From Floating-Point Precision to Human Perception: Reimagining Approximation as Nature’s Algorithm of Mathematical-Politics and Human---Computing Symbiosis

Floating-point arithmetic is often treated as a minor implementation detail in computer science, yet it profoundly influences how humans model, interpret, and trust digital systems. This study reframes floating-point representation—particularly the IEEE 754 standard—as both a mathematical framework and a cultural artifact that mediates human reasoning un- der uncertainty. Drawing on four decades of research (1985–2025), it traces the evolution of numerical precision across technological, political, and psychological domains. Through comparative analysis of modern programming languages (Python, C/C++, Java, JavaScript, Rust) and a synthesis of cognitive-science literature, this paper argues that approximation is not a computational defect but a natural algorithm—bounded, adaptive, and resilient. By replacing figures with data-driven tables, the work highlights reproducibility, cross-language behavior, and perceptual thresholds that link computation to human cognition. The paper concludes with design pathways for ethical, transparent, and ecologically inspired compu- tation, positioning numerical humility as the foundation of trustworthy human–machine symbiosis.