Thermodynamically optimal governance

How information theoretical principles can be applied to social systems

It may seem unsavory to apply the principles of control theory and physical systems to society. However if we do not understand these principles to design a decentralized way to do this, it will be done by centralized systems, which will inherently elevate some group while suppressing their opposition. If the pieces exist to do this in decentralized way, then they certainly exist to do so in a centralized way. Doing so will be massively profitable to whoever can wield that power. So it’s essential to design decentralized systems, implement them at a small scale, and then scale them as quickly as possible.

The short story: Society can be modeled as engaging in active inference as defined in the free energy principle (FEP) just like any intelligent organism or life in general, which inherently presents an optimization problem. If we want to optimize active inference, we’re trying to minimize the amount of free energy in the environment relative to the internal structure of the entity in question. So by understanding what that free energy looks like, we can understand what properties an optimal governance system would have.

For the sake of communication, I’m going to jump in from that starting point. However below that will be a fleshed-out argument for why we can model society as this particular kind of optimization problem.

The thermodynamic context of governance

Society has not been as thoroughly explored from the FEP lens as other forms of life & organization. We have a much more established thermodynamic understanding of atoms and cells. In a cell, atoms are networked together in specific configurations, and the cell can manipulate their position by oxidizing or reducing them or their environment, by configuring them in certain ways that can result in hydrogen bonds, by changing the composition of the cytoplasm, etc.

The cell is not really a physical thing by itself, but an pattern of organization of other physical things. It can only interface with reality through the atoms that make it up. Ultimately it’s a group of atoms controlling each other, acting as proxies of the “will” of the cell. This is a special case of self-organization. Some weaker forms of self-organization are things like snowflakes and other crystals, clock reactions, etc. They spontaneously organize and even self-propagate to some extent but they stop short of an adaptive self-reproduction. We can also look at the organization of atoms as a form of interconnected feedback, bidirectional coupling or mutual constraint. In society, we as participants work to maintain society, which is composed of ourselves. However we only work to do this if we’re incentivized to do behaviors to that end. These incentives are the social equivalent of the inter-atomic forces on display in the cell.

Minimizing free energy in the context of a cell means arranging atoms in such a way that they can accept free energy from the environment. This probably most often takes the form of being on the reduction end of a redox reaction. It can also take the form of excitation from photons, ion pumps, or even mechanical excitation. The diversity of life we see is testament to the many ways there are to extract free energy.

The organization of the atoms themselves, including the kinds of bonds they have, is critically tied to the way the energy is extracted. An atom which becomes excited or reduced and then does not transfer its newfound energy down the chain no longer can serve the same purpose again because it has not moved back to a “ready” state to accept more energy. We can think of it like a bucket of water raised to a certain height. The bucket is not capable of moving more water up until it has been emptied.

When a coal miner extracts coal from a seam, they’re literally harvesting free energy from the environment. They then generally transfer this to another party they have some contractual relationship with. Sometimes this is an employer/employee relationship. Other times it’s a contractor relationship. In that contract there are a few constraints at play. First, the company must pay less for its operations than the coal is worth, otherwise it will eventually be unable to incentivize humans to work on its behalf and will cease to exist. Second, the miner has to be incentivized in some way to transfer that coal… like the water bucket getting emptied. The company must pay him. Or more exactly, they must provide the workers at least as much expected value as they would see from mining that coal themselves and selling it off individually. In effect the source of this latter value is the governance mechanism they provide. In the company’s absence, the miners would be duking it out over who gets to mine which areas, and they would be spending redundant resources getting their coal to market.

We can see these chains of energy transfer in society where they correspond to profit sharing or partnership patterns. In different industries, we see different patterns. The military organizes into strict hierarchy relative to other industries. R&D-heavy tech companies are highly coupled to financial institutions which are engaged in assessing risk. They often give equity to employees. Mining companies rarely have equity arrangements. Similarly in the absence of a common governance structure, all these various industries also incur redundant ad-hoc costs for protecting their resources, property, access to labor, as well as getting products to market, so they tend to organize and promote one. So we can see a direct relationship from the minimization of free energy to the creation of a governance structure.

