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THE NORMAL, AND THE PERILS OF THE SYLLEPTIC ARGUMENT EDMOND A. MURPHY, M.D., ScD* The basic notion of syllepsis can be simply represented. Two attributes separately predicated of two quantities may be confused and make it appear that the two quantities have an attribute in common . Algebraically we might say that A is predicated of B and A* of B*; confusion of the quantities A and A* may make it appear that B and B* have the attribute A in common. Syllepsis is widely used for literary effect. For example in Mrs. Packletide's Tiger the heroine wishes to shoot a tiger so that she can give a party to gloat over her friends with the "tiger-skin rug occupying most of the background and all of the conversation" [I]. Here the word "occupied" is being applied to the words "background" and "conversation"—in the former in a literal sense, in the latter as a metaphor. Syllepsis may be carried over into the field of argumentation. In Molière's Le bourgeois gentilhomme (act 1, sc. 2) the dancing master argues that the diplomat should learn dancing because the errors of diplomacy are false steps, and that the best prophylactic against taking false steps is to know how to dance. There is little danger of error from such transparent cases. But this kind of absurdity is often perpetrated quite unconsciously with words which have many meanings. A brief classification of such words is given in table 1. A typical misuse in an argument, which it seems appropriate to call the "sylleptic syllogism," is provided at the top of table 1. Here the same word, "fitness," is used in two different senses in the two premises: in a medical sense in the first, in a genetic sense in the second. The attendant problems are admirably illustrated in the use of the word "normal." Doubtless many different meanings can be attached to the word, but at least seven are sufficiently different to involve some peril of syllepsis (table 2). From top to bottom of table 2 * Division of Medical Genetics, Department of Medicine, The Johns Hopkins University School of Medicine, Baltimore, Maryland 21205. 566 j Edmond A. Murphy · Perils of Sylleptic Argument TABLE 1 Proper and Sylleptic Syllogisms Proper Syllogism Sylleptic Syllogism* A implies B ........ A is true .......... Therefore B is true . A implies B. A* is true. Therefore B is true. Examples All men are mortal ......... Socrates is a man ........... Therefore Socrates is mortal . Fitness is always desirable. Fitness implies having many healthy children. Therefore it is always desirable to have many healthy children. * Some classes of words which lead to sylleptic arguments: (1) Words which refer tointrinsically human acts (love, responsibility, consent, faith). (2) Words involving value judgment (good, true, beautiful, scientific, democratic). (3) Common words inadequately focused (normal, gene, lawful, the ether, democracy). (4) Words with a common meaning adopted in a specialized sense (random, fit, measurable, probability) or in a generalized sense (bias, myth, disease). (5) Technical words misappropriated by the laity (hysteria, allergic, fractured, tumor, abortion, assault, libel, replica). (6) Euphemisms (malnutrition, promiscuous, privilege). (7) Words which have been watered down, perhaps deliberately (libido, homosexual, education, freedom, home). TABLE 2 Seven Meanings of the Word "Normal" Paraphrase Domains of Use Preferable Term 1. Having probability density function '<^-K(^)'] (predicated of a metrical character) . 2. Most representative of its class. 3.Commonly encountered in its class. 4.Most suited to survival and reproduction .................... 5. Carrying no penalty 6.Commonly aspired to. . . 7.Most perfect of its class. Statistics Descriptive science (biology, etc.) Descriptive science Genetics, operations research , quality control, etc. Clinical medicine Politics, sociology, etc. Metaphysics, esthetics, morals, etc. Gaussian Average, median, modal Habitual Optimal or "fittest" Innocuous or harmless Conventional Ideal there is increasing loss of simplicity and objectivity and increase in complexity and subjectivity. For each sense there are spheres of study in which the term is so used, and for each an alternative term is suggested which is preferable because it is less ambiguous. 