biologists who understand that we live together in a small fragile biosphere and that science should be widely shared in democratic societies. Furthermore, they are steeped in the Western (Greek-derived) intellectual tradition of polar mythologies or Aristotle's excluded middle. While Western interpreters of Oriental notions of yin-yang stress complementarities in union or Buddhist and Zen notions of inclusion of both/and rather than either/or, nonetheless I hope that my audience will bear with the development of another dichotomous comparison for the sake of illuminating a paradox in models of scientific research or science education in Western circles. A similar comparison of humility versus hubris could be equally informative and say much about values among our cultures. Two questions drive this alternative perception: "How do we know that we don't know?" and "How do we educate neophyte scientists to explore questions about the unknown and the unknowable?"

For the past ten years I have been associated with a major curricular reform movement in American college and university education in biology called the BioQUEST Curriculum Consortium (Jungck, 1995). We have been devoted to enabling students to pose problems, to learn problem solving as a series of long term strategies and iterative processes of contemporary research, and to understand that solutions to scientific problems are hypotheses for which the scientific peer community must be persuaded. This pedagogical philosophy has been commonly come to be known as "post-Socratic pedagogy" (Jungck and Calley, 1985) or the "three P's: problem posing, problem solving, and persuading peers" (Peterson and Jungck, 1987). However, in order to inform the inadequacy of the above cross cultural comparison, let the following illustration center our differences in this public dispute (Figure 1).

Figure 1: A BioQUESTian learning paradigm: Ignorance, Error, and Chaos

Please note that we have used the sense strand of this antiparallel double helical representation of learning biology as containing three bases or cornerstones of this alternative mode: (1) ignorance, (2) error and chaos; and (3) collaborative learning. Since the latter is so much a part of most American higher education reforms in science education (e.g. Priscilla Laws' and Ron Thorton's "Workshop Physics," David Smith's and Lang Moore's "Project Calc" {a calculus reform project}, and Brock Spencer's and George Lisensky's "ChemLinks"), we simply refer readers to them (links describing their projects are connected to the BioQUEST Curriculum Consortium homepage). One critical element of the collaborative learning approach where BioQUEST differs from some of the other reforms is that we distinguish between simple cooperation in the acquisition of already known scientific principles and the collaborative construction of meaning in the world promoted by educational constructivists (Bruffee, Driver, Stewart, von Glaserfeld), by "strong programme social studies of science" theorists (Latour, Woolgar, Barnes, Knorr-Cetina, Shapin), and many feminists (notably Longino).

In order to instantiate science education with a more robust possibility of preparing students (all future citizens, some future scientists) to comprehend and/or participate in scientific decision making or investigations, we will lay out below those aspects of ignorance, error, and chaos that might lay a better philosophical foundation for such enabling possibilities. Also, scientists may better appreciate why "the public" frequently misunderstands them if they see that usual measures of education based on knowledge, mastery, control, and individual competition misconstrue much of their own motivation for pursuing science based on curiosity, love of puzzle solving, desire to collaborate with their peers and respond responsibly to criticism, and ability to persevere with enormous frustration in their pursuits. Thus, I introduce ignorance, error, and chaos below in each of several different contexts. How does this "sense strand" influence: Individual student learning? Collaborative student learning? Interest, confidence, and competence in scientific problem solving? Ability to cope with frustrations in pursuing unsolved problems and to deal with resistance to change? An ability to do scientific research and draw warranted inferences from research? The context of scientific research whether by a student or a professional? An appreciation for history of science? Roles of science in society? Professional responsibilities?

Ignorance

Why ignorance? We assert that the purpose of science education is to help citizens understand scientific values of humility about the current state of our knowledge, the limits of our practice, social responsibilities of scientists, and respect for the processes of investigation and communal peer review as well as the education of future scientists who are able to explore new and difficult problems creatively, rigorously, and responsibly. Michael Smithson, a fuzzy set theorist in the social sciences who is concerned with public decision making about environmental risks, has laid out a decision tree for ignorance (Figure 2).

Figure 2: Michael Smithson's "Taxonomy of Ignorance" (1989)

Why ignorance as a value for informing science education?

