Giants, pygmies, and the social costs of fundamental research or price revisited

TECHNOLOGICAL

FORECASTING

AND SOCIAL CHANGE

32, 323-340

(1987)

Giants, Pygmies, and the Social Costs of Fundamental Research or Price Revisited STEPHEN

P. DRESCH

and KENNETH

R. JANSON

ABSTRACT Social resource and opportunity costs of fundamental science are explored utilizing a model which integrates a) the determinants of the talent distribution of the cadre of fundamental scientists, b) the relationship of individual scientific productivity to scientific talent, c) the scientific value of aggregate scientific product, and d) the value of scientific personnel in nonscientific pursuits. On this basis, total, average, and marginal resource and opportunity costs of varying degrees of realization of “scientific potential” are derived. This comparativestatic analysis is then applied to the United States over the period 1940 to 1975-85, suggesting a four- to fivefold increase in the marginal resource cost and a five- to tenfold increase in the marginal opportunity cost of fundamental science over this period. In light of these findings and of the “free-good’ aspect of the products of fundamental science, it is concluded that the level and mode of support for fundamental science must, ultimately, be determined with reference to the non- or quasiscientitic contributions of fundamental scientists.

Prelude Thus, although we recognize that [scientific] saturation is ultimately inevitable, [w]e now maintain that it may already have arrived. It may seem odd to suggest this when we have used only a few percent of the manpower and money of the country, but it will appear that this few percent actually represents an approach to saturation and an exhausting of our resources that nearly (within a factor of two) scrapes the bottom of the barrel. [p. 311 in the density of good scientists we have left one more order of magnitude at the most and, even at the expense of all other high-talent occupations, science is not likely to engross more than 8 percent of the population. Even so, it looks as if the decreasing return of good scientists to every 100 Ph.D.‘s will make it more and more difficult to reach a level of this magnitude. [8, p. 541

Introduction Debates concerning science and technology policies are distinguished by the pervasiveness of confusion and obfuscation. At one level, there is confusion and obfuscation concerning what it is that science (as opposed to technology) contributes to society. Thus, even the scientific participants in the debate proclaim the pragmatic justifications for support of science as an “investment” in useful knowledge, but frequently object when they are forcefully encouraged to conduct their purely scientific endeavors under the guise

STEPHEN P. DRESCH is Dean and Professor of Economics and Business and KENNETH R. JANSON is Associate Professor of Accounting, School of Business and Engineering Administration, Michigan Technological University, Houghton, Michigan 4993 I.

0 1987 by Elsevier Science Publishing Co., Inc.

0040-1625/87/$03.50

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STEPHENP.DRESCHANDKENNETHR.JANSON

of responding to particular practical exigencies (wars on cancer, strategic defense initiatives, etc.). At another, politicians protest the unequal (institutional, geographic, etc.) distributions of the public largess devoted to science, as though the potential for scientific contribution (whatever its source of value) were (or should be) uniformly distributed; but to these protests the scientific community is unable to respond effectively because of its unwillingness to admit the existence of limits on scientific potential and the ultimately meritocratically elitist character of research-front science. In a tentative attempt to clarify several of the underlying issues, here we posit a very simple conception of what we will characterize as “fundamental research”: First, apart from the currency of the knowledge of the research scientist himself, free contributions to the “international knowledge system” constitute the only “products” of fundamental research. “Research-front” knowledge of fundamental science may well be of high practical value in a number of pursuits; however, particular research front developments are rarely motivated by the specific “applications” that are eventually observed. In fundamental research, claims that specific scientific achievements were motivated by their eventual practical applications almost inevitably have a “post hat, ergo propfer hoc” character. Thus, fundamental research is in contrast to “technological research,” the potential consequences (applications) of which can be reasonably confidently anticipated and have a high likelihood of realization (whether or not the accomplishments are ever adopted in practice). The difference between fundamental and technological research is suggested by Price’s [9, p. 2561 distinction between that for which an interested party can contract, which we characterize as technological research, and that for which, because of the unknown nature of the result, it is not possible to contract, which we characterize as fundamental research. Correspondingly, via either patents or trade secrets it is possible for the contracting party to have a proprietary interest in the results of technological research; in contrast, the results of fundamental research enter as free goods into the international knowledge system. A comparable distinction is made by Aranson and Sommer [ 1). Second, the capacity to contribute to the advance of scientific knowledge is a rare talent, possessed in uneven degrees by a relatively small proportion of the population, and the likelihood that an individual will be selected (or self-selected) into the ranks of fundamental scientists is a positive function of scientific talent or potential. By implication, an expansion of the “scientific cadre” will, ceteris paribus, result in a downward shift in the talent distribution of fundamental scientists. As a result of this adverse shift in the talent distribution and of such phenomena as duplication and fragmentation, increases in the size of the fundamental science cadre will result in diminishing scientific returns. Perhaps even more importantly, increases in the scale of fundamental research will be accompanied by rising social losses as nonscientific sectors (most notably, those concerned with technology, its development and utilization) are progressively drained of talent. Our concerns in this analysis are 1) the degree to which the “social potential” for augmentation of fundamental scientific knowledge is realized and 2) the social costs of that degree of realization. However, we would note that a finding of a high degree of realization of scientific potential and of high and rapidly rising costs of incremental additional realizations of potential would not necessarily imply an excessive social allocation of resources to fundamental research. Specifically, as developed in Dresch I41, there exist at least three essentially different justifications (or warrants) for fundamental research. First, fundamental research may be valued as collective social consumption, com-

