God and Nature Summer 2024
|
|
By James Bradley
Game theory is the study of mathematical models of conflict situations. In his book Divine Games (1), Steven Brams uses game theory to analyze situations recorded in the Hebrew Bible that involve conflicts between God and individuals. While Brams’ understanding of God’s thinking differs from that of historic Christian thought, his idea that game theory can enrich theology is intriguing.
Game theory is the study of mathematical models of conflict situations. In his book Divine Games (1), Steven Brams uses game theory to analyze situations recorded in the Hebrew Bible that involve conflicts between God and individuals. While Brams’ understanding of God’s thinking differs from that of historic Christian thought, his idea that game theory can enrich theology is intriguing.
To illustrate how such analysis works, I will use God’s and the Ninevites’ possible choices in the story told in the Book of Jonah. In the biblical account, when Jonah arrived in Nineveh, he proclaimed, “Forty more days and Nineveh will be overthrown” (2). The Ninevites believed Jonah and repented. The Scripture then reports that “When God saw what they did and how they turned from their evil ways, he relented and did not bring on them the destruction he had threatened” (3). Here’s a game-theoretic model reflecting (my understanding of) the situation:
God may respond in the best possible way to another player’s decision, but the outcome may not be God’s first preference. |
The numbers in the matrix denote the ranking of each participant’s preferences among the four possible outcomes—God’s first; Nineveh’s second. God’s most preferred outcome is to have Nineveh repent and not overthrow it; God’s second preference is overthrow Nineveh if they continue sinning. Nineveh’s first preference (most likely) is to continue as they are—still sinning and not overthrown. But their second preference is to repent and not be overthrown.
A key concept in game theory is that of the optimal solution: a pair of choices that is stable in the sense that neither player has an incentive to change the decision. In this case, that’s the outcome in the lower right corner. Brams suggests that God is an optimal decision maker: in every conflict situation, God chooses his best option taking the other player’s choice into account.
Another key concept is the distinction between a tactic and a strategy. A tactic is a particular choice such as Nineveh’s option to repent or God’s option to overthrow Nineveh. A strategy is an overall plan that specifies what a player will do for each option of the other player. Thus, God’s strategy is to overthrow Nineveh if it continues sinning, and to not overthrow it if it repents. As another example, consider a military battle. A tactic is a plan that specifies what one side will do. A strategy is more comprehensive—it spells out what that side will do for every tactic the opponent might choose.
There are several theological issues that game theory can shed light on—first, the classical question of whether God can change his mind. The above quote from the book of Jonah seems to say yes, but many theologians say no. Here’s R.C. Sproul’s view (4): “The mind of God does not change for God does not change. Things change, and they change according to His sovereign will, which He exercises through secondary means and secondary activities. The prayer of His people is one of the means He uses to bring things to pass in this world. So if you ask me whether prayer changes things, I answer with an unhesitating 'Yes!'”
What game theory suggests is that this theological issue arises from not distinguishing the tactical and strategic perspectives. From a tactical perspective, God changed his mind—from a plan to overthrow Nineveh to one in which he did not. From a strategic point of view, God did not change his mind. He maintained the same plan throughout—to overthrow Nineveh if it would not repent and to preserve it if it would. In short, it is possible for one person to say “No, God doesn’t change his mind” and for another to say “Yes, God does change his mind,” and for both to be correct—it depends on which level of God’s thought each person is considering.
Secondly, God being an optimal decision maker does not imply that God necessarily gets his first preference. That is, God may respond in the best possible way to another player’s decision, but the outcome may not be God’s first preference. For example, if the Ninevites had chosen not to repent, God would have overthrown them—God’s second preference. As in the previous issue, from a strategic point of view, God’s will would have been done, but God’s first preference for an outcome would not have been achieved. The discrepancy arises because God respects human choices, but those choices may not be his will.
Thirdly, game theory shows us how it is possible to affirm divine sovereignty without affirming determinism. Determinism requires absolute control of all events. Being an optimal decision maker means that God knows what’s best in every situation, has the power to act on it, has good will, and acts accordingly. Having those qualities seems to me to be an adequate definition of being sovereign. But it still allows for human freedom, and thereby avoiding determinism. (I think it also allows for genuine randomness in nature, but that’s a separate issue (5).)