First, while ignorance is socially constructed, it is usually less commodified or reified than "knowledge" (usually with an inferred capital K). Smithson (1989) elaborates this thusly: "Ignorance is a social creation, like knowledge. Indeed, we cannot even talk about instances of ignorance without referring to the standpoint of some group or individual. Ignorance, like knowledge, is socially constructed and negotiated (p. 6). " One of the widely shared values of scientists that is usually difficult for students to understand is widespread skepticism. The poet Kenneth L. Patton asserts this positively in his poem, "The Faith of Doubt" of which I only share a few verses:

Doubting is but the forefront of faith,

a faith in the inexhaustibility

of growth and the illimitable

extent and wonder of the universe.

A doubting age is an age in the restlessness

and discontent of growth; a doubt is an

idea that is still alive.

To doubt that the past has uncovered

all things is to express faith

that many things are still to

be uncovered.

Thus, the wonder, awe, and mystery that drives many scientists throughout full and long careers can be more easily shared with students. Science can be a search for deeper questions rather than a quest for eternal, absolute truth. The fallibility of science can help to differentiate our practice from aspects of religious conversion. In The Encyclopedia of Ignorance, the editors Ronald Duncan and Miranda Weston-Smith (1977) introduced the volume by stressing these values: "Compared to the pond of knowledge, our ignorance remains atlantic. Indeed the horizon of the unknown recedes as we approach it. The usual encyclopedia states what we know. This one contains papers on what we do not know, on matters which lie on the edge of knowledge. In editing this work we have invited scientists to state what it is that they would most like to know, that is, where their curiosity is presently focused. We found that this approach appealed to them. The more eminent they were, the more ready to run to us with their ignorance." One such famous scientist, Charles Darwin, notes that being: "Deeply stirred by the excitement of hard scientific thought, he succumbed to the full force of ambition. To chase a theory through the mind like this was marvelous: an intoxicating combination of effort, skill, caution, and bravery - and in this case too, a healthy dose of ignorance which encouraged imaginative leaps in the geological dark... (Browne, 1995, pp. 185-186)." Note that this approach flies directly in the face of Jeremiads such as most recently John Horgan (1996) who proclaims in his book: The Ends of Science that "further research may not yield much." Today's students have infinite possibilities for problem solving opportunities that are as likely to radically transform science as in the past: with an explosion of knowledge, there is a parallel development of associated questions that have never arisen before.

Second, while the power of scientists' claims of ignorance (see Holly Stocking and Holstein, 1993) may assert similar authority to other ploys such as datum anthropomorpha (data suggest, research tells us, the results show ...) that disarm the reader into thinking that inferences are universal and unassailable as well as surely not the responsibility of the writer or speaker, to claim that something is unknowable, untestable, unprovable, incalculable, uncomputable, etc. is usually perceived by most readers as "not yet" because of deeply held beliefs that science and mathematics can continue to overcome enormous impediments to investigation.

Third, Marlys Witte (1988), University of Arizona School of Medicine, has developed a curriculum for future physicians that is explicitly devoted to educating these clinicians that most of medicine has a weak scientific underpinning for most common practices other than simple empirical associations that "they work." She asserts that the most important pages in their texts are the blank ones which leave room for what we currently don't know. She leads students in "pondering" sessions and does "wondering" rounds through clinical wards. Since American physicians are usually noted for airs of "god-like" authority, contemplating ignorance can promote healthier humility in the face of difficult medical problems. Donald A. Schön (1987) has studied the practices of professional education of psychoanalysts, architects, and musicians and concluded that the critical stage in becoming a professional is to become a "reflective practitioner."

Fourth, ignorance's various dimensions include many variables as Smithson suggests in Figure 2. If we consider these factors from a social level, Val Woodward suggests that these pose tremendous challenges for democratic societies: " Our mode and manner of teaching signals whether, as a society, we are ready to live with sustained and open-ended uncertainty ..." (1972).

