Explaining Huffman’s Impossible Pyramid
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Explaining Huffman’s Impossible Pyramid
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Re: Explaining Huffman’s Impossible Pyramid
#2People are brainwashed by their prior experience: they have seen so many puzzles with specific assumptions that they assume them to exist here, as well.
The quasi-pyramid is impossible if you assume that there are no hidden nodes and edges. That assumption is not an explicit requirement, so you can posit any number of nodes and edges that are hidden from the specific perspective of the drawing -- it could be as crenellated as the interior of an English muffin.
Re: Explaining Huffman’s Impossible Pyramid
#3People are brainwashed by their prior experience: they have seen so many puzzles with specific assumptions that they assume them to exist here, as well. The quasi-pyramid is impossible if you assume that there are no hidden nodes and edges. That assumption is not an explicit requirement, so you can posit any number of nodes and edges that are hidden from the specific perspective of the drawing -- it could be as crene…
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Re: Explaining Huffman’s Impossible Pyramid
#4I didn't really get it at first, in fact, I might still not be getting it, but if you draw a line from A to C, then you can see that the triangle ABC will not be similar to DEF... when it should be? I don't know.
Re: Explaining Huffman’s Impossible Pyramid
#5https://aitopics.org/download/classics:E29CE08E - Source of the image
The image being discussed is on page 16 of the PDF (p. 310 by the document's page numbers).
EDIT: From my very quick, pre-coffee and woken-up-early-by-the-cats reading:
To everyone saying, "Well, if we choose a different set of assumptions it becomes possible." Yes. The discussion in the paper I link above goes into the assumptions used and rationale for why figures would be impossible in the context of his discussion. Basically, if you start with the image and treat it as an accurate (as accurate as it can be, a necessarily lossy process in most cases) 2d representation of a 3d object/scene, is there a valid 3d interpretation? In the case of the pyramid, with the assumption that it is an accurate drawing of a 3d pyramid, it's an impossible 3d pyramid. You'd have to add more information for it to become possible.
Re: Explaining Huffman’s Impossible Pyramid
#6I personally don’t see the image as “impossible”, in terms of seeing it as a projection of a 3D object. I didn’t interpret ABDE as being flat (A, B, D, and E coplanar), and I didn’t expect G, I, and H to be intersections of lines in 3D.
Re: Explaining Huffman’s Impossible Pyramid
#7The implied fact, which makes it an impossible figure, is the assumption that ACFD is a plane. If, on the other hand, there is an edge CD or an edge AF, the figure becomes possible.
That’s what my intuition tells me, in any case.
Re: Explaining Huffman’s Impossible Pyramid
#8[deleted]
Re: Explaining Huffman’s Impossible Pyramid
#9Here, 'impossible' is defined very loosely, as 'not what it appears to be'. But what does it appear as? Try imagining it, per Necker Cubes, as a concave shape.
Re: Explaining Huffman’s Impossible Pyramid
#10> I read about Huffman’s Pyramid from the consistently excellent blog Futility Closet.
Yes, I can also recommend Futility Closet for HN readers.