The Problem of Problems - Science Direct

J. theor. Biol. (1982) 99, 193-201

The Problem of Problems ROBERT Scorr

ROOT-BERNSTEIN

The Salk Institute for Biological San Diego, California

Studies, P.O. Box 85800, 92138, U.S.A.

(Received 14 August 1981, and in revised

form

12 Jufy 1982)

Problems of generating and evaluating problems are discussed and the subjective nature of these processes highlighted. Criteria for problem evaluation are presented as a means to minimize this subjectivity. Areas of continuing ignorance concerning problem generation and evaluation are defined and suggestions made for investigating them.

is there any way in which to increase either the rate or the efficiency of the discovery process in science ? One way to answer this question is to turn to the old saying that scientific “gerGus” lies as much in asking the “right” questions of nature as it does in answering them (Bancroft, 1928). If this saying is correct, then one way in which to facilitate the discovery process would be to learn how to generate and evaluate new problems more efficiently. Unfortunately, problem generation and problem evaluation are themselves unsolved problems. The purpose of this paper is to define the outlines of this “problem of problems” and to suggest some possible ways of addressing it. The Problem of Problems

Linus Pauling was recently asked, “How do you have so many good ideas?” Pauling answered, “Well, you just have lots of ideas and throw away the bad ones. And I think that this is part of it: that you aren’t going to have good ideas unless you have lots of ideas and some sort of principle of selection” (Pauling, 1977). What Pauling says about ideas in general applies in particular to the “problem of problems” as well. To generate a single “good” problem, one must think up lots of problems and then select out the “bad” ones. Certainly, that is how many successful scientists have worked in the past. Darwin, for example, admits in his Autobiography to incessant hypothesizing accompanied by constant self-scepticism (Darwin, 1887, 1958). J. B. S. Haldane was parodied by Aldous Huxley in Point Counter Point for his ability to 0022-5193/82/210193+09%03.00/0

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perceive a new problem in virtually every event he witnessed (Huxley, 1928). And Neils Bohr is said to have posed dozens of new problems each month in search of one that might be important (Rozental, 1967). The problem of problems therefore consists of two “subproblems”: problem generation and problem evaluation. Unfortunately, how scientists invent or perceive new problems is, at present, a mystery. It is not even clear that sufficient evidence now exists to permit meaningful research into this subproblem. The difficulty is lack of basic information. Scientists, for obvious reasons, rarely record or remember problems that do not merit subsequent research; and scientific recognition accrues to individuals for solving recognizably important problems, not for stating them. If the problem of problem generation is ever to be solved, then, techniques of data collection and incentives to scientists to pay attention to the processes by which they work will have to be formulated. Only two conclusions concerning problem generation seem to be undeniable based upon extant evidence. First, scientists individually tend to pose many more problems than they can actually address for reasons of time, money, or expertise. Second, the greater the number of scientists posing problems, the greater the number of problems that cannot be addressed. It follows that the need for criteria by which to select promising from unpromising problems increases with the number of problems being posed by any individual and with the number of individuals posing problems. Fortunately, sufficient evidence of the evaluation process used by various scientists exists to allow some tentative conclusions to be reached. The rest of this essay will therefore deal with the subproblem of problem evaluation. The Subjectivity

of Problem

Evaluation

The problem of problem evaluation is, like the problem of problems itself, too general to be addressed directly. It needs to be restated in terms of more approachable subproblems. The most obvious of these is that problem evaluation is subjective. T. H. Huxley recognized this subjectivity when he wrote the famous line, “It is the customary fate of new truths to begin as heresies and end as superstitions” (Huxley, 1880). The philosopher R. D. Carmichael concluded his study of the problem solving process by stating that, “discovery itself may be relative to the point of view of the investigator” (Carmichael, 1930). The subjectivity of problem evaluation has been further studied in Root-Bernstein’s (1981) analysis of four Nobel prize winners who founded physical chemistry: Svante Arrhenius, J. H. van? Hoff, Wilhelm Ostwald, and Max Planck. Each man claimed to address a problem considered to

