Information, Boundary, and Reality:
A Mathematical Exploration
of the Holographic Principle
with Philosophical Implications
This is the home page for my current research project, a senior thesis that will investigate whether there is a mathematical framework that inherently connects information and holography to philosophy and theology. This research will try to determine the extent to which, if at all, purely scientific concepts can inform the purley philosophical.
Specifically, this project will use information theory and the holographic principle to examine the merits of the “Simulation Hypothesis.” The final results will then use this as a bridge to consider the possibility that science and mathematics are describing a reality that theology has predicted since the beginning of time. The project aims to leave its readers, after carefully scrutinizing the research to be presented, asking: is it possible that science and religion are saying the same thing?
This page will be updated as research continues and progress is made on the project. In the meantime, a detailed overview of the project, as well as a tentative research map, can be found below.
Expected completion date: December 2026
Project Goals
This research project aims to investigate the mathematical relationship between information, boundaries, and dimensional reduction; explore how these concepts relate to holographic descriptions of reality; and examine the philosophical implications of such models.
Abstract
This research will examine the relationship between boundary data and interior structure, motivated by ideas related to the Holographic Principle. In particular, the project explores how information about a system may be encoded on lower-dimensional boundaries and what limitations exist in reconstructing interior behavior from such data.
The mathematical portion of the project focuses on dynamical systems, chaos theory, and boundary value problems, examining how sensitive dependence on initial conditions and information growth affect the recoverability of system states. These ideas are then placed in dialogue with conceptual frameworks inspired by holography, including the interpretation of physical systems as informationally encoded structures.
Finally, the results will include a carefully delineated philosophical discussion considering whether such mathematical and physical perspectives provide a useful framework for interpreting broader questions about the nature of reality, including simulation-based interpretations and their structural parallels to longstanding philosophical and theological ideas. These reflections are not presented as proofs, but as reasoned explorations grounded in the preceding mathematics.
Motivation
Recent developments in theoretical physics (particularly those associated with the AdS/CFT correspondence) have suggested that the information contained within a physical system may be fully represented on its boundary. While these ideas originate in high-energy physics, they raise fundamental mathematical questions about the relationship between dimensionality, information, and structure.
This project is motivated by the observation that similar questions arise in classical mathematical contexts. In particular, boundary value problems in partial differential equations, as well as the behavior of chaotic dynamical systems, both address the extent to which limited or partial information determines the evolution or structure of a system.
The goal of this project is to explore these mathematical ideas rigorously while examining how they relate, at a conceptual level, to broader interpretations of reality as fundamentally informational.
While such interpretations have appeared in both contemporary philosophical discussions (such as simulation theory) and historical philosophical or theological traditions, this project approaches them cautiously and analytically, using mathematics as the primary foundation.
Research Objectives
The primary objectives of the research will be:
- To analyze the role of boundary data in determining interior behavior
a. Study classical boundary value problems
b. Investigate conditions under which solutions are uniquely determined - To examine the behavior of chaotic dynamical systems from an informational perspective
a. Explore sensitive dependence on initial conditions
b. Consider implications for predictability and informational growth - To investigate mathematical structures related to dimensional reduction and encoding
a. Compare properties of systems in different dimensions
b. Analyze how information may be preserved or lost under projection or restriction - To interpret these mathematical results in light of holographic ideas
a. Provide a conceptional account of holography
b. Identify meaningful analogies with the mathematical results - To explore philosophical implications cautiously and rigorously
a. Examine whether mathematical and physical models of information suggest simulation-like interpretations
b. Discuss structural parallels with philosophical and theological ideas
Methodology
This project will employ a combination of analytical and expository methods, including:
- Mathematical analysis
a. Study of differential equations and boundary value problems
b. Examination of dynamical systems and chaos (including qualitative behavior and sensitivity) - Theoretical synthesis
a. Translation of physical concepts such as holography into mathematically meaningful language
b. Identification of structural similarities across domains - Philosophical reflection
a. Careful analysis of implications derived from mathematical results
b. Clear separation between proven results and interpretive discussion
Expected Contributions
This project aims to:
- Provide a clear mathematical exploration of boundary-driven information and system behavior,
- Demonstrate connections between classical mathematical theory and modern conceptual frameworks in physics, and
- Offer a disciplined approach to interdisciplinary inquiry, showing how mathematical results can inform philosophical interpretation.