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Explore a thought-provoking lecture on the limitations of current AI and neuroscience in explaining ancient forms of spatial reasoning and mathematical consciousness. Delve into the evolutionary origins and diverse functions of consciousness across species, from portia spiders to humans. Examine the importance of understanding possibilities, constraints, and implications in spatial competences and mathematical reasoning. Investigate how evolution's repeated discoveries of complex mathematical structures have led to increasingly sophisticated species with complex needs and behaviors. Learn about the layered control requirements in biological mechanisms and their role in supporting higher-level possibilities and necessities. Discover the connections between these concepts and Immanuel Kant's observations on mathematical consciousness, essential for creative science, engineering, and everyday actions. Compare the power of spatial mathematical reasoning to modern logic and statistical approaches, and consider the potential need for new models of computation, such as sub-neural chemistry-based systems, to better explain these ancient cognitive achievements.