14. The Duck-Rabbit Illusion This is a figure where the brain switches between seeing a duck or a rabbit. The drawing was first used by psychologist Joseph Jastrow in 1899 to make the point that perception is not only what one sees but also a mental activity. His research is based on how quickly one can see the second animal and how fast you can change your perception from one animal to the next. The faster you can do this, the quicker your brain works. What animal do you see? Just as we describe the graph of the function y = x2 above as a parabola opening up because we tend to think of y being a function of x, most people initially see a duck rather than a rabbit. If you turn the graph 90o, the rabbit becomes obvious. At different times during the year, the result of the test seem to change. During the Easter period, people are more likely to see a rabbit first but in October, seeing the duck first is more common. www.mastermathmentor.com

15. The Tribar Illusion What’s wrong with this MC Escher picture Waterfall? This shape is called a tribar or Penrose triangle. Follow the shape of the triangle starting at the top point; the left side seems to extend away from you, and the right side seems to extend towards you, yet they seem to lie on the same plane when they reach and are connected by the bottom vertices. It is an impossible shape. On the left, we see the impossible tribar. On the right, we view it from a slightly different perspective. Note the “top” bar sticking out slightly. Realize this bar is lying flat on the surface of the table. But when this bar is exactly aligned to the vertical bar (the left image), our brains decide the bars are connected – although it is impossible. Escher’s Waterfall: On the right, the water seems to be flowing uphill, then pouring down to the bottom. Realize that this is merely two tribars. On the left, the vertical posts are cut off so our brains don’t connect them to the zig-zagging water channels. The channels are lying flat in one plane! www.mastermathmentor.com

16. The Ouchi Illusion Some other variations. Click to add motion to make the effect more pronounced. The Ouchi illusion, illustrated above, is an illusion named after its inventor, Japanese artist Hajime Ouchi in 1977. In this illusion, the central disk seems to float above the checkered background when moving the eyes around while viewing the figure.  www.mastermathmentor.com

17. Ponzo Illusion B A Which yellow line is longer, A or B? The Ponzo illusion was first demonstrated by Italian psychologist Mario Ponzo in 1911. He suggested that the brain judges an object's size based on its background. He drew two identical lines across a pair of converging lines, similar to railway tracks. The upper line looks longer because we interpret the converging sides according to linear perspective as parallel lines receding into the distance. In this context, we interpret the upper line as though it were farther away, so we see it as longer. The front and back cars, the same as the car in the middle were Photoshopped in. Note how the Ponzo illusion takes over. B A Most people perceive the horizon being farther away than the point straight over their heads. When the Moon is on the horizon, your brain thinks it’s far away, much farther than when it’s overhead. The size of the moon is the Ponzo illusion (the moon is actually slightly closer to the earth when at the horizon). You’d swear that the red vertical line on the right is much longer than the one on the left, wouldn’t you? But the Ponzo illusion is in effect. www.mastermathmentor.com

18. Rotating Face Mask Illusion This is a rotating face mask. Note that the hollow (negative) version of the face immediately switches back into a positive view, one cannot ‘hold’ it. Also, the direction of rotation seems to change. If we cannot rely on shadows (and in the computer image there are different lighting conditions than in your room), there is nothing that can tell us if the face is really hollow or normal. www.mastermathmentor.com

19. Spine Drift Illusion In the image you see square array of spines with a gap showing a square in the middle. Does the central square appear to float, to move relative to the background? If so, you are perceiving the non-existent movement. This is Kitaoka’s “Spine Drift” illusion. It is strongly affected by eye movements. People perceive this from non-existent to strong. The same phenomenon occurs to an extent in “The Autumn Color Swamp.” And the center square is not tilted as well. To enhance the illusion, shake your head from side-to-side. www.mastermathmentor.com

Sources 14. Duck-Rabbit - https://www.illusionsindex.org/i/duck-rabbit, 15. Tribar - https://www.opticalillusion.net/optical-illusions/eschers-waterfall-explained/ 16. Ouchi - http://mathworld.wolfram.com/OuchiIllusion.html, https://michaelbach.de/ot/mot-eyeJitter/index.html 17. Ponzo - https://en.wikipedia.org/wiki/Ponzo_illusion, http://blogs.discovermagazine.com/badastronomy/2010/05/13/ why-does-the-moon-look-so-huge-on-the-horizon/#.XZdMiS3MzFw 18. Rotating Face Mask - https://michaelbach.de/ot/fcs-hollowFace/index.html 19. Spine Drift - https://michaelbach.de/ot/mot-spineDrift/index.html www.mastermathmentor.com