GIANTS,

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325

parable to the value placed on other forms of cultural endeavor. Second, such research may (but may not) contribute to the advance of scientific knowledge. Third, engagement in fundamental research may be the only effective means by which to monitor scientific developments which might (but might not) be relevant to “technological research” endeavors addressing particular practical exigencies. The principal conclusion of our analysis, that rapidly diminishing returns and rapidly rising social costs are associated with increasing allocations of social resources to fundamental research, would have seriously negative implications in the context of the first two of these warrants for societal support of fundamental science. However, in this light one can argue, with Price [9, pp. 2532541, that the important consideration in the determination of the scale (and modes of financing and organization) of fundamental research is not its contribution to scientific knowledge per se, but is, rather, the usefulness of research front knowledge in pursuits other than fundamental research itself. ’ We emphasize that this analysis deals almost entirely with “unobservables,” e.g., “contributions” to scientific knowledge, the “value” of these contributions, the “scientific talents” of individuals and the “scientific-talent distribution” of the population, and the “opportunity costs” of allocations of individuals to scientific pursuits. While these variables are actually (if not inevitably) unobservable, they are, nonetheless, of great social significance. Moreover, we will demonstrate that quite plausible representations of these can be developed despite their unobservability. The principal conclusions of the analysis will be found to be quite robust with respect to the specifics of these representations. Fundamentally, however, the objective is not to present a precise “quantitative” representation of an unobserved reality, but is, rather, to capture the qualitative essence of that reality. Even partial success in this endeavor should have substantial value in clarifying the issues surrounding public policy toward fundamental scientific research. Modeling the Production of Fundamental Scientific Knowledge This analysis begins with a conception of “scientific talent,” T; the distribution of the population over scientific talent is given by the function f(T). The likelihood that an individual will pursue a scientific career, i.e., the probability that he will offer himself to science and that his offer will be accepted, will depend upon his scientific talent and on the scientific relative to nonscientific demands for his services, as reflected in a scientific membership function p(T;M), where M reflects the relative societal demand for scientific talent. The talent distribution of the subpopulation of scientists is then the productp(T;M) * f(T), the integral (over T) of which gives the size of the scientific subpopulation, S. Having been recruited into the subpopulation of scientists, the individual attempts to make a scientific contribution, with the magnitude of his contribution, g(T), dependent on his scientific talent. Aggregate contributions G are then given by the integral (over T) of the product g(T).p(T;M) *f(T). The scientific “value” of these contributions, V, is given by a value function v(G) in which the value of the marginal individual contribution decreases as the aggregate mass of contributions increases (as a result of such phenomena as simultaneous and overlapping discovery, fragmentation of effort, etc.). The size of the scientific cadre, S, provides an index of the real social resources

‘Thus, Price [9, p, 2561 concludes: “Only in very limited cases of support for purely cultural objectives, humane consideration of otherwise unemployable persons, should support be given for research leading into the international knowledge system where that research is taken to have intrinsic but uncontractable value. Fulltime research careers without otherwise useful services are to be discouraged.”

326

STEPHEN P. DRESCH AND KENNETH R. JANSON

Density

100

120

140

160

180

200 Talent

Fig. 1. Distribution

of scientific talent.

devoted to science. However, the “opportunity cost” of science, the value of the nonscientific services foregone as a result of the expansion of science, rises more than proportionately as the proportion of the population drawn into science increases; these “foregone alternatives” have a value, C = c(S), which represents the true social cost of science. The specific functions employed in this analysis can be briefly summarized. 1. DISTRIBUTION

OF SCIENTIFIC

TALENT

where t.~ = 100 and o = 20. For purposes of intuitively grasping the character of this function, it might be noted that its distribution is identical to that conventionally employed in intelligence tests, scores of which are distributed normally with mean 100 and standard deviation 20. However, it is not our intention to argue that scientific talent is equivalent to “intelligence,” however defined or measured. Scientific talent, simply, is whatever it is; we assume only that it follows the indicated distribution.’ Figure 1 provides a graphical representation of the relevant upper half of the distribution of scientific talent. 2. SCIENTIFIC

p(TJw

MEMBERSHIP

=

FUNCTION

u 1

+

,-NT-W’

*Following Dresch [3], one might argue that the talent distribution should exhibit positive skewness, thus suggesting a distribution such as the log-normal. However, with our focus on the upper tail the implications of positively skewed alternatives would not differ greatly from those obtained here. Also, while we do not equate talent with IQ, available IQ data are utilized to calibrate several components of the model, arguing for the assumption of the indicated distribution.

GIANTS,

PYGMIES, AND THE SOCIAL COSTS OF RESEARCH

321

p(T;M)

0.5 -

o.q-* 100

120

140

160

180

200

Talent Fig. 2. Scientific membership

functions.

where U = 0.5, OL= 0.095, and M is an indirectly policy-determined parameter. Interpretively, p(T;M) is a standard (symmetric) logistic function, the upper asymptote of which is U. The “shift-parameter” M determines the level of talent T at which the probability of entering science is equal to one half of its upper limit (0.5U), which is also the point of inflection of the function (transition from increasing at an increasing rate to increasing at a decreasing rate); thus, changes in M serve to shift the membership function horizontally in the [T,p(T;M)] plane. The parameter (Y determines the “thickness” of the tails of the logistic and the function’s steepness at its inflection point (M), higher values of (Ycompressing the tails and increasing the steepness of the function at M. Figure 2 graphically portrays the scientific membership function for values of M equal to 142, 154, and 166, clearly indicating the horizontal-shift effect of variations in this policy parameter. Although the horizontal placement parameter (M) is characterized as a policy parameter, the relative size of the scientific cadre can be altered via changes in other parameters of the membership function as well, raising the issue of which parameter, in fact, appropriately captures the effects of variations in policy. Specifically, because the distribution of the scientific cadre is the product p(T;M) *f(T), the size of that cadre, given by the integral over T of the product p(T;M) . f(T), can be increased, given initial values of all parameters, by either (1) raising the value of U, (b) reducing the value of (Y, or (c) reducing the value of M. Society, obviously, induces alterations in the size of the cadre by altering the resources devoted to science, thus inducing a greater flow of individuals to science; the critical question is, which of these parameters can be plausibly anticipated to be altered by changes in the flow of social resources to science? Clearly, an increase in resources devoted to science should have its greatest impact (induce the greatest rate of flow from nonscience to science) for those nearest to indifference between entry and nonentry into science, i.e., near the midpoint of the logistic. Further, the relative impact should be less in the upper tail of the scientific talent distribution than in lower ranges, in light of

