These are exploratory notes, not a settled physical theory. They ask what follows if accessible reality is treated as pure informational structure, without assuming a separate material substrate behind it. These ideas should earn confidence only by becoming clearer, more compressive, and eventually testable.
Any finite history can be represented as a finite sequence of bits. A sufficiently rich infinite sequence (such as the digits of pi) will contain that sequence somewhere. But pointing to this containment explains nothing: an arbitrary decoder can encode as much information as the dataset it claims to recover.
Physical theories are distinct because their decoders are extraordinarily compact, reusable, and predictive. A short mathematical law can compress vast oceans of empirical data and continue making accurate predictions for unobserved phenomena. Explanatory power lies in net algorithmic compression: the length of the generative rule, plus the boundary conditions and the unexplained residual, measured against the volume of phenomena explained.
Microscopic variation often cancels out when observations are averaged across scales, while coherent correlations reinforce one another. At macro scales, trillions of turbulent micro-states condense into stable, predictable thermodynamic properties: temperature, pressure, fluid flows, and solid objects.
What we call physical structure is the residue of invariant correlations that remains predictive across different scales, observers, and changes of representation.
Randomness does not disappear; what counts as noise is relative to an observer's scale, sampling method, and frame of reference. The deeper claim is that physical laws and durable objects are not autonomous substances—they are classifications of stable correlations that survive the transformations relevant to observers like us.
Mathematics is the formal study of structure, relations, transformations, and invariant patterns. If physics is the systematic search for durable regularities within accessible information, the unreasonable effectiveness of mathematics ceases to be a mystical coincidence: mathematics is the exact tool designed to express structural invariance.
Yet a deeper puzzle remains. Abstract mathematical models routinely predict physical phenomena decades before experimentalists can observe them, and formalisms invented for pure geometry turn out to describe the physical universe. This demonstrates that reality is not merely fitted with mathematics after the fact; it possesses an extraordinary, objective degree of compressible coherence.
We ordinarily experience reality as a dynamic sequence of states evolving through time. From an informational frame, however, the same history can be represented as a single, static multi-dimensional structure containing relations among all states—a block universe. In this description, nothing physically moves the "present moment" forward; rather, embedded observer-states contain differing internal memories, records, and predictions.
The experienced arrow of time is driven by entropy. A mind can record only the low-entropy past, use energy gradients to maintain internal organization, and perform irreversible computation. An apparently open future reflects an observer’s limited, embedded position within an incomplete information field, rather than fundamental metaphysical indeterminacy.
Dynamical evolution, block structures, and boundary-constraint models are alternative mathematical representations of the same invariant pattern. Unless they produce differing empirical predictions, they describe the same reality.
Observers cannot exist at extremes of complexity:
Observers require a precise middle regime:
Any observer capable of discovering physical laws must inhabit a universe compressible enough to be modeled and asymmetric enough to sustain memory. This observer selection effect is a necessary filter, though it is not yet a complete explanation for why such a universe exists.
When sequences of fixed length are counted uniformly, nearly all of them are incompressible noise. Highly compressible, lawful structures are vanishingly rare exceptions.
Lawful universes can receive higher probability only under a measure that explicitly rewards algorithmic simplicity—such as Solomonoff's algorithmic probability, which weights programs inversely by their length ($2^{-K}$).
Justifying this measure is the foundational challenge of informational physics:
Until these questions are answered with testable constraints, informational physics remains an illuminating heuristic rather than a completed physical theory.