An optimal governance system will tend to provide an environment where either party has a predictable set of incentives, because this increases the amount of free energy internally versus externally. The effect is a general reduction of environmental noise which is a decrease in the amount of entropic energy internal to the system. If there’s too much uncertainty, a contract cannot reliably be agreed upon. Just like if there is too much randomness within the cell, biochemical pathways can cease to function. Just as an inefficient engine produces more entropy relative to the amount of energy it transmutes.

The governance system also has an incentive to make sure that the entities engaging with the environment are in a state where they will readily accept free energy. In the case of a redox reaction, an atom which has just accepted an electron cannot accept another. In the case of a miner, they will need someone to pay them for the coal they just extracted. Or at least they need to be able to transfer it into a process that ensures they will get paid in the future. If they cannot, eventually they will stop working until they can somehow exchange the coal for their necessities. Thus interruptions in supply chains don’t just impact the demand side, they also impact the supply side.

Aside from the thermodynamic view, we can also look at this from the information-theoretical view. If a member of society finds a novel process to extract free energy from the environment, it’s likely that that process will yield more energy in other places as well. As such, replicating the process with a certain frequency in certain places should yield more free energy with a certain probability. These energy-producing processes can be extraction processes like mining, but they can also be meta-processes which increase the efficiency of existing processes, like surveying to find the best places to mine, or governance processes.

The active inference model divides this problem up into internal states, hidden states, sensation, and action. However the boundary between internal and hidden states is simply a matter of perspective. When you’re looking at the inference boundary of humanity as a whole, the state of the UN is an internal state, but if you’re looking from the perspective of your local community, it’s a hidden state. This is true of our brains as well. From the perspective of your frontal lobe, your motor neurons are presenting as hidden states.

This means there’s a progression of further and further inward inference boundaries contained within outer inference boundaries, and they cooperate to varying degrees to align on state as well as cooperative actions, or signals to send across that boundary to affect the “environment”. When we update our “internal” processes, we can view that as a process of: retreating one level deeper and externalizing the parameter in question; using “sensation” to update a more internal parameter based on the state of that parameter; and then using “action” to modify that parameter, just as we modify the environment. Thus learning and modifying the environment are equivalent processes.

Each layer configures the internal parameters it has access to with respect to the inferred hidden parameters in order to minimize “surprise”. This the statistical view of free energy. Each layer minimizes the discrepancy between what it models from the external environment, and what the external environment actually produces. To the extent that it fails to do so, that discrepancy results in a lack of ability to do work on the environment.

So each layer “in” is receiving fluctuations of energy from outer layers and translating that into the ability to exert some control on those outer layers/the environment. It does so by interpreting and eventually anticipating those fluctuations.

This appears at first glance as a centralized process where the inner layers govern the outer layers. However we see clearly that in life the outermost layers of the environment are the ones we have the least control over. In this basic model, there are no opinions about how each layer manages to anticipate those fluctuations, or how they exert control on the outer layers.

If we are trying to understand how to optimize such a process, so far all we can say is that we can use something like signal processing or various probabilistic inference methods to anticipate the signal that arrives via sensation.

Distributed Systems

But sensation itself is organized via networks. We receive stimulus on certain neurons and then aggregate over those neurons using other neurons. We then might think and integrate with other senses, or even talk to other people to determine how to update our internal state in response to a stimulus. Not only that, but our neurons might themselves react to the stimulus in a way that affects other neurons around them, even those ostensibly in the same “layer”… in other words the information/control flow is not strictly hierarchical. It can be lateral as well. It can even flow downstream as well. We know that upstream neurons can also affect the sensory neurons’ behavior.

We can also see that no single neuron has the entire picture, so to the extent that this “layer” exists, it’s at least not physical. It’s made up of a collection of smaller units. So the picture we have is of a set of inferring agents which have partial state, communicating over noisy channels,

This then leads to a completely different kind of optimization problem. Instead of just trying to minimize the discrepancy between a set of hidden states and internal states or inner and outer layers, it also becomes a problem of distributing state and processes across many agents. In other words a distributed systems problem. This view allows us to bring other tools into optimizing the problem

Each layer receives its signal from a stimulus or set of stimuli. In the case of the former, that stimulus was produced by the combination of many previous interactions aggregated into a single one passed as a message somewhere else. In the case of the latter, the layer receiving the set of stimuli must itself aggregate those various messages.