328

STEPHEN P. DRESCH AND KENNETH R. JANSON

evidence, e.g., Price [8] and Cooley [2], that the upper tail of the talent distribution relatively quickly approaches saturation, with an exhaustion of the nonscience pool of the highly talented. As a policy variable, U, the upper limit on the proportion of the population at any talent level entering science, would give rise to variations in the probability of entering science which violate these expectations concerning the effects of policy, an increase in U inducing equiproportionate increases in the probability of entry into science at all talent levels. The consequences of variations in the steepness parameter CX,were it the implicit policy variable, would be even less plausible and more at variance with expectations. A decrease in (Y would induce an increase in the rate of entry into science through the flattening of the logistic. This would have the anomalous implication that any increase in the aggregate scientific population would be accomplished through a) a reduction in the number of scientists at high talent levels, i.e., at levels of talent above which the probability of entering science was greater than 0.5U, a reduction which would be more than compensated by b) an increase in the representation of less able scientists, for whom the ex ante probability was less than 0.5lJ; the increase in the latter would outweigh the decrease in the former because of the much greater density of the population at lower talent levels. The horizontal shift parameter M is left as the only potentially plausible representation of changes in social resource flows to science. A change in the horizontal shift parameter has relatively greater consequences at levels of talent for which the probability of entry into science is one-half of its maximum, i.e., at the inflection point of the function. Thus, characterization of M as a policy variable is intuitively quite plausible, since policy is then represented as having its greatest impact on those who are indeed indifferent between entry and nonentry into science, while impacts in the lower tail (where the function is moved away from its lower asymptote) are relatively greater than those in the upper tail (where the function is converging toward its upper asymptote). Because the horizontal shift parameter M is interpreted as a policy parameter, it is the principal parameter varied in deriving alternative solutions of the model. While not directly determined by policy, changes in the social resources devoted to science serve to alter M, which rises with reductions in resources and falls with increases. Thus, variations in M (between 142 and 170) will provide the focus for much of the analysis. Given appropriate values of the other parameters, this range of values of M generates a scientific cadre which, as a percentage of the population, ranges from values below those observed in the last half century to values which, by comparison to observed values, are implausibly high, approaching the level identified by Price [8, pp. 53-541 as a constituting scientific saturation. The parameter (Y, determining the thickness of the tails and steepness of the logistic, was derived experimentally, searching for a value which would result in a modal value of T [from the product p(T;M) . f(T), i.e., for the scientific cadre] between 130 and 140 throughout a reasonable range of values of M. That this is an appropriate range for the mode is suggested by Harmon’s [6] data on modal IQ scores of Ph.D. holders,’ although we would reiterate that IQ, although identically distributed, is simply a convenient surrogate for our generalized conception of scientific talent.

%ited by Price [8, p. 521

GIANTS,

PYGMIES,

AND THE SOCIAL COSTS OF RESEARCH

329

The upper bound on the probability of pursuing a scientific career, U = 0.5, reflects the observation that many of even the most highly talented, although quite capable of productive scientific careers, have always elected nonscientific pursuits, devoting themselves instead to music, engineering, art, accounting, law, medicine, philosophy, etc., with a few electing even such intrinsically unrewarding careers as academic administration. Because the model is homogeneous of degree 1 in U and can be normalized to be homogeneous of degree 0 in U, this stipulation of the upper bound has no consequences for the critical variables, e.g., resource and opportunity costs, which constitute the focus of this analysis. In light of Price’s [8, pp. 51-541 reflections on the IQ distributions of Ph.D. holders, it would not be unreasonable to impose a critical value of talent, e.g., T = 120, below which the probability of entering science would be forced to zero. However, as indicated by Figure 2, in light of the relatively low probability of entering science at a value of T below 120 (for the specified values of other parameters of the logistic membership function), such an externally imposed constraint would have only minor impact. Thus, no entry constraint is imposed on Price’s [8, p. 841 “gentleman from Baffinland who would be a distinguished researcher on fundamental particles if only he could.” 3. INDIVIDUAL

SCIENTIFIC CT-

g(T)

=

CONTRIBUTION

FUNCTION

13OV1~1

e

Having entered into fundamental science (whatever his probability of electing a scientific career), the individual scientist’s (expected) contribution to fundamental scientific knowledge will be a function of his scientific talent. Here, although we are dealing with an unobserved variable, an observed variable, the number of scientific publications, suggests a functional form and its calibration. Again, Price [8, pp. 50-511 provides the basic elements, deducing from the IQ distribution of scientists and the proportions ever publishing that an IQ of 130 is necessary for even the minimal lifetime contribution of one article in the scientific literature; he further notes that the maximum observed lifetime number of publications is on the order of 1000 and that the logarithm appears to rise linearly with IQ, reaching In 1000 at a level of talent which we posit to be about 5 standard deviations above the mean of the talent distribution. Our measure, which, we emphasize, is not meant to be restricted to publications, was calibrated to these observations, with the consequence that it has a value of 1 at a level of talent T = 130 and a value of 1000 at T = 199. If this contribution function were simply intended to measure scientific publications, then the lower bound on the value of In g(T) would be In 1 = 0, simply because one cannot publish less than one article (ignoring the possibility of fractional treatment of multiauthored articles); scientists with talent less than T = 130 would fail to make any scientific contribution at all, although they might make nonscientific contributions (e.g., teaching, consultation, management) which benefit from their participation in science.4 Here, however, our conception of contribution is more general. Thus, the primary scientific contribution of a scientist, author or nonauthor, may be relatively unobservable,

4For discussions

of nonscientific

contributions

of scientists, see Dresch [4, 51.

