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Every human society faces a common challenge: to develop the best possible mix of tools that can help them solve problems. But tools, ranging from simple hunting and cooking implements to technology to ways to transport goods and people, require time and resources to develop, says SFI External Professor Marcus Hamilton, an anthropologist at the University of Texas at San Antonio, and small-scale societies must balance that cost against innovation.

"Technology is an expensive thing," he says.

To better understand that tradeoff, Hamilton and his colleagues have developed a mathematical model that captures the relationship between technological complexity—the diversity of tools in a society's toolkit—and the cost of development. The model, described in Science Advances, reveals an optimal toolkit that maximizes its utility in solving real-world problems while minimizing costs.

"It predicts, basically, that there should be an optimal set of solutions that you need to solve a certain number of problems," he says.

The model also shows that as a society's toolkit becomes more diverse, tools become more specialized and solve a narrower range of problems. A simple, sharp stick has a wider range of uses than a harpoon, which is made of many smaller parts.

"As you invent a new tool, you increase your toolkit, but you have to pay by inventing another part," says Hamilton. The more diverse the assemblage of tools, the higher the cost.

The researchers used their model to analyze data collected over the last few decades about tool use in small-scale societies—populations that have historically focused on subsistence through farming and foraging—and were surprised to see the same sublinear relationships appear, no matter where in the world the society was located.

In future work, they plan to dive deeper into specific environmental conditions that produce these patterns in diverse geographic settings.

The new model could be useful not only to anthropologists and archaeologists but also to economists who study ways that societies build and use new technologies.

Economics tends to focus on the present, says Hamilton, but "there's a whole evolutionary history of humans solving problems going on in the background."