Fifth, incompleteness, imprecision, uncertainty, and other forms of ignorance are cornerstones of contemporary theories of modeling practices. Every model we ever build we know is false before we ever run it because we know that we have made simplifications and comprises to build tractable, comprehensible systems. Levin (1966) argues that models must satisfy a triangle of constraints (see Figure 3): generality, realism, and predictability. He encourages biologists to decrease their reliance on precision and to build models that emphasize generality and realism. No one model can satisfy all constraints; hence, classical models of optimization of single variables are woefully inadequate to deal with multivariate, multidimension, complex problems. Furthermore, the philosopher of biology Bill Wimsatt (1987) has argued that "False models build locally truer theories" because they isolate aspects of our ignorance and allow us to progress. His supposition is: "the creative use of falsehood is one of the best tools the practicing realist-scientist ... has for discovering truths about nature." Wimsatt (1980), Koichiro Matsuno (1995b), and Gregg Michelson(1995) have all recently re-raised the concept of Ceteris paribus in order to deal with counterfactuals in scientific discourse. Wimsatt, in particular, argues that: "Ceteris paribus is viewed as a qualifier on environmental variables" (p. 233) and that the reductionistic problem solvers' focus on "control" leads them to "often tend to miss dependencies of system variables on" environmental variables that are held constant. This will become even more important when we discuss the movement from linear, optimization models to nonlinear, multivariate models where "control" may not even be conceptually possible.

Figure 3: Levin's Triangle of Models

Sixth, a focus on ignorance might help students better comprehend our history of science and not be so surprised that scientists behave in very human ways. In a clever article entitled "Should the History of Science be Rated X?", Stephen G. Brush (1974) summarizes this aid thusly: The history of science could aid the teaching of science by showing that such puzzling concepts as force, energy, etc., are man-made and were evolved in an understandable sequence in response to acutely felt and very real problems. They were not handed down by some celestial textbook writer to whom they were immediately self-evident."

Finally, if you study Figure 2 as a lens to understanding of one's personal (or in Matsuno's (1995c) language, from an internalist perspective), current state of comprehension of a problem, then you might see that the taxonomy is enabling because you can use it as a guide to where you haven't already gone or what you might have missed. Glucksberg and McCloskey (1981) cite the importance of "Knowing that you don't know." Frequently, it is helpful to differentiate between simple lack of having not sufficiently explored the literature on a topic and an expert's intuition that a problem is insoluble with current theory and technology. Instead of feeling inadequate or stupid, this "tree" offers alternative paths to distinguish amongst a variety of possibilities.

Error

Why error? Early on in the debate over artificial intelligence, Marvin Minsky took considerable exception to the knowledge engineering approach of experts systems and production rules. In The Society of Mind (1985), he focuses instead on Learning from Failure: "Accordingly. it may be more important that we learn from how we fail. What should you do if some well-established method - call it "M" - has failed to reach a certain goal? One policy would be to alter M, so it won't make the same mistake again. But even that might be dangerous because it might cause M to fail in other ways. Besides, we might not know how to change M to remove the error. ... Learning has at least two sides. Some parts of our minds learn from success - by remembering when methods work. But other portions of our minds learn mainly when we make mistakes, by remembering the circumstances in which various methods failed to work. Later we'll see how this can teach not only what we shouldn't do, but also what we shouldn't think! (p. 96)." He believes that allowing ourselves to make considerable mistakes to learn from leads systematically to the possibility of generating more new ideas and humorous situations.

This, first and foremost, a learning strategy that help students appreciate error will most likely contribute to their success as creative idea generators. As Minsky (1985) phrases it: or in the early stages of acquiring any really new skill, a person must adopt at least a partly antipleasure attitude: "Good, this is a chance to chance to experience awkwardness and to discover new kinds of mistakes!" (p.97).

Second, a moral problem in contemporary science education is solved by this alternative focus. If the teacher is not the singular authority who judges the credibility of student claims, but instead students are given the opportunity to learn what good scientific, constructive peer review is about, then they not only are empowered by receiving multiple criticisms of their work, they also can become reflective practitioners. Students can critique published primary literature and thereby understand that "texts" are not the final word. As peer reviewers, they also benefit from seeing others' mistakes and thereby avoiding them in the future. One obvious benefit that teachers have long enjoyed is having the privilege of seeing so much work full of so many different kinds of mistakes. If the students are supposed to be the primary learners in a classroom, they should demand equal opportunity.