330

STEPHEN P. DRESCH AND KENNETH R. JANSON

e.g., advice and assistance

to colleagues, and even in the case of those who make significant direct contributions to knowledge, the published literature may provide only a very imperfect record. Thus, there is no reason in principle to constrain the contribution function, i.e., to impose zero contributions on those with talent less than 130, although the magnitude of the contribution below this level of talent will be rather marginal, asymptotically approaching zero.5 4. AGGREGATE

SCIENTIFIC

VALUE OF SCIENTIFIC

CONTRIBUTIONS

V = lnG, where G = J g(T)p(T;M)flT) dT. Increases in the scale of scientific activity are hypothesized to result in contributions of decreasing marginal value. Again, Price [8, p. 551 suggests an appropriate specification, arguing that the advancement of science should be measured by the logarithm of the aggregate number of publications (contributions). In this logarithmic form the elasticity of value with respect to quantity, (dV/dG)*(GIV) = 1 /In G, i.e., the percentage increase in value associated with a 1% increase in quantity, declines with increases in quantity. Several justifications can be suggested for the declining elasticity of scientific value with respect to contributions. For example, as the total number of contributions increases, the probability of duplicative contributions increases; thus, utilizing data developed by Merton and Barber,6 Price [8, p. 67) demonstrates the plausibility of a Poisson distribution of simultaneous discovery in science. Moreover, to the degree to which simultaneous discovery is consciously and successfully avoided, this is achieved by the choice of individual scientists to toil in less promising areas of science; to attempt to secure a niche for which others are not competing results in a deleterious fragmentation of scientific effort, with substantial energy devoted to the achievement of contributions of relatively small value in isolated domains.’ 5. RESOURCE

AND OPPORTUNITY

S = _IPUXY(T)

c =

COSTS OF SCIENCE

dT,

S”,

where q = 1.5. Ignoring nonpersonnel costs (or assuming these to be a constant proportion of total costs) the size of the scientific cadre, S, provides an index of the total social resources devoted to scientific activity. However, this resource index fails to recognize the progressively increasing marginal opportunity costs associated with increases in the scale of scientific activity, i.e., the rapidly increasing value of the foregone alternative

‘In the solutions of the model, a lower bound on the evaluation of the various functions is placed T = 100, i.e., the median of the population distribution. At this level of talent, the implied contribution 0.05, i.e., 5% of that of a scientist for whom T = 130, or vanishingly small. 6As cited by Merton [7]. ‘Price [B, p. 561 notes that this logarithmic specification implies, historically, a linear development science over time, corresponding with the observed lack of progressively greater compression in time unexpected and crucial advances, in contrast to the observed exponential growth of the scientific literature.

at is

of of

GIANTS,

PYGMIES,

AND THE SOCIAL COSTS OF RESEARCH

331

uses of these resources (in technology, medicine, management, etc.), sacrificed in the interest of increases in the scale of scientific activity. Thus, the “opportunity cost” index C, which recognizes the increasing value of foregone alternatives, stipulates a relationship in which the elasticity of opportunity costs with respect to resources, rt, is greater than unity, i.e., a 1% increase in resources devoted to science induces a greater than 1% increase in opportunity costs. The true value of this opportunity cost elasticity is, of course, unknown; however, a value of 1.5, while not exceptionally high, will be shown to have severe consequences. Nonetheless, it will be demonstrated that the results would not be qualitatively altered were a lower (e.g., unitary) value of this elasticity to be stipulated. 6. IMPLICIT

RELATIONSHIPS

s=

s(V)

COSTS TO VALUE

= Key" + p,

dSldV = s’(V) c = c(V)

OF RESOURCE/OPPORTUNITY

= Kye”“,

= [s(V)]” =

dCldV = c’(V)

[Key”

+

= q[KeYV +

P]“, p]T-‘[Ky~yv]

where, for values of the policy parameter M ranging between 142 and 170, holding constant the stipulated values of all other parameters of the model, fitted values of the parameters of the implicit function relating resource and opportunity costs to scientific value of contributions (with all variables normalized, as indicated subsequently) are K

=

0.028,

y = 0.062,

p = 0.158.

Representing the aggregate (total) social resource cost of fundamental research by the size S of the scientific cadre, the aggregate social opportunity cost C as a function of aggregate resource cost S, and aggregate scientific value V as a function of the size and talent distribution of that cadre, implicit functional relationships are created between total resource (S) and opportunity (C) costs, on the one hand, and the scientific value of contributions (V), on the other. The indicated resource cost function s(V), fitted to solution values of S and V for values of A4 ranging between 142 and 170, very accurately describes the derived relationship between resource cost and scientific value, given the other parameters of the model; the implicit opportunity cost function, c(V), is simply derived from the resource function, s(V), given the opportunity+ost elasticity 7 ( = 1.5). These implicit cost-value functions are useful because they permit the derivation of average costs (S/V and C/V), marginal costs [dSldV = s’(V) and dC/dV = c’(V)], and elasticities of cost with respect to value [(dSIdV)(V/S) and (dCldV)(V/C)] as the value of scientific contributions is altered through changes in social support of the fundamental science system. The marginal costs and elasticities are especially important, because they indicate the magnitudes of the increases in costs implied by incremental increases in the scientific value of contributions.8

*The specific form of the fitted resource cost function, s(V), implies a constant elasticity of contributions, G, with respect to the size of the scientific cadre, S, the value of this elasticity being about 0.45. Clearly, a constant elasticity of G with respect to S is appropriate only over the relatively narrow range of M (and S) examined.

