Theoretical Boundaries of Agency

Or why it cannot be zero or absolute

Epistemic status: frantic hand-waving, probably illegible.
Importance: either complete garbage or fundamental science.

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TL;DR:

• Agency of any object is never zero if we zoom in close enough.

• Maximum, or absolute agency means total control over the state of the universe. But there is an important nuance that renders absolute agency impossible.

• Overall, agency is better measured in relative terms.

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World

First of all, let’s map all possible configurations of spacetime to a graph: the vertices will be physically possible states of the universe while the edges will be physically possible transitions between states. What does “physically possible” mean? Simply that there are laws of physics that any configuration of energy and matter must conform to, and that all such states are present in the graph. Any two states may be totally different or almost identical but never strictly identical.

As an example, imagine a simple world of a cellular automaton that has 3 cells, each featuring two possible states, and the rule: over any step, only one cell can change its state. We will get the following graph for that world:

As you can see, there are 8 states yet not all of them are connected. In this graph, it’s very easy to visit all the nodes (you will need exactly 8 steps if you plan wisely) but if the graph is sufficiently large, the states may be so many that there won’t be enough time until the heat death of the universe to traverse even a tiny fraction of those. It’s also easy to imagine a graph with the rules that make it nearly impossible to get to a previously visited state. Our world is exactly like that (and it also generates an immense, if not infinite, graph of states).

Let’s get to our world’s graph.

Every single moment—right now as well—our universe is in a state that corresponds to a single vertex in that unimaginably gigantic graph. The next moment, it will jump to one of the connected vertices. And then another one. This is when agents get to the scene. For they and they alone are the entities that decide what trajectories the world will travel in the graph of world-states. But what are agents?

Agents

For an ideal reductionist, at the maximum resolution, each elementary particle would be an agent. For a normal person, anything that they perceive as a separate object will do. It will do for us too.

At each step, agents assign “priority weights” to all the edges they have access¹ to. In all practical cases, they do that to bundles of edges, as there are billions of variations that are meaningfully the same from an agent’s perspective. That is, whatever state I transition to in the next picosecond, that won’t affect a person next to me because information most likely cannot travel faster than light², and light will traverse less than a millimeter in that time. But of course, we don’t make decisions anywhere near that temporal resolution so let’s get back to the more relatable units.

Right away comes a very important realization: the minimum amount of one-step agency is not zero! Every object (however defined) has its own default next state.

Sure, we only call agents those that can plan and execute their planning (and we will continue to do so) but that requires an arbitrary threshold for the “raw” agency. At the same time, every rock, every grain of sand in and by itself has exactly one³ default next state of existence. But rocks and such don’t have any effective reach into their environment nor are they capable of planning (or we just haven’t caught them yet). Still, for the sake of generalization, I will maintain that the minimum amount of “raw” agency is only infinitely close to zero but never exactly zero.

Now, actual agents will need multi-step modeling, planning, and decision-making. They will have different temporal and spatial horizons, and they’ll be able to contest what parts will comprise the next state of the world. The more powerful an agent is, the more ability it has to impose its will on the contested parts of reality.

Absolute agency

Now that we have set everything up, let’s drop the bomb.

The absolute agency is the ability of an agent to choose any physically possible transition without losing that ability.

And it is impossible.

Because in some states, an agent cannot choose just any transition. Therefore, it cannot choose it at the current step without losing that ability the very next moment.

Conclusion

There is no conclusion, sorry. It’s an exploratory essay, and I’ve learned about as much as you just did. (And even more, I also learned how an essay may rot as a draft for half a year to be finally revived and finished.)

1. There are limitations related to the speed of light which I won’t go into right now. IYKYK.

2. If you wonder why, as I do, you can start here on Quora. If you are generally interested in studying physics, you might like my Twitter alt dedicated to physics studies.

3. Strictly speaking, inanimate objects can transition to a very large subset of states where the specific object’s local state is simply the next one according to the laws of physics.

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