The distinction is more than philosophical hair-splitting. In explicit-time models, chronological information is fed into the simulation from the outside, usually as georeferenced radiocarbon dates calibrated against the calendar. Time acts as an independent variable, much as it does in Newtonian mechanics, where the letter t enters equations of motion as a given axis along which everything else unfolds. In emergent-time models, by contrast, no calendar is imposed at the start. Instead, temporality arises endogenously from repeated cycles of local interaction, adaptive feedback and cumulative transformation, and only afterward does the researcher assign a time scale to the model’s internal steps so that its outputs can be compared with dated evidence. The authors argue that this difference has profound implications for how computational models of social dynamics can be tested against the historical record.

To give the argument formal teeth, the team proposes a deceptively simple unit of analysis: the event, defined as a bounded, identifiable occurrence that marks a discernible difference in the state of a system. Formally, each event is a tuple binding an agent, an action, a location and a time—e = (agent, action, location, time). This structure, the authors contend, can remain invariant across wildly different kinds of evidence. In textual history, all four slots are filled directly: named individuals, described deeds, toponyms and calendar dates. In archaeology, the tuple must be reconstructed inferentially—agents are anonymous, actions are read from material traces, locations are known with centimeter precision, and time is probabilistic rather than calendrical. In depositional events, the raw sedimentary record, the agent slot may be filled by gravity, water or frost rather than any human intention at all.

As one moves from texts to artifacts to sediments, the authors describe a gradient of epistemic directness: agency dissolves from named persons to impersonal forces, action shifts from described intention to measured process, location gains precision while losing meaning, and time loses resolution while gaining depth. This is precisely where the distinction between time as a parameter and temporal information becomes critical. A list of radiocarbon dates provides time-as-parameter—numbers without relational structure. A model of early farming dispersal extracts temporal information by asking how those dates relate to one another across space, what patterns of proximity and sequence they form, and what processes could have generated the observed distribution.

The Mediterranean Neolithic serves as the paper’s empirical proving ground. The spread of farming from the Levant to the Iberian Peninsula between roughly 7000 and 5500 BC is one of the best-documented large-scale social transitions in prehistory, supported by thousands of georeferenced radiocarbon dates. The region’s geographical heterogeneity—mountains, seas and ecological gradients—produced strikingly uneven spread rates, with rapid coastal expansion standing out against slower inland diffusion. This makes the Mediterranean an ideal benchmark for comparing how different temporal representations shape our understanding of prehistoric process.

Equation-based models, the first of the three simulation families analyzed, treat time as explicitly parametric. Reaction-diffusion systems, descended from the classical wave-of-advance framework of Ammerman and Cavalli-Sforza, combine a demographic reaction term—population growth—with a diffusion term describing spatial spread. The authors draw an analogy with Newton’s second law: demographic pressure, climate change, contact with farming groups and social incentives act as forces pushing a population toward agriculture, while the society’s cultural resistance functions as an inertial mass that must be overcome. The velocity term represents the rate at which farming spreads, and its derivative captures whether adoption is accelerating or decelerating. Crucially, the integrated equation shows that the current rate of spread is not determined solely by present conditions but by the entire accumulated history of driving forces—a genuinely historical property.

In these models, empirical dates enter at only two moments: to set the starting conditions and to validate the output. Between those points, time is purely parametric. But this apparent limitation becomes a strength when the framework is inverted: because the arrival dates at specific locations are known, the model’s free parameters—growth rate, dispersal distance, and the balance between demic migration and cultural transmission—are constrained by the data. Only parameter combinations that reproduce the observed chronology remain admissible. The authors note that the cultural transmission parameter can only be broadly bounded from chronological data alone, and that genetic clines were needed to pin down its actual value, illustrating how different strands of evidence complement the temporal constraint.

Agent-based models operate in almost the opposite mode. Here, autonomous computational agents—individual farmers, households or entire settlements—follow simple decision rules within a shared virtual environment, planting crops, fallowing land, relocating or exchanging goods based on local conditions. Time is not a pre-existing axis but an organizing framework for discrete interactions: each timestep is one iteration of an economic cycle in which agents perceive, decide, act and update their state. The historical tempo that emerges—pulses, pauses, leapfrogs—comes from internal feedbacks such as resource depletion, density dependence and learning, not from any external database. Only after the simulation completes does the researcher assign calendar years to the iteration steps, converting the model’s internal ordering into comparable chronological information. The result is a dataset of emergent adoption events, each tying a who, a what, a where and a when.

Network-based models offer a third path, representing history as temporal event graphs in which nodes are events, agents or entities and edges encode dependencies. In timestamped versions, each node carries a duration and edges can be given birth and decay times, allowing the network to be grown as a sequence of snapshots. In a more radical variant, no time parameters are supplied at all: distance-weighted diffusion on a static spatial graph generates emergent timestamps from iterative message-passing, with nodes activating stochastically based on local history. Time steps are calculated from interactions rather than introduced as external input, producing a stream of relational events with internally generated temporal order.

The authors conclude that the two approaches are complementary rather than competing. Emergent-time simulations excel at reconstructing how processes may have unfolded mechanistically, illuminating contingency, feedback and path dependence. Explicit-time analyses excel at confronting hypotheses with empirical chronological evidence, ruling out scenarios that fail basic chronological tests and constraining equifinality. Their combined use encourages a cyclical research strategy in which exploratory emergent models generate hypotheses, explicit analyses evaluate them against dated evidence, and discrepancies prompt refinement. By expressing both as variations of a single event tuple, the framework provides a common ground for integrating heterogeneous simulation approaches—turning time from an invisible backdrop into a measurable, testable dimension of historical explanation.

Subject of Research: Temporal representation in computer simulations of historical social processes, including the spread of early farming in the prehistoric Mediterranean

Article Title: Time as event: bridging explicit and emergent temporal representations in computer-based social simulations

Article References: Time as event: bridging explicit and emergent temporal representations in computer-based social simulations. (n.d.). https://doi.org/10.3389/fcpxs.2026.1838587

Image Credits: AI Generated

DOI: 10.3389/fcpxs.2026.1838587

Keywords: computational archaeology, agent-based modeling, reaction-diffusion, Neolithic transition, temporal representation, simulation, Mediterranean prehistory, radiocarbon dating, event-based analysis, social simulation, emergent time, historical dynamics