332

STEPHEN P. DRESCH AND KENNETH R. JANSON

7. NORMALIZATION

flT) /

OF THE MODEL

dT = 100, 100 G=

I

g(T)p(T;M)f(T) u

/

g(Tlf(T)

100 In

”=

dT

dT

g(TMT&WV) V

in[ UJg(Tlf(T)

dT

1

dT]

Because the model is homogeneous of degree 1 in total population, the solutions presented in the next section are scaled to a population of 100; thus, the “size” of the scientific cadre can be interpreted as its percentage of the population (e.g., labor force). To render the scientific-contribution and value-of-scientific contribution variables (G and V) more readily interpretable (homogeneous of degree 0 in total population and in the upper limit U on the proportion of persons entering science), contributions and the values of contributions are expressed as percentages of their maximum potential values (dividing by the contributions and values were the maximum proportion, U, of all persons at all talent levels to pursue scientific careers).’ As a consequence of this scaling of the population and of the scientific output (contribution and value) variables, the resource cost variable can be interpreted as a percentage of the population; thus, total resource cost is the scientific cadre (as a percentage of the population), the average resource cost is the scientific cadre (as a percentage of the population) divided by the value of contributions (as a percentage of maximum possible value of contributions), and the marginal resource cost is the change in the scientific cadre (as a percentage of the population) required to obtain a one-unit (percentage-point) increase in the value of contributions (expressed as a percentage of the maximum possible value of contributions). Because total opportunity cost is simply total resource cost (scientific cadre as a percentage of the population) raised to a power greater than unity (specifically, 1.5), total opportunity cost will equal total resource cost when 1% of the population is entering science (as will be observed subsequently, at a value ofM between 154 and 158, with approximately the currently observed scientific cadre as a proportion of the population). Apart from this “anchoring” of the resource and opportunity cost functions at unity when 1% of the population enters science, the only permissible quantitative comparisons of the resource and opportunity costs involve elasticities and relative order-of-magnitude changes as the policy variable (the horizontal positioning variableM in the scientific membership function) is changed. Exploitation of Scientific Potential and Its Social Cost Solution of the foregoing model for a range of alternative values of the indirect policy parameter (M) of the scientific membership function permits an assessment of implications for the social costs (resource or opportunity) of fundamental science of

9For a population normalized equations)

of 100 and (I = 0.5 the variables G and V attain saturation values (denominators of 17.95 for potential contributions and 2.89 for potential value.

in the

GIANTS,

PYGMIES,

AND THE SOCIAL COSTS OF RESEARCH TABLE 1 Solutions of the Fundamental

Support of Science U.S. Approximate Year M [in p(T; Ml Science cadre (S) S % of population Modal talent of S Contribution Quantity G (% of max) Value V = In(G) (% of max) Elasticity (dvIdC)(G/v)” Costs and cost elasticitiesb Resource Cost s (*loo) s/v (8100) S’(v) (* 100) S’ (v) * (V/S) Opportunity Cost c (*loo) c/v (*lOO) C’(v) (*lW C’ (v) l (V/C)

333

Science Model

LOW ________________________________________________ .__________.-_________. HIGH c. 1940 170 166

162

c. 1975-85 158 154

150

146

142

0.33 136

0.66 135

0.91 134

1.69 132

2.26 131

2.98 129

0.47 136

1.25 133

13.7

17.2

21.2

25.7

30.8

36.3

42.1

48.0

31.1

39.0

46.3

53.0

59.2

64.9

70.0

74.6

1.16

0.89

0.75

0.65

0.58

0.53

0.49

0.46

Total 33. Avg. 1.08 Marg. 1.18 Elast. 1.10

47. 1.21 1.92 1.58

66. I .43 3.02 2.12

91 1.72 4.58 2.66

125. 2.11 6.72 3.19

169. 2.61 9.57 3.67

226. 3.23 13.16 4.07

298. 4.00 17.52 4.38

Total 19. 32. Avg. 0.62 0.83 Marg. 1.04 1.97 Elast. 1.68 2.36

53. 1.16 3.63 3.14

87 1.64 6.51 3.96

140. 2.36 11.27 4.78

220. 3.39 18.73 5.52

340. 4.86 29.81 6.13

516. 6.91 45.40 6.57

“Elasticity of v with respect to G, (dV/dG) (G/V), is elasticity of normalized v (value as percentage of maximum possible value) with respect to normalized G (contributions as percentage of maximum possible contributions). r’Total and average resource and opportunity costs are derived from “actual” values of s obtained in the solutions of the model. Marginal costs and elasticities are obtained utilizing solution values of s and the relevant coefficients of the fitted implicit resource cost functions, s(V).

variations in the degree to which the purely scientific potential of society is realized. Focusing on the proportions of the population actually engaged in fundamental science, it is possible to make general inferences concerning changes in the exploitation of scientific potential which have occurred historically in the United States and the implied social costs of those changes. 1. COMPARATIVE

STATICS

Table 1 presents the principal results of variations in the policy parameter (M) of the scientific membership function between values of 142 and 170. The talent distributions of the scientific cadre under the three regimes corresponding to values of A4 of 142, 154, and 166 are portrayed graphically in Figure 3. Over this range of regimes, the scientific cadre as a percentage of the population (S) varies between 0.3 (M = 170) and 3(M = 142), i.e., by 1 order of magnitude, with the current ratio of scientific cadre to labor force, approximately l%, ‘Oreached at M = 158: thus, at the lower end of the range examined, the scientific cadre is about one-third its current relative size, while at the upper end it is about three times its current relative size. “‘The proportion of the “appropriate” (e.g., 30-year-old) cohort earning Ph.D. degrees in science is employed as a surrogate measure of the fundamental science cadre in that cohort, recognizing a) that all Ph.D. recipients do not engage in fundamental science and b) that all fundamental scientists do not possess Ph.D. degrees.

