CARPE GRADUM Lagom, Curiosity, and the Geometry of Human Development

This paper proposes a geometric framework for understanding progress and decline in human learning and development. The framework's central proposition is that the path of any learning system — individual or civilizational — is more precisely described as an asymptotic step function than as a continuous linear progression. The hyperbola — two mirrored arms opening eastward along the axis of time from a shared origin — is bounded above by an asymptote of perfection and below by an asymptote of abysmal decline; neither is ever reached. Within this framework, the paper argues for a critical and underexamined geometric property: the steps are non-uniform. At the lower reaches, progress is frequent and the jumps dramatic. As the ascending arm approaches the perfection asymptote, the plateaus lengthen and the jumps diminish. This geometric observation, the paper argues, has direct implications for the psychology of expertise, the failure of prodigies, and the structure of learning itself — implications that invite empirical investigation across developmental psychology, education research, and cognitive neuroscience. The paper further proposes that the Swedish concept of lagom — not moderation as a statistical range but optimization toward a precise point — provides a more adequate governing principle for describing healthy ascent than the conventional concept of moderation. The plateau/eureka relationship is advanced as the fundamental mechanism of genuine learning: consolidation precedes the jump; the jump cannot be forced or scheduled but arrives when preparation is complete. The paper proposes that several engines drive ascent: striving, which includes adaptive response to changing conditions; play, which sustains the curiosity that makes striving generative; and suffering, which can act as a powerful motivator to change adverse conditions. Dementia is examined as the philosophical limiting case of the model: the paper argues that dementia is better understood not as descent to the abysmal asymptote but as the flattening of the hyperbola to a line — the loss of curvature itself, not merely the loss of position. The temporal framework of Veritas Opportunus (Collins, 2025) is proposed as a candidate mechanism for the temporal architecture the model requires, though the connection between the geometric framework advanced here and the neurological architecture of the VO window invites further empirical and philosophical development. The paper concludes by drawing out implications for educational philosophy. Where the paper makes arguments, it does so on philosophical and conceptual grounds. Where it advances hypotheses, it does so explicitly, inviting the empirical investigation they require.