Faith Across the Multiverse: Parables from Modern Science

Chapter 3: Sovereignty in a Time of Spanners

By Andy Walsh

We are blogging through the book, “Faith Across the Multiverse, Parables from Modern Science” by Andy Walsh.  Today is Chapter 3: Sovereignty in a Time of Spanners.  In this chapter Walsh takes up the issue of God’s sovereignty and man’s free will.  He raise the following questions:  Is every outcome foreordained by God and do we bear any responsibility?  Or do we have free will and are agents who make independent choices, and can be held responsible for our choices?  In what sense can God claim to be in charge or have a plan if we can do whatever we please?  Is God always playing catch-up, adjusting his plans to account for our choices?  Can any such being claim any sense of sovereignty, or must he acknowledge that he is in fact secondary to the agents making the choices that he has to react to?  I’m sure by the end of this OP and through the comments, we will settle this question once and for all /sarcasm off.

A conflict between control and freedom is popular in fiction.  The classic book about this is George Orwell’s 1984.  The Matrix and its sequels explore control of humanity through elaborate computer programs. The TV show, Lost, was about experiments and rules designed to exert order and control.  This tension is apparent in the Bible as well, for example, the Moses-Yahweh dialogue in Exodus 4:10-14:

Moses said to the LORD, “Pardon your servant, LORD. I have never been eloquent, neither in the past nor since you have spoken to your servant. I am slow of speech and tongue.” 11. The LORD said to him, “Who gave human beings their mouths? Who makes them deaf or mute? Who gives them sight or makes them blind? Is it not I, the LORD? 12. Now go; I will help you speak and will teach you what to say.” 13. But Moses said, “Pardon your servant, LORD. Please send someone else.” 14. Then the LORD’s anger burned against Moses and he said, “What about your brother, Aaron the Levite? I know he can speak well. He is already on his way to meet you, and he will be glad to see you.

In this passage, God clearly asserts his sovereignty, reminding Moses that he has given Moses all he has, even the capacity to speak; if God is telling Moses to go and speak to Pharaoh, then surely God will have made sure Moses is up to the task.  But if all things go according to God’s plan, how does God justify getting angry at Moses?  Isn’t Moses just acting the way God made him?  Or if instead Moses has agency and free will, then what value do God’s assurances have?  If Moses can act independently, then doesn’t mean he has the capacity to screw up the mission, regardless of God’s preparation?  And then what do we make of the resolution, where God consents to send Aaron along?  Was that God’s plan all along?  Was that a contingency option built into the plan?  Or was God genuinely scrapping his plan for a new one in response to Moses’ choices?  My favorite juxtaposition of this conundrum is Acts 2:23; “Him, being delivered by the determinate counsel and foreknowledge of God, ye have taken, and by wicked hands have crucified and slain…”

Walsh’s mathematical analogy to help us relate to this issue is the parabola.  Parabola refers to a group of shapes rather than a single arc, but all parabolas have the same mathematical form and all thrown objects follow parabolas.  On the surface of the Earth, all of these parabolas can be described in terms of the initial velocity of the object and angle from which it was launched.  Just knowing those two things tells you the path the object will follow.  Our brains seem wired to calculate the path of parabolas without thinking about it every time we throw or catch a ball.  This psychological preference for parabolas may explain the mass appeal of various sports.  A hit in baseball, a football pass, or field goal kick, a basketball shot, a tennis volley—all these are parabolas in action.

Parabolas, and similar models, are determined by initial conditions.  If you know how things are set up at the start, you can figure out how they’ll end up.  Given how useful these properties are, and given how strongly our brains are wired to expect the world to operate this way, it is little wonder that we make so many of our models to have those properties.  More to the point, Walsh says, it’s not surprising that we expect the world to actually work this way.  And with this kind of metaphor for how the world works, it seems fairly natural that those who believe in God would start to think in those terms.  If God does have a plan for the world, then surely it would be expressed in the natural laws that govern his creation.  And since natural laws are fully specified by initial conditions, then really his only opportunity to influence that plan is at the start.  From there, we would seem to have only two options.  Either everything proceeds as planned or else there are other agents which can influence the system, in which case it will then be on a new trajectory requiring further intervention to get back to the original trajectory.