334

STEPHEN P. DRESCH AND KENNETH R. JANSON Density

100

120

140

160

180

200

Talent Fig. 3. Talent distribution

of the scientific cadre.

Notwithstanding the ninefold increase in the relative size of the cadre over the full range examined, the modal talent (T) of the scientific cadre declines only from 136 to 129, reflecting the continuing capacity to draw unexploited talent from the higher range of the underlying talent distribution; however, with the scientific cadre approaching 3% of the population (at M = 142, the “Big Science” extreme of the examined range), this untapped potential is obviously approaching exhaustion, with the consequence that modal talent is declining more rapidly with decreases in M than is observed at higher values of M. In contrast to the ninefold increase in the size of the scientific cadre, the total quantity of scientific contributions (G) increases by a factor of about 3.5, from 14% of its maximum at M = 170 to 48% at M = 142. Stated somewhat differently, with a scientific cadre constituting slightly less than 1% of population (M = 158), about 25% of potential scientific contributions are realized; reducing the cadre by two-thirds would reduce contributions by less than one-half, while a tripling of the cadre would result in a less than doubling of contributions. This is the result, primarily, of the rapid approach to saturation of the highly productive upper tail of the talent distribution of the scientific cadre, as indicated by Figure 4, which presents the distribution of contributions as a function of scientific talent. The increases in contributions as the cadre expands are attributable primarily to increases in contributions made by the only modestly productive, i.e., those with talent between 130 and 150. Above a talent level of 170 or 180 the number of contributions is quite insensitive to policy, since individuals at or above this level are likely to be among the first to enter and the last to leave science. Conversely, while policy has major consequences for the absolute numbers of the less talented (T < 130) drawn into science, this group is so unproductive that the magnitude of its contributions is small in any event. Thus, the middle range of talent provides a progressively higher share of total contributions, with the consequence that the mode of the contribution distribution shifts downward, from a talent of 164 (M = 170) to talents of 159 (M = 158) and 151 (M = 142); correspondingly, the mean number of contributions per scientist declines from 7.3 (M = 170) to 5.1 (M = 158) and 2.9 (M = 142). This downward shift in the talent distribution of contributions is of significance

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180

160

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120

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Talent Fig. 4. Distribution

of contributions.

because it explains the much more rapid growth of the scientific cadre than of aggregate contributions; essentially, as the cadre grows, the pool of those making relatively few contributions rises relative to the pool of those making very high contributions. For example, at M = 170 the modal contribution is made by a scientist (T = 164) who makes 30 contributions, while at M = 142 the modal contribution is made by a scientist (T = 151) who makes only eight contributions. This has obvious consequences for the resource costs of scientific contributions, since, e.g., 30 contributions from one highly productive individual will be likely to entail lower costs than eight contributions each from 3.75 less productive individuals; measuring costs in simple units of labor (scientists), this is definitionally true.

__rcv ______ C(V),

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40 -

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5'0

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8:

Value as % of maximum Fig. 6. Average and marginal

costs of contributions.

Turning to the logarithmic (Price) measure of scientific value as a function of aggregate contributions, the relative increase in the value of scientific contributions, from 30% of its maximum at M = 170 to 75% at M = 142, i.e., by a factor of 2.5, contrasts even more starkly with the ninefold increase in the size of the scientific cadre and the 3.5fold increase in the raw quantity of scientific contributions. Thus, with only 0.3% of the population recruited into active science, almost one-third of the maximum value of scientific potential is being realized, while, with 3% of the population in science, three-quarters of potential scientific value is realized. Using as a reference point a regime with slightly less than 1% of the population in science (M = 158), with realization of slightly more than half of potential scientific value, a two-thirds reduction in the scientific cadre would reduce realized potential by only two-fifths, while a tripling of the scientific cadre would increase realized potential by less than one-half. The difference between the trajectories of value and of quantity is attributable to the devaluation of all individual contributions as the gross quantity of contributions rises, with value rising as the logarithm of quantity. Thus, over the range examined the elasticity of scientific value with respect to the quantity of contributions (percentage increase in value implied by a 1% increase in quantity) declines from 1.16 (M = 170) to 0.65 (A4 = 158) and 0.46 (M = 142). Implications for the resource and opportunity costs of science are intuitively obvious from the foregoing discussion. However, these implications are made explicit by the fitted implicit relationships between resource and opportunity costs, on the one hand, and the value of scientific output, on the other. Utilizing the estimated coefficients of the resource-value equation (K,y, and p), the lower panels of Table 1 present the implied average and marginal resource and opportunity costs and cost elasticities with respect to value. The derived resource and opportunity cost measures (total, average, and marginal) presented in the table are multiplied by 100, while the measure of scientific value is normalized, expressed as a percentage of its maximum potential; thus, the average and marginal cost variables can be interpreted as 0.01% of the population required to obtain

GIANTS, PYGMIES, AND THE SOCIAL COSTS OF RESEARCH 7

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Fig. 7. Cost elasticities.