1. The word "normal" may mean that it is a metrical variate with Perspectives in Biology and Medicine · Summer 1972 | 567 a particular probability density function which is better described by some such term as "Gaussian." Why the term "normal" ever became applied to it is not clear, but there is no reason for thinking that it has anything whatsoever to do with the word normal in any other sense. There is no reason at all why an attribute of "normal" people should have this distribution: indeed it is usually impossible for it to do so, since this distribution has no limits, and most variables in man (height, weight, blood sugar, etc.) cannot assume negative values. Nevertheless this use of "normal" is a constant source of confusion. The statistician commonly asks, "Is it reasonable to suppose that the data are normally distributed?" The investigator often mistakes the sense, and because he has examined these people himself and considered them normal, he is liable to say that it is a reasonable assumption. In fact, the use of methods based on at least approximate normality must be justified either by serious mathematical theory or by analysis of empirical data. There are several other uses of "normal" in mathematics (for example, in geometry and in measure theory) which are of little interest to the biologist and will be ignored. 2.Then normality may be used in the sense of simple descriptive statistics. The man in the street asked what the normal height of a giraffe is might reply, "Ten feet." This figure may be wrong, but at least what he is trying to do is to give the most representative height of a giraffe from his own knowledge. The most representative value which he is trying to guess might be the mean or (for the size of a mouse litter) the mode. 3.A more sophisticated witness might feel that some kind of a range of values would be more appropriate, and might reply, "Nine to 14 feet." What he means by this, it would be hard to say exactly; but in some undefined sense he considers that this encompasses the values habitually encountered in these animals. It implies that if he saw one 2 inches high he would experience genuine difficulty in calling it a giraffe. Attempts have been made to formalize this kind of statement by defining a "normal range," which is "the mean plus or minus two standard deviations" (see below). But these three ways of looking at normality are of a neutral character . They are in some sense descriptive of what happens without regard to effects. 4.A more practical but also less objective way of using the term "normal" is to consider it in relationship to some kind of criterion 568 [ Edmond A. Murphy · Perils of Sylleptic Argument of fitness. Here, of course, the trouble starts because value judgments have been introduced. Geneticists take the ability to reproduce as a mark of excellence. This statement requires some qualification because the production of a large number of sterile offspring would not be evidence of fitness. Perhaps the best definition would be that the fitness of a genetic line is the probability that the line will not become extinct. A technologist or an expert in operations research would use a somewhat similar criterion—the probability that the instrument used will continue to function and to function well. But whereas there would be little doubt as to what a good function in an automobile tire would be, it is much more difficult to see that mere fecundity is a satisfactory criterion of normality in an organism. It can be, and indeed is, widely used in this sense. But then the word "fitness" itself must be used in syllogisms with circumspection. 5.A further rather loose usage of the term "normal" to describe a characteristic is to imply that it carries a trivial burden with it. A pediatrician consulted by a mother who complains that her child is a somnambulist may tell her that this is "normal," not because it is common but because the ill consequences are trivial. Here, perhaps the preferred term would be "innocuous" or "harmless." This criterion implies the methods of the decision theorist. 6.Normality may be used in a still more subjective sense, and then even definition of the criterion, however arbitrary, becomes difficult. There is the "democratic" criterion of conforming to the consensus. The politician is acutely sensitive to the aspirations of the "common man" and projects the corresponding image. The sociologist 's notion of the normal would be somewhat similar: he is not concerned with the outlier but with the typical man. But the form of the consensus becomes progressively less rational as the characteristic under consideration becomes more and more personal. Society might reason with some force that in the interests of self-protection, and the design of clothes, furniture, houses, and so forth, it is desirable that there should not be too much variation in body size. But in the psychological sphere judgments of this kind look more arbitrary than ever. What is normal behavior and what psychotic is a particularly sensitive matter. Herbert writes [2, chap. H]: "It's normal to share the delusions of one's society. . . . It's abnormal to develop private delusions," which probably has a certain justification in that at least such a policy is not disruptive. But there is also a widespread apPerspectives in Biology and Medicine · Summer 1972 \ 569 proach to madness which does not even put on the trappings of a principle: "For to define true madness, what is it but to be nothing else but mad?" (Hamlet, act 2, sc. 2, line 93), which (it need hardly be pointed out) says nothing at all and leaves the whole matter prey to the bias of minds which are themselves part of the system being judged. 