This paper introduces the theory of Material Semantic Systems (MSS): the idea that ancient artifacts functioned as physical information structures performing computation through matter. By synthesizing cognitive archaeology, information theory, materials science, and computer science, this work argues that Bronze Age societies developed sophisticated non-electronic information technologies—including packet-switching amphora networks, cryptographic seals, morphological computation in rope design, and ceramic-based data preservation. Using the “Ancient Post System” of standardized shipping amphorae as the central case study, the paper demonstrates how morphology, material, and spatial placement encoded routing, authentication, and payload data in a manner directly analogous to modern digital infrastructure. The study concludes by showing how these ancient systems anticipate emerging fields such as the Internet of Materials, mechanical neural networks, and physical cryptography.