the average or incremental percentage point of exploitation of scientific potential. In the case of resource costs this statement refers literally to the proportion of the population engaged in science; with reference to the opportunity costs, this “raw science input” is converted to its equivalent in foregone opportunities (i.e., to compensate for the transfer of an additional increment of the population to science would require a more than equivalent increase in the size of the total population, because of the rising value of the foregone alternatives, reinforced by the differentially high talent distribution of those drawn into science). Definitionally, total resource costs rise identically with the size of the scientific cadre. However, because the value of scientific contributions rises at only one-fourth the rate of increase in the mass of the cadre, average resource costs rise by a factor of almost 4 as the policy parameter is varied between M = 170 and M = 142. Thus, marginal resource costs are substantially higher than average resource costs and are rising rapidly; while the value of output increases by a factor of 2.5, marginal resource costs increase by a factor of approximately 15. Summarizing the relationship between resource costs and value, the elasticity of resource costs with respect to value is substantially greater than 1 throughout and rises rapidly with increases in the scale of scientific activity. Thus, with 0.3% of the population in science, a 1% increase in the realized scientific value of fundamental research implies a 1.2% increase in resource costs, but with 3% of the population engaged in science, a 1% increase in value implies more than a 4.4% increase in resource costs. Note that these increases in resource costs with respect to value would also describe increases in opportunity costs (total, average, and marginal costs and the cost elasticity) if a unitary elasticity of opportunity costs with respect to resource costs were stipulated (rather than the elasticity of 1.5, which has been assumed). Even more dramatic than the 2.5-fold increase in value of output and the ninefold increase in the size of the scientific cadre, total opportunity costs increase by a factor of 27 over the range examined, assuming an elasticity of opportunity cost with respect to resource cost of 1.5. As a result, average opportunity costs rise by a factor of approximately 11. Necessarily, the increase in marginal opportunity cost is, then, an astounding factor

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of 44, rising from 1 at a V of 31 to 45 at a V of 75. Thus, the elasticity of opportunity costs with respect to value rises from 1.7 for “small science” (M = 170) to 6.6 with “big science” (M = 142). 2. U.S. QUASIHISTORY

Considering the historical allocation of human resources to science in the United States, the situation prior to the second world war would be characterized by an M of between 166 and 170, with between one-third and one-half of 1% of relevant age cohorts entering science.” Under those circumstances, between 30 and 40% of potential scientific value was being realized, at an average resource cost (per percentage point of potential value realized) of about 0.01% of the population (age cohort), and a marginal resource cost of substantially less than twice the average resource cost. In light of the small proportion of talent being absorbed into science, marginal opportunity costs (reflecting the value of the talent in nonscientific pursuits) were not substantially higher than marginal resource costs. By the 1970s the proportions of successive cohorts absorbed into science had approximately tripled by comparison to the prewar period, with approximately 1% entering scientific careers, creating a situation characterized by an M of between 154 and 158. Under these circumstances, between 50 and 60% of the potential value of scientific activity was being realized, but at extremely high average and marginal costs. Thus, the average resource cost was approximately twice as great as before the war, while the marginal resource cost was four to five times greater. With a tripled entry rate into science, talent deprivation in other sectors had raised marginal opportunity costs to levels five to ten times higher than had been confronted before the war. The elasticity of opportunity cost with respect to value had increased from about 2 to between 4 and 5. Under these circumstances, it is not surprising that the rapid growth of science which prevailed between roughly 1950 and 1970 (an acceleration of the already rapid growth experienced over the preceding century) came to an abrupt halt after 1970. The loss of talent in other sectors (especially those related to technology) had become exceptionally high, while the purely scientific benefits of marginal additional resources absorbed by science had become vanishingly small. Inevitably, the “golden age” of fundamental science had come to an end. Conclusion The foregoing analysis, suggesting that the historical growth of fundamental science could not be rationalized on purely scientific grounds, reinforces Price’s [8, p. 321 anticipation that “Big Science . becomes an uncomfortably brief interlude between the traditional centuries of Little Science and the impending period following transition” (to logistic saturation). It does not, however, provide evidence that the scale of the scientific enterprise has become excessivelygreat. Were fundamental research to be “The science entry rates which we cite reflect the pace of award of technical doctoral degrees by U.S. graduate schools. Admittedly, career paths of doctoral recipients evolve to place differential emphasis on “basic and even “management” of research organizations. The focal research,” “applied research,” “development,” point of our analysis, however, remains the aggregate product accruing to the more fundamental, “basic,” research effort. We expect that, to the extent to which each of these competing activities represents an absorbing state, they will attract cadres with different talent distributions (means). Further their elasticities of output with respect to human input will certainly differ and, in at least one category, may even assume a negative sign. We acknowledge the insightful comments of D. F. Stein and of an anonymous referee for clarifying this important point.

