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Explaining Huffman’s Impossible Pyramid

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Re: Explaining Huffman’s Impossible Pyramid

#51

Post by drcongo »

Jtsummers wrote: post #26
drcongo wrote: post #24

Earlier quoted context omitted.

Downvoted, but can anyone explain how it's impossible if the base is quadrilateral? [1] [1] https://imgur.com/a/C3tDi50

I upvoted your original comment because it shouldn't have been downvoted. But I'd suggest reading the paper I linked elsewhere in this discussion which helps to explain why Huffman called it impossible. The image is "impossible" under the assumptions of that paper. If it were known to be a real object, then it implies that something about the image is wrong (there is hidden information, like the edge you add in your…

Thanks, that definitely wasn't in my mind when I looked at the original diagram and instantly pictured the quadrilateral base that makes "possible".

Re: Explaining Huffman’s Impossible Pyramid

#52

Post by red_trumpet »

dragontamer wrote: post #29

If you draw a "dotted line" from "A to C", it becomes blatantly obvious that the backside must be curved or warped in some degree (where the "dotted line" represents the bottom base). Assuming that the front-faces are flat, the triangle on the top of the figure is too warped to match the readily assumed triangular base. In fact, my brain is bouncing between many different interpretations of the base when I saw this f…

If the top triangle is not parallel to the base (which you picture by your method), then the two triangles don't match, even in a real picture.

Re: Explaining Huffman’s Impossible Pyramid

#53

Post by dragontamer »

red_trumpet wrote: post #52
dragontamer wrote: post #29

If you draw a "dotted line" from "A to C", it becomes blatantly obvious that the backside must be curved or warped in some degree (where the "dotted line" represents the bottom base). Assuming that the front-faces are flat, the triangle on the top of the figure is too warped to match the readily assumed triangular base. In fact, my brain is bouncing between many different interpretations of the base when I saw this f…

If the top triangle is not parallel to the base (which you picture by your method), then the two triangles don't match, even in a real picture.

The "impossible" part is trying to imagine a "flat" ADFC face.

There is no such "ADFC" face that can result in a triangle in the shape of DEF.

-------

To imagine what "ADFC" could possibly look like, I suggest trying to visualize the ABC-base at first, and then trying to imagine different "ADFC" faces to match the ABC-triangle with the DEF-triangles.

The only way you can get this shape to look like this, is if ADFC is bent or twisted somehow. No "straight/flat" ADFC could possibly connect the bottom with the top.

Re: Explaining Huffman’s Impossible Pyramid

#54

Post by SilasX »

Jtsummers wrote: post #44
SilasX wrote: post #40

Earlier quoted context omitted.

Okay, it's fair to call it impossible if you restrict the domain like that. But, per my other comment, this feels like a non-standard use of "impossible figure", as the conventional meaning is such that, just from the image, there is no reasonable figure that results in that image. That's not the case here. https://news.ycombinator.com/item?id=29879788

The context of the creation of this "impossible pyramid" is where the definition for "impossible" comes from here. Under Huffman's assumptions (the image is not deliberately misleading, there is no hidden information, each side lies entirely within a plane, and the image is meant to represent a polyhedron), the pyramid is, indeed, impossible. Relaxing his assumptions (which he discusses) would make it possible, but t…

I don't know how you can call it misleading if my immediate, natural, non-clever interpretation of the image matches a valid possibility. If anything, it's the insistence that "no no it's got a be a [truncated] pyramid with three sides at the base" that feels bolted on and arbitrary.

Also, the solution I responded to adheres to "each side entirely within a plane"[1] and "is a polyhedron". To make this impossible, you have to add information -- the assumption that this must be a triangular pyramid -- that is not present in the image itself.

Furthermore, the solution here, does not require that you be looking at it at a very precise angle that gets everything to line up perfectly, as you'd need for e.g. the Penrose triangle: https://en.wikipedia.org/wiki/Penrose_triangle

Bottom line, it is a different kind of thing than usual impossible figures.

[1] Assuming I'm interpreting "side" correctly? But any definition where the solution violates it, also feels arbitrary.

Re: Explaining Huffman’s Impossible Pyramid

#55

Post by SilasX »

Jtsummers wrote: post #25
Jtsummers wrote: post #5

https://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 rationa…

Too late to edit again, but here is one of the critical assumptions from the original paper: > One assumption we shall make throughout this paper is that all pictures are taken from a 'general position'; that is, that a slight change of the position from which the picture is taken would not change the number of lines in the picture or the configurations in which they come together. In the case of pictures of polyhedr…

But there's a solution where the camera is in a general position. See this thread:

https://news.ycombinator.com/item?id=29877311

Re: Explaining Huffman’s Impossible Pyramid

#56

Post by Jtsummers »

SilasX wrote: post #55
Jtsummers wrote: post #25

Earlier quoted context omitted.

