Re-discussion: Using Euler's Formula to Examine the ReformDirections of Social Systems in the New Era

Summary: Euler’s Formula as the Ultimate Criterion for Institutional Reform in the Nuclear AgeThis paper argues that Euler’s formula (e^{i\theta}=\cos\theta + i\sin\theta) provides more than a mathematical metaphor—it offers a geometric blueprint for sustainable social systems. In an era where nuclear weapons have permanently eliminated war as a redistributive reset mechanism, humanity must design institutions that achieve endogenous stability without relying on civilizational collapse.The author derives three core institutional prerequisites from the geometry of the complex plane. Any viable system for the new era must satisfy all three:1. Flowing without accumulation – Maintain full economic liquidity while preventing wealth hoarding, capital concentration, and the Matthew Effect.2. Spinning without rupture – Replace physical spatial expansion (which hits planetary limits) with iterative growth along the time axis, escaping involution and systemic collapse.3. Orthogonal checks and balances – Abandon the single monetary real-axis measurement. A sustainable order requires two orthogonal, mutually restraining dimensions: a real axis for market transactions and an imaginary axis for institutional constraints (e.g., social credits, behavioral rights).Traditional systems fail precisely because they violate these geometric constraints. Liberalism retains only the monetary real axis (violating propositions 1 and 3); Keynesian interventionism suppresses liquidity and spatial expansion (violating 1 and 2); egalitarian arrangements freeze time‑axis iteration (violating 2).The proposed solution is a dual‑track institution aligned with Euler’s two axes:· Real axis (currency) – Spontaneous competitive order, external wealth creation, cross‑border flows, and technological innovation.· Imaginary axis (symbiosis points) – Constructed order for internal equilibrium, preventing wealth monopoly, hereditary stratification, and capital polarization, while unlocking infinite civilizational progress along the time axis.This two‑dimensional orthogonal framework enables what history has never achieved: spontaneous market vitality without social chaos, equitable distribution without rigidity, free capital flow without hoarding, and sustained growth without collapse. War as a redistributive tool is obsolete; Euler’s geometry becomes the ultimate test for all institutional reforms in the nuclear age.