apart from shadows, and representations on paper, can a 2D object exist in the 3D world? If 2D requires the 3D world to exist, what are the requirements for the 3D world to exist?

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apart from shadows, and representations on paper, can a 2D object exist in the 3D world? If 2D requires the 3D world to exist, what are the requirements for the 3D world to exist?

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It might help to think of it in more abstract terms – as sets of data with features.

For example, your address contains a street and a state. This is ‘two dimensional’ data. If we then add a street number, we now have ‘three dimensional’ data. If we have a list of streets/states and want to plug them into our number/street/state databases, we need to assign a value for ‘number’ to all of those two dimensional entries.

The same is true with spatial dimensions. If we have a two dimensional object with length and width, we’d need to assign it a height for it to make sense in a three (spatial) dimensional frame.

The question is difficult to interpret because it isn’t clear what “world” and “object” means? If you mean this universe made of matter and energy, then 2D objects made of matter does not exist. A shadow is not made of matter and so if you define it as an object, the discussion becomes rather unclear.

If the definition of world is abstract and sort of mathematical world, then a slice of a 3D object in that “world” is a 2D object. It is possible in an abstract definition to think of a 2D world in which 2D objects reside. It doesn’t require any embedding in a 3D world for that 2D world to “exist”.

That depends on what you mean by ‘object’. If by object you mean a physical thing that has its own physical properties, than no – a 2D object can’t exist in a 3D world.

You can have 2D representations of an object in a 3D world. Think of a photograph, it’s a 2D representation of 3D objects, but the photograph itself is a 3D object (it has thickness). A shadow isn’t really an ‘object’, so it’s not a ‘2D object in a 3D world’.

The closest we can get to a 2D object might be a slice of a substance called graphene. It’s a hexagonal lattice of carbon atoms that is only one atom thick but can be big enough in width and height to see it with your naked eye. But even that isn’t truly 2D. The single-atom thickness is still 3D, even though it’s super thin.

As far as we can tell, our 3D universe isn’t “embedded” in a higher-dimensional space. There’s no mathematical reason to believe it is.

Along with what people have said about drawings, shadows aren’t actually two dimensional either.

If you hang a tennis ball in front of a lamp and turn it on, you’ll see a flat, round shadow on the wall–but the actual shadow extends from the edges of the ball to that spot and fills all the space between. We just think of shadows as flat because the way our eyes work makes it easier for us to notice the part of the shadow that touches the wall, the same way we don’t actually see the light coming from the lamp unless we look right at it or it reflects off of something.