Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA.
Proc Natl Acad Sci U S A. 2011 May 31;108(22):9008-13. doi: 10.1073/pnas.1017298108. Epub 2011 May 16.
We study a simple model for the evolution of the cost (or more generally the performance) of a technology or production process. The technology can be decomposed into n components, each of which interacts with a cluster of d - 1 other components. Innovation occurs through a series of trial-and-error events, each of which consists of randomly changing the cost of each component in a cluster, and accepting the changes only if the total cost of the cluster is lowered. We show that the relationship between the cost of the whole technology and the number of innovation attempts is asymptotically a power law, matching the functional form often observed for empirical data. The exponent α of the power law depends on the intrinsic difficulty of finding better components, and on what we term the design complexity: the more complex the design, the slower the rate of improvement. Letting d as defined above be the connectivity, in the special case in which the connectivity is constant, the design complexity is simply the connectivity. When the connectivity varies, bottlenecks can arise in which a few components limit progress. In this case the design complexity depends on the details of the design. The number of bottlenecks also determines whether progress is steady, or whether there are periods of stasis punctuated by occasional large changes. Our model connects the engineering properties of a design to historical studies of technology improvement.
我们研究了一种简单的模型，用于研究技术或生产过程的成本（或更一般地说，性能）的演变。该技术可以分解为 n 个组件，每个组件都与一组 d-1 个其他组件相互作用。创新是通过一系列试错事件发生的，每个事件都包括随机改变一组组件的成本，并仅在降低了集群总成本的情况下才接受这些更改。我们表明，整个技术的成本与创新尝试次数之间的关系在渐近上是幂律关系，与经验数据中经常观察到的函数形式相匹配。幂律的指数α取决于找到更好组件的内在难度，以及我们所谓的设计复杂性：设计越复杂，改进的速度就越慢。令上述 d 为连接度，在连接度恒定的特殊情况下，设计复杂性就是连接度。当连接度变化时，可能会出现瓶颈，其中少数几个组件会限制进度。在这种情况下，设计复杂性取决于设计的细节。瓶颈的数量也决定了进展是否稳定，或者是否有偶尔出现较大变化的停滞期。我们的模型将设计的工程特性与对技术改进的历史研究联系起来。