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be “impossible” by the majority of his colleagues. Each met great resistance and scepticism in pursuing that problem. Yet, each man, by introducing an unorthodox technique or idea into science, succeeded in solving his “impossible” problem. These episodes in the history of science suggest that the evaluation of the solvability of a problem is linked to contemporary evaluations of the limitations of existing problem-solving techniques. If existing techniques are deemed irrelevant to the posed problem, then the problem will, in all likelihood, be deemed impossible of solution. Yet, as Arrhenius said some years after receiving his Noble prize: “Just such things will promote science and knowledge very much, which are said to be impossible” (Arrhenius, 1912). Indeed, the history of science suggests that the major difficulty encountered by innovators from Copernicus to Einstein has not been only in persuading their colleagues to accept their resolution to a problem; usually it has been in persuading their colleagues that a problem so important that it calls for innovation exists in the first place (Kuhn, 1977). Unorthodoxy, be it in problems or solutions, is necessary to science, yet it is always suspect (Schachman, 1979). There is always a great deal of what Hans Gaffron calls “resistance to knowledge” (Gaffron, 1970). In consequence, one may rephrase the problem of problem evaluation as follows: how can suspicion of unorthodoxy and the subjectivity of problem evaluation be minimized so that truly important questions will be given appropriate attention? The answer to this question, it seems to me, lies in the development of explicit criteria for problem evaluation. These criteria will have to be capable of sorting worthwhile problems from worthless ones; of determining whether or not worthwhile problems are resolvable; and, if resolvable, by what methods. I propose here to essay a list of such criteria. I hope that they will provide the basis upon which a more complete and functional set may one day be developed. Some Criteria

for Problem

Evaluation

To begin with, it must be realized that not all problems are created equal. Problems differ in a number of characteristics, the first of which might be called “class.” There are at least nine “classes” of problems (though there may be more): (1) problems of definition; (2) problems of theory; (3) problems of data; (4) problems of methodology or technique; (5) problems of criteria; (6) problems of integration; (7) problems of extension; (8) problems of comparison; and (9) artifactual problems. “Classes” of problems deal with subject matter.

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A problem of definition is one of classification or distinction; e.g., “What is life?” or “What species is this ?” A problem of theory concerns the explanation of data according to some unifying concept; e.g. the explanation of the fossil record and the geographical distribution of species by evolution; or the explanation of the observed characteristics of falling bodies by gravity. Data problems concern the verification and the collection of data in sufficient quantities and of sufficient quality to verify or falsify a theory. Problems of methodology or technique concern the means by which data are collected; e.g., “I need the following kind of data: how do I get it?” The next five “classes” of problems concern interactions between the first four and thus might be classified as “interclass”. Problems of criteria concern the interpretation, meaning, or validity of any of the first four “classes”. For example, some definitions, such as that of velocity, are very useful to scientists while others, such as entelechy, are not. Clearly criteria must exist by which one may-evaluate definitions. Similarly, a theory must provide criteria for the evaluation of data as fact (data that verifies a theory), artifact (data that is inapplicable to testing a theory because it results from causes defined to be outside the bounds covered by the theory), or anomaly (data that contradicts theory but can be demonstrated to fall within the bounds in which the theory should be valid). Scientists spend a great deal of time, often unknowingly, resolving problems of criteria and determining the boundaries within which problem statements and resolutions are valid. Problems of integration arise from attempts to integrate two or more theories or data bases in a coherent fashion. Reduction of biological theories to those of chemistry and physics is an example of an integration problem. Problems of extension are exactly opposite in nature. They deal with the export of a technique, criteria, or a theory to a new field of science in which the application is problematic: e.g., does genetics provide a sufficient basis upon which to build sociobiology? Problems of comparison, on the other hand, treat competition between two or a more definitions, theories, etc. For example, if two sets of data are incompatible, how does one establish which set is valid for any particular use? Or, how does one test the relative merits of two theories invented to explain the same data base, but which employ contradictory assumptions (e.g., the wave-particle duality in physics)? Finally, in a “class” by themselves, are artifactual problems. Artifactual problems result from misclassifying problems. For example, the validity of a theory may be thrown into question as a result of data collected by a technique inappropriate to the particular experiment. What at first appears to be a theory problem is actually a combination data problem (verification) and criterium problem (is the technique for data collection suitable?) It