7. If there is any reference standard outside of mere convention, then the consensus may bear little relation to it. Pi cannot be made equal to three by a legislative body, though the task has been attempted . It may be politically dangerous to say so, but it is nevertheless true that the aspirations of the common man call for guidance by the reformer and the visionary. It seems clear that the normal man should be the ideal man, and the study of the nature of the ideal man falls within the various branches of philosophy. Needless to say, this is the most controversial and the most subjective way in which to define the normal. But such a criterion, even if consensus is impossible , seems better than an unambiguous definition based on a narrow viewpoint. But it is important to distinguish personal prejudices from arbitrary usages. If an investigator takes as normal "the mean plus or minus two standard deviations," then we know what he means by the term, and in any argument he constructs about the normal, wherever the word occurs it can, and perhaps should, be replaced by his definition. Such arguments may have a trivial character, but at least they will not mislead if the rules of logic are followed. But if, for instance, he pushes his argument to mean that people not within this range should be exterminated or should be admitted to mental hospitals or require thorough medical investigation, then he is guilty of syllepsis. A hundred years ago he would doubtless have joined forces with the fifth group in observing with approbation the "laudable pus" which was present after all the best surgical operations. A Synthetic Approach The approach to the problem so far has been cautionary: it suggests that in current usage great ambiguity exists. It might be more helpful to start at the other end of the problem to see what use is to be made of the notion of normality and then consider how it is to be formulated. To this end it will be advantageous to consider three questions at increasing levels of epistemological difficulty. 570 I Edmond A. Murphy · Perils of Sylleptic Argument 1 . WHAT IS THE BEST METHOD OF DISTINGUISHING BETWEEN A NORMAL AND AN ABNORMAL GROUP? Of course, some criterion of "best" is needed, perhaps that which minimizes the cost of the process. A decision is to be made on the basis of a set of measurements or attributes; the criterion may be a complicated one because the various measurements will provide different amounts of information but will not, in general, be independent . Thus, impaired intelligence is a more secure sign of phenylketonuria than blond hair [3]. But in principle, at least, all the pieces of information going into the decision can be reduced to a single quantity or index. Thus, by dealing with the interpretation of a single value we lose nothing in generality. This consideration should meet the common criticism that the following kind of argument oversimplifies the nature of diagnosis. In simple fashion, suppose that a false positive is just as undesirable as a false negative. Then it is an easy matter to find a dividing point which will minimize the total misclassification. One such instance which we have worked out in detail elsewhere [4] is the diagnostic value of the lipoprotein fraction Sf 0-12 in coronary artery disease. To make this method pertinent to real life, factors other than the probability density of the curves must be taken into account. First, the relative frequencies of the normal and abnormal states should be considered. So also should the effect of bias of ascertainment. For example, in coronary disease the family physician is liable to see all manner of cases, whereas the hospital resident will see disproportionately few of the trivial cases and of the cases producing sudden death. The two physicians will be sampling from different populations, and the best cutoff points between the normal and the abnormal they should use will differ. Again, it is said that the very mildest and the totally incapacitating errors of refraction do not cause headache, that it is the intermediate cases which do and which come to the attention of the neurologist. If so, the notions of what the neurologist and the oculist consider normal will likely be different. Further, the results must take account of the cost of misdiagnosis. A satisfactory formulation of "cost" may be hard to give, but in principle the point is clear enough. Where cost of the false negative is high, the diagnosis will be made on slighter grounds. The adjustment Perspectives in Biology and Medicine · Summer 1972 | 571 is achieved by introducing a "cost function." The details may be found elsewhere [4, 5]. Now, how exactly we construct these decision schemes depends, among other things, on the alternative to normality under consideration . This seems to show that any attempt to cut the Gordian knot of diagnosis by any such simple device as "the mean plus or minus two standard deviations" will inevitably fail. The other fact to be borne in mind is that the decision is not often made between the normal and one disease state only, but between the normal and a variety of alternatives. 