PAST PROJECTS / MATRIX VISUAL ARCHIVE

The remainder — a visual hypothesis

Original portal visual design, edited for public reading. Diagrams are interpretations and learning analogies, not claims about how a real brain or the film’s fictional technology works.

01 / Approximation and remainder

                  f'(a)         f''(a)              f⁽ⁿ⁾(a)
f(x) = f(a) + ─── (x-a) + ─── (x-a)² + ... + ─── (x-a)ⁿ + Rₙ(x)
                  1!            2!                  n!
       └────────────── Pₙ(x) (n차 polynomial) ──────────────┘   └ remainder ┘

The original formula diagram is retained. The remainder is the difference from the approximation; it can be zero. Convergence depends on the function and the interval.

02 / Reading the analogy

MODEL                         WHAT IT LEAVES OUT
Pₙ(x)                         Rₙ(x) = f(x) − Pₙ(x)
  │                              │
  └── a useful description       └── a reason to look again

FILM INTERPRETATION
A system’s expectations  ──────  A character’s unexpected choice

The original branching-diagram format connects two ideas. This is a metaphor, not a mathematical explanation of Neo.

03 / Layers of a story

VIEWER’S QUESTION
  │
  ├── The world shown as everyday reality
  │     │
  │     └── The simulated world within the story
  │            │
  │            └── What the characters believe they can change
  │
  └── What evidence would distinguish one interpretation from another?

The earlier portal imagined nested layers. Here the diagram remains a question about interpretation rather than a claim that another simulation is established.

04 / Revising a model

OBSERVE → DESCRIBE → COMPARE → FIND A MISMATCH
              ↑                         │
              └──── REVISE / TEST ───────┘

An unexpected result invites a closer look. Changing the description is useful only if it improves what we can explain or test.

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MATRIX · VISUAL ARCHIVE