Rowlando Morgan
Journal of Economics, Theology and Religion, vol. 4 (2024): 60-77
Abstract
This paper explores the role of the Sabbath as an economic institution and its relationship with the concept of debt. The Sabbath’s function is explored, both as a special day of abstinence from work, as well as a wider symbol of social liberation. The paper develops a geometric model that correlates the way the Sabbath commandment interacts with a law that institutes a de facto seven-year debt cycle. This shows that it is possible to use modern mathematics and economic concepts to model biblical laws that have economic content. It thereby shows a way to frame key biblical laws inside of a rational framework where they can be seen as a harmonic economic system that co-ordinates the real and financial sides of the economy. The key technical contribution of this paper is an application of Pythagoras’ theorem to the modelling of the macroeconomics of debt.
Keywords
Commandments, Sabbath, debt, geometry, Pythagoras
Publication history
Received: 17 June 2024
Accepted: 13 September 2024
First view: 25 November 2024
Published: 18 December 2024
1. Introduction
This paper uses the ideas of economic cycles and mathematical geometry to model the economic and mathematical content embodied within key biblical scriptures which relate to economics. The study of economic and financial cycles has long played a role in economics. Economic historians, for instance, have often used the concept of cycles to assess long and short swings in economic activity. These sorts of cycles have been associated with terms such as the Kuznets Swing, the Juglar cycle and the Kondratiev wave.
More modern macroeconomic literature also considers both business and financial cycles as well as their interactions. A range of studies find that the financial cycle is of longer duration than the business cycle (Drehman et al. 2012; Galati et al. 2016; and Herman et al. 2015). One study finds that “on average financial cycles last 7.2 years” (Schuler et al. 2015), whilst another finds the business cycle to be 6.3 years in duration (Herman et al. 2015). Whilst these are just two estimates within a large range of empirical values found in the literature, these sorts of numbers are not far away from comparative respective lengths of financial and non-financial cycles implied by considering biblical scriptures that relate to the concepts of the Sabbath and debt. The rest of the paper will firstly explore the concept of the Sabbath and its relationship with debt before developing a novel geometric model to replicate the numerical and economic content found in biblical scriptures in relation to these same concepts.
2. The Sabbath
In the biblical cosmology, God established the seven-day week as a key unit of time, of which the Sabbath was its culmination. In this way, God instituted the Sabbath, which is an institution related to time which is in contrast to the physical elements of creation. Not only was the Sabbath a part of Creation but Isaiah 66:23 (New International Version, NIV) says that “From one New Moon to another and from one Sabbath to another, all mankind will come and bow down before me,” says the Lord.” This suggests that it will be an eternal institution. These biblical references are taken by the Seventh-day Adventist denomination, for instance, to be an argument for the enduring and perpetual relevance of the Sabbath in Christian religious practice. This paper supports this idea by identifying general properties of the Sabbath, as well as another key law related to debt; both of which are independent of any particular type of economy such as the agrarian-focused Ancient Israelite economy.
The Sabbath, whilst first appearing in Genesis, takes more of a central role in the bible in Exodus 20:8-11 (NIV), where in the fourth commandment of the decalogue, it says to
Remember the Sabbath day by keeping it holy. Six days you shall labour and do all your work, but the seventh day is a sabbath to the Lord your God. On it you shall not do any work, neither you, nor your son or daughter, nor your male or female servant, nor your animals, nor any foreigner residing in your towns. For in six days the Lord made the heavens and the earth, the sea, and all that is in them, but he rested on the seventh day. Therefore, the Lord blessed the Sabbath day and made it holy.
This commandment describes the Sabbath as an institution that regulates economic activity. The Sabbath is, of course, much more than a form of economic regulation. It is a day that was made holy and was sanctified by God at the time of creation, and so serves as a central day of worship for Jews and some Christians such as Seventh-day Adventists. Heschel, for instance, describes the Sabbath as “a sanctuary which we build, a sanctuary in time” (Heschel 2005, 29). Nevertheless, the root-meaning of the word Sabbath is “to cease”; it is a day of rest where work was to cease along with associated buying and selling. From the vantage point of biblical cosmology, it can be seen that the “environment in which God placed humans is social” (Cafferky 2015, 36), and this is embodied by the institution of the Sabbath. It provides a general regulation on the extent to which economic agents could work or require others to work (including animals). There is also limited, if any, direct reference to any particular type of economy which further indicates a general applicability of this commandment.