2. HOW IS A DISEASED GROUP TO BE DEFINED? This is a more fundamental and a more difficult question. There are really two problems here. If there were some external reference on the basis of which to group the cases, it would be easy by discriminant analysis to find the best set of decision rules [6]. This method is used if the objective is to replace a definitive but costly, and perhaps dangerous, procedure (such as an exploratory craniotomy) by cheap, simple, and harmless tests such as X-ray of the skull. But much more commonly—and this is a major problem in modern epidemiology—not only is there no external reference on the basis of which to minimize the cost, but there is no very clear idea of what is being sought. There is a vague idea that atherosclerosis is bad because it leads to high morbidity and mortality, but it is very far from clear what is really meant by this term. Is a fatty streak atherosclerosis ? Is an organized thrombus atherosclerosis? What is the difference between a thrombus and a hemostatic plug? These are by no means trivial or impractical questions, and an appeal to the state of confusion of the field after vast expenditure of time and money on basic research gives support to the claim that at least part of the problem rests on these fundamentally semantic questions. Fortunately—or unfortunately, it is difficult to say which since nothing succeeds like success but also nothing misleads more than success—not all problems are of this kind. Some Mendelian characters at least separate the subjects into unambiguous groups, not quite so perfectly as the categorical geneticist thinks but well enough for any possible practical purpose. The matter of defining discrete enti572 I Edmond A. Murphy · Perils of Sylleptic Argument ties and the methods and criteria for doing so are discussed in some detail by McKusick [7]. There are other conditions which segregate into somewhat less secure groups, such as certain infectious diseases or intoxications. The common run of measurable characteristics, however, do not behave in this way, especially in higher organisms. Height, which in the pea segregates as a Mendelian character, in man shows no evidence of grouping (ignoring a number of genetic diseases causing dwarfism, all of them rare). There are, in fact, good arguments from population dynamics why characteristics tend to be multilocal, especially where disease is concerned [8]. Where there is incomplete separation into groups, analysis is a much more difficult matter and probably cannot be solved except by putting arbitrary constraints on the parameters. If the task set is to find the description which conforms most closely to the data, it transpires that the best way is to put each individual in its own class. Now the whole scientific endeavor implies that the number of terms required to describe the universe is less than the number of data to be obtained from it. A classification which yields as many classes as there are data points is useless. So to start with it must be supposed that the number of classes is small, and known. But even then the problem is difficult and in certain cases still gives absurd results [9]. But then there is the other half of the question. Suppose that two groups of people are demonstrated, how can we decide which is the normal and which the diseased? Obviously, neither might be diseased . There is grouping with respect to handedness, and there is no reason to believe that either is diseased. There is no doubt which should be regarded as the disease, the hemophilic or the nonhemophilic state. In the case of sickle trait, we could give a reasonably sure answer if the environmental conditions were specified. Such answers could be defended in terms of morbidity and mortality. But in many cases who is to say? The old proverb that the creaking gate lasts the longest implies that there is survival value in not always feeling on the top of one's form. A previous generation used to describe some members of society as "delicate" or "not very strong," and it is impossible to discover any discernible meaning in the term. Many such persons lived to very advanced ages. But in making judgments, however obvious they may appear, our prejudices, conscious or unconscious, get in the way. Rightly or Perspectives in Biology and Medicine · Summer 1972 | 573 wrongly we are appalled at an eighteenth-century society which sent a child of six to the gallows for the crime of stealing sixpence. Rightly or wrongly they would have been appalled at our society, which tolerates abortion of a fetus. The tendency is to think that their standards are only conditionally true whereas ours are absolutely true.1 McKusick has remarked that we think it reasonable to study the height of Pigmies, whom we regard