"time_

abstract

learning algorithms assume meaningful input-state, context, relational structure. a continuous stream provides none of this. before a system can learn from time, it must translate time into state. we argue that the central obstacle to embodied continual learning is not inadequate optimization but inadequate translation: credit assignment is ill-posed until temporal history has been rendered into a representation where responsibility is locally computable. we characterize the constraints on temporal translation — causal, bounded, continuous, locally interpretable — and show they admit essentially one solution class among linear, time-invariant, finite-state summaries: exponentially decaying measurements at geometrically spaced timescales. when spaced by the golden ratio to maximize incommensurability, this decomposition provides a minimal temporal language in which the past is present and credit assignment becomes tractable. we instantiate this in the spectral online machine architecture (soma), demonstrating continuous adaptation without catastrophic forgetting, under fixed resources, with no replay buffer and no sequence storage, reaching 1.87 bits per byte under streaming constraints with bounded memory. the architecture satisfies a requirement that theories of consciousness increasingly emphasize: temporal integration must be intrinsic to the system's state, not externalized as retrievable data. a system with translated time is its history; it does not merely have access to it. the failure of continual learning is not a failure of learning rules. it is a failure to give them a language for time.