aasb-ch02-inside-causality

Chapter 2: Embeddedness and Causality

Premises 1 and 2

Premise 1: Embeddedness

Statement: The observer is a subsystem of the universe, with only local access to state.

Definition

Let U be the universe (the total system). Let O ⊂ U be an observer (a proper subsystem). The embeddedness constraint states:

Proper containment: O ≠ U. The observer is strictly smaller than the whole.
Local access: O can only directly access state within its boundary ∂O.
Mediated access: Information about U \ O (the complement) must cross ∂O to reach O.

Formal Consequences

From proper containment:

There exist states of U not directly accessible to O
O's representation of U is necessarily incomplete

From local access:

O's inputs are boundary-crossing signals, not global state
O's outputs affect only what its boundary contacts

From mediated access:

Information about distant regions arrives via channels
Channels have bandwidth limits and propagation delays

Why No One Argues

Any claim to observe "the whole system from outside" raises: where is the observer standing? If outside U, they observe something other than U. If inside U, they satisfy the constraint. There is no third position.

The observer is always embedded. The map is always inside the territory it maps.

Interlude I: Echoes of Embeddedness

The same constraint, different vocabularies

In Physics

Generalized observer models treat observation as boundary-crossing input that updates internal record, shaping subsequent responses. The observer:

Has a boundary (inside vs outside)
Receives signals that cross the boundary
Updates internal state based on those signals
Generates outputs that cross the boundary outward

This is substrate-independent. A photoreceptor, a thermometer, a scientific instrument, a conscious mind—all satisfy the same formal structure.

In Markets

No market participant sees the whole market. Each trader:

Observes local price signals
Has private information about their own position
Receives delayed information about others' actions
Makes decisions based on incomplete, locally-available data

The efficient market hypothesis is a claim about what happens when many embedded observers each act on local information. Prices aggregate distributed knowledge precisely because no one has global access.

Insider trading laws exist because locality matters. If someone could access information before it propagated, the game breaks. The regulations enforce what should be natural: you're inside the system.

In Theology

The Christian doctrine of incarnation is a claim about embeddedness: God enters the system. Not observing from outside, but participating from within, subject to locality constraints.

"The Word became flesh and dwelt among us" is a statement about topology. The infinite becomes local. The unbounded accepts bounds.

In John 10:30, "I and the Father are one"—the observer and the observed system share structure. The part and the whole are not separate kinds. The map is inside the territory, yet the map can be accurate, because both are made of the same stuff.

Premise 2: Causality

Statement: State updates respect a partial order. Information propagates along causal structure.

Definition

Let events in U be partially ordered by ≤ (causally precedes or equals). The causality constraint states:

Partial order: ≤ is reflexive, antisymmetric, and transitive
Information flow: If event A causally influences event B, then A ≤ B
No backward signaling: If A ≤ B and B ≤ A, then A = B (antisymmetry implies no causal loops across distinct events)

Formal Consequences

From partial order:

Not all events are comparable (spacelike separation exists)
Causal structure defines what can influence what

From information flow:

Signals propagate forward along causal chains
Effects cannot precede their causes

From no backward signaling:

You cannot send information to your own past
Paradoxes (grandfather, bootstrap) are structurally excluded

Why No One Argues

Every attempt to violate causality generates paradoxes. Physics confirms information cannot travel faster than light. Thermodynamics gives time an arrow. Causality survives across quantum mechanics, relativity, and thermodynamics.

This is the weakest possible claim about time: causes come before effects. Deny it and nothing is predictable.

Interlude II: Echoes of Causality

The same constraint, different vocabularies

In Control Theory

Theorem: Agency is control theory applied to ontology.

Control Element	Ontological Mapping
Reference Signal	"What state should I be in?"
Sensor	"What state am I actually in?"
Error Signal	Reference − Actual
Actuator	Mechanism that acts to reduce the gap
Plant	System being controlled (including self)

The Anterior Cingulate Cortex generates the error signal—detecting mismatch between expectation and actuality. The experience of "witnessing" is what it feels like to be a control loop monitoring itself.

Control loops respect causality: sense → compute → act. The sensing must precede the acting. There is no acausal control.

In Supply Chains

Supply chains are causal graphs. Raw materials → processing → manufacturing → distribution → retail → consumer. Each node:

Sees upstream through orders and contracts
Sees downstream through demand signals
Cannot skip the causal chain

The bullwhip effect—small demand fluctuations amplifying into large supply swings—is causality plus delay. Information propagates at finite speed. Each node reacts to signals already stale.

In Theology

Karma is causality over long horizons. Actions have consequences. Consequences propagate. You cannot act and escape the causal chain.

This isn't metaphysics about reincarnation. At core, it's the observation that causality doesn't stop at convenient boundaries. If causes precede effects, and effects become causes, then every action participates in a chain extending beyond local observation.

Providence—divine action in history—works through causal chains, not around them. Miracles, in most sophisticated theology, are not violations of causality but unexpected causal paths. The burning bush burns but is not consumed; the effect is surprising, not acausal.

The Half-Derivation

From these two premises alone:

If embedded: Your state is incomplete relative to the whole. Gaps are structural.

If causal: You cannot act on information you haven't received. Lag between events and knowledge of events is guaranteed.

Together: Coherent action must begin by detecting a gap (something needed but not possessed), then addressing the system to retrieve it. You cannot act on what you don't have. You must fetch.

This is the first half of the loop: PAUSE → FETCH

The system pauses (recognizes incompleteness), then fetches (queries along causal channels).

Chapter 3 completes the derivation.

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