MB · The Lab

EXP. 010 · The Tesseract Room

n = 4 · vertices 16 · edges 32
the fourth right angle — drag to rotate where you can't point

The Lab — EXP. 010 · the other half of the ask

The fourth right angle.

A point, swept: a segment. Swept again: a square, a cube — and once more, along an axis this room doesn't own: a tesseract. Drag to rotate it through planes you can't point at. The inner cube isn't inside — it's just farther in w.

EXP. 010 — Notes

The Tesseract Room

The n-cube genealogy, performed: sweep a point and get a segment; sweep the segment, a square; the square, a cube; then the same move once more along a fourth axis perpendicular to all three. What renders is a shadow of a shadow — 4D projected to 3D projected to the screen — and rotation happens in planes rather than around axes, which is why turning in x–w looks like the object pulling itself inside-out. The inner cube isn't inside. It's just farther in w.

Adding a strategic dimension — a channel, a geography, a pricing axis, an AI capability — doesn't replace your business; it makes everything you had one face of a larger object. Competitors studying your 3D shadow can't reconstruct the 4D shape. Dimensionality is a moat that looks like a distraction.

And the reading habit: when a metric looks paradoxical — segments all improve, the total declines — you're usually looking at a projection with an axis missing. Mix shift is a shadow artifact; Simpson's paradox is this room. Find the w before you act on the shadow.

The room has one more direction than you do. Everything you know is still here — it's just a slice now, a face of something patient standing at right angles to your entire world, waiting for you to learn to point.

  1. Mechanism under test: the n-cube genealogy made drivable. Vertices are every sign-choice in n coordinates (2ⁿ of them), edges join pairs differing in one coordinate (n·2ⁿ⁻¹); stepping n up SWEEPS the current figure along a new perpendicular axis, animated, so you watch the square become the cube become the tesseract by the same single move.
  2. Rotation you can't point at: dragging rotates in the x–w and y–w planes — perfectly ordinary rotations, just in a plane this room doesn't contain. The projection is double perspective: 4-D → 3-D (divide by distance in w), then 3-D → 2-D. Ember marks the edges swept along the newest axis; bone is everything older.
  3. The mind-bend: the "inner" cube of the projected tesseract is not inside anything — it is the same size as the outer one, merely farther away in w, exactly as a far wall is not smaller than a near one. Rotate until they trade places.
  4. Lineage: the site's dim-hypercube plate (Annotation & Schematic family) drew this genealogy as a still; here it becomes an instrument. Readouts (2ⁿ, n·2ⁿ⁻¹) are computed, not typeset.
  5. What might graduate: the sweep-as-explanation (one gesture defining a whole family) as figure grammar for essays; the double-perspective projection for any future dimensional figure.

PHYSICS — raw WebGL2, RGBA8 only, no libraries, single file · all projection in JS (2ⁿ ≤ 16 vertices), edges drawn as screen-space quads + additive glow · seeded opening rotation settles by inertia decay → zero idle frames (visibility-gated) · reduced motion = settled figure, stepper jumps without sweeping · no-GL = designed fallback · zero console errors.

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