The Sabbath commandment was the lynchpin of a series of laws that, at least in principle, engendered liberation across the social hierarchy within Ancient Israel. It was part of a body of stipulated economic cycles that also occurred over years and decades, culminating in the Jubilee. More generally, the concept of Sabbath rest is a motif that is woven throughout the Hebrew Scriptures and the New Testament. Whilst it refers to one day in a week, it also refers to one year out of seven. The concepts of sabbatical years (Exodus 23:10-1; Leviticus 25:4-5; 26:34-5; 2 Chronicles 36:21) and the year of Jubilee (Leviticus 25: 10-54; 27:17-24) present the Sabbath as a means of establishing liberation in a general sense. Moreover, in the New Testament, Christ made clear that the Sabbath was created for people, and was not intended to be a rules-based system of oppression (Mark 2:27-8) (Gallagher 2019, 141). There are also applications of the concepts of the Sabbath and debt forgiveness in the modern world. For instance, the economist Ched Myers (2023, 4) believes that:
… the theology of Sabbath economics, with its ethic of regular, systemic redistribution of wealth and power … continues to offer communities of faith today a way out of our historical and persistent slavery to the Debt system – with its alienating cruel practices of social stratification and the concentration of wealth and power.
The Sabbath also references the specific inclusion of marginalized groups, such as foreigners, servants, and slaves, thereby highlighting the importance of social justice (Gallagher 2019, 138-40). All factors of production were to experience rest related to the number seven. For instance, the sabbatical principle of rest applied “as much to the earth as it [did] for humans” (Cafferky 2015, 36), as the land was to lie fallow every seventh year (Exodus 23:11).
Every seven days slaves would experience rest along with all of their respective masters’ household, including animals. Then, every seventh year, slaves were to be set free, and debts were to be forgiven. This represented a release from responsibility of meeting financial debt obligations. So, whilst the Sabbath related specifically to the labor market, there was also another macroeconomic regulation related to the functioning of the credit market.
Moreover, slavery as reported in the bible generally emerged through a failure to pay debts. In general, slavery itself was a boundary solution to the problem of a person not being able to afford one’s day-to-day needs. If daily needs could not be met, debt was the solution. If debts could not be repaid, slavery was a solution. As such, the seven-year release from debt obligations and the freeing of slaves can be viewed as being primarily all about debt, whether it was the forgiveness of debt directly or the release of fellow Israelites from debt-induced slavery.
A different version of the Sabbath commandment, found in Deuteronomy 5:12-5 (NIV), reads:
Observe the Sabbath day by keeping it holy, as the Lord your God has commanded you. Six days you shall labour and do all your work, but the seventh day is a sabbath to the Lord your God. On it you shall not do any work, neither you, nor your son or daughter, nor your male or female servant, nor your ox, your donkey or any of your animals, nor any foreigner residing in your towns, so that your male and female servants may rest, as you do.Remember that you were slaves in Egypt and that the Lord your God brought you out of there with a mighty hand and an outstretched arm. Therefore the Lord your God has commanded you to observe the Sabbath day.
This version, referring to the slavery and oppression experienced by the children of Israel and the mixed multitude that accompanied them out of Egypt, provides a more direct link between the Sabbath, slavery, and debt. Here, the Sabbath commandment emphasizes that bondage was not to be a theme of God’s economy. In this way we see that the Sabbath also engendered a moment of equality, whilst reflecting the freedom that God had granted upon freeing his people from the bondage experienced in the land of Egypt. Indeed, the Sabbath can be interpreted as intermittent moments of salvation. The weekly Sabbath represented a moment of freedom that mirrored the liberation from the Egyptians. It established periodic rest days where the master-servant bondage relationship was to be suspended and then re-established as the week reverted back to its first day. The Sabbath thereby reflects both the nature of liberation provided by Jesus Christ as well as the freeing of the Israelites from Egypt. This thereby links the creation story directly to the salvation provided by Christ via the institution of the Sabbath due to these periodic moments of liberation.
Consider also the Jubilee year, which occurred just after the 49th year of a 50-year cycle. It was to be a year of rest, a sort of super-sabbatical, where property was to revert to its original owners, and debts were to be forgiven (Anderson 2005, 27). The inherited land of families would also be returned if it had been sold due to debts that could not be repaid. In this way, the “jubilee year … [affirmed] the fundamental unity of creation, since both people and the land [were] intended to observe the sabbath” (Fanucci 2014, 6). Overall, whilst the ratio of one-seventh was applied to both people and their land, the nature of the enforcement of the liberation was to vary in ways that aligned with the nature of the entity experiencing the liberation.
3. Debt, the Sabbath, and time ratios
The key scripture about financial market regulation is found in Deuteronomy, where it says the following:
At the end of every seven years you must cancel debts. This is how it is to be done: Every creditor shall cancel any loan they have made to a fellow Israelite. They shall not require payment from anyone among their own people, because the Lord’s time for canceling debts has been proclaimed (Deuteronomy 5:12-5, NIV).