But not all systems in the physical world can be described by models that behave like parabolas. Surprisingly, it doesn’t require terribly sophisticated mathematics to get a completely different kind of behavior, a behavior so counterintuitive it was initially called chaos theory.  Chaos theory describe systems that are very complex and very sensitive to initial conditions.  The prime example are weather systems.  Most people have heard of the butterfly effect—the butterfly flapping its wings in Japan can mean the difference between rain or sunshine in New York City.

Jeff Goldblum’s character Ian Malcolm famously illustrates a similar principle in the movie Jurassic Park by putting drops of water on Ellie Sattler’s (Laura Dern’s) hand.  The first drop flows one way down her hand, the second a completely different way; according to Malcolm, small deviations in drop placement, the arrangement of the tiny hairs on the hand, or other conditions cause the difference in outcome.  Nothing is exactly the same way twice; small changes get amplified into big ones, and thus everything is unpredictable chaos.  Malcolm uses this idea to argue the dinosaurs in Jurassic Park can never be controlled—in fact control is an illusion.

Chaos Theory can be summarized in a few simple maxims:

• A tiny difference in initial parameters will result in a completely different behavior of a complex system.
• The Uncertainty Principle prohibits accuracy. Therefore, the initial situation of a complex system cannot be accurately determined, and the evolution of a complex system can therefore not be accurately predicted.
• Complex systems often seek to settle in one specific situation. This situation may be static (Attractor) or dynamic (Strange Attractor).

Walsh introduces a system that shows a strange attractor; the Hénon Map.  Without getting exceedingly more complex, the Hénon Map shows a bounded region that a dynamic chaotic particle will stay within, even though its position at one point or time cannot be predicted.  Walsh says:

This tendency of certain dynamic systems to stay with certain bounds despite perturbation, or what might be seen as bumps in a predetermined road, helps me to think about grace. More precisely I find it easier to believe that grace can coexist with God having a purpose or will for how the world turns out.  The metaphor of a bump in the road, a little deviation from the expected before returning to the intended path, conveys a similar idea.  At the same time, a road is static; these strange attractors are dynamic.  The stability of the pattern emerges out of the dynamic activity of the system, not in contrast to it.  Thus I find strange attractors a useful additional metaphor when thinking about grace.

So what would a strange attractor look like as part of the trajectory of our lives?  If we think everything behaved like parabolas, then it seemed as if either God had a plan and everything was following it, in which case there was little room for free will and little need for grace and mercy, or we as humans have free will, in which case we can sin and be in need of grace and mercy, but then God’s plan seems to need so many contingencies and adjustments that it becomes hard to see it as a plan at all.  Again Walsh says:

Consider what happens when we think of God’s will in strange attractor terms.  On the one hand, it is absolutely a well-defined, pre-specified plan.  The behavior that led to strange attractors was completely defined by our equations; we didn’t have to make adjustments as we went.  And yet on the other hand, there is room for free choice in the system as well.  We can get off the pattern, and eventually events will come back to that pattern.  There are still consequences to that choice, in that the exact spots with the pattern that get visited will change, but overall the system stays in the attractor.

In the passage from Exodus, God asserts his sovereignty and Moses chooses to decline the commission to speak to Pharaoh.  This is genuinely a choice on Moses’ part, which explains God’s anger at that choice.  Moses’ choice could have real consequences which might be bad for Moses and the Israelites, and thus represents a true sin which would displease God.  One of those consequences, however, is that Aaron will accompany Moses and speak to Pharaoh, so Israel gets led out of Egypt after all, accomplishing God’s overall plan to deliver them.

