A key challenge when trying to understand innovation is that it is a dynamic, ongoing process, which can be highly contingent on ephemeral factors such as culture, economics, or luck. This means that any analysis of the real-world process must necessarily be historical - and thus probably too late to be most useful - but also cannot be sure what the properties of the web of connections between innovations is or was. Here I try to address this by designing and generating a set of synthetic innovation web "dictionaries" that can be used to host sampled innovation timelines, probe the overall statistics and behaviours of these processes, and determine the degree of their reliance on the structure or generating algorithm. Thus, inspired by the work of Fink, Reeves, Palma and Farr (2017) on innovation in language, gastronomy, and technology, I study how new symbol discovery manifests itself in terms of additional "word" vocabulary being available from dictionaries generated from a finite number of symbols. Several distinct dictionary generation models are investigated using numerical simulation, with emphasis on the scaling of knowledge as dictionary generators and parameters are varied, and the role of which order the symbols are discovered in.

翻译：理解创新的一个关键挑战在于它是一个动态的、持续进行的过程，高度依赖于文化、经济或运气等短暂因素。这意味着对现实世界创新过程的任何分析都必然是历史性的——因而可能为时已晚而无法发挥最大效用——同时也无法确定创新之间连接网络的属性无论是现在还是过去究竟是怎样的。本文试图通过设计并生成一组合成创新网络"词典"来解决这一问题，这些词典可用于承载采样的创新时间线，探究这些过程的整体统计规律和行为特征，并确定其对结构或生成算法的依赖程度。受Fink、Reeves、Palma和Farr（2017）关于语言、美食与技术领域创新研究的启发，我研究了新符号的发现如何通过从有限符号生成的词典中额外"词汇"库的可用性来体现。通过数值模拟研究了多种不同的词典生成模型，重点考察了当词典生成器和参数变化时知识的扩展规律，以及符号发现顺序所起的作用。