This verse dictates that the debt cycle was to occur over seven years but at the end of the seventh year the debt cycle was to cease. More precisely, while debt contracts could be initiated by individuals at any time, these contracts (unlike the process of buying and selling) would not cease to exist every seventh day, but only at the end of the seventh year. Concurrently, six years of work (i.e., buying and selling) will have occurred in this time period, if the observance of the Sabbath commandment were to be simultaneously observed by the same society. The first key mathematical observation to be noted is that this implicitly leads to a ratio of time spent on the two most primary economic activities: buying and selling, and lending and borrowing. This ratio is 6:7, as six-sevenths of time would have been associated with buying and selling, whilst the full seven-year period would be associated with lending and borrowing. These laws can also therefore be interpreted as macroeconomic regulations of both the goods and credit markets. Moreover, the laws dictated two cycles were to run in harmony: a continuous cycle related to debt instruments being used (lending and borrowing) and a cycle of discrete activity, related to what we now might term as ‘goods-market’ activity (buying and selling).
We now develop a model that provides a novel geometric derivation of two economies: a non-debt economy versus a debt-based economy which aligns with the economics embodied in the Sabbath and debt laws referenced above. Our model shows that these laws can be viewed as regulating the interactions between non-debt-related activity (a No-debt economy) and debt-related activity in a temporal sense. It will be shown that the concept of a ‘rest’ for the agents exacting labor can be derived in a generalized depiction of a closed economy which has debt transactions, and that the time associated with this rest period in equilibrium is approximately one-seventh of the total time allocated to economic activity.
4. The model
The model assumes a closed economy, subsequently considering a scenario where debt is not an available instrument, and then comparing this scenario to scenarios where it is available. The model thereby identifies the contribution of the debt instrument to equilibrium output. This equilibrium result is then compared to the economics embodied in the Sabbath and debt laws.
It is assumed that a unit of output requires a unit of labor effort. In a No-debt economy (an economy with no access to debt instruments), the income levels of any agent over a given period cannot diverge from their respective expenditure levels. An economy with a debt instrument, however, allows income and expenditure levels to diverge.
We assume a finite length of discrete periods of equal length (i.e., years). We then consider each group and how they interact through their intertemporal budget constraints. The basis of this model is the familiar intertemporal budget constraint model found in standard macroeconomic textbooks. However, two amendments are made, one of which is standard and the other more novel. Regarding the non-novel amendment, the intertemporal budget constraint is made into a finite-time intertemporal budget constraint. The second, more novel, amendment is two-fold: we partition the economy into two interacting groups of net creditors and net debtors, and then describe their interactions by depicting each group by a distinct intertemporal budget constraint. It is assumed that both intertemporal budget constraints are met with equality.
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5. Visualizing a geometry
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6. Pythagoras’ theorem
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7. Linking the geometric model to the biblical laws
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8. Discussion: the wider context
This analysis begs the question of whether there is a ‘normative’ argument for Sabbath observance for any arbitrary society, given the ‘positive’ evidence related to the interactions of real and financial cycles. The analysis discussed above suggests that the Sabbath has a policy function of aligning two cycles of differing lengths: the real and financial cycles. The analysis indicates that the financial activity related to debt functions over a temporal cycle that is seven-sixths the length of real activity. According to this viewpoint of the weekly Sabbath institution, the Sabbath is a means of elongating the length of the real cycle by a ratio of seven-sixths, and thereby aligning it to coincide with the financial cycle related to debt-based transactions. Given that the analysis is related to general properties of any arbitrary economy, these findings also indicate that this is a normative principle that could therefore be applied to any arbitrary economy and not only one that fits the profile of the agrarian Ancient Israelite economy. One caveat is that other laws related to the ownership of land suggest that the wider economic implications of biblical laws served to engender an agrarian economy, for instance through ensuring tribes and families had long-term rights to land to be used for agrarian purposes. Notwithstanding this, the Sabbath can be viewed as an institution that enhances social welfare by coordinating economic cycles. Given, however, that the framework used is not utilitarian, the present analysis is insufficient to support any idea of the Sabbath maximizing social welfare.
There are also archaeological reasons for accepting the general applicability of the biblical commandments insofar as the Israelite economy (which it may reasonably be argued that laws were intended specifically to cater for) was itself non-uniform. McNutt, for instance, references David Hopkins (1996), who emphasizes that there was not even “an ancient economy” in ancient Israel, but rather a multiplicity of economies that were induced by the ‘complex and fragmented’ geography. Two major economic zones are identified as being, firstly, rural areas and small villages and, secondly, a more fully developed and interregionally integrated town- or urban-based economy (McNutt 1999, 154).
