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Impossible Figures Library

im-possible.info

I like these. Some of them are even non-obviously impossible. They may pass at first glance, but then one sees why it shouldn't work.

I recently posted my figures [0] here. It's also a kind of impossible figures, however they are actually printable in real life but still tricks the mind.

[0]: https://github.com/Matsemann/impossible-objects

It cracks me up that I'm getting tons of ads for 3D printing on a website for impossible objects.

Then I'll suggest https://www.kleinbottle.com

"Glass Klein Bottles for sale - inquire within"

You could be the future of advertising..

I'm struggling to understand why the illustration at the bottom left of https://im-possible.info/english/library/grey/grey4.html is impossible. If you don't assume the two horizontal bars are parallel, and the top one is farther back than the bottom one, it make seems to make sense.

Eg it has a side profile of;

                ----
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            ----

I guess it's because the bottom and top bar look like their edges are actually touching which should be impossible with the middle bar going between them without it being squished.

I was able to recreate it in FreeCAD:

https://i.imgur.com/atOSXbc.gif

I don't think your idea would work in an ortho projection (like the one in the drawing). If the two horizontal bars were separated vertically you would have to see a space between them instead of the them sharing an edge. You idea should work if there is perspective distortion involved and the top bar is closer to the viewer and is also longer than the other.

The "bottom" and "top" pieces have the same length (transversal in your projection), as the 3d figure shows. But if you try to place the pieces so that their edges match on a projection, then they cannot start and end at the same point (one is "nearer" the camera than the other).

A agree, and I just reproduced it physically using three rectangular objects that were to hand on my desk.

Presumably the impossibility is meant to be that the edges of the two parallel bars are actually touching, rather than just being aligned in the angle of view. But it is certainly possible to reproduce this physically.

I wonder what the text equivalent would be.

Are there sentences which are locally consistent[1] but globally impossible?

(the question is on my mind because earlier on HN I'd had a nice convo about a folk song embedded in a protest song in which the quoted verse worked nearly as well as polish under a functor as in the original ukrainian.

https://news.ycombinator.com/item?id=24101696 )

[1] on a longer scale than "colourless green ideas sleep furiously", of course.

Garden-path sentences. Or comparative illusions.

https://en.wikipedia.org/wiki/Garden-path_sentence

https://en.wikipedia.org/wiki/Comparative_illusion

ขอบคุณ! The garden-path admits of a consistent, yet initially unpredicted reading, while the comparative illusion is exactly what I'd been groping for: locally cromulent but globally uffish.

First you need to map geometric concepts to language. What is grammar, what is syntax? (I propose that 'syntax' is 'local coherence', and grammar is 'global coherence'.)

And the trick of these figures is using symmetry to fool the brain into creating imaginary 'grammatical structure' that simply are not there.

What is important to note is at symmetric axis, graphical duals are present which are syntactically correct -- a beam intersecting a plane for example -- but are no longer semantically equivalent.

So probably, homonyms will be required liberally.

Language Log occasionally discusses "Escher sentences", with the prototype being "More people have been to France than I have."

I suspect this is the kind of thing you're going for?

Paradoxes, like: This sentence is a lie.

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