Mathematics 🔐 Opening

On the moral geometry of power (δ) and legal capacity(∆)

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Abstract

This paper develops a symbolic and mathematical interpretation of legal power (δ) and

juridical capacity (∆), proposing a dynamic equation of moral geometry: 1 = 2 = 3 = δ = ∆.

Through comparative reasoning inspired by Al Khwarizmi and civil law theory, the

author defines power as the relational emergence that binds capacities, forming a third

juridical entity. The study suggests that moral regimes—domination, equilibrium, and

altruism—represent distinct geometric structures of social interaction, where power can

either dominate, balance, or dissolve itself.

I. Historical Background

The term, derived from Latin potestas or potere, itself translating the Greek kratos

(κρaτος), finds its roots deep in the history of civilizations. Among the Egyptians, as early

as 3150 B.C., power was embodied within a cosmic and juridical order. Understanding the

notion of power requires examining its origin in the individual and then its evolution within

human relations between subject A and subject B.

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