Discussions of the future trajectory of humanity often focus on the contrast between extreme scenarios, such as extinction vs. a utopian or dystopian future, or light-speed expansion throughout the universe vs. maintaining the status quo. I think this is simplistic, and tends to neglect less salient possibilities of what the future might look like.
In this post, I will develop a more complex framework to describe the future evolution of human civilisation.
First, we need a way to describe the world state at any given point. One could do this in many different ways, but the following dimensions are most relevant:
- The relative power of different value systems: We will describe this using a vector p that sums to 1.
- The degree of cooperation between different value systems (and agents that represent them): We will condense this into a single number c, where 1 corresponds to all agents pursuing a perfect compromise, and 0 corresponds to everyone acting purely in self-interest. (This could be extended to a multi-dimensional model, i.e. a vector that captures all relevant aspects of how different actors / values interact.)
- The overall technological capabilities of civilisation: We model this using a scalar a, where 1 corresponds to a state where every physically possible technology is available (or could easily be made available), and 0 corresponds to a state without any technology. (Again, this could be expanded to a vector that captures many different capabilities.)
- The overall world state can be describe as s = (p,c,a), or s(t) = (p(t), c(t), a(t)) if we consider it as a function of time.
Now, the world state evolves over time as a result of innovation, value drift, influence drift, and other dynamics. We use a vector field1 f(s) = (f_p(s),f_c(s),f_a(s)) to describe the evolution of the world state. That is, if the world state is s(t) at time t, then s(t+1) = s(t) + f(s(t)).
Given this, we can consider the possible asymptotic behaviour of this dynamical system:
- An attractor is a set of numerical values toward which a system tends to evolve, for a wide variety of starting conditions of the system.
- Fixed points (steady states) are the simplest and most plausible attractor.2 The following are plausible fixed points:
- For any value system, there’s a possible fixed point3 where p is the corresponding unit vector, i.e. 1 for that value system and 0 for all others. This is called a singleton – it means that all power is held by that value system. In this case, c does not matter. The parameter a could in principle be any number from 0 to 1.
- Alternatively, p could be a some non-singleton distribution of values. This is often called a multipolar outcome.
- The c = 1 case corresponds to a fully cooperative multipolar outcome. This is in many ways equivalent to a singleton with compromise values.
- For c < 1, the result is a stable not-fully-cooperative multipolar outcome.
- There are broadly three cases for the a parameter:
- a = 0 corresponds to extinction – a state where civilisation does not have any capacity whatsoever to shape the universe. In this case, other parameters don’t matter.
- The one extreme end is “technological maturity”, i.e. any possible technology is available.
- Civilisation could also reach a technological plateau at any level in between these extremes, i.e. 0 < a < 1, and then stagnate at that level.
- In principle, any (non-zero) value of a could go along with any value of c and p, and vice versa. That is, the fixed point could be a technologically advanced non-cooperative multipolar outcome, or a singleton at a low level of capabilities, or a fully cooperative multipolar outcome at a medium level of capabilities, and so on.
- Another possibility is convergence to a limit cycle, where the world state oscillates periodically.
- The cycle could be such that all parameters vary, or a and/or c could be constant and only other parameters vary, or vice versa.
- Attractors can also be more complex (cf. strange attractors).
- Of course, there is no guarantee of convergence to any kind of attractor. An attractor is what you converge to for lots of starting conditions (formally, there is a basin of attraction). But in reality, there is only one starting condition: the way the world actually is, which may not be in any basin of attraction.
- It is also possible that the asymptotic behaviour is like a log function4, or that there is no regularity whatsoever.
- Perhaps some aspects converge, while others don’t (or only at a later stage).
A lot could be said about how likely each of these outcomes is:
- While more complex attractors (limit cycles or strange attractors) may seem to be a mathematical oddity, I don’t see a strong argument for why this couldn’t happen for the evolution of civilisation.
- The a parameter is special in that it tends to increase rather than decrease, except for the possibility of extinction or catastrophe. It doesn’t seem that likely that a will go up and down in a cycle (or a more complex shape), although there is some precedent (cf. “Dark Ages”).