In Numbers, we see the Israelites who left Egypt arrive at the Jordan River across from the land of Canaan.  We are told that it is God’s plan for them to live in Canaan, and yet they choose not to cross the river.  The strange attractor model affirms this a genuine choice, with the consequence that the Israelites wander in the wilderness for forty years and the generation of adults that chose not to cross the river don’t live to return to Canaan.  And yet, their descendants do return, cross the river, and wind up living in Canaan, just as God’s plan indicated.

On the eve of his death, Jesus appears to contemplate the possibility of alternatives to crucifixion.  This is a challenging passage.  Walsh says it makes the most sense to him if Jesus genuinely has a choice in that moment, rather than perpetuating the illusion of choice for out benefit.  And if Jesus is wondering whether there is an alternative, then it would seem that he must be comfortable with the idea that there is more than one way to achieve a given goal.  How could Jesus consider the idea of an alternative if he knows that God’s plan is as fixed as a parabola?  Walsh says:

A gracious universe is also a universe in which life is possible.  Life is dynamic; every change holds the potential to make things worse instead of better.  A universe that recover from missteps, and organism that tolerate error, those are systems that can persist, remaining coherent over time.

We can practice such grace in our own lives as well.  Rather than making plans that require everything to go perfectly, we can expect and allow for disruption.  We can especially prepare for our fellow humans to make their own choices and perhaps even their own mistakes.

Faith Across the Multiverse: Parables from Modern Science
Chapter 2: The Hound of Heaven across the Multiverse

By Andy Walsh

We are blogging through the book, “Faith Across the Multiverse, Parables from Modern Science” by Andy Walsh.  Today is Chapter 2: The Hound of Heaven across the Multiverse. Walsh begins the chapter by recounting the story of the recent movie, “The Martian”.  The Martian is the story of astronaut Mark Watney inadvertently stranded on the surface of Mars and his struggles to survive and be rescued.  Walsh notes there are a couple of math equations vital to the story and to Watney’s survival.  One would be C_T=ϵd, where ϵ represents Watney’s eating rate in calories per day and C_T the total calories needed to survive d days. Looking in his pantry tells him he does not have enough food to survive the 400 days until he can be rescued.  The equation is straightforward reality; to survive he has to change one of the variables.  He can lower his eating rate ϵ, but only to a certain extent because he still has to be able to function.  He can hope for rescue sooner, but that is out of his control.  His third option is to increase C_T by ingeniously fashioning a garden and growing his own food.

Another equation relevant to The Martian is the rocket equation:

Δ V = V_ex log [(m_r + m_f )/ m] – gt

At some point, Watney will have to accelerate his rocket, or change his velocity (ΔV) into orbit around Mars to rendezvous with his rescue ship.  He knows how much fuel (m_f) he has, which is fixed by what’s in his tanks, and he knows the required exhaust velocity (V_ex) or propulsion needed to get high enough into orbit.  Acceleration due to gravity (g) is in the opposite direction and is constant for a given planet over the time (t) to achieve the necessary height.  The only factor he can change is the mass of rocket (m_r) by discarding as much material as he can that he doesn’t need.  As Walsh says:

All of that drama flows from the equation, because it encapsulates the relationship of gravity and rocket fuel.  The cleverness of the storytelling is to connect that relationship with Watney’s relationship to his home, his future, and his fellow astronauts.  The narrative establishes a new equation: lowering rocket mass equals increasing thrust equals Mark Watney catches a ride home.  We intuitively understand the human elements, the need to commune with other people and to return home.  By constructing the narrative equation this way, we now have a connection between something we understand well and the less familiar physics of rocket science.  As we go forward here, we can build on what we have learned about rocket science and the math involved to understand more about God.

Walsh is talking about a mathematical principle called “optimization”.

In the pictured example, the optimal or “highest” point on the figure is indicated by the blue dot.  In everyday life, optimization often means finding an alternative with the most cost effective or highest achievable performance under the given constraints, by maximizing desired factors and minimizing undesired ones. We all do this on an almost daily basis; we shop for groceries where we can find the most food that is the most nutritious and best tasting or freshest at the lowest price.  If price and quantity are what we want to optimize, we shop the bargain bins, if freshness and nutrition are to be optimized, we shop the pricier stores.

