The Role of Higher-Dimensional Categories in Foundations of Mathematics and Physics
Understanding Reality Through Mathematics and Physics
Humans strive to comprehend the foundations of information and mathematics, but often find themselves at a loss when trying to grasp the true nature of these concepts. The actual physics of the universe is a stateless system where every entity influences every other entity, including those not yet discovered. This complexity requires us to consider both state-based and stateless systems as orthogonal, with special cases where they intersect.
The Limitations of State-Based Systems
State-based systems, such as those used in information and mathematics, approximate conditions to provide limited predictability, which is very useful in engineering contexts. However, in the realm of science, these systems must account for quantum mechanics and the probabilistic nature of physical interactions. This skewed probability, often represented by phased distributions, accounts for hidden influences within engineering units.
Exploring Infinite Dimensions and Approximations
For a stateless system to be best approximated, an infinite number of state-based dimensions may be necessary. The concept of infinity here is a fudge factor: it allows us to extrapolate beyond reasonable considerations. Despite the precision of mathematical models, they cannot exactly represent the complexity of actual physics, as we cannot fully model how everything interacts with everything else, including currently unknown phenomena like dark matter, dark energy, and the mechanisms of subatomic particles.
Implications for Current Scientific Understanding
Examples such as the decentralized expansion of galaxies, the formation of a flat thermal universe from non-optical foundations, the propagation of light through subatomic interactions, and the mechanisms supporting quantum entanglement underscore the limitations of current scientific models. Theories explaining these phenomena often rely on vague, partial perspectives and are far from absolute truths. The quest for understanding is inherently ongoing and context-dependent.
Artificial Intelligence and Technological Singularity
While humans may not be able to know any absolute truth about the universe, there is hope that artificial intelligence could help bridge this gap. By modeling a stateless system, a potential technological singularity could enable AI to relate to the actual physics and its underpinnings. This raises exciting possibilities for integrating advanced computational techniques with fundamental physical understandings.
Dimensions and Physics
Traditional human models of dimensions, often used in explanations and analogies, do not directly correspond to the stateless nature of actual physics. These models help in relating the perceived dominant features of physics, but their significance is often trivial compared to the vastness of what remains unknown. The true nature of dimensions remains a frontier in both theoretical and applied physics.
Understanding the relationship between higher-dimensional categories and the foundations of mathematics and physics is crucial for advancing scientific knowledge. It pushes us towards a more nuanced and accurate representation of our universe, leading us closer to a deeper understanding of its true nature.