Third, we must differentiate between philosophy of science and philosophy of learning. Three important texts on this distinction are Tweeny, Doherty, and Mynatt's (1981) On Scientific Thinking, Berkson and Wettersten's (1984) Learning from Error: Karl Popper's Psychology of Learning, and Gorman's (1992) Simulating Science: Heuristics, Mental Models, and Technoscientific Thinking. All three focus on disconfirmatory evidence in learning situations. Other readers besides myself may also be amazed at their descriptions of how refractory most of us are to negative evidence. They observed that we sustain belief in ideas despite enormous observations to the contrary. While this helps make an even stronger case for the social construction of knowledge, it provides us with an opportunity to explore the conditions in education that may be more conducive to students (including all of us) making sufficiently clear hypotheses that we will recognize situations where they clearly are rejected. In light of Wimsatt's observation above that we know all models are false even before we run them, Popper's falsifiability is dead in a global sense even before we begin. In the post-positivist interpretation of Popper, all science is conjectural knowledge; even the asymmetry between multiple confirmations and singular falsifications are insufficient to posit "truth." In an essay on Popper, Agassi (1988) states: "Fallibilism ensures that science is literally endless: we can always seek errors in our past successes (p. 499)." Similarly, local problem solving (Matsuno, 1995a) makes progress by the ability of the solver to be able to debug their own computer program, to edit their own writing, and to redesign their own experiments or models. This level of student competence is justly associated with a confidence that frees themselves from their teachers such that a co-researcher relationship can develop. Furthermore, Lawrence Schwartz (1983), a creative writing teacher, extends these activities to the student - teacher interaction: "To learn to debug is to overcome the fear of being wrong, replacing it with the drive to untangle the problem. This is the real goal of making writing personally meaningful and relevant. It encourages the student to become an active participant and creates a truly collaborative relationship with the writing teacher." Similarly, Minsky says that it "creates a positive attitude toward error" and "a whole new set of attitudes toward making mistakes."

Fourth, in terms of students' increasing appreciation for the history of science, by recognizing "alternative conceptions" as appropriate sets of beliefs based upon the theories, methodologies, and data at any point in time, they have a possibility for more than the simple Whiggish history of the winner's side. Also, they might come to appreciate that controversy is a lifeblood of science. We constantly seek to resolve multiple working hypotheses, incongruencies in data, and differences of competing paradigms and their holders. While traditional science education may caution a student to be wary of arguments from authority, re impossibility, or association by innuendo, if students have to actively, openly, and publicly persuade peers of the plausibility, significance, elegance, etc. of their hypothesis, then they are more likely to both recognize and respect the variety of talents that their colleagues bring to bear on problems as well as the context of their own interpretations, experiences, and values.

Fifth, student laboratory exercises have been consciously chosen to be valuable precisely because they don't adhere to scientific practice. Where scientific investigations aim to solve problems that are real, significant, and frequently troubling, student laboratory exercises have been chosen because they "work well." That is, they demonstrate some already well known concept, behavior, phenomenon, or technique without much probability that something other than this was wished to be shown will come up. Black tars in organic chemistry labs are to be tossed before the instructor sees them, cats with upside-down kidneys are discounted as pathological in a dissection lab rather than opportunities for investigation of Darwinian variation, and kinetics of an enzyme that don't obey simple Michaelis-Menten relationships are because the student measured out the reagents wrong, couldn't read the spectrophotometer appropriately due to parallaxes, or graphed wrong. The whole notion of an "unknown" is to come up with the answer that the instructor has secretly held to themselves. All these behaviors condition student laboratory exercises to be oriented towards pleasing the instructor and coming up with the "right" answer rather than being open to the possibility that we learn from our mistakes or from surprisingly different results than we expected. Furthermore, the whole ideology on "hands-on" learning is not sufficiently empowering. As Nancy J. Nersessian (1989) points out: embedded in much of what is said about the need for students to have more laboratory experience is the implicit assumption that 'the scientific method' involves primarily induction from data. This assumption has been taken over from empiricist/positivist accounts of scientific method, and these have been severely challenged by contemporary philosophy of science. ... Construction of the conceptual structure of a science is not entirely, and perhaps not even primarily, 'data driven'. ... Second, implicit also in the belief in the primacy of laboratory experience is the assumption that if students have the correct data, they will recognize when these conflict with their preconceptions (pp. 179-180)." Since so many labs are designed to "work well," there is even less chance of the standard empiricist/positivist accounts even being challenged by students.