as dwarfs; but we would think it unreasonable that Pigmies study the height of Americans, whom they would consider giants. Yet one would be hard put to think of any reason we could plead before a cosmic court as to which of the two attitudes is correct. Curiously enough, the problem is easier for the multifactorial trait. Where a large number of environmental factors and genetic loci operate independently with about equal influence to determine some characteristic, the value it assumes should follow a Gaussian distribution approximately, or at least should be bell-shaped. The peak depends basically on the various gene frequencies, which are in turn determined in large part by selection. Thus, an exquisite feedback system is operating: if the peak of the curve does not conform to the optimal for the type of environment, then under selection, gene frequencies will readjust, and a new peak will be established representing that state which is most suited to the environment. This mechanism presumably provides the justification for senses 2 and 3 of the word "normal" and sets up a relationship to sense 4. The argument is sound if two assumptions can be accepted: that the yardstick of normality is biologic (or genetic) fitness and that the present condition of the distribution curve represents a final or steady state. The former point will be ignored, since it is almost certainly not a scientific question at all; the latter raises considerable difficulties. In steady state the rate at which genes are entering the population (for the most part by mutation) is exactly balanced by the rate at which they are leaving it (mostly by selection)—which may in part be the result of a struggle among the members of the population themselves. It might be fairly easy to demonstrate a steady state in a population with a short generation time under controlled and observed environmental conditions. But in human populations, generi These examples are not quoted to start a controversy. They are merely intended to suggest that "being appalled" is neither evidence nor rational argument. In exploring the theory of his judgments a man with a disciplined mind should be able to identify his prejudices and the prejudices of his age. 574 I Edmond A. Murphy · Perils of Sylleptic Argument ation time is long relative to the life of an observer, and what is known about environment in the past is based on inference from indirect evidence, which, while highly imaginative, is rarely coercive. It is thus difficult to establish that a steady state exists, and therefore the argument from central tendency (in any sense other than 2 and 3) is specious. For one thing mutation rate and selection have doubtless changed over the centuries. But besides, it is very far from evident that the human species will not continue to change in the future. Even if it were true that no further evolution will occur, the fact that man has devised so many recording devices and hence can accumulate scientific and cultural information will ensure that his environment will continue to change. Moreover, man is self-conscious and hence will tend to provide his own feedback mechanisms and artificial selection. It has been argued that various chronic diseases represent the results of the time lag between, on the one hand, the environment and the selection it imposes and, on the other, the genetic composition of the population to which it leads [10]. There is one curious logical consequence of the notion of a steady state which seems to have been almost entirely overlooked. If the peak occurs in the distribution at the optimal state, then there must be relatively greater selection against all alternative values. It is freely accepted that people with unusually high blood pressure, weight, or serum cholesterol or glucose have a considerably lower expectation of life than those near the mean. Why does not the force of selection drive down gene frequencies to the point where the resulting phenotypes will almost all lie within the "safe" range? I can think of only two possible answers. First, it may not be possible for a system to be constructed in which, for example, the blood cholesterol or blood pressure does not rise with age, any more than it is possible to devise a machine which will not wear out. This answer seems to be belied by the fact that there are classes of people in whom no rise in blood pressure with age occurs [H]. The other interpretation is that there is also a selection against the low values. Now surely this is a hypothesis which could be very easily tested? Of course blood pressure may be low as a result of Addison's disease or sodium-losing nephritis, and serum cholesterol may be low because of malabsorptive disease; and these conditions lead to low fitness. But that is not the point. If high blood pressure is selected against, in its own right (and not simply because it is a manifestation of something Perspectives in Biology and Medicine · Summer 1972 | 575 more important), low blood pressure should also be selected against in its own right. The standard textbooks emphatically reject "idiopathic hypotension" as a disease. Harrison's textbook [12], for instance , states: "Chronic hypotension is not a disease. . . . Thus, persistent low blood pressure should never be treated as such." If this means that prognosis is good in low blood pressure unassociated with disease, it would be of value to know whether this viewpoint has been formally verified or is based on "common sense" or on vague clinical impressions. Unfortunately the claims are undocumented. Should it prove to be true, then the argument from central tendency would be in peril. 