Dimensionality increase for error correction in the interaction between information space and the physical world

TL;DR

This paper proposes a mathematical framework where the physical world and information space are modeled as submanifolds within infinite-dimensional Hilbert spaces, suggesting that increasing dimensionality can aid in error correction and solution existence.

Contribution

It introduces a novel theoretical model embedding physical and informational submanifolds into higher-dimensional Hilbert spaces, providing an existence theorem for deforming submanifolds to solve problems.

Findings

Submanifolds can be deformed outside their original space with enough parameters.

The model offers a new perspective on error correction via dimensionality increase.

Theoretical foundation for embedding finite models into higher-dimensional spaces.

Abstract

The evolution of human intelligence led to the huge amount of data in the information space. Accessing and processing this data helps in finding solutions to applied problems based on finite-dimensional models. We argue, that formally, such a mathematical model can be embedded into a higher-dimensional model inside of which a desired solution will exist. In our model, the physical world and the information space are submanifolds of infinite-dimensional Hilbert spaces, and the processes, including information transmission, are maps between the submanifolds of the physical world or of the information space. We discuss how our perspective fits in the context of existing literature. Our theorem states that a submanifold in the parameter space of the physical world can be deformed to a target submanifold outside that space, with an appropriate count of the deformation parameters. We interpret this assertion as an existence result for a class of problems and we discuss further steps.