Understanding 2D Worlds: The Perception of Shapes in Flatland

[Pflip]

[SOLVED] Flatland question

In Hyperspace, Mr. Kaku makes several references to a 3D object entering a 2D world. If the object is say, a ball, he notes that the 2D people would see a giant, dark circle.

My question is how they can tell it's a circle. It would seem that if the ball were to come down in front of them, all they would see is a darknesss on the horizon. How could they possibly get a "bird's eye view" and see the outline of the object?

Thanks,
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[selfAdjoint]

In Flatland they would maneuver around it and discover it has no corners, and thus discover it's a priest - i.e. what we call a circle. After all, what they could see of each other was only a dark stripe too- recognition was tactile.

BTW, Welcome to the forums. Nice to have you.

 

[alkaline]

They don't even have to maneuver around the circle - having two eyes, they could make out the shape of the circle using binocular vision to visualize the shape inside their head. Shading would also give clues to its shape. We do these same things in the third dimension when we see spheres. Hold a ball in front of yourself and ask yourself how you know it is a sphere and not a disk.

You can get more explanations of the dimensional interactions at my website:

Fourth Dimension: Tetraspace

 

[Pflip]

OK, I can buy both explanations, of course the examples in the book don't mention the flatlanders moving around, merely that they see a giant circle appear.

As for knowing the ball is a sphere and not a disk, I could only do that if it were close enough.

It's a little hard to imagine seeing something that has NO height. But these are fascinating concepts to consider. I look forward to many more discussions.

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[Hurkyl]

The elite flatlanders practiced the art of identifying the shape based on lighting; the omnipresent fog would dim the figure before them in a characteristic pattern and those who trained in sight recognition could tell the shape from the color pattern.

 

[alkaline]

Generalizing, a person of dimension n will see a hyperplane of dimension n-1 (flatlanders see a line, we see a plane, "tetronians" see a "realm"). Thus, a being in any dimension would only need 2 eyes, because the combination of the two images in the brain adds the last dimension and brings the image up to dimension n.

 

[drag]

Originally posted by Pflip
My question is how they can tell it's a circle. It would seem that if the ball were to come down in front of them, all they would see is a darknesss on the horizon. How could they possibly get a "bird's eye view" and see the outline of the object?

I don't remember precisely but I believe he said that if their plane was to
pass past the object then they'd "see" a circle - the line would first get
wider and then narrower again. (Couldn't read past the middle of that book,
all that art stuff bored me to death, I guess I should finish reading it sometime.)

Live long and prosper.

 

[alkaline]

i think the question was how the flatlander could perceive the shape as a circle, as opposed to them thinking it was a line, square, triangle, or any other shape. If they thought it was a line, then they would see a line grow & shrink instead of thinking it was a circle doing that.