3. WHAT REASON IS THERE TO BELIEVE THAT NATURAL GROUPINGS OCCUR? This is at once the most fundamental and the most difficult of the questions. Every entity is in some sense unique; classification is a convenience of thought and invariably falsifies to some extent. An exact description of anything would not allow it to be put into any category. For the most part, of course, subjects are not looked at in their entirety but from the standpoint of one characteristic. Sometimes measurement of the characteristic shows incontrovertible grouping. Almost invariably, however, even for well-established Mendelian characters, there is some scattering within groups. Whether this scatter should be ignored clearly depends on what its genesis may be. If it merely represents "noise"—that is, irrelevant variation such as experimental error, or variation due to the time of day at which the study is done—it is appropriate to discard it. But if it is due to the action of modifying genes, or to some habit of life, or to some environmental hazard, much may be learned from analyzing it. It is rarely easy to distinguish with confidence between the relevant and the irrelevant, and when in doubt, it is usually wise to retain the pristine data. Categorization even as an arbitrary device has its advantages, and indeed in certain situations it may be indispensible. For example, how can the effect of war on the sex of newborn children be determined ? A simple approach (and there is no virtue in making the problem gratuitously complicated) is to compare the percentage of male children in time of peace with that in time of war. But this 576 I Edmond A. Murphy · Perils of Sylleptic Argument whole method supposes that the division of children into "male" and "female" is possible. There is a further matter, one of convenience. Suppose it is true that all cases of cancer or schizophrenia or congenital heart disease could be divided into a number of classes and an exact prognosis worked out for each. It seems evident that as the number of categories goes up, the greater the burden on the memory of the physician ; but also the price for greater homogeneity within the categories is smaller samples and therefore larger standard errors of the estimates [13]. But this is an oversimplification. Not all members of a category may behave in exactly the same way. But if the variance within categories is small compared with that among categories, lumping them together may mean little loss of information and great gain in simplicity . In such cases the dividing point between cases can be chosen such that a shift in either direction makes very little difference in the classification of actual cases. If the upper limit of one class is five arbitrary units and the lower of the other is twenty, it does not matter whether the dividing point is chosen as ten or fifteen. By contrast, blood pressure does not show this kind of partition of variance. Wherever the dividing line is between normal and abnormal, it will not be true that most of variance is concentrated between groups. Moreover, a small shift in the dividing line will produce a disproportionately larger difference in the allocation of cases. We might then take as a kind of joint index of the usefulness of a classification of a variable the simplicity which results and the proportion of the variance which is distributed among categories. The more categories, the larger the proportion of the variance taken by the differences among them. Consider the following imaginary data points: 117, 121, 129, 131, 139, 140, 156, and 163. They might represent height in centimeters in some rare form of dwarfism. A common clinical problem is to decide into how many groups these values would fall naturally. They can be grouped in various numbers of categories so that the largest part of the total variation is distributed among categories (table 3). If the "best" split into two categories is used (so that the maximum proportion of the total variance is between categories), about threequarters of the total variation is attributable to differences between the two groups. For three categories the variation among groups inPerspectives in Biology and Medicine · Summer 1972 | 577 TABLE 3 Relationship of Homogeneity to The Number of Groups Classes Breakdown None 1-6, 7-8 1-2, 3-6, 7-8 