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Do you think 'impossible' objects from mathematics are 'real,' even if they can't be constructed in our world? Don't try to build a Lego version of one of M.C. Escher's staircases … it would be impossible, as Robert Ghrist points out in this article about an impossible object that he and a colleague invented.
The object fits into the category of visual paradoxes, and in our three-dimensional world it couldn't exist. They started with a variant of a Penrose staircase:'A ladybug walking along a Penrose staircase, for example, will feel like it has climbed a full set of stairs, yet it will have returned to the same height it was at when it started.' Would you consider these types of objects real even if they can't exist in our world?
I am a professor emeritus of Mathematical Sciences, University of Memphis, TN. In my early career, 1969-1970s) I frequently taught 'math for liberal arts' courses and tology courses and assigned the construction of such objects as homework. An excellent example is Lewis' Carrol's construction of a projective plane: take three pocket handkerchiefs, sew two together to make a mobius strip, sew the four edges of the third to the four edges of the mobius strip.
Class discussion: why could you not finish the sewing? Would it be a klein bottle or a projective plane if completed? In one case a student sewed one edge in the wrong orientation and it took two professors with Ph.D.s in topology an hour to determine what object it would be if completed . I still keep that souvenir in my desk, over 50 years later.)
How likely would you be to say 'yes' to being placed in a coma for a lengthy spaceflight to another planet?
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