There are optical illusions and auditory illusions. This week’s Micro Softy concerns logical illusions.  Two optical illusions are shown in Figure 1.    On the left, the “Mad poiuyt” appeared on the cover of MAD Magazine in March 1965.   On the right, stairs repeat themselves in an impossible illusion. If you walk clockwise, you are always going downstairs forever. This staircase was used in the surreal art of M.C. Escher.  Figure 1: Two optical illusions. / WikipediaLeft, WikipediaRight.  The Shepard-Risset glissando is an auditory illusion where the pitch of a sound appears to continuously rise or fall indefinitely. Christopher Nolan’s films like Dunkirk and The Dark Knight used it to heighten the sense of dread or relentless motion. It can be used to create the illusion of an endless climb or descent, or to signify a special event, as in Super Mario 64’s endless staircase.  A tone that decreased in pitch forever is not possible. The Shepard-Risset glissando is an auditory illusion.    Logical Illusions  This week’s Micro Softy is about logical illusions. Here’s a classic example.  Epimenides, a 6th-century BC philosopher from Crete, reportedly said:  “All Cretans are liars.”  The Apostle Paul repeated this claim in the New Testament book of Titus.  “One of Crete’s own prophets has said it: `Cretans are always liars …’ ”  [Titus 1:12]   The logic illusion paradox arises when we consider that Epimenides himself is a Cretan. Suppose …