January 20, 2019

Faith Across the Multiverse, Parables from Modern Science- Part 1, The Language of Mathematics, Chapter 3: Sovereignty in a Time of Spanners By Andy Walsh

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 1984The 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).

Hénon Map

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.


  1. Susan Dumbrell says:

    before we delve further off the present topic.I am sorry I am late for yesterday’s post but:-

    I would like our USA IMonkers to consider the votes that they or others may place affect the rest of the World.
    I think US is introspective and needs to consider the fragile world we all live in and from which we all draw the same oxygen.

    My late comment is, persuade by what ever means is available that we exist outside of your simple view of the world.

    Stressed Susan.

    • Christiane says:

      Hello Susan,
      for as long as we have been a country, we have not ‘cared for’ the environment as a sacred duty, in spite of our honoring God as its ‘Creator’, which makes little sense, except that in our modern time, corporate greed rules the day and blocks decisions that might protect our air and water quality (check out the story of Flint, Michigan).

      But the land we took from the Indians was to them ‘sacred’ and over a century ago, an Indian chief TRIED to share something of his ‘simple view of the world’ that did mention also that ‘we all draw the same oxygen.’ So a long time ago, someone cared enough about the environment to speak these words to our leaders, but the ‘words’ still hold meaning, maybe now more than ever:


  2. Adam Tauno Williams says:

    “””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.”””

    And not only does this allow for better Theology – – – it is simply very good advice. Resilience, and happiness, are best achieved through adaptability.

  3. Adam Tauno Williams says:

    “””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. “””

    Constrained Choice, that’s been my belief all along. Our choices are constrained, and unknowingly influenced by so, so,so many things; we cannot – cannot – be disentangled from our material surroundings.

    Too often the concept of “Free Will” gets mired down in absolutist delusions, engendering theoretical arguments and debates which have no binding to reality.

    But these our tough concepts as our language imposes limitations of this own; even take the sentence: “””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?”””” There are potentially multiple concepts of sovereignty here. The is “sovereignty” as in “I can do [absolutely] anything I want” and “sovereignty” as in “I am accountable to no other.” I read this using the second definition of “sovereignty”, due to the circles I inhabit that is my default definition, and thought “Huh? what does that have to do with sovereignty?” then realized I needed to context switch to the other definition. Many many times I’ve listened to or read through these kinds of arguments – – – watching people **unconsciously** context switching between various meanings of words [and, maybe sometimes deliberately doing so, to try to salvage their side of the argument from certain ruin]. When the meanings of words slide around the arguments rarely move forward.

  4. God has a plan for our life. It is a plan for good. The plan entails us exercising our will and consciously choosing and creating. It’s a living story, not a prescripted one. We are cocreators of the story. Two things are critical to the operation. One is waiting. The other is acting. Waiting is the quiet, the prayer and the chewing the cud. Acting is using one’s volition and choosing to create the thing. One without the other is a mess. Life is of course very complex but we are always responsible for choices along the path as active players, not paper cutouts. Imposition and joy cannot coexist. Neither can love and something imposed, like the law, live compatibley. We can serve one who imposes their will upon us but we cannot befriend them.

    • Christiane says:

      Hello ChrisS,

      you wrote ” We can serve one who imposes their will upon us but we cannot befriend them.”

      and I thought you might appreciate these observances from my faith own tradition:

      ““” In spite of the all-powerful strength of God’s merciful hand,
      which touches, enfolds and bends the souls with so many inspirations, calls and attractions,
      the human will remains perfectly FREE, unfettered, and exempt from every form of constraint and necessity.

      Grace is so gracious, and so graciously does it seize our hearts in order to draw them on, that it in no wise impairs the liberty of our will…
      grace has a holy violence, not to violate our liberty but to make it full of love…it presses us but does not oppress our freedom…”
      (Francis DeSales)

  5. Michael Bell says:

    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.

    Uh, maybe a bit of a simplication. 😀

    You would also need to know the gravitational constant and the drag,

    D = .5 * Cd * r * A * Vt^2

    where r is the gas density, Cd is the drag coefficient which characterizes the effects of shape of the ball, A is the cross-sectional area of the ball, and Vt is the terminal velocity.

  6. Dana Ames says:

    The discussions of our notions of “sovereignty” and “plan” have been frustrating to me, because a) as Finn wrote above, there are different concepts involved and b) those terms are ultimately grounded in what we understand about exercise of power. I see these things as questions arising from the Enlightenment, in the context of the aftermath of the religious wars in Europe. I can’t find them in eastern Christianity or much of western Christianity before the schism – not that we don’t talk about them, but they’re approached with much less stress, because we don’t think of God’s power as like human power, just “more so.”

    Of course God knew and knows in advance everything that did and will happen. That doesn’t negate our freedom, choices and actions. It simply means that we do not understand everything about how God works – what God’s providence entails. And maybe we can’t abide that God would do anything not revealed to us in Scripture where we can look it up and point to it in the Answer Book – and perhaps wield power over others through expounding a certain interpretation of it.

    The longer I know God (insofar as I can understand anything about God), the more I am impressed not with God’s power, but with God’s humility. Just as Mary, Jesus’ human mother, Jesus the human man had to trust the Father and voluntarily take up the task offered and given. That is a huge part of what makes Jesus the first Truly Human Being. We think we see deliberation and choice; I think what’s really presented in the Gospels is a place/space to contemplate that there was actually very little deliberation when the time came (though what there was of it was extremely intense). Unlike Adam, Christ said “no” to the temptation and “yes” to the Father, on a level that we are allowed to say is “choice”, and which we describe as agony – struggle, but nonetheless flowed from the innermost depths of Jesus the True Human Being, who always willed to do what the Father is doing as the right exercise of what our human will was made for. It’s also a place/space, since we know how the story ends, to think about what the fate of humanity would have been if Jesus “chose” the alternative.

    “…for of Thine own will wast Thou well pleased to endure the cross in the flesh, to deliver from the bondage of the enemy those whom Thou has fashioned… This is sung about Christ on the first Sunday of Lent. It also is true of the Father and the Spirit. That is the character of God, not the exercise of Bare Power.

    For more cogent writing, see Fr Stephen’s blog posts “The Secret Hand of God” and “The Agent of Change”, and anything that comes up at his blog under the search term “providence.”


  7. Norma Cenva says:

    And all this from the intersection of a plane and right circular cone huh?

  8. CM,
    I sent a couple emails. The second replaces the first.