# Technology Development Model

Each artifact (products, components, etc.) is constructed by transforming (production capabilities, requiring physical activities, skills, know-how, etc.) other artifacts or raw resources, see Fig. 1. We assume that all the transformations form an innate, universal, directed graph of transformations. The idea is that mankind has to master certain primitive transformations that it uses to bootstrap into mastering more advanced transformations. Mankind thus gradually develops a broader and more sophisticated portfolio of tools and production processes (see e.g. Childe 2003; Basalla 1988). An example of relationships in the transformation blueprint is how the concepts ‘controlling fire’ and ‘containing liquid’ unlock the transformation ‘boiling’. The more transformations mankind has mastered, the more artifacts it can produce and the more combinations of transformations it can make to unlock yet new transformations.

The real-world transformation blueprint is highly complex and only gradually discovered (see e.g. Childe 2003). Here, we operationally define a highly stylized transformation blueprint to be used in our agent-based model. We assume that the blueprint starts with several root transformations at what we call tier *t =* 0 and that it extends indefinitely to more advanced transformations. Much like a phylogenetic network,^{[1]} each transformation either (1) splits into two new, more advanced transformations, or (2) merges with another transformation into one new, more advanced transformation. We assume that, with probability p, a transformation at tier t -1 splits into two transformations at tier t, while, with probability 1 -p, a transformation т at tier t -1 is merged with a second transformation т' at a tier < t -1 into one transformation at tier t. A second parameter q defines where this second transformation comes from. Let ^(т) be the set of all transformations that are ancestors of transformation т. With probability q, the second transformation т' is uniform randomly drawn from the set *Q(*т), which we dub ‘conservative’ accumulation. With probability q -1, the second transformation т' is drawn uniform randomly from all transformations at tiers < t minus ^(т), i.e. all eligible transformations that are not ancestors of т, which we dub ‘progressive’ accumulation. Figures 2, 3, and 4 contain plots of transformation blueprints for p = 0, q = 0, p = 0, q = 1, and p = 1, q = 0 respectively, generated from tier 0 through to tier 6. Note that for p = 1.0, there is no merging, so the blueprint does not change with changes in q.

Fig. 1 Each artifact *(circle)* is the output of a transformation *(square)* applied to input artifacts. The artifacts at the *bottom* tier are raw resources. Each artifact is defined by its bipartite tree of transformations and input artifacts/ raw resources

Fig. 2 *p =* 0.0, q = 0.0

Fig. 3 **p = 0.0, q = 1.0**

Fig. 4 **p = 1.0, q = 0.0**

The blueprint only defines how transformations relate to one another, it does not specify what the transformation does: convert two input artifacts into a unique output artifact of higher advancedness. In this work, transformations at tier t e {0, 1, ... } take two uniform randomly drawn inputs of advancedness t and produce a unique output of advancedness t + 1, both in case of a split and a merger.

Although we provide the actual agents’ heuristics for searching for transformations and constructing artifacts in the next section, there are different variants conceivable. However, each variant of these search heuristics has to meet the following requirements. Firstly, the process of unlocking advanced transformations necessarily starts with the most primitive transformations (i.e. those at t = 0). Agents hence either have to start with a non-empty repository or be able to build a repository of these most primitive transformations. As transformations may split or merge, agents need to be able to investigate whether a transformation in its repository singularly splits into two new transformations (‘splitting’) or whether two transformations combine into a new transformation (‘merging’). As we will see in the next section, we allow agents within reach of each other to pool their respective transformation repositories.

Moreover, a particular artifact can only be produced by an agent if, firstly, this agent has mastered a transformation producing it and, secondly, the necessary input artifacts are available. These input artifacts may be raw resources—and we assume these are inexhaustible and freely available—or yet other artifacts that need to be produced from yet other inputs or raw resources.

- [1] A phylogenetic network evolves due to phylesis (extension), speciation (splitting) and reticulation (merging) of species.