1-2, 3-4, 5-6, 7-8 1-2, 3-4, 5-6, 7, 8 1, 2, 3-4, 5-6, 7, 8 1,2,3,4,5-6,7,8 Percentage of Total Variation among Groups 0.0000 74.7508 93.0648 98.0620 99.4186 99.8616 99.9723 100.0000 creases to about 93 percent of the total. By the time eight categories are used, all the variation is between categories and none within. Clearly if the only criterion is homogeneity within classes, eight categories will achieve it. However, it might be felt that with grouping into, say, four categories the loss of homogeneity within groups is trivial. An Alternative Scheme It might seem, then, that for this problem there is no cure which will work in the general case. If things fall neatly into categories, widely separated from each other, well and good; if they do not, the problem is insoluble, except by unwieldy methods. Now this is an unduly pessimistic viewpoint. The problem as stated is not in general soluble, but it is largely a gratuitous problem. It arises from a confusion between dimensionality and cardinality. A line has an uncountable number of points, and its cardinal number is therefore infinite. Thus it would seem to require an uncountable number of facts to describe it. But this is not so. The line can be described by specifying that it is straight and giving the positions of its ends each of which can be defined by three space coordinates. A distant colleague could reconstruct the line from these seven facts alone. The information can be coded in a seven-dimensional vector. Quite elaborate-looking curves can be unambiguously reconstructed from a comparatively small number of facts. A fair example is given in table 4. For a simple rectangular coordinate system with measurements in inches, a set of data on arcs of circles is given: the extremities for each arc, the radius of curva578 I Edmond A. Murphy · Perils of Sylleptic Argument TABLE 4 The Information in a Diagram Figure IjI Start End Radius (in Inches) Figuhe IB Start End Radius (in Inches) (0.00,0.00). (0.15,4.55). (1.50,1.30) (2.70,1.55) (3.20,1.80) (4.05,5.20) (4.30,7.70) (4.20,9.00) (2.90,9.60) (1.00,8.00) (0.15,4.55) (0.00,0.00) 2.15 5.00 2.20 3.00 OO 3.30 1.50 + 2.50 + 9.50 + 10.00 (7.45,1.40). + + (6.65,4.65). (9.40,0.00) (9.40,4.35) (8.50,8.40) (7.70,9.20) (5.45,0.60) (5.50,7.20) (5.70,6.35) (6.65,4.65) (7.45,1.40) - 2.15 +10.00 + 10.00 + 2.90 + 1.50 - 4.40 - 0.90 -10.00 - 3.30 Note.—By convention, a positive radius means that the arc is concave to the center of the figure; i.e., a line connecting the terminals will separate the arc from the center of the figure. The opposite applies to negative curvature . ture, and whether the curvature is positive or negative (defined in an arbitrary manner). These data were then given to a mathematical colleague who reconstructed the diagram shown in figure 1. He did not identify it, but the physician will recognize the silhouette of a heart and lung field. In fact the reconstruction agrees to within 0.5 percent of the original X-ray. To these tolerances and from the point of view of heart size, the dimensionality of the X-ray is something like forty: a modest content of information. In interpreting the X-ray the radiologist would of course be concerned with other information—for instance the vascular markings. Fig. !.—Silhouette of heart and lung fields Perspectives in Biology and Medicine · Summer 1972 | 579 But they would not contain any information about the size of the heart. It then seems evident that any purpose to which a classification is to be put could be dealt with by using a continuous mathematical function with little increase in complexity (indeed often quite the reverse ) and considerable gain in accuracy. Why, for instance, does the clinician try to set up categories of "hypertensive" and "normotensive "? The answer seems to be because he will use it as a basis for deciding what to do in the way of investigation, what he can say in prognosis, and how he will treat. The matter of investigating cases represents a complex decision procedure which it would not be practicable to pursue here. As for a five-year prognosis, he would have to remember two pieces of information, one for each group. But suppose (for instance) that the five-year mortality rate increases ten per thousand for every 10 mm rise in diastolic pressure: he would still have to remember two facts: what the rate is for the average and the gradient of risk. But this scheme would surely be more helpful than trying to pretend that all cases above 100 mm Hg have an equal prognosis . No sensible physician would attempt to defend this latter policy, but why categorize at all if the same and better results could be obtained from the same number of facts? Both are two-dimensional representations of a set of facts of infinite cardinality. The former distorts. The latter does not. As to treatment, the matter is even more clear. Reputable practice in the treatment of most diseases considers the objective as a restoring of values to the optimum. The vigor with