On the political history of the Milky-Way Galaxy

This is a slightly more technical write up of the work in this blog post: Politics in the milky way.

Summary

Robin Hanson and colleagues recently proposed that “Grabby Aliens” could be the reason why humanity seems to have arrived cosmically early. In the Grabby alien model there is no conflict between aliens. I decided to create a simple cellular automata model where innovation, colonisation and cultural drift are all possible but faster than light travel is still impossible. I assume that meaningful innovation becomes exponentially harder as time progresses. I discuss the possible states that can occur in such a model and the limit state at infinite time. In this model, the galaxy tends towards a divided state where technology has stagnated at some level above our own which I call a tapestry state.

Assumptions:

1. The spread of alien civilisations can be captured using a cellular automata model.

In the model I have created, the rules governing the evolution of a unit depend only on the states of its 4 closest neighbours and itself. As long as the speed of light remains a constraint for advanced civilisations this assumption that interactions are local is valid.

2. The expansion of alien civilisations and the spread of new ideas or technology happens at the same, universally constant rate which is some large fraction of the speed of light.

Given the discretisation used in the simulation below, the spatial scale of each unit is 500 by 500 light years. Each unit would therefore contain O(100,000) stars. I assume it takes 750 years for changes to propagate through a unit of this size. Since the diagonal length of this unit is about 700 ly, this propagation speed is fast. For a developed grabby civilisation any large fraction of the speed of light should be plausible.

3. New alien civilisations have some probability of appearing in any empty unit in any 750 year timespan.

The prediction of the likelihood of intelligent life emerging is an extremely tricky problem. Since new alien civilisations are not allowed to emerge within held territory, the problem reduces to whether civilisations emerge in the time between the first civilisation appearing and that civilisation spreading throughout the galaxy. We call this probability \(p_a\). If \(p_a\) is large then many civilisations will emerge before any one has saturated the galaxy, if it is low then few or none will have emerged.

4. Innovation slows with time.

Counter to the trends of the current era in human history, I propose that on the longest timescales meaningful innovation becomes increasingly rare. The speed of communication may be taken as an example. If the speed of light remains an upper limit on communication speed, with similar constraints from physics on the density of information, then technology can only asymptote towards these upper limits.

The rate that this slowdown will occur at is impossible to predict. In the current model, the probability that a major innovation will happen in any unit starts at 1/1000 and is inversely proportional to time. The probability of innovation in any unit is \(p_i\) and decreases with time.

5. There is some fixed likelihood that cultural drift will occur in a region.

I assume there is some probability \(p_d\) that a unit undergoes revolution or sufficient cultural drift to create a new faction. This probability is also extremely difficult to predict. It will be considered low if civilisations remain coherent in their expansion phase and high otherwise.

6. When two cultures meet, the technologically superior culture will either share their technology or dominate the territory of the other culture.

The probability that a civilisation will choose war or peace with its neighbours is hard to predict, I will denote the probability of war \(p_w\). It is considered low if territory if rarely conquered and high if technology is almost never shared between different factions.

Possible states:

The model has 4 key variables. \(p_a\) (the probability an alien civilisation will appear in the time it takes for a civilisation to spread across the galaxy), \(p_i\) (the probability of innovation), \(p_d\) (the probability of cultural drift) and \(p_w\) (the probability a civilisation will colonise its neighbour rather than peacefully share its technology). This gives 16 possibilities to discuss. However, we will only have to discuss a few of these as many are qualitatively the same and their limit states are all identical.

The limit case of this model is independent of \(p_w\), \(p_d\) or \(p_i\) provided they are each non-zero and the decay in innovation is non-zero. In sufficient time \(p_i\) will become negligible. This will mean cultural drift will be uncorrectable. Since technology level will be uniform war becomes irrelevant and in the limit every resolved unit will belong to a distinct faction. I call this the tapestry state.

Case 1:

Probability of cultural drift is high.

In this case the tapestry state is reached almost as soon as life reaches any region in the universe.

Case 2:

Low probability of cultural drift and civilisations are mostly peaceful. This is Hanson's grabby aliens universe.

Since war is so rare the probability of innovation is irrelevant. Innovation is almost always instantly shared and so has little effect on the political/cultural landscape. If \(p_a\) is high then something resembling the tapestry state will form quite quickly. If \(p_a\) is low then a few cultures will dominate early history before the galaxy tends to the tapestry state.

Case 3:

Low probability of cultural drift and civilisations are mostly warlike.

If \(p_a\) is low then only a single culture will dominate the early history of the galaxy.

If \(p_a\) is high then the early history is characterised by the struggle between alien civilisations. The higher the rate of innovation the more stable this conflict state is, since innovations that lead to territorial gains for one side will quickly be matched by the opposition. As the probability of innovation decreases this state will become unstable and rivals will either eliminate each other or make peace.

Model details:

I discretise the Galaxy into a circle of radius 100 units. The model is self-similar so qualitative conclusions at this resolution will apply to higher resolution runs. There is a small probability for a “dead” unit to become host to a new civilisation. This civilisation will receive a random colour (a float greater than 0 and less than 1) which will parametrise its identity. The aliens also receive an initial technology score between 0 and 1. This value can only be increased by an innovation event. There is a small chance that diminishes linearly over time that a paradigm shifting breakthrough will occur at some occupied unit, increasing the technology score of that unit above its peers. This model then assumes that interactions between civilisations will all be reminiscent of the colonisation of the new world. The technologically superior civilisation will have the option to either wipe out the existing civilisation or share their technology (intentionally or not). The chance that technology is shared is proportional to how close the colours representing the two civilisations are (meant to represent ideological or perhaps physiological closeness).

This is implemented by each unit randomly choosing a neighbour at each timestep. If the neighbour has a higher technological level the unit will either be replaced or gain the technology. If the technological level is lower nothing will happen to the unit.

The last system is cultural drift. There is a small probability that a unit within an empire will randomly change colour while retaining the same level of technology, representing revolution or prolonged isolation.

The code can be found on Github and run in your browser using this binder.

Conclusions:

If the assumptions made here are correct, regardless of the specific values for the four probabilities that govern transient evolution, the late political state of the galaxy will be a divided one where technology has stagnated at some level above our own.

The early political evolution is heavily dependent on the probability of cultural drift, conflict between civilisations and the probability of grabby alien life.

Hanson, R., Martin, D., McCarter, C., & Paulson, J. (2021). If Loud Aliens Explain Human Earliness, Quiet Aliens Are Also Rare. The Astrophysical Journal, 922(2), 182.