On using brain-fuck to simulate the emergence of replication
I wrote this post in a response to a podcast on Sean Carol’s Mindscape where he interviewed Blaise Agüera about his paper which purports to show how self-replication can emerge spontaneously from a computationally rich “soup” in the form of simple computer programs written in a low-level programming language called “Brain Fuck”.
I was very taken by this claim in the podcast:
But the idea of doing simulations that in some sense mimic the actual beginning of life is a somewhat understudied field, if I get the impression. 0:12:00.0 BA: Totally. I think it’s never or very rarely, probably not really happened before,
Oh dear. In fact this has been done to death, and not only by the cellular-automata folks, and not only by Stephen Wolfram. For example, see Moshe Sipper’s overview from 2001, and in his actual paper Agüera himself cites models from the 1990s which were based on a programming game called Core Wars which made use of a language called “red code” instead of “brain fuck”.
So there is a long history of this kind “soup” model in Artificial Life (ALife) research. But as any kind of genuine explanation of real world abiogenesis most of it is deeply flawed. Many of these arguments start with simulations of purportedly very simple ingredients that allegedly do not contain the basis of replication, and then voila, after many iterations we are asked to examine the simulation outputs and imagine that they demonstrate spontaneous complexity and evolution; gee, nothing goes in and something comes out.
But in fact, any simulation model is still just a model. If it were not a simplified model of something, then we should skeptical that it can be used to draw useful inferences about anything that cannot be determined by experiments in the actual real world itself. Given, then, that it is a simplified model of reality, we should be very careful to explicitly state the simplifying modelling assumptions. If we do this we see that in fact replication is built in to the brain-fuck model, and not an emergent property.
Let me start my paraphrase the description of the brain-fuck model.
Pairs of individuals are chosen at random from a large population, and undergo a joint interaction whose outcome depends on the combined properties of the pair.
As a result of this interaction the individuals can modify themselves or each other.
Additionally, they are subjected to random mutation.
The modified individuals are then put back into the population.
This process is then repeated many times.
The original paper makes a big deal about the fact that previous Alife models had copying, i.e. replication, already builtin, whereas in his model replication arises via modification. But, mathematically, what is to distinguish replication verses modification with replacement? Let’s rephrase the description of the brain-fuck model without changing its meaning.
Pairs of individuals are chosen at random from a large population, and undergo a joint interaction whose outcome depends on the combined properties of the pair.
As a result of this interaction, the individuals produce a pair of offspring whose combined properties are a function of the joint properties of the original parents. The parents die and are replaced by their offspring.
Offspring are additionally subjected to random mutation.
This process is then repeated over many generations.
Astute readers will recognize this as a variant of a standard evolutionary game-theory (EGT) model. In evolutionary game-theory individuals are typically hard-coded to a discrete strategy or “type”, e.g. “Hawk” or “Dove” or “Cooperator” versus “Defector”. In most EGT models we only have a few (typically two) strategies allowing us to write a simple matrix showing the fitness accruing to each type in every possible joint interactions. This is called the [“payoff matrix”](https://en.wikipedia.org/wiki/Normal-form_game. Moreover, in EGT, the reproductive success of a type is frequency-dependent, because it is the pairwise combination of types which determines reproductive success, and so in a well-mixed population expected fitness depends on the expected probability of encountering another type, which is given by its current fraction in the population (its “frequency”). The interesting thing about EGT models is that fitness and frequency are “coupled”; fitness determines frequency which in turn determines fitness, and this can lead to interesting dynamics, including not only stationary points and attractors but also limit-cycles and chaos.
The brain-fuck model is no different- it is just a matter of the number of strategies. Here the discrete “types” are “tapes”. Instead of just the 2 types in most theoretical EGT models we have S^N where S is the number of possible symbols and N is the length of the tape. When we “execute” the two tapes and replace the original individuals with the modified individuals, we are in fact subjecting the individuals to an evolutionary “game”. For example, analogous to the PD variant of hawk-dove, one tape could be “altruistic” to another tape by overwriting its own contents with the contents of the other tape, or it could be “selfish” by trying to overwrite the other tape with its own contents. It is then interesting to consider whether there is a steady-state, but possibly dynamic equilibrium, in which both of selfish and altruistic tapes survive.
Again, this type of model has a venerable history in the computer-science and ALife literature, in the now (largely obsolete) field of co-evolutionary algorithms. See e.g. - Ficici, S. G., & Pollack, J. B. (1998). Challenges in Coevolutionary Learning: Arms-Race Dynamics, Open-Endedness, and Mediocre Stable States. In Proceedings of the sixth international conference on Artificial life (pp. 238–247).
Hillis, W. D. (1992). Co-evolving parasites improve simulated evolution as an optimization procedure. Physica D: Nonlinear Phenomena, 42(1–3), 228–234.
For further notes see https://sphelps.net/teaching/egt.html