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appears to this observer that a disproportionate share of problems discussed by scientists are, unfortunately, resolved only after it is discovered that they are artifactual. Indeed, many scientific controversies have their roots in artifactual problem statements (Root-Bernstein, 1982). It should be evident that each of these problem “classes” requires a different methodology for its solution. Much as contemporary biology is tied to empiricism and the experimental method, it is obvious that no amount of experimentation will answer the definitional problem “What is life?” Neither will experiments provide concepts upon which to build theoretical explanations, nor new techniques by which new experiments may be devised. Experiments yield only data. Techniques make experimentation possible; data makes the invention of verified theoretical concepts possible. In short, the experimental method is only one of a series of procedures used by scientists. Thus, part of solving the problem of problems requires the development of a diversity of scientific methodologies of sufficient scope to handle the diversity of problem “classes”. Then, if one could accurately identify the “class” of a problem, one could avoid artifactual problems, and employ the methods appropriate to resolving that “class” of problems. Now, in addition to “class”, problems also have what might be called “order”. Most problems are defined within a very broad “problem area” or what Danielli has called a “major or first-order problem” (Danielli, 1966). An example of a “problem area” or “first-order problem” would be “How does the immune system work ?” There are clearly subproblems of all “classes” here: what constitutes the “immune system” (definitional); how does one describe an immune reaction (data and techniques); how does one explain the description one obtains experimentally (theoretical); is the mechanism describable or explainable in terms of already established mechanisms (integration); etc. To resolve these lower order problems, one must, in turn, address yet further subproblems. For example, to define what constitutes the immune system, one must have anatomical and physiological data; to get data, one must do experiments; to do experiments, one must develop techniques; to develop appropriate techniques, one must have appropriate criteria to define a particular problem and its boundaries; etc. What results from this process of “nesting” questions might be called an “ordered problem tree” (see Fig. 1). “Ordered problem trees” may be made up of any combination of problem “classes.” The “order” of a problem in a “problem tree” is extremely important. Danielli has pointed out that problems may only be solved when the techniques exist for solving them (Danielli, 1966). I would prefer a slightly broader statement than Danielli’s: problems may only be solved when the

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Fifth order problems

Fourth order problems

Third order problems

Second problems

order

First order problem ( Problem area) FIG.

1. Model of an “ordered problem tree”. Adapted from Danielli (1966).

techniques, data, theories, or concepts exist for solving them. The trick of problem solving, then, becomes the ability to propose a tree of logically connected (i.e., “nested”) problems so constructed that one or more branches or twigs connect with the known. The solution of one or more subproblems may then provide the basis for the solution of the problem next in the “order”. In a very well connected “logical problem tree”, the solution of a single minor problem may create a “domino effect” or “chain reaction” leading to the solution of an entire problem area. Galileo (Galilei, 1914) and Einstein (Rothenberg, 1979; Holton, 1973) were masters at this sort of problem “nesting”, sometimes reducing the solution of an entire problem area to considerations of a single, simple thought experiment. In terms of the immunological example introduced above, one might therefore postulate that one way of resolving how the immune system works would be to reduce that problem area through a “logical problem tree” to a subproblem such as “How does one explain the ABO blood system?” Since the ABO blood system has been well-characterized genetically, biochemically, and physically, there is a clear intersection between the known and

