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The rapid advances in the capabilities of Large Language Models (LLMs) have galvanised public and scientific debates over whether artificial systems might one day be conscious. Prevailing optimism is often grounded in computational functionalism: the assumption that consciousness is determined solely by the right pattern of information processing, independent of the physical substrate. Opposing this, biological naturalism insists that conscious experience is fundamentally dependent on the concrete physical processes of living systems. Despite the centrality of these positions to the artificial consciousness debate, there is currently no coherent framework that explains how biological computation differs from digital computation, and why this difference might matter for consciousness. Here, we argue that the absence of consciousness in artificial systems is not merely due to missing functional organisation but reflects a deeper divide between digital and biological modes of computation and the dynamico-structural dependencies of living organisms. Specifically, we propose that biological systems support conscious processing because they (i) instantiate scale-inseparable, substrate-dependent multiscale processing as a metabolic optimisation strategy, and (ii) alongside discrete computations, they perform continuous-valued computations due to the very nature of the fluidic substrate from which they are composed. These features – scale inseparability and hybrid computations – are not peripheral, but essential to the brain’s mode of computation. In light of these differences, we outline the foundational principles of a biological theory of computation and explain why current artificial intelligence systems are unlikely to replicate conscious processing as it arises in biology.