3
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The object came with a few clues to help you figure it out.

I can be viewed on paper
I cannot be viewed in reality by your kind
I am made up of what your mind can truly comprehend
I resemble a shape many learn first in primary

It's freakishly easy if you think in a specific way.

BONUS (for people who don't mind risking not being first for more quality):

How many edges and vertices does it have, and what does it look like?

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  • $\begingroup$ Um... Care to explain the downvote? $\endgroup$ – warspyking Dec 1 '14 at 19:25
  • $\begingroup$ A down-vote seems unwarranted until you at least know the answer. $\endgroup$ – tjbtech Dec 1 '14 at 19:42
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    $\begingroup$ @Josh "How's my faces". That was most likely auto correct. $\endgroup$ – warspyking Dec 1 '14 at 19:58
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    $\begingroup$ This question has many possible answers $\endgroup$ – Julian Rosen Dec 1 '14 at 21:20
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    $\begingroup$ @warspyking I downvoted because there are so many possible answers that fit all the clues, and not enough information to determine which one you happen to be thinking of. For example, a Klein bottle. Or just an n-dimensional tesseract for n>4. $\endgroup$ – Lopsy Dec 2 '14 at 4:28
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A tesseract (a 4-dimensional analog of the cube). You can see the projection of a tesseract. "Our kind" is three-dimensional, so we cannot see it. It is made of cubes which we can comprehend. It resembles a square which we learn in primary (it is actually a generalization).

A really cool gif of a tesseract.

24 faces
32 edges
16 vertices

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  • $\begingroup$ Normally, it is projected into a figure that resembles an octogon. $\endgroup$ – Victor Stafusa Dec 1 '14 at 20:32
  • $\begingroup$ @Victor I really like this projection $\endgroup$ – dmg Dec 1 '14 at 20:34
  • $\begingroup$ This was one of the first things that came to mind based on the first two lines (and having recently watched Interstellar). This would have been my second guess. +1 from me. $\endgroup$ – jliv902 Dec 1 '14 at 20:35
  • $\begingroup$ Nice! :D I added the bonus if you'd like to include that? $\endgroup$ – warspyking Dec 1 '14 at 20:36
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    $\begingroup$ Projections of 3D objects can be viewed on paper, but a tesseract is 4-dimensional. Thus it cannot be viewed on paper. $\endgroup$ – MackTuesday Dec 1 '14 at 23:43
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The number of faces is:

Zero

The object is a:

A point

Line 1: I can be viewed on paper

A point can be viewed on paper.

Line 2: I cannot be viewed in reality by your kind

A point, a dimension-less object, cannot be seen in the real world.

Line 3: I am made up of what your mind can truly comprehend

There is a philosophy tag. As we learn more, we realize how little we actually know. There is no real way to know that we truly comprehend something as technology and science change our perspectives as time advances. Therefore, we can say that there is nothing we truly comprehend. A point can be considered made up of nothing.

Line 4: I resemble a shape many learn first in primary

A point resembles a circle on paper.

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    $\begingroup$ "The mind can truly comprehend nothing"? Really? $\endgroup$ – Rand al'Thor Dec 1 '14 at 20:25
  • $\begingroup$ LOL I can officially comprehend how hilarious this answer is with that comment about how mind not comprehending anything. -1 D: $\endgroup$ – warspyking Dec 1 '14 at 20:26
  • $\begingroup$ @randal'thor There is a philosophy tag. As we learn more, we realize how little we actually know. There is no real way to know that we truly comprehend something as technology and science change our perspectives as time advances. $\endgroup$ – jliv902 Dec 1 '14 at 20:27
  • $\begingroup$ @jliv902 - Sorry, I misunderstood. I thought you were saying the mind can comprehend the concept of nothing! That makes it even funnier, I guess... $\endgroup$ – Rand al'Thor Dec 1 '14 at 20:31
  • $\begingroup$ @jliv902 You deserve a +1! $\endgroup$ – dmg Dec 1 '14 at 20:32
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Probably not the intended answer, but

the real projective plane

seems to work. It "can be viewed on paper" (see the picture at the top of the link I provided), but "cannot be viewed in reality by your kind" (i.e. by 3D beings) since it cannot be embedded into $\mathbb{R}^3$. It can be seen as being made up of lines in $\mathbb{R}^3$, which "your mind can truly comprehend". And it looks like JontheMon's answer (again see the picture at the top of the link)!

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  • $\begingroup$ I few the answers are inching towards what the solution really is. $\endgroup$ – warspyking Dec 1 '14 at 20:24
  • $\begingroup$ @warspyking - Is it some kind of geometric entity then? $\endgroup$ – Rand al'Thor Dec 1 '14 at 20:25
  • $\begingroup$ I refuse to give away too much lol. $\endgroup$ – warspyking Dec 1 '14 at 20:27
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Edges and vertices:

16 vertices

32 edges

24 square faces

8 cubic cells

In 2D, frequently projected as an octogon.

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1
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Well, I'd say it's a square, so 1 face. However, I think that you could view it, just not from the side; unless it's just the boundary of a square. For the 3rd clue, squares are made up of lines, which are made up of points, and points are hard to imagine.

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  • $\begingroup$ "I resemble a shape many learn first in primary" if you said square because of this, I said it resembles a shape, not that it is a shape. $\endgroup$ – warspyking Dec 1 '14 at 19:40
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It is:

photons

Light particles/waves that are reflected by a white paper.

Their quantum nature can't be really comprehended by our minds. But at the same time, light is all that we see.

Their wave resembles sinuidal waves. Although people normally do not know what a sinuidal wave is in the primary, every small kid know their shapes and frequently draws them even without knowing their exact name nor the mathematics behind. If light is considered a particle, then photons are aproximated to spheres, which every small kid knows about.

How many faces? This can't really be determined. :)

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0
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# of faces:

1


The object is any two-dimensional object.
I can be viewed on paper
You can view a two-dimensional object on paper.
I cannot be viewed in reality by your kind
Our universe is defined in three spatial dimensions. No two-dimensional object can be viewed in reality by us; even a drawing on paper has a thickness, however small, and is never two-dimensional.
I am made up of what your mind can truly comprehend
We can comprehend two-dimensional objects pretty easily.
I resemble a shape many learn first in primary
Most people learn two-dimensional shapes in primary school.
How many edges and vertices does it have, and what does it look like?
Any natural number of edges, any natural number of vertices. It looks like whatever you want a two-dimensional object to look like.

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