World model¶

Anoma operates with the fundamental conceptual frame of agents in a world who may often seek to share their observations of the world, pool their storage and computational resources, and coordinate their actions taken within the world for mutually preferred effect.

Agents¶

Agent is a primary notion that aims to unify the notions of process in the distributed systems literature, organism in the theoretical biology literature (e.g. active inference), and the subject of experience as articulated by Kant.

An agent is a corporeal being possessed of memory, the ability to perform computation, internal unity, and transcendental freedom. To spell out each of these in turn:

• An agent is a corporeal being in the sense of being possessed of a physical form and a boundary which delineates that which is part of the agent from that which is not. That which is not the agent is the world. That which is part of the agent is not revealed to the world except through messages sent outwards.
• An agent is possessed of memory which can store the agent's own history of experience, computations derived from it, or any other data.
• An agent is possessed of the ability to perform arbitrary computation. For the time being, we assume that this computation is classical in nature, but the notion could be extended to quantum computation in the future.
• An agent is possessed of internal unity, in the sense that whatever parts compose the agent act in unison and may be modelled both internally and externally as a unified whole.
• An agent is possessed of transcendental freedom in the Kantian sense, in that the agent can originate an action purely from itself, and that in response to certain inputs, the agent can always do otherwise. We furthermore assume that this self-origination of action is sufficient to provide a random oracle whose output is not predictable.

In general, Anoma does not assume that agent identity is fixed and temporally invariant. Agents may split themselves, merge with or absorb other agents, or otherwise alter their boundaries continuously. However, reasoning about the evolution of the system over time will require the assumption that the information known to the agents at the start of the period in question is in some form preserved.

Agents may be composed of many parts which may be variously of physical or biological natures. Roughly, Anoma understands the identity of an agent on the basis of unity of corporeality, memory, computation, and freedom of action. For example, a person and their smartphone or personal computer held in hand would together comprise a singular agent in the sense defined here, while two separate people or a person and a computer across the world would not.

World¶

An agent always exists in a world. The world, in some sense, is simply the sum totality of that which is not the agent. The world, we assume, is generally of interest to agents: they may seek information from it, send information into it, depend on physical resources from it for their continued survival, and simply care about it for transcendental reasons of their own. It is only through the world that one agent can communicate with another, and the distinction in the identity of the other from the rest of the world must simply be inferred.

Observations & actions¶

Agents can interact with the world in two ways: by taking observations of it, and by performing actions within it. Observations can be understood as messages received from the world, while actions can be understood as messages sent to it.

Observations may be directed by a particular conceptualization of phenomena, in which case they are called measurements, and accompanied by a name of semantic significance to the agent taking the measurement, or undirected, in which case they are called perceptions and unaccompanied. Observations may be initiated by the agent itself or initiated by the world.

Actions, similarly, may be directed by a particular conceptualization of the agent-world boundary, in which case they are accompanied by a name of semantic significance to the agent taking the action, or undirected, in which case they are unaccompanied.

Causal structure¶

In general, the world which the agents inhabit is assumed to have causal structure which is unknown but connected and agent-invariant, i.e.:

• The world is connected: for at least some actions, the probability distribution of at least one other agent's future observations, conditioned on an agent's action, is not equal to the probability distribution not so conditioned. In other words, we assume that actions have effects. In a world where this does not hold, coordination would be pointless.
• The world is agent-invariant: - Agents observing the world in the same way (the definition of this is left a bit vague, but suppose e.g. measuring the temperature at the same time in the same place) will receive the same result. - Agents taking actions in the same way (the definition of this is left a bit vague, but suppose e.g. setting the same thermostat to the same level) will result in the same effects.

In order for the agents to build up a model of the behaviour of the world over time which will be useful in predicting the results of future actions, the world's causal structure must also be invariant under spatial and temporal translation (as, say, the known laws of physics are).