Finally, a focus on valuing errors, surprises, miscalculations, mismismeasurements, and misinterpretations has the ever present reinforcement of Marlys Witte's (see Blum, 1993) notion of our own fallibility: "Everybody knows the tune of ignorance: 'Yes, we have no pat answers.' " If we are less arrogant in our presentation of scientific facts, are we also not more likely to be able to engage in more responsible relationships to societal issues and "move from the absolute certainty of ignorance to the cautious uncertainty of scholarship?"

Chaos

Why chaos? Unfortunately, ignorance and error collectively would be inadequate to a substantial transformation of the assumptions of science education because each could be assumed to be static equilibria rather than open-ended, dynamic driving forces of self-organization, dissipation, or strange attraction. Chaos provides the constant source of disequilibration, the awareness of complexity, and sensitivity to initial conditions.

Hence, first and foremost, Bill Doll (1986) suggests that: "Any curriculum which emphasizes the active and reflective - the only way to achieve internality - must by nature run the risk of disequilibrium ... Disruption, or disequilibrium, is the motor which drives reorganizational behavior ... The teacher must intentionally cause enough chaos to motivate the student to reorganize. Because no preset formula can tell the teacher what [the right amount of chaos] will be for individual students, teaching becomes an art. Behavioral objectives with their set predeterminations have no place in this art. Immense responsibility is placed on the teacher, and curricula need to be teacher manipulated, not teacher proofed (pp. 10-16).

Second, critical education forces us to be self-reflective and this frequently leads to frustration. In bell hooks' (1994) reflections on her own struggles to legitimize theory in practice, she cites "the many women and men who dare to create theory from the location of pain and struggle, who courageously expose wounds to give us their experience to teach and guide, as a means to chart new theoretical journeys. Their work is liberatory. (p. 74)." So many recent science education researchers have focused on students' alternative conceptions and on conceptual change; yet few of them address the angst associated with going through a personal scientific revolution. While few students might use hooks' language of "profound and unrelenting misery and sorrow (p. 75)" associated with the regular and systematic "pain of sexism and sexist oppression (p. 75)" to describe their scientific worldview shifts, the transformations from an anthropocentric universe to a geocentric to a heliocentric to a view where our solar system is in one corner of a small insignificant galaxy out of millions or from special creation to Darwinian evolution have been associated with major philosophical, social, and cultural upheaval. Why if these are recognized as major problems for societies, do we not recognize the important aspects of personal upheaval?

Third, "chaos has allowed [many scientists] to renew their sense of wonder. ... For them, chaos is an image for what can be touched but not grasped, felt but not seen. At a time when resistance to mastery is so sophisticated that it cannot help but be perceived as masterful, chaos presents them with a resistance that alleviates the fear of mastery. ... They take chaos as demonstrating that there is something more than novelty, something other than the precession of simulacra. For them , chaos signifies the truly new (Hayles, 1990, p. 293)." I have opposed chaos and mastery in Figure 1 for both of these tensions of connotations between the student being transformed from a slave to a master with all of its sexist and racist overtones as well as the exclusionary sense of mastery which precludes the tension to humbly explore new ground. Without childlike awe, a scientist or a science student is severely handicapped.

Fourth, society and corporations have a vested interest in maintaining equilibrium. Yet science is a constant source of innovation and change. How, therefore, should educational institutions that are part of a larger corporate society stimulate innovation while maintaining social cohesion with larger society? Schön (1982) argues that: The society of a corporation attempts to maintain a stable state. This effort is not inertia, but conservative dynamism. The various forms of corporate resistance to change which reflect themselves as obstacles to technological innovation are processes of conservation - processes which are essential to the survival of any social or biological organism. ... It is nonsense to say that companies should throw off this old-fashioned habit. But it is the crisis of the modern industrial corporation that it is required to undertake technological change - change that is destructive of its stable state - in order to survive (pp. 301-302." Meanwhile when students are caught in the middle of academic wars in the construction of new disciplines such as biochemistry earlier in this century and recently molecular bioinformatics, additional challenges arise. Thus, chaotic change is a force in social readjustment because of the commitments and cohesion of organizations, but adjust they must if scientific research is to be supported. Similarly, science education curricula are socially constructed and the status quo does serve the interests of many who will be substantially at risk in a more open-ended curriculum. Hodson and Prophet (1986) conclude their discussion of curricular change by asking three critical questions: "Whose 'way of looking at the world' is being advanced? Whose interest is being promoted by the curriculum? Whose view of society is to be projected (p. 178)?"