And those aggregation processes are themselves subject to the optimization problem of propagating certain processes and information. We know in these kinds of problems that there’s a trade-off between holding onto all information and acting on information when it’s available. The attention mechanism has proven extremely powerful in machine learning by this principle.

All of this leads to the idea that if we want to optimize governance, we can treat it as a distributed learning problem. Information comes from many sources, and a hierarchical approach will fail to compete with one which can adjust to more dynamic environments. Decentralized systems have popularized and developed consensus mechanisms from distributed systems research, which end up looking suspiciously like governance mechanisms because ultimately that’s what they are. This is not a coincidence. They’re solving the same problem which is the lateral aspect of inference. In other words, how agents at the same layer align on state and collectively decide upon and trigger actions.

Optimization

So, we’ve made a case that society can be viewed as a collection of distributed systems which engage in processes designed to minimize the amount of free energy exterior to them as compared to their interior. But then what are the parameters for optimizing this. Distributed systems have a notorious set of trade-offs. The CAP theorem describes that there’s an inherent set of trade-offs between Consistency, Availability, and Partition Tolerance. In the realm of human governance these would correspond roughly to rule of law, responsiveness to public needs / speed of execution, and local rights. We can see that many of the political fault-lines that occur are about which trade-offs should be made.

We can compare the differing resources and constraints of various regions within a political entity to the various capabilities and constraints that different devices in a distributed system might have. Some might have access to certain data. They might transform that data into a form that another part of the system can use in order to prevent them from having to process it, etc. One of the biggest lessons of this correspondence actually goes the other way. Markets are exceedingly efficient at allocating resources, and this lesson has yet to be used on a large scale in distributed systems except in the case of app stores and plugin markets. That said, the fact that they have not also speaks to their limits.

So for different models of a nation as a distributed system as well as different weights for the various trade-offs, we would end up with potentially different optimal treatments for governance protocols. That said, if we were able to explicitly describe what choices we’re making about that and arrive at consensus on that, then we could begin to attempt an optimization. This requires a formal language which can describe our society as system over which optimization can occur, as well as a method for proposing and arriving at consensus on updated versions of that description. This could induce a sort of self-awareness in the system which would allow it to respond to changing environmental circumstances more effectively and allow us to engage in more long-term decisions rather than being constantly biased toward the short term.

In some ways this is sort of what the government already does. The constitution outlines the structure of the government and congress, the judiciary, and the executive administration follow processes to update it. What it does not do is take advantage of the past 100 years of intensive study about these topics which provide extremely useful tools for managing such a system. If laws could be written formally, we could type-check the law and find contradictions. That alone would likely be worth billions. Not to mention directly integrating administrative processes and allowing them to be similarly checked against the laws.

We also know that the amount of economic activity and speed of communication has massively increased from the time the constitution was laid out. As that decreased latency, increased throughput, and changes in capabilities and constraints has occurred, the optimization landscape has changed dramatically while the core architecture has not been updated or even really put on more powerful hardware. The result is that we are essentially trying to steer a massive ship with a rudder made for a rowboat.

Systematizing these governance processes and integrating them with administrative procedures would also lead to one of the most important advantages, which is the ability to trigger processes automatically and remove the ambiguity of human interpretation which gives too much room for corruption.

This is in contrast to AI governance, which even if it could properly sustain itself would not have a direct feedback loop requiring it to serve human needs. Rather than taking advantage of the mechanistic execution of logic that computers excel at, we’d simply be replacing our own biases and misinterpretations. Though there might be pieces which could integrate neural nets for identifying events and triggering procedures in response, these processes would all be proposed and consensus would be arrived upon by humans.

