problems/computation-through-a-surface.md

# Computing through a reusable surface

Can a change of representation replace repeated computation with operations on a reusable surface?

Explore encoding a spatial or temporal structure in an interference-like representation and computing changes or views from it; evaluate preparation cost, reconstruction cost, approximation, and representational limits.

Status: open problem. Formulation and comparisons: reconstruction. Development: independent branch.

## Alternative representations

### An interference-based physical representation

Affords: Connects spatial information with a physical surface.

Limits or losses: Capacity and reconstruction depend on the actual physical setup.

### A computed surface for rendering or simulation

Affords: Moves repeated work into a reusable representation.

Limits or losses: Preparation and dynamic updates may cost more than direct computation.

## Tension

A cheap view after expensive preparation is beneficial only for a suitable pattern of reuse.

## Challenge

Which updates remain local after the transformation, and which require recomputing the surface?

This challenge is an editorial prompt, not a claim that the evidence already resolved it.

## Proposed next move

Compare total preparation, update, and query costs against direct computation for several reuse counts.

Status: new model-proposed experiment or extension; not a reported result.

## Related problems

- [How much of a whole can a part carry?](part-whole-traces.md) — shares a word with different meanings (retrospective_connection). Physical or computed surfaces and distributed social information can invite a holographic analogy, but they need separate encodings and validation.
- [Finding a strategy by changing the representation](strategy-through-transformation.md) — asks whether transformation saves work (retrospective_connection). Both move effort into a representation. Preparation, planning, and execution costs must remain separately counted.

## Evidence anchors

- basis-computation-through-a-surface: The material proposes translating physical interactions into changes in an interference pattern and asks about storage capacity. A later rendering proposal stores stable structures in a computational hologram and simulates moving parts through the surface, while asking whether the calculation becomes more complex or requires recomputing every section. [Editorial paraphrase; presence of a proposal does not verify its truth.]

Root evidence and private recovery mappings are not part of this public release.

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