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339

justified solely by the augmentations of scientific knowledge purported to result, then the rationality of public subvention at the current rate (or indeed, at any rate at all) would be open to serious question. At the margin, clearly, the costs of those augmentations of knowledge have become extremely high by even relatively recent historical standards. And, regardless of their cost, because those augmentations of knowledge enter as free goods into the international knowledge system, there would be little incentive for any social entity, including the state, to underwrite their acquisition. In short, if the current scale of fundamental science is to be justified, this analysis does suggest that the justification must involve considerations other than the augmentation of scientific knowledge. The development of an alternative possible rationale for the allocation of resources to research is beyond the purview of this analysis. However, the principal elements have been developed elsewhere by Dresch [4] and can be briefly sketched here. In searching for an alternative rationale for the allocation of resources to research, the fact that the products of fundamental research enter as free goods into the international knowledge system can be argued to have a critical implication: To be able to appropriate the knowledge contributed (freely) by others, one must be aware of that knowledge. But the only effective means by which to monitor research-front developments and to be in a position to exploit those developments which, fortuitously, have practical implications is to be engaged in work at the research front; to attempt to track the advance of science from a distance necessarily implies that the “front” which is observed falls significantly short of the active front. I2 Thus, ironically, the opportunity to exploit (for commercial, military, and other “practical” purposes) the contributions of others provides a rational and effective motivation for contributing to the international knowledge system. Stated more generally, the capacity to perform what is conventionally characterized as “applied research” and “development” is critically dependent on knowledge which can only be obtained through participation in what we have characterized as “fundamental research.” However, if the capacity to exploit fortuitously relevant augmentations of fundamental knowledge is to provide the justification for the support of fundamental research, then that exploitation must have a nonscientific purpose, i.e., fundamental research can no longer be an end in itself, and, by implication, fundamental research cannot provide a justification for the existence of fundamental researchers. Rather, that justification must be found in other activities and functions of fundamental scientists, whose performance of which is sufficiently enhanced by participation in research-front science as to warrant supportfor that research. This conclusion has profound implications for the organization and financing of fundamental research. Among these: l

l

First, “full-time research careers without otherwise useful services are to be discouraged” [9, p. 256].13 Second, the costs of part-time research careers should be recognized as costs of those nonresearch services provided more effectively by research-front scientists, whose fundamental research should be financed accordingly.

“See Price’s [8, pp. 62-911 discussion of “invisible colleges.” 13This should not be interpreted to preclude the utilization ofprivate wealth to underwrite full-time research careers, e.g., the endowment of the full-time, tenured fundamental research careers of the permanent “faculty” of the Institute for Advanced Study by department store heir Louis Bamberger and his sister, Caroline Bamberger (Mrs. Felix) Fuld. Conditional on their conformity with income and inheritance tax statutes, the wealthy (and everyone else) should be permitted to devote private resources to any form of “consumption” desired, including conspicuous consumption of the talents of fundamental scientists.

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STEPHEN P. DRESCH AND KENNETH R. JANSON

l

Finally, third (as a corollary to the first and second), there is no justification public subvention of research careers, either full or part time.14

for

Effective realization of these implications will confirm Price’s [8, p. 311 prescient expectation of “a break with the traditions of centuries . . giv[ing] rise to new escalations, violent huntings, redefinitions of our basic terms, and all the other phenomena associated with the upper limit.” Postlude About this process there is the same sort of essential. built-in undemocraq~ that gives rise to a nation of cities rather than a country steadily approximating a state of uniform population density. Scientists tend to congregate in fields, in institutions, in countries, and in the use of certain journals. They do not spread out uniformly, however desirable that may or may not be. In particular, the growth is such as to keep relatively constant the balance between the few giants and the mass of pygmies. The number of giants grows so much more slowly than the entire population that there must be more and more pygmies per giant, deploring their own lack of stature and wondering why it is that neither man nor nature pushes us toward egalitarian uniformity [8, p. 591.”

The authors appreciate the advice and criticism of MTU colleagues James R. Gale, Wen-he Lu, Karol I. Pelt, Donald R. Beck and Dale F. Stein, and the the TFSC reviewers. Dresch acknowledges, especially, the incalculable bent@ (personal as well as scholarly) of over a decade of close association with Derek J. de Solla Price, Avalon Professor of the History of Science at Yale Univrrsity until his death in 1983; the subtitle of this paper was suggested not only by its content but also by a chapter title (“Galton Revisited”) of Price’s Little Science, Big Scirnc~e [ 81. References 1. Aranson,

P. H., and Sommer, J. W., Science and Technology Policy: Public Choice and Private Response, and the State. John W. Sommer, ed., Independent Institute, San Francisco, 1987 (forthcoming). Cooley, W. W., Career Developmcnf of Scientisrs, Harvard University Graduate School of Education, Cambridge, Mass., 1963. Dresch, S. P., Ability, Fertility and Educational Adaptation, in Research in Population Economics, vol. I. Julian Simon, ed.. JAI Press, Greenwich, Conn., 1978. Dresch, S. P.. The Economics of Fundamental Research, in Higher Education and rhe State. John W. Sommer, ed., Independent Institute, San Francisco, I987 (forthcoming). Dresch, S. P., On the Nature and Pathologies of Meritocratic Collectivities, Working Paper, School of Business and Engineering Administration, Michigan Technological University, Houghton, Mich., 1987. Harmon, L. R., The High School Backgrounds of Science Doctorates, Science 133, 679 (1963). Merton, R. K., Singletons and Multiples in Scientific Discovery, Proceedings ofrhe American Philosophical in Hi@~e’r Education

2. 3. 4. 5. 6. I.

Sociefi

105, 470 (1961).

8. Price, D. J. de S., Little Science. Big Science. Columbia University Press, New York, 1963 [republished, with additional papers, as Lirtle Science, Sig Science and Beyond, Columbia University Press, New York, 1986.1 9 Price, D. J. de S., A Theoretical Basis for Input-Output Analysis of National R&D Policies, in Research. Development. and Technological Innovation. D. Sahal, ed., Lexington Books, Lexington, Mass., 1980. Received

13 August 1987;

revised

27

October

1987

“‘This is not to say that the state would not indirectly provide part of its procurement of directly valued goods and services, e.g., which would be enhanced by access to research-front knowledge. “Note the implicit contradiction contained within this passage: more slowly than the entire population,” then “the balance between cannot be kept “roughly constant, ” i.e., indeed “there must be more a minor lapse is rare in Derek Price’s writings.

support for part-time research careers as military hardware, the effectiveness of If “the number of giants grows so much the few giants and the mass of pygmies” and more pygmies per giant.” Even such