The notion of God as optimal decision maker and the distinction between tactic and strategy also have implications for how we interpret Scripture. For example, consider the issue of women in church office. In First Corinthians, Paul wrote, “Women should remain silent in the churches. They are not allowed to speak but must remain in submission, as the law says. If they want to inquire about something, they should ask their own husbands at home; for it is disgraceful for a woman to speak in the church” (6). Some Christians today have taken this and other related passages to oppose allowing women to be pastors or elders in churches. Other contemporary Christians have argued that this passage is not divinely inspired but is simply Paul’s opinion (and have often added some uncomplimentary comments about Paul). But let’s assume that Paul was divinely inspired. The notion of God as optimal decision maker suggests that this was indeed the right thing for Paul to say at that time and in that place, probably because of cultural factors that we don’t understand very well. In short, it was an optimal tactic at that time. But that does not make it the optimal tactic for today. Rather, we need to step back and ask what the strategic perspective would be. The role of women in contemporary culture is so dramatically different than it was in Paul’s day that it’s reasonable to consider the possibility that that tactic is no longer optimal and thus not appropriate for us.
Discerning what is optimal from God’s point of view can be hard. While one must consider the situation, one must also think strategically in terms of God’s nature and objectives. God’s ethical commands to us are clear: we should love God and love our neighbor. God’s overall goal for us is that we be shaped into the image of Jesus Christ. Scripture presents these commands and this goal as transcending cultures. Thus, given that there are no obstacles in contemporary Western culture to women serving in leadership roles, it seems reasonable to say that the decision of whether a woman should be an elder or pastor in a contemporary Western church should be primarily shaped by the question of whether she loves God and people and whether she has the gifts to facilitate people’s growth in Christ, not by a first-century tactic.
That’s one example among many others. It is controversial in some denominations and churches, but not in others. To my mind, it illustrates well an important principle in scriptural interpretation: we should always look to the bigger picture of God’s overall strategy for humans because tactics optimal in one situation may not be optimal in another.
References
1. Brams, Steven J. Divine Games, Cambridge, Massachusetts: MIT Press. 2018.
2. Jonah 3:4 (NIV).
3. Jonah 3:10
4. Sproul, R.C. Does Prayer Change Things? p.15, Crucial Questions Series. Reformation Trust Publishing. 2019.
5. Bradley, James. Randomness and God’s Nature, PSCF, Volume 26, Number 2, June 2012.
6. 1 Corinthians 14:34-35 (NIV)
James Bradley is an emeritus professor of mathematics from Calvin University. He was co-editor of the books Mathematics in a Postmodern Age: A Christian Perspective and Mathematics Through the Eyes of Faith. He also served as editor of the Journal of the Association of Christian in the Mathematical Sciences. He has a BS from MIT and a PhD from the University of Rochester. His dissertation was in game theory.
A key concept in game theory is that of the optimal solution: a pair of choices that is stable in the sense that neither player has an incentive to change the decision. In this case, that’s the outcome in the lower right corner. Brams suggests that God is an optimal decision maker: in every conflict situation, God chooses his best option taking the other player’s choice into account.
Another key concept is the distinction between a tactic and a strategy. A tactic is a particular choice such as Nineveh’s option to repent or God’s option to overthrow Nineveh. A strategy is an overall plan that specifies what a player will do for each option of the other player. Thus, God’s strategy is to overthrow Nineveh if it continues sinning, and to not overthrow it if it repents. As another example, consider a military battle. A tactic is a plan that specifies what one side will do. A strategy is more comprehensive—it spells out what that side will do for every tactic the opponent might choose.
There are several theological issues that game theory can shed light on—first, the classical question of whether God can change his mind. The above quote from the book of Jonah seems to say yes, but many theologians say no. Here’s R.C. Sproul’s view (4): “The mind of God does not change for God does not change. Things change, and they change according to His sovereign will, which He exercises through secondary means and secondary activities. The prayer of His people is one of the means He uses to bring things to pass in this world. So if you ask me whether prayer changes things, I answer with an unhesitating 'Yes!'”
