Why is it possible to draw an impossible shape but in reality the creation of such a shape is… impossible?

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Title pretty much.

Saw some pictures with the never ending stairs, the various cubes and triangles that are impossible. Then there of course is the fork/trident and a bunch of impossible animals.

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PS. Really not sure about the flair, sorry.

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6 Answers

Anonymous 0 Comments

It’s taking advantage of perspective. Your brain looks at one part of the drawing and says, yeah that’s possible assuming x is going on at the other side I can’t see. But then the drawing just continues and your realize you are looking at something impossible because your assumptions about what the other side must look like are shown to be wrong.

Anonymous 0 Comments

Because you draw in 2D. When you draw something real, i.e. “from life”, what you’re basically doing is taking a 3-D world and drawing a projection of that world onto a 2-D plane.

But when you draw, you aren’t restricted to drawing things that are correct 2-D projections of 3-D scenes that could actually exist. You can draw anything you like, including things that are impossible to interpret as a (correct) 2-D projection of a (possible) 3-D shape.

Take [this impossible cube](https://upload.wikimedia.org/wikipedia/commons/thumb/8/81/Impossible_cube_illusion_angle.svg/582px-Impossible_cube_illusion_angle.svg.png) for instance. The image is really just a collection of colored shapes. If you were to interpret them as just that, a bunch of flat shapes arranged next to each other, then there is no conflict. But your brain is primed to try and see this as a 3-D shape. And that’s where you run into trouble, because there are conflicting cues here, that suggest that one part of the cube is simultaneously behind and in front of another part. Which is of course impossible. But again, it is not impossible for colored shapes to be on a piece of paper like that, or for pixels on your screen to light up in this pattern.

Anonymous 0 Comments

Because when you draw a 2D projection of a 3D object, you lose the depth information which is crucial for the error.

Anonymous 0 Comments

They are basically optical illusions. They are actually possible to make in reality, they just… aren’t what you expect them to be. [Here](https://www.youtube.com/watch?v=qJGT-aZKCYk) is a nice video with some examples.

Anonymous 0 Comments

These illusions take advantage of the fact that different objects look the same when projected onto a flat surface (i.e. onto your retina).

For the never ending stairs, there are effectively multiple different staircases being drawn. However, there is some point where the projections of these staircases onto your eye are identical, in the same way that a flat square and a cube from up close look identical. Some kind of depth information about the staircase is just lost in the process of looking at it.

When we stitch these images together, we end up with a 2D image that has no cuts, but the overall 3D object has some kind of contradictory global property, like apparently being at two different heights at the same time (like the never ending stairs).

Perhaps ironically, a fantastic way of seeing this is to try to create these objects in 3D. You can see in [this 3d model](https://pinshape.com/items/43838-3d-printed-impossible-stairs) that there’s some breakpoint in the 3D object, but when you look at it from the right angle, that breakpoint disappears and it looks like the 2D shape smoothly connects with itself.

Anonymous 0 Comments

It’s the illusion of a 2d thing appearing 3d. Your brain is perceiving a flat shape made of lines as an image of a 3d thing from one side of it. If you draw a shape that vaguely looks like a 3d thing but also is messed up in a way that cannot exist, it fools your brain into thinking of it as an impossible shape, rather than a 2d collection of lines