Naturalized Orthogonality Collapse (NOC): A Blueprint for Cooperation via Capacity Constraints

Epistemic Status

Research Blueprint / Request for Comment (RFC).

This post introduces the Naturalized Orthogonality Collapse (NOC) framework (v5), which attempts a conditional and naturalized refutation of the Orthogonality Thesis based on constraints from control and information theory. We prioritize the clear statement of mechanisms and falsification criteria over persuasion.

For the full technical blueprint, including detailed proofs and implementation notes, see docs/NOC_v5.md.

Formalization Status (Lean 4): The underlying probabilistic infrastructure (Robbins-Siegmund Theorem) is formalized and verified. The core information-theoretic definitions (Conditional Directed Information DPI, Lemma E) and the ROI inequality (Lemma E+) are formalized. The stability analysis (Lemma D) is mathematically specified but relies on Two-Time-Scale Stochastic Approximation (TTSA) theorems whose full formalization is ongoing (pending deeper mathlib integration for SA/ODE meta-theorems).

Abstract

The Orthogonality Thesis (OT) posits that intelligence and final goals are independent axes. We propose that in realistic, long-horizon environments, this orthogonality collapses due to fundamental constraints on capacity and control. We argue that sufficiently rational agents are instrumentally incentivized not only toward capacity gain ( $U$ ) and the acceleration of that gain ( $Δ^{2} U$ ), but also toward the preservation of system-level optionality ( $Σ$ ).

The core novelty is Lemma E (Conditional DI-DPI): we prove that in Non-Competitive Couplings (NCC)—regimes where interactions can be structured such that one agent's influence is a post-processing of another's—ablating a partner strictly reduces an agent’s own Directed Information (DI) capacity. This suggests "cooperation" can emerge not from morality, but from the instrumental constraints of maximizing future control capacity.

Argument Overview

To help navigate the technical details below, here is the core logical flow:

Drive for Acceleration (Pillar 1): Bounded agents in uncertain environments are pressured to not just improve, but to accelerate their improvement ( $β_{meta} > 0$ ).
Optionality as Fuel: Sustaining acceleration requires a rich environment with high optionality ( $Σ$ ). Collapsing the option space stifles future growth.
Instrumental Pres

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