How much can we influence the rate of innovation?

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Science Advances  09 Jan 2019:
Vol. 5, no. 1, eaat6107
DOI: 10.1126/sciadv.aat6107


  • Fig. 1 We studied products and the components used to make them from four domains.

    (A) In language, the products are 39,915 English words and the components are the 26 letters. (B) In gastronomy, the products are 56,498 recipes and the components are 381 ingredients. (C) In mixed drinks, the products are 3053 cocktails and the components are 350 beverages. (D) In technology, the products are 1158 software products and the components are 993 development tools used to make them. For each domain, we show the number of products we can make when we acquire components in alphabetical order (points) and the average number of products we can make over all possible orders in which to acquire the components (lines).

  • Fig. 2 We compared the innovation rates for different distributions of product complexity.

    (A to C) The same set of components can be used to make different sets of products. We show toy examples of 10 components used to make 30 products with (A) constant complexity, (B) binomial complexity, and (C) Poisson complexity. (D to I) To test our prediction that the average innovation rate depends only on the distribution of product complexity, we glued together all 56,498 gastronomy recipes end to end to form a giant strip of 464,405 components. We then cut these into pieces with different lengths to make new recipes. We chose the lengths to be constant (D), binomially distributed (E), and Poisson-distributed (F), all with mean length Embedded Image. When we added components to our basket in a random order and measured the size of the product space (points) (G to I), we found that it follows our prediction in Eq. 3 (lines).

  • Fig. 3 We computed the distribution of product complexity and the rank frequency of components for our four domains.

    (A to D) The distribution of product complexity is shown for each of our four domains. (E to H) The number of products that each component appears in, where the components are in rank order from most to least frequent, is shown for each of our four domains.

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