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the unknown. The problem is then to develop a “logical problem tree” in which a particular subproblem provides the key to the rest. One caveat concerning “logical problem trees“lmust be mentioned. Logic is not sufficient to the resolution of problems. It is possible to construct logical trees that infinitely regress into the unknown. To resolve one problem requires knowledge that raises another problem that requires knowledge that raises another problem. . . . In such instances, infinitely regressing “problem trees” will only be useful if the “tree” may be grafted at some point onto another “tree” that connects to the known. One way of making such grafts is by analogy: “This problem, about which we know nothing, is like that problem which can be solved; perhaps, therefore, the solution to that problem provides an analogy by which this problem may be resolved”. Examples of this sort of analogical grafting are evident in current attempts to understand memory in terms of immunological A second way of making grafts is to “memory” or computer “memory”. build models. Several excellent studies of the roles of analogical thinking and model-building as problem-solving techniques have been written (SEB, 1960; Hesse, 1966). Several criteria for problem evaluation follow immediately from considerations of problem “order”. A problem, even if valid, is not worth pursuing if a logical tree of subproblems cannot be built or grafted between it and established techniques, data, theory, or concepts. A problem that meets this criterium may be worth pursuing if it meets other criteria. The problem should not be trivial. Triviality may be difficult to determine a priori, but clues do exist. The importance of a problem is at least partially a function of its connection to lower order problems, or to a problem area. In other words, it is not sufficient that a problem connect to the known; it should also have strong connections to other unsolved problems so that its solution promises their solution. Otherwise a scientist may spend his whole life posing and resolving problems that have no logical importance to the integration or extension of knowledge. It is a choice, as Kant has said, between being curious or wise: “To yield to every whim of curiosity, and to allow our passion for inquiry to be restrained by nothing but the limits of our ability, this shows an eagerness of mind not unbecoming to scholarship. But it is wisdom that has the merit of selecting, from among the innumerable problems which present themselves, those whose solution is important to mankind” (Popper, 1960). Many scientists, unfortunately, only put on the trappings of wisdom and abuse logic in so doing. It should not be acceptable to justify trivial problems by saying that “if we understand this, then we will understand (e.g.) cancer.” To argue in this manner is to make direct connections between nth order

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problems and a problem area without specifying the “logical problem tree” in between. One way of evaluating a problem is to analyze the strength of the logical connections linking it to its problem area. The stronger and more numerous the logical connections, and the better these connections are specified, the greater the probability that the resolution of the problem will not be trivial. A final criterion that may be used in problem evaluation concerns the specificity of the problem statement itself. A well-defined problem states (implicitly if not explicitly) the criteria by which its solution can be recognized. On the contrary, a problem that is stated so that its solution set cannot be imagined a priori is unlikely to be resolved. Thus, it is important to reduce a problem to known constituents. For example, if one asks how the ABO blood system works, then the extensive data on the ABO blood groups provide the criteria for evaluating the success of any explanation: can the theory explain all of the available data in terms of fact or artifact? It follows that the greater the data base, body of techniques, theories, or concepts that a problem tree can be linked to, the more clear-cut the critieria will be for recognizing an appropriate resolution to the problems at the unknown/known juncture. Resolving the Problem

of Problems

By carefully de*fining the “class” and “order” of problems, a set of criteria immediately follow by which appropriate methods and resolutions may be evaluated. Regrettably, even this will not entirely solve the problem of problems, for the criteria presented here for problem evaluation are undoubtedly incomplete, while the process of problem generation remains unknown and appears to be a random one governed by chance. It seems likely, however, that problem generation could be altered from a stochastic process to a heuristic one by analyzing the failures and successes of many scientists. No doubt some such learning already occurs informally and implicitly in research laboratories, but knowledge needs to be made explicit if it is to be useful. This knowledge is not, at present, explicit. As Medawar has pointed out, “what scientists do has never been the subject of scientific inquiry” (Medawar, 1967). In consequence, Dedijer states that “there is a need for summation of practical knowledge” in the form of a “science of science”: “What do we know? Fourteen generations of scientists have been trained. Every one of those scientists had a teacher. That teacher had know-how. But very few have summed up that know-how. I like to cite the example of J. J. Thomson, who had nine Nobel prize-winners, thirty-two fellows of the Royal Society, and eighty-three professors of physics among his pupils. . . Yet, when

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you look-what were his rules of thumb? how did he teach?-you find practically nothing.” (Dedijer, 1966). You find practically nothing, not because the knowledge about how to do these things is lacking, but because the problems associated with preserving and teaching that knowledge are not considered part of science itself. The lack of interest is stultifying. Nothing could be more important to each and every scientist than the problem of problems in all its ramifications. For if the problem of problems is stated accurately here, then the need to resolve it-the need to understand how to interrogate nature and what about-is the central issue of science itself. It is time that the issue be faced squarely, and not just by those who study scientists, but by scientists themselves. It is scientists, after all, who have the most to gain.

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