Applying the Event Time Interval Approach to Big Future

Plotting time intervals between major events (Δtime) or simply event time vs. event number (event#) have been used as a method to corroborate qualitative trends of accelerated complexity increase in (big) history. Emphasis of such event time (interval) studies has been on fitting the Δtime data with appropriate mathematical models ([super]exponential, logistic, hyperbolic). This is typically followed by a discussion on the occurrence of a possible singularity or inflection point around the present time. The event time (interval) approach is attractive, because of its simplicity and the impressively linear correlations observed in plots of logarithm of Δtime [log(Δtime)] vs. event#. However, a variety of concerns has been expressed related to the basics underlying this method, which big historians should take at heart. Amongst others, there is no objective definition of a major event nor is there a quantitative criterion for the selection of such an event. Therefore, the selection of major events is subjective. Next, there is no sound support for the underlying assumption that all selected events have equal importance. The event selection is also biased from the perspective of today, resulting in an even spread of events over a logarithmic time scale. To further explore these issues, the event time interval approach is here applied to a series of cosmological events, calculated from first principles by Adams and Laughlin (in Review of Modern Physics 69:337–372, 1997) in their study “A dying universe”. This series of events starts at the Big Bang, proceeds via the formation and subsequent development and degeneration of stars, planets, galaxies, and black holes, as well as the decay of matter to, eventually, a dark, cool universe. The series of 37 major events span 200 orders of magnitude of time and is mainly situated in the future, hence big future. In contrast to previous event time interval studies exploring the past, Δtime increases continuously with cosmological event# both in the past and in the future. This corresponds to a continuous deceleration of change and, thus, points to a slow “death” of the universe instead of a dramatic singularity. This is most probably the result of the continuously expanding and, thus, cooling and thinning universe, resulting in a slowdown of cosmological processes. Log(Δtime) increases with event# via three stages, viz. first an S-shaped increase, followed by a linear, relatively flat part though still somewhat increasing, and, finally, an upswing. The two transitions between these three stages are probably the result of two changes, i.e. first from a homogeneous universe to a universe with local heterogeneity, structured matter and energy-dissipating systems, and next to an increasingly homogeneous universe. Alternatively, the three-stage log(Δtime) curve may be interpreted as evidence for a time bias, looking at both the past and future from the present time. As a result, log(Δtime) values are rather small for events in both the near past and future, as well as an increase for events further away in both the distant and diffuse past and future. Finally, simple simulations with different event time series have shown that an even spread of events over the whole log(time) range results in a linear correlation between log(Δtime) and log(time) vs. event #. In addition, large Δtime values relative to the event times themselves result in a linear correlation between log(Δtime) and log(time). In conclusion, the most reliable way to corroborate qualitative trends in (big) history is the study of objective, quantitative parameters, either for the magnitude of a characteristic or for the diversity of a system, over time. In addition, researchers are encouraged to further develop and explore other and/or new metrics for complexity in a big history context.