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View Diary: Godel, Escher, Bach series: Mumon and Godel (56 comments)

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  •  Left and right spheres (2+ / 0-)
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    Dave in RI, plf515

    Escher's drawing on p238 is a fascinating study in surface and bulk properties of materials, among other things. Hofstadter uses it in a way (and in a context) that doesn't really allow much reference to the left and right spheres, and glosses over the fact that the side spheres don't really reflect the other two spheres at all, despite the text.

    The middle sphere is reflective but the left hand sphere is transparent, and reacts in a very different way to the ambient light, as evidenced most obviously by the slightly reflective table top on which the three spheres rest. The same surface interestingly shows almost no difference between the mirror sphere and the matt sphere.

    An allegory might be the perception of various groupings of different phenomena. Looking at the top left reflection of the window in the glass sphere and the mirror sphere, one might regard them as similar; seeing the lack of reflected detail of the artist, one might regard the glass and matt spheres as similar; and seeing the dark shadows on the table, one could see the mirror and matt spheres as similar. All possible pairings can be justified.

    This is not a sig-line.

    by Joffan on Sun Mar 22, 2009 at 10:05:19 PM PDT

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