Two Dimensional (2D) Objects

Two Dimensional Objects; do they really exist?

My answer is no; two dimensional (2D) objects cannot exist in the real world, only in mathematical calculations and in theoretical scenarios.

In order to exist, an object must be made of three dimensions; length, width and height. If you can see it or detect it, it must be a three dimensional object.

Now you may be thinking, aren’t the very words written on paper or even in this blog an example of 2D objects? Again, the answer is no.

If you take a piece of paper with writing on it and look at it from the edge, you probably won’t see the height of the ink as it rises above the paper, but it is there. The ink has height and rises from the paper, if it didn’t you wouldn’t be reading this sentence right now. Take that paper and place it under an electron microscope and the ink on the page will look like a mountain range.

Electronically, the words on your screen have a depth to them. You can't really see the depth by moving the moniter, but the depth is there.

Even though there is no possible way a 2D universe can exist with the current laws of physics, this hasn’t stopped people from thinking about a theoretical 2D universe. For example, an author by the name of Edwin A. Abbott wrote a book in 1884 named Flatland. This book introduced characters that lived in a two dimensional universe. In this universe the rain came from one direction, north, since there was no “up” for it to rain down on and people were triangles, squares, circles and straight lines. Somehow light exists in Flatland from somewhere as the residents actually view other residents and things happening around them. Since there is no “up”, the author cannot say the light comes from a sun or another light source so he never answers that question. Since people in three dimensions actually see things (and colours for that matter) after light reflects off of the surface of an object, the author doesn’t say how objects without a surface facing them (that is, without height) can be seen. The author also doesn’t say how anyone can tell a triangle from a square.  If the “person” can only see its edge, how can a figure be discerned? In fact, if a triangle person doesn’t have an edge, that is it doesn’t have any height at all, how can it see? The only place for the eyes would be in the centre of the object facing “up”. However, since there is no “up” or third dimension, how can eyes be placed there? If they could, they still couldn’t look all the way to what is beside it as this requires height. Also, in order for an object to move freely like the people described in Flatland, they would need to be independent of the ground; that is, they must be unattached or untethered. In order to be unattached, there must be space between the two objects and in order to have space this requires a third dimension; height. Finally, if 2D objects did become “people”, like in Flatland, how do they interact? Sound needs three dimensions in order to work, light wouldn’t work as it too needs three dimensions to work and sexual intercourse and general interaction would be impossible as each “person” has no height and therefore would pass through each other because there is no thickness to stop them from doing so. Things may be incredibly flat in Flatland, but they are not two dimensional.

However, for some reason, even great scientists have not figured out these problems with two dimensional objects. Even Albert Einstein used 2D objects in some of his “thought experiments.” For example, in a lecture before the Prussian Academy of Sciences on January 27, 1921, Einstein talked about how you could take a “disc” and put it on a spherical surface and then push that disc across the spherical surface forever as you would not reach anything to obstruct you. He calls this, “two-dimensional continuum that is finite, but unbounded.” Einstein then takes the disc that is on the sphere and, using an outside light source and a flat object below the sphere like a giant piece of paper, manages to create a shadow of the disc on the object below. His theory was that by manipulating the disc on the surface of the sphere, one changes the size and shape of the shadow formed by the disk. Einstein then goes on to say that this can be translated into the, “three-dimensional case.”

Huh?

By using the three dimensional sphere, a light source shining down on the sphere from above and an object below the sphere, you are actually already in three dimensions! Just because the main focus of your concept was on the sphere’s surface, does not negate the three dimensional objects you were using.

Today scientists use the concept of 2D objects to help them understand a three dimensional universe better. Scientists and those without a scientific background seem to like the idea of two dimensional objects as it ‘simplifies things’ when trying to deal with complex ideas. For example, how would gravity work in a two dimensional universe? There isn’t a “down”, so gravity cannot pull from below an object, so would there even be gravity? If there isn't an "up" and a "down", does gravity matters? Some scientists believe that gravity could still exist but that it can warp the universe like someone taking a piece of paper and rolling it into a torus or doughnut-shaped object. The creatures of this “two dimensional” universe would live on the surface.

Now first of all, paper is not two dimensional, it is three dimensional but if you start “curling” a two dimensional universe, it is no longer two dimensional, it is now three dimensional. Second of all, how can you step out of the two dimensional universe in order to curl it? You can only move in two directions, if you moved outside the universe to curl it, you automatically have another dimension.

Also, two dimensional brains would, by their very limited nature of just two dimensions, find thinking much more difficult as a third dimension adds volume and extra space for a brain to exist. I mean, if you took a three dimensional brain and pulled it apart molecule by molecule, took those molecules an formed a "sheet" or one incredibly thin layer, the sheer size would take up the size of a football field! Two dimensional “people” would have to be huge in order to incorporate the brain alone or suffer a vast lack of intelligence!

While scientists may be able to mathematically create a 2D universe, the reality is that it just doesn’t work. As I have shown above, there are far too many problems with a universe limited to two dimensions so much so that it is not truly two dimensional.

It might be fun to think up a two dimensional universe as a concept but like thinking of pigs that spontaneously sprout wings and fly to the moon, it is just not possible.