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Comments on Lecture 1 "Right-Facing Arrow"
Comment 1. About the appearance in the mirror placing to the right
This object changes its appearance in an unusual way when reflected in a mirror sanding behind the object. On the other hand, it reflects normally in the mirror standing to the right. This normal behavior looks like strange because the top curve of the object is a space curve instead of a planar curve. This phenomenon comes from the fact that the view direction does not change in the mirror because the mirror is parallel to the view direction. Note that the actual view direction is not strictly parallel to the mirror becuase we see the mirror image in a slated directin. This implies that the illusion is strlong in the sense that the illusion does not disappear even if we change the viewpoint slightly.
Comment 2. To those who want to touch the real object
A plastic model of the arrow is included in the next set.
Fushigi Rittai SET, Tokyo Shoseki Publisher, Tokyo, 2018. See
here.
This set includes four plastic models of amgibuous objects, which change their appearances drastically in a mirror, and three unfolded surface diagrams of partly invisible objects, part of which become invisible in a mirror.
Shogaku 8 Nensei, Issue 6 (published from Shogakkann in February, 2018) includes a diagram of the unfolded surface of the right-facing arrow. See
here.
Comment 3. Reference for the mathematical backgraound of the right-facing arrow
K. Sugihara: Anomalous Mirror Symmetry Generated by Optical Illusion. Symmetry, vol. 8, no. 4 (2016), p. 21.