Too late to edit again, but here is one of the critical assumptions from the original paper: > One assumption we shall make throughout this paper is that all pictures are taken from a 'general position'; that is, that a slight change of the position from which the picture is taken would not change the number of lines in the picture or the configurations in which they come together. In the case of pictures of polyhedr…

But there's a solution where the camera is in a general position. See this thread: https://news.ycombinator.com/item?id=29877311

Which I was also in, just look at Huffman's paper, it's not that long, which lays out his various assumptions which lead to why the figure would be an impossible pyramid. That it has a valid interpretation does not make it suddenly a possible pyramid just a possible polyhedron, if you introduce information that isn't evident in the image.

There's no sense in discussing Huffman's Impossible Pyramid without also considering Huffman's definition for impossible. If we discard his definition, what we're talking about is something else entirely.

Re: Explaining Huffman’s Impossible Pyramid

#57

Post by Jtsummers »

SilasX wrote: post #54
Jtsummers wrote: post #44

Earlier quoted context omitted.

The context of the creation of this "impossible pyramid" is where the definition for "impossible" comes from here. Under Huffman's assumptions (the image is not deliberately misleading, there is no hidden information, each side lies entirely within a plane, and the image is meant to represent a polyhedron), the pyramid is, indeed, impossible. Relaxing his assumptions (which he discusses) would make it possible, but t…

I don't know how you can call it misleading if my immediate, natural, non-clever interpretation of the image matches a valid possibility. If anything, it's the insistence that "no no it's got a be a [truncated] pyramid with three sides at the base" that feels bolted on and arbitrary. Also, the solution I responded to adheres to "each side entirely within a plane"[1] and "is a polyhedron". To make this impossible, you…

I meant "face", not "side".

However, almost all the solutions to make this a possible polyhedron make it not a pyramid and operate under the assumption that there is hidden information (that is, that the image is misleading, deliberate or not). It still remains an impossible pyramid in Huffman's context.

Re: Explaining Huffman’s Impossible Pyramid

#58

Post by SilasX »

Jtsummers wrote: post #56
SilasX wrote: post #55

Earlier quoted context omitted.

But there's a solution where the camera is in a general position. See this thread: https://news.ycombinator.com/item?id=29877311

Which I was also in, just look at Huffman's paper, it's not that long, which lays out his various assumptions which lead to why the figure would be an impossible pyramid . That it has a valid interpretation does not make it suddenly a possible pyramid just a possible polyhedron , if you introduce information that isn't evident in the image. There's no sense in discussing Huffman's Impossible Pyramid without also cons…

Sure, and I addressed your point there[1], that this still requires a non-standard, new definition of "impossible figure".

Furthermore, I don't see how it introduces information that "isn't evident in the image" when several people automatically assumed a 4 sided base (me among them) without trying to be clever.

[1] https://news.ycombinator.com/item?id=29879862

Re: Explaining Huffman’s Impossible Pyramid

#59

Post by Jtsummers »

SilasX wrote: post #58
Jtsummers wrote: post #56

Earlier quoted context omitted.

Which I was also in, just look at Huffman's paper, it's not that long, which lays out his various assumptions which lead to why the figure would be an impossible pyramid . That it has a valid interpretation does not make it suddenly a possible pyramid just a possible polyhedron , if you introduce information that isn't evident in the image. There's no sense in discussing Huffman's Impossible Pyramid without also cons…

Sure, and I addressed your point there[1], that this still requires a non-standard, new definition of "impossible figure". Furthermore, I don't see how it introduces information that "isn't evident in the image" when several people automatically assumed a 4 sided base (me among them) without trying to be clever. [1] https://news.ycombinator.com/item?id=29879862

"assumed", because it wasn't presented. It wouldn't need to be assumed if it were present. That's pretty much the definition of assuming.

Re: Explaining Huffman’s Impossible Pyramid

#60

Post by SilasX »

Jtsummers wrote: post #57
SilasX wrote: post #54

Earlier quoted context omitted.

I don't know how you can call it misleading if my immediate, natural, non-clever interpretation of the image matches a valid possibility. If anything, it's the insistence that "no no it's got a be a [truncated] pyramid with three sides at the base" that feels bolted on and arbitrary. Also, the solution I responded to adheres to "each side entirely within a plane"[1] and "is a polyhedron". To make this impossible, you…

I meant "face", not "side". However, almost all the solutions to make this a possible polyhedron make it not a pyramid and operate under the assumption that there is hidden information (that is, that the image is misleading, deliberate or not). It still remains an impossible pyramid in Huffman's context.

>I meant "face", not "side".

Okay but if you're going to ground your position in "hey, this is just what you get when you're super rigorous about terms and assumptions and all", it's incumbent on you to be a little more careful about that.

>However, almost all the solutions to make this a possible polyhedron make it not a pyramid and operate under the assumption that there is hidden information (that is, that the image is misleading, deliberate or not). It still remains an impossible pyramid in Huffman's context.

And again, that's adding information that is not present in the image itself, the exact problem you claimed would invalidate the offered solution (in this subthread), and it's still a different definition of "impossible figure" than the conventional one.

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