- However, oscillation is not that implausible for values.
- Extreme outcomes, like a future in which any physically possible technology is available, are very salient when thinking about the future. But I think it is actually not implausible that civilisation would get stuck in some local optimum; this depends on how difficult it is to innovate, and what the corresponding incentives are. (There is, however, a wager to assume a technologically advanced future.)
- Some conjectures in cosmology suggest that eventual extinction is inevitable (e.g. heat death of the universe). However, what matters for effective altruists is what happens before that.
- It’s hard to see how a lock-in of values (convergence to a fixed point) could occur in the foreseeable future. It would arguably require a radically different structure of society.
- One could argue that, on a cosmic timescale of millions or billions of years, civilisation is likely to end up in an attractor, simply because that state is stable while persistent random drift (outside of an attractor) isn’t.
- There is, however, no guarantee of convergence. For instance, one may make a similar argument about biological evolution: rather than constant drift, shouldn’t we expect the distribution of animals and plants to converge to some stable equilibrium (or a cycle)? Yet this hasn’t happened over billions of years.5
(Cf. Brian Tomasik’s Will Future Civilization Eventually Achieve Goal Preservation?) - If civilisation will drift indefinitely, or even only for a very long time, then perhaps extinction is all but inevitable, because there will be a dangerous combination of values and technological capabilities at some point. However, this argument is also very abstract, and it’s possible that extinction risk would, despite continuing drift, decrease over time.
- Even if the argument holds, it doesn’t mean that we live in a “Time of Perils”, i.e. that extinction risk is high in the foreseeable future.
- On the other hand, it’s just really hard to go extinct. For instance, biorisk or nuclear war is unlikely to kill everyone, considering remote villages, people on submarines, people who are in the middle of a flight when a catastrophe happens, people on the ISS, and so on.
How can we, given this framework, have a lasting altruistic impact?
- We can model our impact as a small perturbation of the current world state, leading to ripple effects through time (as described by the evolution function f(s)).
- This perturbation could then result in convergence to a different – hopefully better – attractor, compared to the non-perturbed trajectory:
- If there is a singleton, the perturbation could change which values win out.
- The distribution of power (p) in multipolar outcomes could change.
- The perturbation could change whether civilisation ends up with a singleton or a multipolar outcome.
- It could increase or decrease c
- It could increase or decrease a
- Positive-future-oriented EAs tend to prefer a higher a, while suffering reducers tend to prefer a lower a, at least in so far as higher a correlates with (much) larger populations. (This generalises the divergence regarding extinction.)
- Note that many of these possibilities are gradual, which is at odds with the usual conception of a trajectory change as leading in a completely different result. A small perturbation could, depending on the evolution function f, lead to big differences down the line, but this is not obvious either way.
- Lock-in is generally associated with opportunities for exceptionally large impact, but this isn’t necessarily true. For instance, in the case of gradual convergence to an equilibrium or compromise, there may be no unusually effective levers or “phase transitions” in terms of the outcome. (However, such lock-in would still make our influence more predictable compared to indefinite drift.)
- If civilisation never converges to any attractor, then this is not the right way to model our impact. But it is still possible that we have a lasting impact; depending on f, a small perturbation may lead to a) smaller, b) larger, c) equally large differences after more time passes.
- In cases b) and c), our impact is prima facie not smaller than in the case of convergence to an attractor. But it’s harder to have a predictably positive impact.
Footnotes
- Alternatively, we could use a stochastic model.
- Note that not every fixed point is an attractor. See here for an example.
- This is only a fixed point if stable goal preservation is achieved. Depending on how the values are embodied in agents, this may not be easy. Plus, some values may intrinsically disvalue goal preservation, or value continuing change.
- The model parameters are bounded, so it’s not directly comparable. But the rate of change could go like 1/t (the derivative of log), so that there is no convergence.
- However, there are examples of species that changed very little over long timespans.