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Explaining Huffman’s Impossible Pyramid

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Re: Explaining Huffman’s Impossible Pyramid

#41

Post by [deleted] »

norrius wrote: post #22
jerf wrote: post #15

Earlier quoted context omitted.

If my "geometric intuition" is working properly, the "problem" is that the figure in the picture wouldn't meet in a point. There would be a line at the top, and it wouldn't be a pyramid. But there's nothing "impossible" about that. The impossibility simply seems to be an assertion of impossibility. It feels like it's a problem similar to spending to much time doing "2 + 5 = _" problems and thinking the equality symbo…

Sure, if you want to allow non-flat, curved faces, this body is possible. I'd argue this is not in the spirit of the question, similar to the triangle statue mentioned in the article.

[deleted]

Re: Explaining Huffman’s Impossible Pyramid

#42

Post by JumpCrisscross »

thaumasiotes wrote: post #35
thaumasiotes wrote: post #20

Earlier quoted context omitted.

> If my "geometric intuition" is working properly, the "problem" is that the figure in the picture wouldn't meet in a point. There would be a line at the top, and it wouldn't be a pyramid. But there's nothing "impossible" about that. The proof given in the article seems fine. Assuming the figure has three flat faces, the arrangement of those faces is impossible. A figure such as you describe, with a line on the top,…

Try approaching the problem from another direction: imagine you're positioning three planes (which will form the side faces of the truncated pyramid, but imagine infinite planes). How would you position them so that they didn't come to a single point? It can't be done; the first two planes will form an infinitely long "trough" in more or less the shape of a Λ (well, an X, but we're only interested in the part below t…

> It can't be done

Cheeky: it can, but they must be parallel.

Re: Explaining Huffman’s Impossible Pyramid

#43

Post by marcosdumay »

norrius wrote: post #22
jerf wrote: post #15

Earlier quoted context omitted.

If my "geometric intuition" is working properly, the "problem" is that the figure in the picture wouldn't meet in a point. There would be a line at the top, and it wouldn't be a pyramid. But there's nothing "impossible" about that. The impossibility simply seems to be an assertion of impossibility. It feels like it's a problem similar to spending to much time doing "2 + 5 = _" problems and thinking the equality symbo…

Sure, if you want to allow non-flat, curved faces, this body is possible. I'd argue this is not in the spirit of the question, similar to the triangle statue mentioned in the article.

> I'd argue this is not in the spirit of the question

What question? I don't see any question.

I only see the drawing of a solid and a statement that it's impossible for such solid to exist.

And the only thing that is supposed to make the solid impossible is that it's named a "pyramid". What only means that the author uses a definition of that word that is more lenient than the strict usage I see in use, and more strict than the lenient usage.

It's an interesting math problem, that exists on the contexts of its definitions (like any other). But given that the definitions aren't stated, it's not reasonable to expected people to come aware of them.

Re: Explaining Huffman’s Impossible Pyramid

#44

Post by Jtsummers »

SilasX wrote: post #40
Jtsummers wrote: post #26

Earlier quoted context omitted.

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…

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 then, well, you've relaxed the assumptions (there's a hidden edge not seen, the image is meant to mislead, each side does not, in fact, lie entirely within a plane, etc.).

Re: Explaining Huffman’s Impossible Pyramid

#45

Post by dandanua »

The "impossibility" proof actually uses 3 assumptions:

1. A, D, E, B lie in one plane

2. B, E, F, C lie in one plane

3. A, D, F, C lie in one plane

Any of these assumptions can be wrong. It's easy to perceive that number 3 is not flat, if you think that 1 and 2 are flat.

Re: Explaining Huffman’s Impossible Pyramid

#46

Post by Jtsummers »

marcosdumay wrote: post #43
norrius wrote: post #22

Earlier quoted context omitted.

Sure, if you want to allow non-flat, curved faces, this body is possible. I'd argue this is not in the spirit of the question, similar to the triangle statue mentioned in the article.

> I'd argue this is not in the spirit of the question What question? I don't see any question. I only see the drawing of a solid and a statement that it's impossible for such solid to exist. And the only thing that is supposed to make the solid impossible is that it's named a "pyramid". What only means that the author uses a definition of that word that is more lenient than the strict usage I see in use, and more str…

> It's an interesting math problem, that exists on the contexts of its definitions (like any other). But given that the definitions aren't stated, it's not reasonable to expected people to come aware of them.

That's why I linked to the the definitions in my own comment:

https://news.ycombinator.com/item?id=29875085

https://aitopics.org/download/classics:E29CE08E

This entire thread is mostly suffering from excessive pedantry because the linked blog failed to properly frame the problem.

