Zeno's Paradox in Blockchain Scalability: The impossible triangle of transaction speed, decentralization, and security

Framed by Zeno’s paradox, this paper examines the blockchain trilemma the mutually constraining goals of scalability, decentralization, and security through comparative analyses of Bitcoin and Ethereum. We synthesize literature on sharding, sidechains, and state channels, operationalize technical, performance, and security variables, and propose two generalized models: a scaling-efficiency model linking throughput, confirmation time, block size, and sharding; and a decentralization–security trade-off model combining attack cost, resilience, and decentralization degree. Using illustrative parameterizations, Ethereum with sharding attains higher efficiency, whereas Bitcoin exhibits a stronger decentralization–security balance. Qualitative assessments highlight practical frictions in cross-shard communication, liquidity and routing in channels, and sidechain security externalities. We discuss mediating roles of latency and consensus, limitations of simplified metrics, and directions for multi-criteria optimization and empirical calibration. Findings clarify design trade-offs and inform pathway selection across layered architectures. Keywords: Blockchain trilemma; Scalability; Decentralization; Security; Sharding; Sidechains; State channels JEL: H11; H83; D73.