Metamodeling and rulology represent two foundational activities for understanding complexity: metamodeling asks 'what underlying Primitives operate beneath a model?' while rulology catalogs 'what do simple rules actually do?'—these are the bedrock beneath applied complexity research.

Relativity emerges necessarily in the Wolfram Physics model because observers embedded in the system can only know causal relationships between events, not absolute orderings of events, and causal invariance (the property that the causal graph is the same regardless of the order in which updates are applied) ensures that different reference frames will agree on these causal structures.

Rule space is a third fundamental space (beyond physical space and branchial space) where each point represents a possible rule or law of physics; observers have positions in rule space, and the Ruliad represents all points in rule space, with our perceived laws of physics corresponding to our particular position in rule space.

The key scientific insight from studying cellular automata and simple computational rules is that even with extremely simple rules (like Rule 30 with just one black cell as initial condition), very complicated and seemingly random behavior emerges, contradicting the intuition that simple rules produce simple behavior.

Multiway computation is a new computational paradigm where instead of a single deterministic sequence of states (as in classical computation) or a single probabilistic thread (as in traditional quantum mechanics), there are multiple asynchronous, parallel threads of execution happening simultaneously with no inherent ordering—and observers embedded in such a system can only detect causal relationships between events, not a global ordering.

The universe at its most fundamental level is a hypergraph—a collection of atoms of space with only identities and relationships to each other (like a 'friend network')—not a continuous geometric space, and all features of reality including particles and forces are tangles or patterns in this hypergraph structure.

Time is not a coordinate that can be arbitrarily moved forward or backward (as in mathematical equations) but rather an irreducible computational process—a sequence of rewrites of the hypergraph—that necessarily advances in one direction, making time fundamentally different from space.

Consciousness is fundamentally characterized by two constraints: computational boundedness (observers can only process limited information about the universe) and a single thread of time (sequential experience), which together distinguish consciousness from mere computational sophistication or intelligence.

Branchial space is the space of possible quantum histories and quantum branches, where motion in branchial space corresponds to changes in quantum state; the analog of the speed of light in branchial space is the maximum entanglement speed, which determines how quickly quantum correlations can spread.

Time dilation in relativity can be understood as a consequence of the fact that the universe is computing, and objects moving through space must use some of their computational budget to maintain their identity at different positions, leaving less computational resource to update their internal clocks, thus causing time to run slower for moving objects.

Quantum mechanics is not an add-on feature to the universe but an inevitable consequence of multiway computation—since there are multiple possible update sequences of the hypergraph (multiple possible histories), quantum branching is fundamental; what we experience as definite outcomes results from our branching brains selectively conflating different branches of the multiway graph into consistent narratives.

Mathematics can be understood as having two levels: an underlying 'molecular dynamics' level (axiomatic formalization) where Gödel's incompleteness applies and there are proofs of arbitrary length, and a higher 'hydrodynamic' level where mathematicians operate and experience mathematics as comprehensible and unified.

The elementary length scale at which space becomes discrete is approximately 10^-100 meters, derived from fundamental constants (speed of light, gravitational constant, Planck's constant) modified by a parameter representing the number of simultaneous quantum threads in the universe (approximately 10^170).

Complexity is defined not as a property that can be precisely measured but rather as the difficulty of determining what a system will do—when you cannot easily tell what a system will do despite knowing the rule, that is complexity; formally, this relates to computational irreducibility.

We perceive the universe to be 3-dimensional because at human scales the volume of a ball grows as r^3 (cubic growth), but the universe is not inherently 3-dimensional; in the early universe it may have been higher-dimensional, and as the universe evolved it became lower-dimensional, with dimension being an emergent property of the scale at which you're observing.

Dimension fluctuations in the early universe (the universe having slightly non-integer effective dimension at the cosmic microwave background era) might be detectable through unusual photon propagation patterns predicted by Huygens' principle, providing a potential test of the Wolfram Physics model.

Chemistry can be understood as a multiway computation system where molecules and their reactions form a dynamic network graph, and the different possible observers in this system (such as molecular-level observers sensitive to momentum and orientation, or human-level observers focused on concentrations) would perceive different effective laws.

The immune system may be better understood through a dynamic network theory where immune memory and function arise from complex interactions between T-cells, B-cells, and antibodies (anti-antibodies, etc.) rather than from the traditional clonal selection model of individual cells, and this network structure may store information in ways not captured by concentration measurements.

Four epochs can be identified in the history of scientific modeling: (1) ancient structural models (water, atoms, crystal spheres); (2) mathematical models with equations (17th century onward); (3) computational models where time is discrete and deterministic but sequential (early 1980s onward); (4) multiway computational models with asynchronous, branching time.

Mathematica, Wolfram Language, and related computational tools represent a 40-year effort to build symbolic computation infrastructure that can represent and transform abstract concepts; many of the core ideas (like the notebook interface) took 25 years to be widely adopted even after implementation.