Re: Explaining Huffman’s Impossible Pyramid

#47

Post by WhitneyLand »

Jtsummers wrote: post #46
marcosdumay wrote: post #43

Earlier quoted context omitted.

> I'd argue this is not in the spirit of the question What question? I don't see any question. I only see the drawing of a solid and a statement that it's impossible for such solid to exist. And the only thing that is supposed to make the solid impossible is that it's named a "pyramid". What only means that the author uses a definition of that word that is more lenient than the strict usage I see in use, and more str…

> It's an interesting math problem, that exists on the contexts of its definitions (like any other). But given that the definitions aren't stated, it's not reasonable to expected people to come aware of them. That's why I linked to the the definitions in my own comment: https://news.ycombinator.com/item?id=29875085 https://aitopics.org/download/classics:E29CE08E This entire thread is mostly suffering from excessive p…

>entire thread is mostly suffering from excessive pedantry

It is? The comments here don’t seem pretentious and dogmatic to me, I prefer to use pentantry for cases where basically people can tell they’re being a little bit of a dick.

It seems here in the comments people are simply saying, it’s hard to see the contradiction, that they can’t see any contradiction, and I think their implication is not to be a dick, it’s to hope someone will reply and say well here’s how it works or to correct a mistake.

In other words to simply get to the bottom of understanding.

Re: Explaining Huffman’s Impossible Pyramid

#48

Post by aaroninsf »

SilasX wrote: post #38
teddyh wrote: post #7

The 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.

Yes! Thank you! I was wondering what's so impossible about this and I think that's what I was missing -- yes, if you go with the assumption that the back side is a plane, then it's not possible, but that was never my initial assumption. I interpreted it as like a ... 3D trapezoid (?), with a rear support for D and fourth point on its base (though maybe that has its own issue). This is IMHO very different from usual "…

I am in agreement with y'all.

In particular with you observation that this is a different class of "impossible figures."

Though I can also understand the counter-argument, that one can also construct objects which from a privileged perspective also "technically" are possible solutions for such figures.

I believe the (compelling) counter-counter-argument is that such solutions are AFAIK unique to privileged perspectives, but in this case, there is a whole set of such perspectives. You can rotate the thing through quite a range and still assert you're looking at an impossible pyramid.

Adding a single edge to defeat the premise that it's a "pyramid" is I suspect a formalizable distinction which reduces the impossibility (as others have said) to whether you want to hinge all on the word "pyramid."

Re: Explaining Huffman’s Impossible Pyramid

#49

Post by thaumasiotes »

JumpCrisscross wrote: post #42
thaumasiotes wrote: post #35

Earlier quoted context omitted.

Try approaching the problem from another direction: imagine you're positioning three planes (which will form the side faces of the truncated pyramid, but imagine infinite planes). How would you position them so that they didn't come to a single point? It can't be done; the first two planes will form an infinitely long "trough" in more or less the shape of a Λ (well, an X, but we're only interested in the part below t…

> It can't be done Cheeky: it can, but they must be parallel.

Good luck positioning parallel planes to form the sides of a pyramid. ;D

Re: Explaining Huffman’s Impossible Pyramid

#50

Post by thaumasiotes »

marcosdumay wrote: post #43
norrius wrote: post #22

Earlier quoted context omitted.

Sure, if you want to allow non-flat, curved faces, this body is possible. I'd argue this is not in the spirit of the question, similar to the triangle statue mentioned in the article.

> I'd argue this is not in the spirit of the question What question? I don't see any question. I only see the drawing of a solid and a statement that it's impossible for such solid to exist. And the only thing that is supposed to make the solid impossible is that it's named a "pyramid". What only means that the author uses a definition of that word that is more lenient than the strict usage I see in use, and more str…

> I only see the drawing of a solid and a statement that it's impossible for such solid to exist.

> It's an interesting math problem, that exists on the contexts of its definitions (like any other). But given that the definitions aren't stated, it's not reasonable to expected people to come aware of them.

You know, we aren't supposed to accuse people of not reading the article.

But this is what the article says:

> The drawing appears to represent a polyhedron with two triangular faces and three quadrilateral faces. The triangular faces are ABC and DEF. The quadrilateral faces are ABED, BCFE, and CADF. It also appears that AD and BE intersect at I, AD and CF intersect at G, and BE and CF intersect at H. If we accept this interpretation of the drawing, then the shape that it represents is impossible.

It would be difficult to be more explicit about the definitions.

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