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## Another Paradox?- Consider the image below, which I will call
*Three To Five*.
It is constructed from a Rubic Cube, which has 27 sub-cubes. How then is it possible to have a tower of 5 cubes stretching from the bottom front to the top back? Where did the two extra translucent cubes come from? This appears to be different from Reutersvaard?s Attempting to simplify the effect, consider the next image, The black latticework on top serves to make the top surfaces of the two cubes on top, to be coplanar. But the black latticework is not essential: This seems to have a certain ambiguity, and therefore is automatically suspect as a paradox, for as we have seen elsewhere in these pages, ambiguity does not generate contradiction but rather incompleteness (eg. the duck-rabbit isn't impossible, only under-determined). Ambiguity abounds for Necker-like structures, of course. But the ambiguity is itself curious. A consistent way to see this image, is as two sub-cubes with the top square face of the bottom front cube co-planar with the bottom square face of the top back cube. Then two lines in this plane join the corners of the two coplanar squares. The ambiguity arises because there is another way to see this, namely as a tower of three cubes with a translucent cube in the middle position. This makes it like a simplified or cut-down version of Smaller, proto-versions exist, such as
The right hand image is the simplest. It shows a square out of which a cube grows, or a top cube suppressed to be coplanar with the top of the bigger square . There is also a recipe, therefore, for stacking further levels on top: just add a
The tower structure is surprisingly like Brancusi's sculpture
Tesselations with many directions are possible:
Structures which more obviously manifest ambiguity abound in this area. Consider the following image:
The following is called The Little ImpossibleTheatre.
Another form of the paradox exploits the other three planar symmetries instead of the four diagonal ones. The extra cubes in theses cases appear as the orthogonal splines of the three-cube, emerging as the middle most cube on each face. For a sketchbook of images exploiting this other kind of paradoxicality, click here. ----------------------------------------------------------------------
Other images and gallery: Steve Leishman and Chris Mortensen
This project is conducted within the Department of Philosophy, University of Adelaide, and funded by The Australian Research Council. |

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