The stabilizing role of the Sabbath in pre-monarchic Israel:a mathematical model

Abstract

The three monotheistic cultures have many common institutions and some of them germinated in pre-monarchic Israel. Reasonably, the essential institutions were in place at that starting point; this work explores the possibility that the Sabbath is one of these institutions. Our mathematical examination points to the potential cultural, civic, and social role of the weekly Sabbath, that is, the Sabbath institution, in controlling deviation from social norms. It begins with an analogy between spread of transgression (defined as lack of conformity with social norms) and of biological infection. Borrowing well-known mathematical methods, we derive solution sets of social equilibrium and study their social stability. The work shows how a weekly Sabbath could in theory enhance social resilience in comparison with a similar assembly with a more natural and longer period, say between New Moon and Full Moon. The examination reveals that an efficient Sabbath institution has the potential to ensure a stable organization and suppress occasional appearances of transgression from cultural norms and boundaries. The work suggests the existence of a sharp threshold governed by the “Basic Sabbath Number ש0”—a critical observance of the Sabbath, or large enough ש0, is required to ensure suppression of transgression. Subsequently, the model is used to explore an interesting question: how old is the Sabbath? The work is interdisciplinary, combining anthropological concepts with mathematical analysis and with archaeological parallels in regards to the findings.Electronic supplementary materialThe online version of this article (doi:10.1007/s10867-014-9373-9) contains supplementary material, which is available to authorized users.

Cultural Evolution of an Institution: The Sabbath

“…In Livni and Stone (2015) we showed that the Sabbath was a solution to the problem of justice administration of pre-monarchic Israel; this work makes the case that the Sabbath was the only solution.…”

“…In (Livni and Stone 2015), we established that these convocations played an essential role in keeping the egalitarian lifestyle due to its odd seven-day frequency. Tribes with convocations at known time units like monthly or halfmonthly could not.…”

“…The Sabbath institution is essential to the covenantal society (Livni and Stone 2015); therefore I shall treat its evolution in parallel with the evolution of the covenantal society. The "supercomplex chiefdoms created by some nomads of Eurasia" (Bondarenko, Grinin, and Korotayev 2004) are a proper point of start.…”

“…The mathematical model of Livni and Stone (2015) studies whether the justice administration of a covenantal society may fail because the society has no dedicated police force. Next to the Creator only the assembly, has the authority of judging wrongdoers and punishing them by ridiculing, gossiping, finger pointing, condemning, snubbing, excommunicating and possibly even stoning.…”

“…It will follow it as an evolutionary process of a random cultural mutation growing into a widely accepted cultural trait that gave us not only the weekends but it also fundamentally shaped our current way of life. 1 The report is a follow-up of a previous investigation (Livni and Stone 2015). That article used the bio-mathematical analogy between spread of misconduct and propagation of infections.…”