Parallax Cipher — Depth Perception from Two Viewpoints

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> PARALLAX CIPHER

parallax difficulty: 3–6 field: stereoscopic vision / astronomy

The idea in plain English: Hold your thumb up at arm's length and close one eye, then switch eyes. Your thumb appears to jump against the background. That's parallax — the apparent shift of an object when viewed from two different angles. The closer the object, the bigger the shift. In this puzzle, multiple objects at different distances are viewed from two positions. The displacement (how far each object appears to shift) encodes an ASCII code. Objects closer to the viewer shift more; objects farther away shift less.

Why this really exists: Parallax is how we perceive depth (our two eyes give two slightly different views, and the brain calculates distance from the shift). It's also how astronomers measure distances to nearby stars — they measure the star's apparent shift against distant background stars as Earth orbits the Sun. This is the stellar parallax method. The nearest star, Proxima Centauri, has a parallax of 0.77 arcseconds (a tiny shift!). The Gaia spacecraft is currently mapping billions of stars using parallax.

▸ Concrete Example

Two viewpoints at x = -10 and x = +10. Objects at various distances:

Object A at distance 50: shift = 20/50 = 0.4 pixels
Object B at distance 100: shift = 20/100 = 0.2 pixels
Object C at distance 25: shift = 20/25 = 0.8 pixels

Shifts: [0.4, 0.2, 0.8] → scaled to ASCII
Scale factor of 100: [40, 20, 80] → '(' , NUL, 'P'
Different scale: [72, 69, 76] → 'H', 'E', 'L'

The puzzle provides the scale factor → shift values map to ASCII codes

▸ How to Solve (Step by Step)

1. Get the two viewpoint positions and object 3D coordinates from puzzle data

2. Project each object onto both viewpoints' image planes

3. Calculate the displacement (difference in projected positions) for each object

4. Apply the given scale factor → round to integer → ASCII character

5. Join → the answer word

def displacement(obj_pos, vp1, vp2):
  proj1 = obj_pos / (obj_pos - vp1) # simplified projection
  proj2 = obj_pos / (obj_pos - vp2)
  return abs(proj1 - proj2)

word = ''.join(chr(int(round(disp * scale))) for disp in displacements)

▸ Real-World Applications

Stellar distance measurement: Parallax is how we know how far stars are
3D vision: Stereo cameras (like the ones in iPhones and VR headsets) use parallax for depth
Autonomous driving: Cars use stereo cameras + parallax to detect obstacles
Astronomy: The Gaia spacecraft maps 1.8 billion stars using parallax

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