So to answer the question of “what does optimal governance look like?”: the answer is it depends intimately on the conditions of the system under governance, however the tools of information theory, distributed systems, signal processing and other fields would yield drastic gains upon what we currently have. This is a call for the research development of of a formal model of human processes and governance as well as its integration into our political and corporate structures. Given the degree to which national governance now impacts individuals and institutions on a daily basis in terms of both time and cost, this would be one of the single most beneficial ways that the federal government could spend money.

Why is governance describable by the free energy principle?

As promised in the first paragraph, this is an argument for why we can say that governance is described by the free energy principle. First, we need to define what we mean by governance, and what optimizing it might look like. At it’s core, governance is the creation, maintenance, and execution of policy, or code. However these policies are created, maintained and by the same agents who the policies apply to.

Let’s set up some definitions. A governance system G is defined as a process executed by a society. Each process (P1, P2, etc.) takes as parameters a set of resources (some of which can be energy e, agents a as well as other processes), and outputs another set of resources. And society is defined by its agents, resources, as well as the set of continuations of its processes or “contracts” (c1, c2, etc).

Executing policy involves causing these agents to behave differently than they otherwise would, and as such requires increased energy to carry out. This allows us to establish some assumptions.

1. A governance system is failed when the agents no longer carry out its processes.

2. Energy must be used to incentivize agents to carry out those processes.

We can also say something about the agents involved in the execution of this policy. An agent will be dis-incentivized from doing work that gives less energy in return than it could otherwise acquire independently. Further, an agent which does more work on behalf of a governance system than it receives in return without another source of energy will eventually die. Behaving this way is heavily suppressed by natural selection. Thus we can say the probability of an agent doing this is nearly 0.

It’s possible that we only want a temporary governance system. In that case, it’s fine to consume energy without replenishing it. In this case agents are essentially seeding the governance system with their energy acquired elsewhere. However, the dissolution of a temporary governance system will eventually lead to the same class of problem that encouraged the development of the governance system to begin with. Not only that, but some problems that groups of people face are constant enough to warrant a persistent governance system. Attacks from outside, excessive extraction of resources from the vulnerable, cooperation on significant projects, etc. Hence some more assumptions.

3. Agents will only willingly consistently do work on behalf of a governance system if they acquire more energy or opportunity than they otherwise would in its absence.

4. A persistent governance system is desirable

Given those assumptions, we can extend to some helpful theorems.

1. The policies of a governance system must lead to the acquisition of more energy than is expended to incentivize the processes to be carried out. If it’s merely equal, then there’s no net benefit to the added complexity.

\(\Delta E_{execute\_policy} \lt \Delta E_{acquired\_via\_policy}\)

2. An indefinitely sustainable governance system must provide at least as much energy to its members as they would acquire without it.

\(\Delta E_{acquired\_via\_policy} \gt \sum_{i} \Delta E_{agent\_no\_governance_i}\)

Now, how does this relate to thermodynamics? To see this, first we can restate the previous assumptions and theorems in terms of probability. A governance system has failed when the probability of an agent carrying out its processes is no greater than if the governance system did not exist. In order to increase the probability of an agent carrying out the processes, energy must be expended.

We can model certain configurations of the “society” (i.e. agents, the processes that govern them, and the accessible environment) as providing some anticipated increase in energy to some part of the system. If we imagine the system just shuffling through states randomly, then we can consider the growth of the system as being dependent only on the average amount of energy gained across the states.

However in a society, certain states are coupled to other adjacent states. If an agent discovers and exerts control over a high-energy resource, they can decompose it and transfer parts of it to other agents, or store it in a central hub for later distribution. They may have contracts or processes that need to be filled which make certain transitions much higher probability than others. The particular configuration of the adjacent states is critical for understanding the time evolution of the system.

A governance system is a set of such societal processes which enable redistribution of resources. An optimal governance system from the point of view of thermodynamics would maximize the amount of energy absorbed into the system, and ultimately increasing the number of accessible states the system can achieve. In other words it would attempt to minimize the amount of free energy in the environment.

This exactly corresponds to the optimization problem described by the Free Energy Principle. As such we can model society as engaging in a form of active inference.