Fifth, if students are to solve open-ended problems, then their local research practices must reflect the possibility of being "stuck," so much so that you need to greatly rework your fundamental underlying assumptions about operative causal relationships. "The importance of chaos theory does not derive, then, solely from the new theories and techniques it offers. Rather, part of its importance comes from its re-visioning of the world as dynamic and nonlinear, yet predictable in its very unpredictability (Hayles, 1990, p. 143)." While I would argue that Hayles has conflated LaPlacian prediction and determinism again in this passage, she catches my eye because I believe that her "re-vision" is precisely what students, teachers, and classes must collectively address as they attempt serious, "real" problems. Agassi (1988) connects these aspects of open-endedness with disruption in a series of questions: "Can we think of all of our concepts as inherently open-ended? Can we imagine that perhaps all the wonderful ideas humans have ever created fall short of our ideals - of truth, beauty, goodness? And finally, the key question: Is this idea disturbing to you (p. 500)?"

Sixth, many students believe, usually based upon some Whiggish history of the contributions of geniuses, that in order for them to plant the seeds of a scientific revolution they must make extraordinary claims. However, Porush (1991) notes that while "Gleick obviously wrote his book to confirm the model of paradigm change that Kuhn explicates in The Structure of Scientific Revolutions . Prigogine entertains the notion that scientific change is a sort of dissipative process and takes Kuhn to task, a bit, for not recognizing the extent to which scientific change can come from normal processes of science, and that no 'revelation' is necessary (p. 81)" In addition, Steven Shapin (1989) has celebrated "The Invisible Technician" who may have made some of the greatest potential for revolutionaries to have made their claims. Thus, I believe that Prigogine's sense of chaos in the history of science can be very democratizing in students' perception of their possibility for contributing significantly to science. Small efforts can have enormous consequences or in chaos lingo, there can be tremendous sensitivity to initial conditions.

Finally, what does the metaphor of chaos offer us for practicing responsible science in and of society? Dunbar (1993) offers five heuristics for achieving high possibilities for making discoveries: "(1) Members of a research group should have different, but overlapping research backgrounds. This will foster group problem solving and analogical reasoning. (2) Analogical reasoning should be engaged in when problems arise in the research. In particular, the scientists should engage in making both local and regional analogies. (3) Researchers should be encouraged to engage in combinations of high and low risk projects. This increases the probability that each scientist will have achieved a tangible result. (4) Take note of surprising results. Use the surprising results to generate new hypotheses and research programs. (5) Provide opportunities for the members of the research group to interact and discuss the research by having overlapping research projects and helping the lab to break up into smaller groups working on similar problems (pp. 16-17)." Dunbar also stresses serendipity and risk taking. If society is to support science and if science is to serve society well, then we need a more robust, chaotic model of science to be more widely understood in opposition to a cold, sterile, rational, turn-the-crank view of science which can produce results simply on demand.

Ignorance, Error, and Chaos

"An assumption underlying much of this work, according to Smithson, is that ignorance will always be with us. To the extent that this assumption is correct, human beings must learn not only the traditional strategies of reducing and eliminating ignorance, but also strategies for managing and coping with it (Stocking, personal communication)." Scientific research and science education share much in common; I argue here that they should become almost indifferentiatable or seamlessly connected in order to be more fully effective in the generation of new knowledge and of new problem solvers. I believe that shifting the attention from knowledge to ignorance, from mastery to error, from control to chaos, and from individualized instruction to collaborative learning that this integration of science and science education could be more easily approached. There will, most likely, be several benefits that I have summarized above: First, research and problem solving is more easily kept open rather than assuming premature or artificial closure. Second, researchers and students by being more self-reflective about their ignorance and errors are less likely to prematurely convince themselves or become overly arrogant about their insights. Third, the recognition of the social construction of knowledge and ignorance can be more explicit in classrooms and research labs and, hence, the complex relationship of science to society can be deconstructed. Fourth, for science to responsibly serve open, democratic societies and organizations, not only must science not be secret, but an open acknowledgment of the discomfiture of innovation with tradition has to be recognized and openly negotiated. Fifthly, an understanding of history of science and roles of ordinary scientists in this history can more easily be understand from this more humble and human perspective. Finally, less us hope that curiosity, awe, risk taking, and social responsibility would be stimulated by an alternative philosophical grounding of science education because students may be empowered rather than silenced because "the data did not suggest" those cannonical inferences to them or because a proof may have not been "intuitively obvious."