This analysis, however, does presuppose that barter was not a central feature of the Israelite economy, or indeed economies in general. This is reasonable to suppose, as money is mentioned in the bible as early on as in Genesis. Genesis 17:23 (NIV), for instance, says: “On that very day Abraham took his son Ishmael and all those born in his household or bought with his money, every male in his household, and circumcised them, as God told him.” The story of Joseph also mentions the use of money, where it says in Genesis 47:15 (NIV): “When the money of the people of Egypt and Canaan was gone, all Egypt came to Joseph and said, “Give us food. Why should we die before your eyes? Our money is all gone.” A specific aspect of tithing laws also indicates a general usage of money in the Ancient Israelite economy. Deuteronomy 14:25 (New English Translation, NET): “you may convert the tithe into money, secure the money, and travel to the place the Lord your God chooses for himself.” Furthermore, “money makes debt possible” (Graeber 2011, 21). This suggests that given that there was a law on debt in the bible, money must have played a sufficiently significant role in the Ancient Israelite economy for that law to make sense as an economic institution. Isaiah 24:2 (NIV) suggests that buying and selling, and lending and borrowing were considered typical economic activities in the Ancient Israelite economy, as they are in any modern economy. It reads: “it will be the same … for seller as for buyer, for borrower as for lender, for debtor as for creditor.”
Moreover, sociologists such as David Graeber and Caroline Humphrey argue that according to anthropological evidence, no barter economy ever existed anywhere. According to Humphrey, “no example of a barter economy, pure and simple, has ever been described, let alone the emergence from it of money; all available ethnography suggests there never has been such a thing” (Humphrey 1985, 48). Humphrey also has written that “There are few if any whole economies of any sizable scale which are known to have operated by barter alone” (Humphrey & Hugh-Jones 1992, 6). Graeber describes the idea of barter systems being the forerunners of modern monetary economies as the “the founding myth of our system of relations” and that “there’s no evidence that it ever happened, and an enormous amount of evidence suggesting that it did not” (Graeber 2011, 28).
More generally, Brueggemann presents the Sabbath as an economic system that contrasts with the system experienced within Egypt, with no significant reference to the specific realization of the Israelite economy, such as being predominantly agrarian. In referring to the Egyptian socio-economic system, he refers to it as being a system in which “there can be no Sabbath rest. There is no rest for Pharoah in his supervisory capacity, and he undoubtedly monitors daily production schedules …; and of course there can be no rest for the slaves who must satisfy the taskmasters in order to meet Pharaoh’s demanding quotas.” In contrast the Sabbath based system was one there was no longer exploitation and the “Israelite economy is no longer determined and compelled by the insatiable production quotas of Egypt” (Brueggemann 1989, 3-5). Hence, although the territory into which the Israelites were to enter was agricultural in nature, its system was to be one where there would be “no permanent underclass,” and the poor would not be seen as objects to be targeted through economic abuse but rather seen as neighbors to live in community with (Brueggemann 1989, 44).
Heschel describes the Sabbath as being independent of a particular economic context: “On the Sabbath we live, as it were, independent of technical civilization: we abstain primarily from any activity that aims at remaking or reshaping the things of space. Man’s royal privilege to conquer nature is suspended on the seventh day” (Heschel 2005, 28-9). This presents a generalized view of the Sabbath, unconnected to a specific spatial context. Even writing in the context of the United States in the 1950s—an advanced modern non-agrarian economy—Heschel considered the Sabbath to still remain as “a concrete fact, a legal institution and a social order” (Heschel 2005, 16).
9. Conclusion
This paper has shown that the biblical Sabbatical cycle is more than merely a day of worship. It can be viewed as a key part of a form of macroeconomic regulation that spans time periods and types of factors of production. It can also be viewed as being part of a wider macroeconomic framework that encompassed the regulation of debt and bondage more generally. The Sabbath was a weekly moment of economic equality, where both the slave and slave master could be considered equals, as their slave-master relationship was suspended for a 24-hour period. It was part of a wider system that ensured liberation was an essential part of the ideal Israelite economy. Not only humans, but animals and land were incorporated in this regime of liberation. Moreover, the yearly cycles of Sabbatical rest, release and forgiveness bore a symmetric relationship to the weekly cycle of Sabbath rest. The Sabbath precepts closely relate to biblical precepts on debt, and this relationship is modelled using the simple geometry of the Pythagorean theorem. This correlates well with an implied ratio of time to be associated with the economic activities of buying and selling, and lending and borrowing, which is a ratio of 6:7. Whilst Heschel (1989, 10) describes the meaning of the Sabbath in terms of a celebration of time rather than space, this paper models the economics of Sabbath commandment, in combination with a key debt law, using the abstract geometric spatial object of the circle.
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