What is money in the future worth today? In the seventeenth century, questions about the “present value” of future wealth became matters of practical concern, as businesspeople and governments deployed future-oriented financial technologies like mortgages, bonds, and annuities. Those questions also attracted the attention of mathematicians. This essay examines the excursions two English mathematicians, the indefatigable mathematical gossip John Collins (1625–83) and the lesser-known Thomas Watkins (fl. 1710s–20s), made into the mathematics of financial time. In capitalist practice today, present-value problems are invariably dealt with using a single technique, compound-interest discounting, which has become deeply embedded in commercial, governmental, and legal infrastructures. Yet, for early modern thinkers, the question of how best to calculate the financial future was an open question. Both Collins and Watkins explored imaginative alternatives to what would become the compound-interest orthodoxy. With help from his network of correspondents, Collins explored simple-interest discounting, which provoked thorny mathematical questions about harmonic series and hyperbolic curves; Watkins crafted multiple mathematical techniques for “correcting” the compound-interest approach to the financial future. Though both projects proved abortive, examining those forgone futures enables us to examine the development of a key element of capitalistic rationality before it became “black-boxed.”

中文翻译：

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复利修正：早期现代英国金融未来的富有想象力的数学

未来的钱今天值多少钱？在 17 世纪，随着商界人士和政府部署面向未来的金融技术，如抵押贷款、债券和年金，有关未来财富“现值”的问题成为实际关注的问题。这些问题也引起了数学家的注意。本文考察了两位英国数学家，不知疲倦的数学八卦约翰柯林斯（1625-83 年）和鲜为人知的托马斯沃特金斯（1710-20 年代）在金融时间数学中的远足。在今天的资本主义实践中，现值问题总是使用单一的技术——复利贴现——来处理，这种技术已经深深植根于商业、政府和法律基础设施中。然而，对于早期的现代思想家来说，如何最好地计算财务未来的问题是一个悬而未决的问题。柯林斯和沃特金斯都探索了将成为复利正统观念的富有想象力的替代方案。在通讯员网络的帮助下，柯林斯探索了单利贴现，这引发了有关调和级数和双曲曲线的棘手数学问题；沃特金斯 (Watkins) 精心设计了多种数学技术来“纠正”金融未来的复利方法。尽管这两个项目都被证明是失败的，但检查那些被放弃的未来使我们能够检查资本主义理性的一个关键要素在它成为“黑箱”之前的发展。在通讯员网络的帮助下，柯林斯探索了单利贴现，这引发了有关调和级数和双曲曲线的棘手数学问题；沃特金斯 (Watkins) 精心设计了多种数学技术，以“纠正”金融未来的复利方法。尽管这两个项目都被证明是失败的，但检查那些被放弃的未来使我们能够检查资本主义理性的一个关键要素在它成为“黑箱”之前的发展。在通讯员网络的帮助下，柯林斯探索了单利贴现，这引发了有关调和级数和双曲曲线的棘手数学问题；沃特金斯 (Watkins) 精心设计了多种数学技术来“纠正”金融未来的复利方法。尽管这两个项目都被证明是失败的，但检查那些被放弃的未来使我们能够检查资本主义理性的一个关键要素在它成为“黑箱”之前的发展。