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John_Maxwell_IV comments on Reaching young math/compsci talent - Less Wrong Discussion

6 Post author: lukeprog 02 June 2012 09:07PM

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Comment author: Kaj_Sotala 03 June 2012 12:55:27PM 4 points [-]

(part 2)

if one calculates the age curves separately for major and minor works within careers, the resulting functions are basically identical. Both follow the same second-order polynomial (as seen in Equation 1), with roughly equal parameters. Second, if the overall age trend is removed from the within-career tabulations of both quantity and quality, minor and major contributions still fluctuate together. Those periods in a creator's life that see the most masterpieces also witness the greatest number of easily forgotten productions, on the average. Another way of saying the same thing is to note that the "quality ratio," or the proportion of major products to total output per age unit, tends to fluctuate randomly over the course of any career. The quality ratio neither increases nor decreases with age nor does it assume some curvilinear form. These outcomes are valid for both artistic (e.g., Simonton, 1977a) and scientific (e.g., Simonton, 1985b) modes of creative contribution (see also Alpaugh, Renner,& Birren, 1976, p. 28). What these two results signify is that if we select the contribution rather than the age period as the unit of analysis, then age becomes irrelevant to determining the success of a particular contribution. For instance, the number of citations received by a single scientific article is not contingent upon the age of the researcher (Oromaner, 1977).

The longitudinal linkage between quantity and quality can be subsumed under the more general "constant-probability-ofsuccess model" of creative output (Simonton, 1977a, 1984b, 1985b, 1988b, chap. 4). According to this hypothesis, creativity is a probabilistic consequence of productivity, a relationship that holds both within and across careers. Within single careers, the count of major works per age period will be a positive function of total works generated each period, yielding a quality ratio that exhibits no systematic developmental trends. And across careers, those individual creators who are the most productive will also tend, on the average, to be the most creative: Individual variation in quantity is positively associated with variation in quality. There is abundant evidence for the application of the constant-probability-of-success model to cross-sectional contrasts in quantity and quality of output (Richard A. Davis, 1987; Simonton, 1984b, chap. 6; 1985b, 1988b, chap. 4). In the sciences, for example, the reputation of a nineteenthcentury scientist in the twentieth century, as judged by entries in standard reference works, is positively correlated with the total number of publications that can be claimed (Dennis, 1954a; Simonton, 1981 a; see also Dennis, 1954c). Similarly, the number of citations a scientist receives, which is a key indicator of achievement, is a positive function of total publications (Crandall, 1978; Richard A. Davis, 1987; Myers, 1970; Rushton, 1984), and total productivity even correlates positively with the citations earned by a scientist's three best publications (J. R. Cole & S. Cole, 1973, chap. 4). [...]

The constant-probability-of-success model has an important implication for helping us understand the relation between total lifetime output and the location of the peak age for creative achievement within a single career (Simonton, 1987a, 1988b, chap. 4). Because total lifetime output is positively related to total creative contributions and hence to ultimate eminence, and given that a creator's most distinguished work will appear in those career periods when productivity is highest, the peak age for creative impact should not vary as a function of either the success of the particular contribution or the final fame of the creator. Considerable empirical evidence indeed demonstrates the stability of the career peak (Simonton, 1987a). In the sciences, for instance, the correlation between the eminence of psychologists and the age at which they contribute their most influential work is almost exactly zero (Zusne, 1976; see also Lehman, 1966b; of. Homer et al., 1986). And in the arts, such as literary and musical creativity, the age at which a masterpiece is generated is largely independent of the magnitude of the achievement (Simonton, 1975a, 1977a, 1977c). Thus, even though an impressive lifetime output of works, and subsequent distinction, is tied to precocity, longevity, and production rate, the expected age optimum for quantity and quality of contribution is dependent solely on the particular form of creative expression (also see Raskin, 1936).