Occasional Tales

But does the ladder mind? Another of Escher’s cunning pictures of the impossible. This one, Belvedere , is done by taking two rectangles and turning one 90°. In reality, that would form a cross, but on paper, one rectangle will merely be above the other in spite of its orientation. I don’t find this picture quite as satisfying as Waterfall because the columns to the left and right of the ladder, supporting the upper level, look wrong, just as the one to the left of the figure at the other end of the balcony seems wrong because both rest on something that is forward of their position. But if the columns were allowed to sit where they ought to be (at least in two dimensions), the illusion of the picture would probably be spoilt. I also note that the picture is based on a skewed, flattened hexagon. Also, I suspect that the two tiers would have to be tilted if you attempted to do this in reality even although they look horizontal in the picture. (In an unrelated exclamation, it seems that...

But you have to love the architecture. I’ve always liked this picture using Penrose impossible triangles. Even if this really was possible in three dimensions, the water would have to go uphill, thus appearing to make the picture impossible on two counts. I also note that this is a reverse capital sigma (Σ). I’ve seen the triangle itself done in three dimensions, but it can only look real when viewed from the right direction. Basically it’s three pieces, but the two at either end are angled away from each other. When you rotate the structure to make it look like a triangle, it’ll seem to be an impossible triangle. Who said two dimensions were boring? Anyway, more of the same tomorrow.

Just where do you think you’re going? The white birds fly towards the night and the black towards the day. My brain is too mediocre to work out what metaphorical (or metaphysical) import these tessellated flocks might have. Opposites attract? Night will become day just as day will become night? Between black and white, there is a spectrum of shades of grey so that only what is extreme can be absolute? An artist’s purpose is impossible to fathom? Looking at the book may resolve the intention that the author had when he included the picture in it? Well, according to Martin Cohen, the birds are swooping down to become part of the landscape while that produces more of them. I looked at the picture (the thumbnail above) and more readily saw the birds emerging from the landscape, which is, I think, how I’ve seen it in the past. I don’t see some sort of cycle here, but that’s just me. Apparently one physicist thinks this is a good model for the nature of the universe in that there ended up be...