References:

Agassi, Joseph. (1988). ""Sir Karl Popper in Retrospect: the positive power of negative thinking." The Gentle Art of Philosophical Polemics: Selected Reviews and Comments, Open Court Publishing Company: La Salle, Illinois, Chapter 43, pp. 479-501.

Berkson, William and John Wettersten. (1984) Learning from Error: Karl Popper's Psychology of Learning. Open Court Publishing Company: La Salle, Illinois.

Blum, Debra E. (1993). "Arizona Professor Offers Curriculum on Ignorance to Give Medical Education a Wake-Up Call." The Chronicle of Higher Education (January 27): p. A27.

Browne, Janet. (1995). Charles Darwin: Voyaging. Alfred A. Knopf: New York.

Brush, Stephen G. (1974) "Should the History of Science be Rated X?", Science 183: 1164-1172.

Doll, William E., Jr. (1986). "Prigogine: A New Sense of Order, A New Curriculum." Theory into Practice XXV(1): 10-16.

Dunbar, Kevin. (1993). "How scientists really reason: Scientific reasoning in real-world laboratories." In R. J. Sternberg and J. Davidson, editors. Insight. MIT Press: Cambridge, Massachussets.

Duncan, Ronald and Miranda Weston-Smith, editors. (1977) The Encyclopedia of Ignorance. A Wallaby Book/Pocket Books: New York.

Glucksberg, Sam and Michael McCloskey. (1981). "Decisions about Ignorance: Knowing that you don't know." Journal of Experimental Psychology: Human Learning and Memory 7(5): 311-325.

Gorman, Michael E. (1992). Simulating Science: Heuristics, Mental Models, and Technoscientific Thinking. Indiana University Press: Bloomington, Indiana.

Hayles, N. Katherine. (1990). Chaos Bound: Orderly Disorder in Contemporary Literature and Science. Cornell University Press: Ithaca, New York. (See especially Chapter 8: "The Politics of Chaos: Local Knowledge versus Global Theory."

Hodson, D. and R. B. Prophet. (1986). "Why the science curriculum changes - evolution or social control?" In Joan Brown, Alan Cooper, Tim Horton, Frederick Toates, and David Zeldin, editors, Science in Schools, Open University Press: Milton Keynes, U. K., pp. 163 -180.

hooks, bell. (1994). Teaching to Transgress: Education as the Practice of Freedom. Routledge: New York.

Horgan, John. (1996). The Ends of Science. Helix Books/Addison-Wesley Publishing Company: Reading, Massachussets.

Jungck, John R., editor. (1995) The BioQUEST Library. Press: University of Maryland, College Park, Maryland.

Jungck, John R. and John N. Calley. (1985). "Strategic Simulations and Post-Socratic Pedagogy: Constructing computer software to develop long-term inference through experimental inquiry," American Biology Teacher 14(2): 137-146.

Levins, Richard. (1968). Evolution in Changing Environments: Some Theoretical Explorations. Princeton University Press: Princeton, New Jersey.

Matsuno, Koichiro. (1995a). "Global Idealism/Local Materialism." Biology and Philosophy 10: 309-337.

Matsuno, Koichiro. (1995b). "Being Free from Ceteris paribus: A Vehicle for Founding Physics on Biology Rather than the Other Way Around." Applied Mathematics and Computation 56: 261-279.

Matsuno, Koichiro. (1995c). "Internalist stance and the physics of information." BioSystems 38: 111-118.

