“Durdle Dwarves” is a simulation where little “Dwarf” pixels dig-through and build rock-like structures. They do this according to a set of 20 rules. A rule tests a Dwarf’s vicinity and provides a response. (For example, if a Dwarf notices a drop-off to his left, he’ll build a new piece of “bridge”; that’s 1 rule of the 20.)
The simulation is 100% deterministic, and the state of the world at a certain time is a strict function of those initial rules, plus the starting state.
For instance, this starting state:
Yields this world state after 13,500 ticks:
Let’s pretend we don’t like something about this result. Perhaps that structure just below the middle — the one that looks a bit like a road with a lane divider — displeases us.
We could just pause the simulation and erase it, of course.
Because we have the arbitrary power to change things at any time, you and I are sovereign over this world.
But each interruption like this comes at a cost. Even though we were displeased by the road-like shape, we’re also displeased to intrude upon the natural flow of events. In our set of innate interests, one interest is that the world have as few of these intrusions as feasible.
Another option is to change the starting state of the world. Let’s make our initial two “Adam & Eve Dwarves” one block farther apart.
And here’s what things look like after 13,500 ticks:
Hooray! We got rid of that nasty road-like pattern.
But there was a cost here, too. The world is dramatically different now. Here’s the “Before & After”:
This kind of thing is nicknamed the “Butterfly Effect” in chaos theory. The tiniest of changes, over time, produces explosive world differences in nonlinear and/or interactive systems.
This is irritating, too, because we liked the world basically how it was, we just didn’t like the road pattern. Now everything is way, way different.
Let’s define micromanagement as, “Controlling things with surgical precision.” Is there a way to micromanage-away that road, so that we keep the rest (through our precise surgery), but also without using the blunt force of the eraser?
You might be thinking, “Why don’t we alter the starting rules, so that the road never appears?”
Unfortunately, merely altering one of the 20 core rules, or adding just a few rules, has the same explosive “Butterfly Effect” that dramatically changes the world state at frame 13,500. So, this would fail to micromanage.
As it turns out, the only way to pull this off is to have tons and tons and tons of core rules.
And this, of course, has the cost of being horribly ugly and inelegant.
Some folks would tolerate that inelegance. But you and I agree that this basically defeats the point of creating these guys at all. We take pleasure — let’s say — in the emergence of these forms out of an elegant, simple foundation.
Where This Leaves Us
“Durdle Dwarves” is just a computer program.
However, it’s such an obvious deterministic cloister that it serves as the “worst case” for verifying whether determinism always means full micromanagement.
The answer? It doesn’t.
If we have an innate interest in maintaining systemic elegance, then the degree to which the world is micromanaged is equal to the degree to which we have found it warranted, in certain rare circumstances, to intrude, even as we’d rather not intrude.
Notice that our innate interests have what’s called “circumstantial incommensurability” at the “13,500 circumstance.”
It’s not power-weakness that makes a wholly-satisfying solution impossible. Remember, we’re 100% powerful over that world.
Rather, a wholly-satisfying solution is arithmetic nonsense.
What This Shows Us
An entity can be 100% sovereign and powerful over an interactive deterministic world, including that world’s core rules, starting state, and modifications to any subsequent state.
But if that entity has innate interests in an elegant ruleset, then the world is not necessarily micromanaged. Then, if the entity never intrudes, then the world is not micromanaged at all. And if the entity intrudes to some limited degree, then the world is micromanaged only to that degree.
Primary Causation & Secondary Causation
If we start with an elegant core ruleset in a sizeable interactive system, then as time goes on, I will lose surgical control over that system, even if I’m 100% sovereign over it.
True, but pretty dang counterintuitive.
It is only when I find it justifiable to intrude that I can wrest-back some amount of surgical control, temporarily.
- The reductive perspective is that since these decisions are all “up to me,” everything in the system reduces to “my causation.”
This is the perspective from which St. Irenaeus wrote in the 2nd century, “The will and the energy of God is the effective and foreseeing cause of every time and place and age, and of every nature.”
But this fails to capture something important to me, doesn’t it? Indeed, a formative perspective is needed to capture my interests.
- The formative perspective is that there is a meaningful — according to my interests — difference between primary causation, the stuff that glows brightly with my exceptional exertions of power, and secondary causation, the “teleologically-dimmer” stuff that starts to act weirder and weirder as time goes on.
This is the perspective whereby we rightly deny that God “authors” sin under chaotic determinism; rather, he broadly suffers it.
These two perspectives are simultaneously true in heterophroneo (a concept we’ve been exploring on this site that’s similar to Aristotle’s hylomorphism, but not exactly).
- Those who say “under determinism, primary and secondary causation have no meaningful distinction” are mistaken.
- Those who say “under determinism, a sovereign entity has 100% micromanagement, irrespective of that entity’s interests” are mistaken.
Please see last year’s article, “The Sun Also Rises,” to explore other philosophical and theological puzzles that “form heterophroneo” finally puts to bed.
Explore “Durdle Dwarves” for yourself here. Press “Start” to see the world erupt chaotically but deterministically, according to a small set of rules.