Abstract
We learned previously that geniuses and outstanding scientists have peak productivities in their 30s but produce little late in life. This time we consider average astronomers who have completed their careers (25 American Astronomical Society members who died recently) and found that they peak in their mid 40s and did half of their life's important output after age 50.
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1. Introduction
There is an extensive literature on the correlation of age and productivity. The peak productivity can be measured by quality or quantity. It can depend on how long it takes individuals (or teams) to master their fields. For instance, Walter Baade, working mostly alone, needed to learn much about the contents of galaxies before he could, at age 51, announce his discovery that they have two population types. It can depend on the nature of the field, e.g., athletes are more likely to peak early and philosophers later. It may differ between past and current generations because the distribution of knowledge has accelerated recently. It can depend on whether the individuals have the financial or health freedom to do research fulltime or need to spend time on non-research activities. And it can depend on whether we are considering geniuses or average researchers. There may be other factors involved. This study considers the peak production years for average versus outstanding astronomers.
A comprehensive study was made by Lehman (1953). He considered the most successful people in many different fields (art, science, inventions, social sciences, music, poetry, literature) but his average is shown in Figure 1. The peak occurs at age 34 years with half-peak points at 24 and 50 years. A more recent study by Simonton (1988) or see Uberti & Simonton (2017) showed a large diversity by fields. Einstein once said "A person who has not made his great contribution to science before the age of thirty will never do so." But some, like Bach and Verdi, did some of their best work in their 70s and 80s.
Figure 1. For hundreds of outstanding scientists, artists, composers, authors, and social scientists, Harvey Lehman (1953) compiled their ages when they did their most significant work. The vertical scale is relative to 100% during ages 35–39. The data points are 5 years averages. Of the various mathematical functions that can be fit to the data, this one has no physical significance but fit best and has a peak at age 34 years.
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Standard image High-resolution imageIn astronomy, my first study (Abt 1983) showed for "outstanding astronomers" a fairly flat peak in productivity during ages 30–70 after allowing for the decrease of citations with time. That is, no maximum in the 30s. A recent study (Abt 2016) of Russell Lecturers showed a peak in the 30s, although 33% of their citations occurred after age 50. However those were the best researchers of their time. What is the production profile (normalized citations as a function of age) age of average astronomers?
2. Results on Average Astronomers
The American Astronomical Society has as members virtually all American astronomers and it started a policy more than a decade ago to publish notices of deaths and obituaries of all members. That listing can be found at website https://aas.org/obituaries in chronological order. Therefore by studying the 25 astronomers who died recently, that would constitute a random sample of astronomers who completed their careers. The dates of death ran from 2016 October 11 to 2017 June 10. Readers can therefore identify by names the astronomers selected, if they wish. In selecting those, I skipped two people: one statistician who started working in astronomy only after 67 years and one who was a co-author on nearly 5000 papers, mostly having hundreds of authors. In counting normalized citations (citations per author) for that author, the numbers rarely exceeded 0.1 citations per paper. That counting became extensive and led to few total normalized citations.
In a multi-author project, one person does not do all of the work. Therefore no one person deserves all of the credit (citation counts) for the project. We are rarely told the distribution of planning, work, and interpretation among the authors. Often, but not always, the most active authors are listed first and the remainder listed alphabetically after. Some lead authors insist that their names be the last among the authors. For statistical purposes we will assume equal credit for each author, so the total citation counts should be distributed equally among the authors. The ADS understands that and lists "normalized citation counts," i.e., the total citation numbers divided by the numbers of authors.
This counting, then, ignores papers that received no citations by 2017. It includes all papers that received citations, although journal papers containing the full data are cited more often than conference papers that are little more than abstracts (Abt 1995). The new research source Research Gate lists papers that were downloaded read but not used as citations. Of course we know that astronomers do many useful things, such as teaching, public education, service on committees both within their institutions and nationally, etc. This study concentrates only on research results that directly aided research by others.
Only one of the remaining 25 authors was Russell Lecturer, so this is a random sample, rarely including a prize winner. The 25 included both three women and 22 men, and five non-Americans who resided abroad for the bulk of their research. Twenty two of the 25 astronomers started publishing in their 20s, so the range in starting dates is not large. The counting was done in 2017 June and July and used the on-line SAO/NASA Astrophysics Data System.
Some astronomers work in popular areas (currently cosmology and exoplanets) and therefore their papers are likely to receive more citations than papers in less popular areas. Most astronomers do not change areas during their lifetimes. That means that some astronomers receive many citations throughout their lifetimes and others fewer. But in Figure 2 we are not comparing results from different astronomers, but only how their citation histories vary during their lifetimes.
Figure 2. For 25 average astronomers, the distribution of their normalized citations per year are plotted against the ages at the times of publication. The normalized citations are the total citations for a paper divided by the number of authors. The data points are averages during five years. The error bars are p.e. in the means. The fitted curve is a 3rd order polynomial and has a peak at age 45 years.
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As an astronomer matures, the types of papers he/she publishes may change. For instance, after collecting data on many different systems (galaxies, star clusters, stars, planets, or asteroids) in many short papers, the astronomer may write some long papers to synthesize the results. Or the astronomer may become involved in space teams that publish many short papers with many authors. Therefore changes in the mean lengths of papers or numbers of papers may not be informative measures of the astronomer's productivity.
The distribution of normalized citations with age at the times of publication is shown in Figure 2. A third-order polynomial fits the data best. It shows a peak age of publication of 45 years. That is very different than the peak age of 33 years for the Russell Lecturers and 34 for most outstanding scientists according to Lehman. The half-peak values for average astronomers occurred at ages 28 and 67.
An interesting result is that 50% of the average astronomers' important output occurs after the age of 50 years. For the Russell Lecturers only 20% of their important output occurred after the age of 50 years. Therefore the average astronomers' output peaked in their mid-40s and they did half of their important work after the age of 50 years. After age 55 the error bars in Figure 2 became larger, indicating more diversity among individuals.
The total lifetime normalized citations for the 25 average astronomers ranged from 19 to 4753 citations and averaged 1722 ± 326 citations.