What could be?
A set of states describes the possibilities inside a model. A state is a description, not a claim that the description exhausts reality.
01 / THE FRAMEWORK
Reality, models,
and the view between.
Reality Calculus is presented here as an evolving mathematical and methodological research program about possible changes and the observations that describe them.
The definitions below are a provisional teaching interpretation. Original foundational publications are unavailable / not independently reviewed.
Four questions.
Four different jobs.
What is allowed?
Constraints select which states the example permits. Changing a constraint changes the model’s possibilities.
What can change?
Directed connections describe allowed changes. Being reachable means a path exists, not that the path will occur.
What can be seen?
An observation map can send different states to the same reading. A measurement need not identify the full state.
INTERACTIVE CONCEPT / SOURCE-QUALIFIED TEACHING EXAMPLE
One world model.
Four different lenses.
Choose U, A, T or o. The same illustrative five-state system appears differently depending on the question you ask.
U / STATES
Continue to the interactive graph Five possible states
U = {A, B, C, D, E}. All five state descriptions exist in this finite teaching model; no physical measurement is involved.
Select a different lens to see which distinctions matter.
FIG. 02 / FOUR-LAYER MODELILLUSTRATIVE
A provisional teaching model, not a measured property of nature. In the observation lens, B/C and D/E share readings.
A LOCAL TEACHING MODEL
C = (U, A, T, o)
Think of a room with several doors. The rooms are states, locked doors impose constraints, doorways are transitions, and a coarse sensor may report only which floor you are on.
The analogy explains information loss. It is not experimental evidence for the research framework.
Technical definitions used in this website
U = {A, B, C, D, E}. Admissibility is represented by a subset A ⊆ U. To avoid confusing the set A with the state named A, the explorer labels its control “excluded state.” T ⊆ U × U is a directed relation restricted to admissible endpoints.
The observation function o : U → {α, β, γ} maps A ↦ α, B and C ↦ β, and D and E ↦ γ. Reachability includes the starting state through a zero-length path. A path is a sequence of admissible states connected by T.
These definitions are explicit choices for this demonstration. They are not asserted to reproduce canonical notation in unprovided original publications.
What would a physical claim need?
A definition alone does not select a new physical theory.
- A distinct prediction
Specify an observable outcome that differs from the comparison model under matched conditions.
- An auditable protocol
State controls, calibration, uncertainty, stopping rules, and analysis before acquisition.
- Independent observations
Collect actual measurements; distinguish synthetic rehearsals from sensor data.
- A source trail
Make data, methods, and limitations inspectable. Include negative and inconclusive results.