Walsh relates this optimization process to having made the choice of faith discussed in the last chapter to know God as an axiom and explore the truth contained in that axiomatic system, we accept the particular behavioral evaluation function that God establishes.  (And he does make the point that there may well be the empirical observation that plenty of people lead functional, socially constructive, and happy lives following another moral code; those alternatives aren’t completely bankrupt or vacuous.)

However, having decided to hold himself to a “biblical” standard, he needs to know what God is trying to optimize.  In Isaiah 28:17 it says, “I will make justice the measuring line and righteousness the plumb line” and Micah 6:8 says, “To act justly and to love mercy and to walk humbly”.  Jesus says in the Sermon on the Mount, “But seek first his kingdom and his righteousness”.  Walsh is trying to say the standards of morality in the Bible are presented within the framework of covenants.  Rather than saying, “You must do this because I said so”, God describes what a relationship with Him entails, both the benefits and the conditions.  Such relationships can then be built on informed consent, not blind obedience.  One common thread through concepts like justice, fairness, and peacemaking is a sense of communal well-being.  We are not simply finding the best possible versions of ourselves independent of everyone else, but the best possible collective version of ourselves.

He points out another notable feature of these values we are trying to optimize is the tension between some of them.  If we were to maximize only justice, there would be little or no mercy, while maximizing mercy would yield very little justice.  In mathematical optimization it is common to have multiple constraints.  The optimal solution across all of them might not correspond to the optimal solution for just a single constraint.  He asserts that the Bible calls us to balance justice and mercy rather than purely optimizing just one or the other.

He cites the conquering of Canaan that is often held up, if not as an example of God’s wrath, then at the very least of his extreme sense of justice.  Yet Joshua also recounts in chapter 9 the experience of the Gibeonites, a group who lived in Canaan.  They convinced Joshua and the other Israelite leaders that they weren’t local as a pretense to secure a treaty.  Even after the truth is revealed, Israel upholds the treaty and the Gibeonites are spared.  This mercy is never condemned, and indeed years later when the Israelite king Saul violates the treaty, he is sanctioned for it (2 Samuel 21).

Jesus also stands up for justice as well as mercy.  He cleanses the temple courts of merchants who are exploiting the poor.  When he spares a women accused of adultery from stoning, he is showing her mercy while also standing against the injustice of prosecuting her alone.

Walsh wants to conceive of sin as deviating from the path of an optimal version of ourselves.  Sin starts when we choose to optimize qualities other than the ones God invites us to optimize.  He thinks the Genesis 3 story of Adam and Eve describes this scenario.  Adam and Eve walk with God, and he leads them down the path to an optimal existence.  The one condition of their arrangement is that they not eat from one specific tree.  This is not a hardship, as food is available in abundance.  Not eating from the tree is how they communicate that they want to participate in the relationship God offers.

The serpent comes along and offers a different interpretation of what God meant.  Adam and Eve could have chosen to use their relationship with God to explore his intended meaning, but instead they decide to make their own meaning.  So in choosing their own interpretation for why God prohibited eating from that tree, Adam and Eve also chose to use their own optimization goals rather than God’s.  They were no longer following God by his map; they were drawing their own map and forging their own path.  And thus their sin was born as they began to deviate from the optimal version of their lives that God offered.  Walsh says:

The idea of choosing one’s own qualities to optimize, to forge one’s own path, to be master of one’s own destiny—these may all sound quite positive.  Self-determination is a core virtue of libertine society in general and the American mythos I grew up with.  I appreciate and respect the value placed on deciding one’s own fate.  A great number of injustices have been perpetrated precisely by taking away self-determination, and restoring self-determination has been an important force for justice.  Therefore, I am not advocating complete rejection of it, especially in the context of how we relate to each other, and I don’t believe God calls us to that either.  At the same time, just as God calls us to balance justice and mercy, he also calls us to balance self-determination with submission to his will.