Very roughly, why do the horizontal lines in the Muller-Lyer illusion (depicted below) appear to be different lengths?

The Müller-Lyer illusion is a well-known optical illusion that shows how our perception can be influenced by contextual visual cues.

Explanation:

1. Contextual Cues: The illusion involves two horizontal lines that are equal in length, but appear to be different due to the addition of arrow-like symbols at the ends of each line. One line has arrows pointing outward (away from the line), while the other has arrows pointing inward (toward the line).

2. Perceptual Scaling: Our brains use perspective cues to interpret depth and size. The outward-pointing arrows suggest that the line is shorter in depth, while the inward-pointing arrows suggest the line is longer. This misinterpretation of scale causes one line to appear longer than the other.

3. Gestalt Principles: The brain organizes visual information according to certain principles. The principle of closure and grouping leads us to perceive the lines as having different lengths, even when they do not.

In summary, the difference in perceived lengths of the lines in the Müller-Lyer illusion arises from the influence of contextual visual cues that affect our interpretation of size and perspective.