1 dimension, 2 dimension, 3 dimension, 4

There is a book out there titled “Flatland, by A Square” written by E. A. Abbott in 1884. It is an amazing little book that tries to explain the fourth dimension by taking you on a trip through the second dimension. Now, if you are confused by the talk of different dimensions of existence, let me simplify things. In our physical world, the dimensions are nothing more than Length, Width, and Height. Those are the three dimensions of our world, and we, therefore, live in the third dimension!

In a two dimensional world there are only two dimensions, Length and Width, kind of like a sheet of paper. A two dimensional being’s world has no height and they, therefore, cannot jump over obstacles but have to go around them. Following this same line of thinking, a one-dimensional creature would live on a line and would only be able to move forward and backward. They would not be able to turn around and would never see what was behind them, nor could they pass whatever was in front of them. Are you still with me?

Imagine, for a moment, that you entered Flatland. The very instant you entered the surface of Flatland, you would appear to the creatures in Flatland as a small dot in front of them. Obviously, only a very small portion of your three-dimensional body could be in the two-dimensional (plane) world at any given time. Compare it to pushing your finger through a sheet of paper. The tip of your finger and fingernail would be below the paper (not in the two dimensional world) and your hand and the rest of your body would be above the paper and also outside the two-dimensional plane. Only a thin whisp of your finger would be in the same plane as the paper and visible to a two-dimensional being. Sometimes I think this is what happens when people see the apparitions we call ghosts. Fourth dimensional beings who can only manifest a “whisp” of their actual selves to a three-dimensional world!

From a world of no dimensions, to our world of three dimensions, you only need to move the original dimension perpendicular to itself to create each new dimension. Move a “no dimensional dot” perpendicular to itself and you create a line (one dimension). Move the line perpendicular to itself and you create a plane (sheet of paper, two dimensions). Move the plane perpendicular to itself and you create a cube (our world, three dimensions). Now comes the part that will stretch your imagination. How do you move our three-dimensional world perpendicular to itself?

Some say you do it by moving in or out like the layers of an onion, but this is only a three-dimensional explanation of a much deeper concept. Einstein said that the fourth dimension is a thing called Space/Time, and amazingly, space and time are interchangeable in many of his formulas. What this means is, we should be able to move around in time just as easily as we do in space, and there are an infinite number of these “times” that we could exist in! Also, we would not, and could not, leave one to enter the other. Like the three dimensional creature that exists in an infinite number of two-dimensional worlds all at the same time (like a stack of paper), a three dimensional creature (us) would exist in an infinite number of three dimensional worlds all at the same time.

Flatland by A Square is a fascinating book and easy to read. Ladies, beware, it is very chauvinistic in its views. The creatures in Flatland are categorized by how many facets they have. Triangles, with only three facets, are relegated to the females of the society with isosceles triangles being the lowliest of women, and equilaterals being the most advanced. The men are all polygons and begin as squares and can graduate to pentagons (business people), hexagons (college professors), octagons (government or church officials), etc. until they have so many facets they appear as complete circles, the priestly class. If you can get past this chauvinistic view, Abbott gives many examples of what we, as three-dimensional beings, would look like to a two-dimensional world. From that, you can cogitate on what a forth-dimensional being would look like in our three-dimensional world. This could be as much fun as contemplating your bellybutton.