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Sic Transit Gloria Manuscriptum: Two Views of the Aggregate Fate of Ancient Papers

When PageRank began to be used for ranking in Web search, a concern soon arose that older pages have an inherent --- and potentially unfair --- advantage over emerging pages of high quality, because they have had more time to acquire hyperlink citations. Algorithms were then proposed to compensate for this effect. Curiously, in bibliometry, the opposite concern has often been raised: that a growing body of recent papers crowds out older papers, resulting in a collective amnesia in research communities, which potentially leads to reinventions, redundancies, and missed opportunities to connect ideas. A recent paper by Verstak et al. reported experiments on Google Scholar data, which seemed to refute the amnesia, or aging, hypothesis. They claimed that more recently written papers have a larger fraction of outbound citations targeting papers that are older by a fixed number of years, indicating that ancient papers are alive and well-loved and increasingly easily found, thanks in part to Google Scholar. In this paper we show that the full picture is considerably more nuanced. Specifically, the fate of a fixed sample of papers, as they age, is rather different from what Verstak et al.'s study suggests: there is clear and steady abandonment in favor of citations to newer papers. The two apparently contradictory views are reconciled by the realization that, as time passes, the number of papers older than a fixed number of years grows rapidly.