What game theory suggests is that this theological issue arises from not distinguishing the tactical and strategic perspectives. From a tactical perspective, God changed his mind—from a plan to overthrow Nineveh to one in which he did not. From a strategic point of view, God did not change his mind. He maintained the same plan throughout—to overthrow Nineveh if it would not repent and to preserve it if it would. In short, it is possible for one person to say “No, God doesn’t change his mind” and for another to say “Yes, God does change his mind,” and for both to be correct—it depends on which level of God’s thought each person is considering.
Secondly, God being an optimal decision maker does not imply that God necessarily gets his first preference. That is, God may respond in the best possible way to another player’s decision, but the outcome may not be God’s first preference. For example, if the Ninevites had chosen not to repent, God would have overthrown them—God’s second preference. As in the previous issue, from a strategic point of view, God’s will would have been done, but God’s first preference for an outcome would not have been achieved. The discrepancy arises because God respects human choices, but those choices may not be his will.
Thirdly, game theory shows us how it is possible to affirm divine sovereignty without affirming determinism. Determinism requires absolute control of all events. Being an optimal decision maker means that God knows what’s best in every situation, has the power to act on it, has good will, and acts accordingly. Having those qualities seems to me to be an adequate definition of being sovereign. But it still allows for human freedom, and thereby avoiding determinism. (I think it also allows for genuine randomness in nature, but that’s a separate issue (5).)
The notion of God as optimal decision maker and the distinction between tactic and strategy also have implications for how we interpret Scripture. For example, consider the issue of women in church office. In First Corinthians, Paul wrote, “Women should remain silent in the churches. They are not allowed to speak but must remain in submission, as the law says. If they want to inquire about something, they should ask their own husbands at home; for it is disgraceful for a woman to speak in the church” (6). Some Christians today have taken this and other related passages to oppose allowing women to be pastors or elders in churches. Other contemporary Christians have argued that this passage is not divinely inspired but is simply Paul’s opinion (and have often added some uncomplimentary comments about Paul). But let’s assume that Paul was divinely inspired. The notion of God as optimal decision maker suggests that this was indeed the right thing for Paul to say at that time and in that place, probably because of cultural factors that we don’t understand very well. In short, it was an optimal tactic at that time. But that does not make it the optimal tactic for today. Rather, we need to step back and ask what the strategic perspective would be. The role of women in contemporary culture is so dramatically different than it was in Paul’s day that it’s reasonable to consider the possibility that that tactic is no longer optimal and thus not appropriate for us.
Discerning what is optimal from God’s point of view can be hard. While one must consider the situation, one must also think strategically in terms of God’s nature and objectives. God’s ethical commands to us are clear: we should love God and love our neighbor. God’s overall goal for us is that we be shaped into the image of Jesus Christ. Scripture presents these commands and this goal as transcending cultures. Thus, given that there are no obstacles in contemporary Western culture to women serving in leadership roles, it seems reasonable to say that the decision of whether a woman should be an elder or pastor in a contemporary Western church should be primarily shaped by the question of whether she loves God and people and whether she has the gifts to facilitate people’s growth in Christ, not by a first-century tactic.
That’s one example among many others. It is controversial in some denominations and churches, but not in others. To my mind, it illustrates well an important principle in scriptural interpretation: we should always look to the bigger picture of God’s overall strategy for humans because tactics optimal in one situation may not be optimal in another.
References
1. Brams, Steven J. Divine Games, Cambridge, Massachusetts: MIT Press. 2018.
2. Jonah 3:4 (NIV).
3. Jonah 3:10
4. Sproul, R.C. Does Prayer Change Things? p.15, Crucial Questions Series. Reformation Trust Publishing. 2019.
5. Bradley, James. Randomness and God’s Nature, PSCF, Volume 26, Number 2, June 2012.
6. 1 Corinthians 14:34-35 (NIV)
James Bradley is an emeritus professor of mathematics from Calvin University. He was co-editor of the books Mathematics in a Postmodern Age: A Christian Perspective and Mathematics Through the Eyes of Faith. He also served as editor of the Journal of the Association of Christian in the Mathematical Sciences. He has a BS from MIT and a PhD from the University of Rochester. His dissertation was in game theory.