Technological complexity and combinatorial invention in small-scale societies

Abstract

Technology plays a central role in all human societies, from foraging to industrial economies. However, technological solutions come with associated costs, and in small-scale societies, technological complexity reflects this trade-off between efficiency and resource constraints. Here, we analyze this trade-off and show a sublinear scaling relationship between toolkit richness and tool part richness in ethnographic societies. This result indicates diminishing returns where each additional part contributes less to overall toolkit diversity. This scaling holds across diverse ecological and cultural contexts, suggesting a general principle of optimization in tool design. Ethnographic toolkits achieve their adaptability by reusing a core set of versatile parts and selectively incorporating more specialized parts. However, increasing richness also increases complexity, and complexity is costly. We formalize these dynamics within a combinatorial optimization framework and discuss the implications.

Fig. 1.. Ethnohistoric examples of subsistence related tools of varying complexity.

(A) Tsimshian fish club (56); (B) Inuit stone hammer (57); (C) Inuit walrus harpoons (57); (D) Inuit bow (57); (E) Seri bone awl (58); (F) Tsimshian fish hook (56); (G) Seri bow, quiver, and arrow (58); (H) Menominee small game trap (59). All images are from the Bureau of American Ethnology and are in the public domain.

Fig. 2.. Tool parts, types, and complexity.

Panel (A) represents a toolkit comprised of seven individual tool types constructed from 20 unique parts with an average tool complexity of 2.9 parts per tool. Panel (B) represents a toolkit of 10 individual tool types constructed from 40 unique parts with an average tool complexity of four parts per tool. $P_n$$T_n$ , $Y_T$.

Fig. 3.. The global distribution of the 127 societies in the dataset.

Spatial coverage is clustered and uneven, as is typical for anthropological datasets. We control for these effects statistically.

Fig. 4.. Descriptive statistics of toolkit types, parts, and complexity.

Violin plots of (A) toolkit types $T_n$ , (B) parts $P_n$ , and (C) average tool complexity $Y_T$ . Farmers have the highest toolkit richness (A), whereas delayed-return system hunter-gatherers have the most complex technologies (C). Vertical bars represent statistically significant pairwise Wilcoxon tests at the 95% confidence level where ${}^{***}P<0.001$ and ${}^{**}P<0.01$.

Fig. 5.. The scaling relationship of toolkit richness and part richness.

Toolkit richness $T_n$ as a function of part richness $P_n$ across the three lifestyle types, immediate-return systems hunter-gatherers (red), delayed-return system hunter-gatherers (blue), and farmers (green). Slopes range between 0.67 and 0.71. Fitted straight lines are ordinary least squares regression models but see Table 1 for full results from the mixed effects model. These data show the remarkably tight sublinear relationship between toolkit richness and tool part richness, indicating diminishing returns. R², coefficient of determination.