Michelson, Gregg. (1995). "Counterfactuals and Ceteris paribus Assumptions in Food-Web Ecology." Presentation at the International Society for the History, Philosophy, and Social Studies of Biology: Leuven, Belgium.

Minsky, Marvin. (1985). The Society of Mind. Simon and Schuster: New York.

Nersessian, Nancy J. (1989). "Conceptual Change in Science and Science Education." Synthese 80(1): 163-183 (July).

Peterson, Nils and John R. Jungck. (1988). "Problem-posing, problem-solving, and persuasion in biology education." Academic Computing 2(6): 14-17, 48-50.

Porush, David. (1991). "Fictions as Dissipative Structures: Prigogine's Theory and Postmodernism's Roadshow." In N. Katherine Hayles, Chaos and Order: Complex Dynamics in Literature and Science. University of Chicago Press: Chicago, pp. 54-84.

Schön, Donald A. (1982). "The fear of innovation." In Barry Barnes and David Edge, editors, Science in Context: Readings in the Sociology of Science. MIT Press: Cambridge, Massachusetts, pp. 290-302.

Schön, Donald A. (1987). Educating the Reflective Practitioner: Toward a New Design for Teaching and Learning in the Professions. Jossey-Bass Publishers: San Francisco, California.

Schwartz, Lawrence. (1983). "Teaching writing in the age of the word processor and personal computers." Educational Technology June 1983: 33-35.

Shapin, Steven. (1989). "The Invisible Technician." American Scientist 77: 554-563.

Smithson, Michael. (1989). Ignorance and Uncertainty: Emerging Paradigms. Springer-Verlag: New York.

Stocking, S. Holly and Lisa W. Holstein. (1993). "Constructing and Reconstructing Scientific Ignorance: Ignorance Claims in Science and Journalism." Knowledge: Creation, Diffusion, Utilization 15(2): 186-210.

Tweeny, Ryan D., Michael E. Doherty, and Clifford R. Mynatt. (1981). On Scientific Thinking. Columbia University Press; New York.

Wimsatt, William C. (1980). "Reductionistic research strategies and their biases in the units of selection controversy." In T. Nickles, editor, Scientific Discovery Volume II: Case Studies, Reidel: Dortrecht, pp. 213-259.

Wimsatt, William C. (1987). "False Models as means to Truer Theories." In M. Nitecki and A. Hoffman, editors, Neutral Models in Biology, Oxford University Press: London, U.K., pp. 23-55.

Witte, Marlys H. (1988). "Seminars, Clinics, and Laboratories on Medical Ignorance." Journal of Medical Education 63(10): 793-795.

Woodward, Val. (1972). "Teaching and Learning through Investigation: A Case for Participatory Evolution." In John W. Thorton, editor, The Laboratory: A Place to Investigate (CUEBS Publication Number 33), American Institute of Biological Sciences: Washington, D.C., pp. 15-25.

Acknowledgments: My deepest apologies to my readers in Japanese; I am terribly sorry that I am not able to write to you directly in your primary language and that I am so poorly educated about Japanese science, philosophy, and customs. My first exposure to Japanese subjects from 1958 until 1966 was through art (paintings, silk screens, architecture, gardens, bonzai, origami), poetry (Haiku, Tanka, and Zen koans), food, plays, and literature. From 1966 through 1968, I worked on testing several ideas of Motoo Kimura on neutralist models of molecular evolution. From 1968 through 1971, I had the personal good fortune to work closely with four Japanese scientists in origins of life studies: Kaoru Harada, Tadayoshi Nakashima, Atsushi Yuki, and Takao Yoshida. While these memories have faded somewhat over the years, I deeply hope that my inferences expressed here do not transgress the bounds of my deep respect for all of you as well as my new colleague, Professor Koichiro Matsuno, for whom I am deeply indebted to explore some ideas that have been long in development. I also want to thank two American colleagues who greatly helped me over many years in developing these concepts: Holly Stocking for introducing me to the richness of ignorance and Chuck Dyke for helping develop what a nonlinear pedagogy should consider.

Author: John R. Jungck, Mead Chair of the Sciences, Beloit College, 700 College Street, Beloit, Wisconsin 53511 USA: e-mail address: jungck@beloit.edu