Positional encodings are fundamental to Transformers, yet explicit methods like RoPE can degrade under length extrapolation and may incur extra arithmetic and memory-access overhead. In this paper, we propose Scoped Position Encoding (ScoPE), a novel framework that reimagines structured sparsity as an intrinsic position encoding mechanism. Instead of relying on explicit arithmetic signals, ScoPE assigns exponentially scaled look-back scopes to attention heads. We theoretically demonstrate that this simple topological constraint transforms multi-head attention into a hierarchical processor, yielding an order awareness horizon that grows exponentially with depth up to the sequence length. Consequently, ScoPE is parameter-free and avoids relying on fragile positional arithmetic. Empirically, it significantly enhances efficiency by masking the majority of attention computations, offering a theoretical 8x reduction in attention FLOPs at long contexts. Extensive evaluations on LLaMA-3-8B architectures reveal that ScoPE achieves superior native length extrapolation and robust retrieval fidelity compared to RoPE, all while substantially reducing training and inference latency. The code is available at https://github.com/oncemoe/ScoPE.