A blue point of view
A couple nights ago I made the unfortunate mistake of reading about The Blue Eyed Islanders puzzle (though I am fond of this less violent version). It kept me up all night. I understood some of the logic but there was one point in particular that I couldn't work out. It got to the point where the problem was threatening to sink me into blathering madness the rest of the next day, and since it was in fact a lovely weekend, that just wouldn’t do. I finally bit the bullet and worked through my concerns with Claude (Opus 4.7) and then went on a lovely bike/run.
I suggest that before reading this post any further you pause to read at least the basic formulation of the problem. I will insert the art for this essay here to mask spoilers below.
Image generated by GPT Image 2, 2026.
Welcome back. (I hope it has been minutes or at least hours rather than days.)
For me, the induction steps that led to the solution were not the main challenge. Rather I was having difficulty understanding the part played by the visitor’s faux pas. One of Tao's comments I found particularly vexing:
It is probably the n=3 case (three blue-eyed people) which causes the first major conceptual difficulty, in which common knowledge separates from both first-order and second-order knowledge. As pointed out above, in this case the three blue-eyed people all know that there is at least one blue-eyed person, and they know that everyone else knows this also… but they don’t know that everyone else knows that everyone else knows this, until the foreigner speaks.
For the n=3 case, if everyone knows that everyone knows that there is at least one person with blue eyes, then why does anything change when an external person says that out loud?
Perhaps this was more evident to you than me, but this is the part that took me working with Claude to understand. This is also where we find connections to HCAI and cybernetics in the guise of perspective-taking, or rather, chains of perspective-takings.
Remember before we dive in that individuals leave the island if people can be sure of their own eye color.
Now then, let's say Alex, Bob, and Candice all have blue eyes. We will be Alex. As Alex, we do not know our eye color but we do see that Bob and Candice have blue eyes, so we know that the proposition, "at least one person has blue eyes" (call this proposition P) is true. Now as Alex we project ourselves into Bob. Alex-reasoning-as-Bob looks at Alex and sees...fog. That's because we are Alex projecting into Bob and so we only have Alex's knowledge about the world, and Alex does not know his own eye color. Now let’s start exploring branching possibilities. Let's pick for now the possible branch in which Alex-reasoning-as-Bob sees Alex as having brown eyes. We'll call this version of Bob Bob-Alex/brown. Still, we know that Bob-Alex/brown will see Candice as having blue eyes (because Alex knows this for a fact!), so he also agrees with P. Now we go one step further and project from Bob-Alex/brown to Candice. Bob-Alex/brown has the same problem as Alex—he cannot know his own eye color—and again here we choose the brown eye branch. Therefore now we are Candice-Bob/brown-Alex/brown. That is, we are now Alex projecting himself into a version of Bob that sees Alex as having brown eyes and who is projecting himself into a version of Candice who sees Bob as having brown eyes. From Candice-Bob/brown-Alex/brown’s perspective, Alex and Bob both have brown eyes: those are the choices we've made on this branch, and crucially, choices we cannot rule out. But Candice of course doesn't know her own eye color. So then Candice-Bob/brown-Alex/brown has to assume it is possible that she, and thus everyone, has brown eyes, and therefore in this particular branch of the tree of perspective-taking possibilities, P is not true! This branch is in fact the bulwark that stops the group from starting the chain of inductive steps that leads to the blue eyed folks having certainty of their own eye color (and thus leaving the island). But as soon as an outsider verifies that at least one person has blue eyes, all possible brown-brown-brown branches disappear in a poof.
Phew.
From perspective-taking to agent design
There are many places we could go from here. This chain-of-perspectives reasoning of course derives from Theory of Mind. This cognitive capacity is usually associated with mechanisms that act to prevent egocentrism and promote empathy and better communication (though it can have less prosocial impacts as well, which Liu Cixin famously explores with the concept of “chains-of-suspicion” in his book The Dark Forest).
But what struck me most about this problem and the ensuing logic of its solution was the unreality of both the mise en scene, the relentless perspective hopping, and the ruthless adherence to logic over common sense. Humans would likely not follow a many-hopped logic but instead dismiss concerns as soon as it became common sense to do so (e.g., once it was clear that everyone knows that there are blue eyed people, folks would shrug and move on with their lives). They would also (unless they are literally imprisoned) be unlikely to act exclusively as lone agents: they would share information (even if told not to do so, they would find a black market method).
This led me to worry that agents in AI system design may be as similarly "alien" in their thought processes as the islanders. And while we probably do want agents to use this kind of ruthless inhuman logic in some cases, we also want them to be properly empathetic with humans and understand that they are likely not to do so. We may also want them to share information rather than hoard it.
When he derived the Viable System Model (VSM), Stafford Beer recognized that recursive coordination requires recursive viability: each subsystem must itself be a viable system, with its own regulators and feedback loops. He was explicit that the VSM is not a command hierarchy but a recursive containment structure with bidirectional flows, control distributed across levels rather than concentrated at the top. This model stands in contrast to the way that many agentic systems are designed now: a rather rigid hierarchy in which an orchestrator manages sub-agents. We might instead envision architectures that give agents more agency at each level of control, and include shared spaces to push information up, down, and across the agent graph. This mechanism would also allow agents to regularly update their shared understanding of the peculiarities of the people or communities they are modeling or interacting with.
This is the space stigmergic blackboard architectures are exploring (the term stigmergy comes from biology: the study of how individual agents [e.g., ants] modify their environment with traces to coordinate with other agents). Salemi et al. (2025) take aim at the master-slave paradigm in current agent frameworks in which subordinate agents are forced to execute instructions from a coordinator even when they hold better information, and a central controller required to maintain accurate models of every agent's capabilities, which is rarely realistic when agents have only partial or shifting knowledge. Their alternative is to have the coordinator post a request on a shared blackboard, with agents self-selecting based on what they can contribute. They report improvements of 13–57% on their data discovery benchmarks over orchestrator baselines.
Han and Zhang (2025) generalize the pattern, building a control unit, a blackboard split into public and private spaces, and a roster of agents with roles like planner, decider, critic, cleaner, and conflict-resolver, all communicating through the shared workspace. Gao et al.’s AutoScientists agents are related but more decentralized, interpreting a shared experimental state, self-organizing into teams around promising hypotheses, critiquing proposals, and running experiments while sharing both successes and failures so the system as a whole avoids redundant exploration. Similarly, the open-source Stigmergic Blackboard Protocol (SBP) is a coordination mechanism for AI agents that work together with two layers: ephemeral "pheromones" that decay over time, and durable traces that persist as institutional memory. A related line of work on reflective modeling, in which agents watch other agents (see Wang et al. 2024 and Storf et al. 2026), fits alongside the shared blackboard pattern since a shared workspace gives these monitoring agents something to watch.
Takeaway
Stigmergic blackboard architectures show how we can leverage some of the ways humans coordinate to design systems that have more regulatory feedback, share more knowledge to deepen understanding, and ultimately help agents act in a way that is overall more humane.
That said, I do think the main takeaway of this article is: never read logic puzzles when you are trying to go to sleep.