A Method for Constructing Higher-Dimensional Theories Using AI

A Method for Constructing Higher-Dimensional Theories Using AI

1. Introduction

This paper proposes a hypothetical framework based on mathematical principles regarding the possibility of constructing higher-dimensional theories using AI. We focus on the inherent cognitive limitations of humans—particularly in terms of the number of dimensions they can intuitively understand—and discuss a method by which higher-dimensional theoretical structures may be constructed and verified using AI as an inference engine.

2. Overview

Humans find it difficult to grasp higher-dimensional structures intuitively and are often only able to perceive them as multiple, independent lower-dimensional theories. However, if these lower-dimensional theories can be organized orthogonally and then unified through AI, it becomes theoretically possible to reconstruct an approximation of the higher-dimensional theory. This paper organizes this process mathematically.

3. The Difficulty of Higher-Dimensional Inference for Humans

The human cognitive system is optimized for the perception of three spatial dimensions plus one temporal dimension (a total of four dimensions), and even abstract manipulation beyond 5–7 dimensions is known to be difficult (e.g., Miller's Law). Beyond this range, visualization, causal structuring, and intuitive manipulation become extremely challenging.

s such, theories that span multiple fields—such as theoretical physics or consciousness studies—often present fundamental challenges to direct human manipulation due to their inherently higher-dimensional nature.

4. Constructing Higher-Dimensional Theories Through Projection

Mathematically, an N-dimensional structure ( S ) can be described using a group of orthogonal projection theories ( {T_1, T_2, ..., T_c} ), each of dimension ( N - c ). Each theory ( T_i ) is semantically independent and captures a distinct partial structure of ( S ).

To integrate these, the projection group must be mutually orthogonal and sufficiently numerous. If an inference engine presented with multiple such projections can generate and validate a consistent structure ( ilde{S} ) in the N-dimensional space, then an approximate reconstruction of ( S ) becomes theoretically possible.

5. AI's Inference Capabilities and the Need for Constraints

Modern large language models (LLMs) and structural inference engines can handle tens of thousands of dimensional vectors and possess the ability to perform abstract reasoning beyond human intuition. However, when the provided structure or context is vague, AI tends to over-generalize, leading to a loss of precision.

Therefore, by providing multiple explicitly structured lower-dimensional theories, AI can be guided to evaluate their consistency and search for a unified higher-dimensional structure. In terms of information theory, this corresponds to collapsing excessive degrees of freedom into a direction defined by "semantic constraints."

6. Conclusion

Constructing higher-dimensional theories poses challenges beyond human cognitive limits. However, by designing orthogonal lower-dimensional theory groups and using AI inference engines to integrate and verify them, approximate reconstructions become theoretically possible. The framework proposed herein has potential applications in highly abstract domains such as theoretical physics, consciousness studies, and ethics modeling.

Thus, AI is no longer merely a computational aid but can be positioned as an "external cognitive space" for handling higher-dimensional structures. Future research may involve concrete structural applications, optimization of inference algorithms, and theoretical formalization of projection groups.