Foreword: Reconstructing Reality via Algorithms and Geometry

(前言：重构实在的算法与几何)

The history of physics is a history of continuously stripping away appearances and seeking deeper invariants. From Newton’s absolute spacetime to Einstein’s curved geometry, from Bohr’s quantum jumps to Yang-Mills gauge fields, we have step by step approached the fundamental nature of reality. However, over the past half-century, this magnificent edifice seems to have encountered an invisible boundary. The continuity of general relativity and the discreteness of quantum mechanics clash like two gears that cannot mesh, emitting harsh friction at the Planck scale. The black hole information paradox, the nature of dark energy, the physical status of consciousness… These unresolved puzzles suggest that we may not need a new equation, but rather an entirely new ontology.

This book, Foundations of Physics in Geometry and Information, is a response to this challenge. It is not a patchwork of existing theories, but an axiomatic reconstruction from the ground up.

Our starting point is extremely simple, even “naive”: physical reality is finite. If we push this seemingly mundane proposition—the Finite Information Axiom—to its logical extreme, we find that the familiar, smooth, continuous spacetime continuum must disappear. In its place emerges a vast and intricate network of Quantum Cellular Automata (QCA) composed of discrete qubits.

In this discrete ontological picture, “matter” and “spacetime” are no longer opposing dualities, but two different manifestations of information.

• Time is no longer an external background parameter, but a statistical property of microscopic scattering processes. As we prove in Volume II, the rate of time flow strictly equals the system’s density of states ($\kappa =\rho$). Time is matter, matter is delay.

• Gravity is no longer a fundamental force, but a thermodynamic response of the spacetime network to maintain holographic entanglement balance. Einstein’s field equations are merely the equation of state for generalized entropy on causal diamonds (IGVP).

• Consciousness is no longer a bystander to the physical world, but a topologically protected self-referential soliton (MSCC) in the causal network. It is the geometric focus of the universe’s self-awareness.

To transform these radical ideas into rigorous science, we have had to develop and borrow a series of powerful mathematical tools: from operator algebras to differential geometry, from cybernetics to category theory. In particular, the categorical quantum mechanics introduced in Volume V proves the logical completeness of this theoretical framework—physical laws are essentially normed morphisms in symmetric monoidal categories.

This five-volume work is not only an intellectual adventure, but also an engineering blueprint. It attempts to tell us: the universe may not be a divine miracle, but a self-consistent structure that can be understood and even constructed through computation, encoding, and topological design. Wheeler predicted “It from Bit,” and this book further proposes: It from Qubit, via Geometry, to Agency.

This is a path less traveled. In the gap between discrete and continuous, at the boundary between information and matter, we attempt to glimpse the ultimate, unified, computational face of the universe.

May this journey bring you intellectual thrill and delight.

Auric

2025, Deep in Discrete Spacetime