which weight reduction is encouraged depends on the degree of obesity; other things being equal, the higher the blood pressure, the more powerful the drugs used and the greater the dosage; insulin or thyroid or adrenal hormones are titrated to a nicety against response. The same is true of the use of most effective drugs. Whitehead [14, p. 43] points out that much of the habit of classifying in science is to be traced to the preoccupations of medieval philosophers with categories, an idea derived ultimately from Aristotle , whose attitudes of mind perhaps reflect the fact that he was the son of a physician. Plato, on the other hand, was a mathematician. Had he gained the hegemony in Western thought, our scientific habits, particularly in medicine, might have been different and, Whitehead believes, better. 580 I Edmond A. Murphy · Perils of Sylleptic Argument At the present time at least, it is difficult to think of disease as other than an intimate interaction between the organism (with its genetic endowment and accumulated experiences) and perturbations in the environment. It has been suggested elsewhere [15] that the word "disease" is used in at least three distinct senses: 1.The manifestations of the body's attempt to maintain a normal interior milieu despite the effects of environmental change. The features of food poisoning (diarrhea and vomiting, which tend to eliminate toxin) might be thought of as an example. In this sense disease is closely allied to homeostasis. 2.Perversion of a normal homeostatic process, which in some cases may conceivably be a compensating process. Hypertension behaves in this fashion. Attempts to lower the pressure (although they would reduce the risk of serious complications) are nevertheless strenuously combated by the body. The hypertension which accompanies raised intracranial tension is presumably a compensating mechanism to maintain cerebral blood flow against outside compression. 3.A completely anarchical state in no way directed to serving the economy of the body. Cancer is the prime example. In the first sense, good clinical practice is directed to aiding the process. In the second it consists of adjusting the settings of the homeostatic mechanisms. In the third it is a matter of destroying the anarchical system. In all three cases the object is to pursue the optimal. But it is clearly desirable that the physician should know what is optimal before he attempts to pursue it. In this decision he must seek the opinions and the support of society. Who knows how much misery has been produced by the arbitrary decree that left-handedness is an abnormality which must be eradicated? But if the optimal can be defined, then it should be pursued as well as possible. The ideal doctor would concern himself with the task of making his patients ever more healthy. And if he did, he could with advantage forget about the word "normal" altogether. REFERENCES 1.H.H. Munro. The short stories of Saki. New York: Modern Library, 1958. 2.F. Herbert. The Santaroga Barrier. New York: Berkley, 1968. 3.L. S. Penrose. An introduction to human biochemical genetics. Eugen. Lab. Mem., vol. 37. London: Cambridge Univ. Press, 1955. 4.E. A. Murphy and H. Abbey. J. Chronic Dis., 20:79, 1967. 5.H. Chernoff and L. E. Moses. Elementary decision theory. New York: Wiley, 1959. Perspectives in Biology and Medicine · Summer 1972 | 581 6.C. R. Rao. Advanced statistical methods in biometrie research. New York: Wiley, 1952. 7.V. A. McKusick. Perspect. Biol. Med., 12:298, 1969. 8.E. A. Murphy. Perspect. Biol. Med., 9:333, 1966. 9.E. A. Murphy and D. R. Bollino. Amer. T. Hum. Genet., 19:322, 1967. 10.J. V. Neel. Amer. J. Hum. Genet., 14:353, 1962. 11.R. J. Jorgenson, D. R. Bolling, O. C. Yoder, and E. A. Murphy. Blood pressure studies in the Amish. In preparation. 12.A. Blalock and T. R. Harrison. In: T. R. Harrison et al. (eds.). Principles of internal medicine, article 135. 5th ed. New" York: McGraw-Hill, 1966. 13.J. Truett, J. Cornfield, and W. Kannel. J. Chronic Dis., 20:511, 1967. 14.A. N. Whitehead. Science and the modern world. New York: Macmillan, 1925. 15.E. A. Murphy. Linacre Quart., 36:158, 1969. SUMMER NIGHT Here and now, past midnight's hour, alone, Unsettled thoughts seek out profound expression, Find only languor, the pen upended by a smile. And the city sleeps without anticipation, Sleeps and dreams in incongruous scenes, These thousands set somehow at cross purposes. We know no more this summer night than ever, And yet we read the world with ease and smile, While gray clouds muster in the firmament, Prepare to wash our souls with summer rain. Jay Cohen 582 I Edmond A. Murphy · Perils of Sylleptic Argument ...

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1529-8795
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0031-5982
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pp. 566-582
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2015-01-07
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