The pursuit of creating artificial intelligence (AI) mirrors our longstanding fascination with understanding our own intelligence. From the myths of Talos to Aristotelian logic and Heron's inventions, we have sought to replicate the marvels of the mind. While recent advances in AI hold promise, singular approaches often fall short in capturing the essence of intelligence. This paper explores how fundamental principles from biological computation--particularly context-dependent, hierarchical information processing, trial-and-error heuristics, and multi-scale organization--can guide the design of truly intelligent systems. By examining the nuanced mechanisms of biological intelligence, such as top-down causality and adaptive interaction with the environment, we aim to illuminate potential limitations in artificial constructs. Our goal is to provide a framework inspired by biological systems for designing more adaptable and robust artificial intelligent systems.

This paper introduces a category theory-based framework to redefine physical computing in light of advancements in quantum computing and non-standard computing systems. By integrating classical definitions within this broader perspective, the paper rigorously recontextualizes what constitutes physical computing devices and processes. It demonstrates how the compositional nature and relational structures of physical computing systems can be coherently formalized using category theory. This approach not only encapsulates recent formalisms in physical computing but also offers a structured method to explore the dynamic interactions within these systems. Keywords: Computation, Computability, Physical Computation, Category Theory 1. Introduction Roots of computability trace back to Leibniz, who invented a mechanical calculator for automating the evaluation of mathematical expressions [23, 20, 9]. At the Paris international conference for mathematics, David Hilbert extended Leibniz's fascination by proposing the Entscheidungsproblem (the decision problem), questioning the existence of an "effective procedure" to determine the truth or falsity of mathematical statements [29]. Alan Turing and Alonso Church independently demonstrated the impossibility of resolving the Entscheidungsproblem. This discovery, known as the "Church-Turing thesis", posited that no effective procedure (or "algorithm" in contemporary terms) can Present address: McGovern Institute for Brain Research, MIT, Cambridge, 02139, MA, USA Prior to the emergence of algorithm(s), procedural calculation through a finite number of exact, finite instructions was labeled "effective procedure (or effective calculation).

Our fascination with intelligent machines goes back to ancient times with the mythical automaton Talos, Aristotle's mode of mechanical thought (syllogism) and Heron of Alexandria's mechanical machines. However, the quest for Artificial General Intelligence (AGI) has been troubled with repeated failures. Recently, there has been a shift towards bio-inspired software and hardware, but their singular design focus makes them inefficient in achieving AGI. Which set of requirements have to be met in the design of AGI? What are the limits in the design of the artificial? A careful examination of computation in biological systems suggests that evolutionary tinkering of contextual processing of information enabled by a hierarchical architecture is key to building AGI.