In the pursuit of a new computational fabric, our work is grounded in a critique of the foundational congruencies that have guided network architecture for the past fifty years. We have found that much of what we get back to in distributed systems--from silent data corruption to unbounded tail latency--are the result of a reflection on what can be described as Forward-In-Time-Only (FITO) thinking. This approach, which usually relies on timeouts, retries, and a new time-board: an illusion of a single, global timeline..fundamentally conflicts against physical reality, where simultaneity is observer-dependent and causality can be indefinite.
The kind of computational thinking needed to grapple with these foundational subjects is often missing from conventional education. While there is a rush to study computer science, this kind of introduction to computational thinking isn't yet a course out there. It should be. It should have been for a long time. The computational objects we present makes it easy to make such a course.
Taking this sentiment to heart, we precede this project with not a mere visualization, but as a "code-as-proof" model for exploring the principles of one whose local action "ways" canonicalize our work. The code below reinterprets Conway's Game of Life in the form a model for creating a deterministic, self-organizing representation from a causal seed, mirroring the true tenets of the DÆDÆLUS philosophy. In this scenario, an initial state acts as a conserved quantity of information. This seed is not broadcast to a global controller; instead, it provides the local rules for a computational fabric--a cellular automaton--that evolves based entirely on "local information only".
From Local Rules to Global Order
Classical cellular automata (CA) are discrete dynamical systems that watch how complex, inspiring behavior can arise from simple, local rules. These systems are defined by a regular grid of cells, a finite set of states, and a deterministic local update rule that determines a cell's next state based on its neighbors. The evolution is inherently and intrinsically parallel, with a global structure developing from purely local interactions. The computational power of these systems is well-established; Elementary Cellular Automaton Rule 110, for example, is known to be computationally universal.
This classical model, how-ever, is limited by its deterministic predictability and definite cell states. To model the physical world more accurately, we must turn to Quantum Cellular Automata (QCA), which extend this framework into the quantum realm by replacing classical bits with quantum systems and deterministic rules with unitary quantum operations. In a QCA, each cell exists in a quantum superposition of states, and the system's global state can exhibit "massive" entanglement, allowing it to process exponentially more information than its classical counterpart. Which segues into, the evolution of a QCA that must be unitary, which en-forces the principles of reversibility and probability conservation --concepts central to our design of reversible subtransactions.
Recent Breakthroughs and Future Directions
The field of QCA is advancing rapidly. Recent breakthroughs include the demonstration of measurement-free quantum error correction using QCA designs, a paradigm shift from traditional methods that require frequent, disruptive measurements. Furthermore, a comprehensive renormalization theory for QCA has been established, providing a rigorous mathematical framework for understanding how these systems behave across different scales by grouping cells into tiles and analyzing the resulting coarse-grained evolution.
This work, which connects computation directly to the principles of modern physics, is essential for building the next generation of distributed systems that the world has never yet seen before already. The following is some Wolfram Language code that provides a hands-on environment for exploring these foundational concepts.
