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That's three dimensions, and they can give us a cube. The formula is 53 = 125, five cubed equals one hundred twenty-five. The solid is one hundred twenty-five cubic inches in size.
Imagine another five-inch line from that point at right angles to the other three lines. Stop before you go blind; it can't be done. We are three-dimensional creatures and have our limits after all. In fact, we can say five squared and five cubed, but we don't have a common word for 54. We have to say something awkward like five to the fourth power, but we aren't limited in mathematics to three dimensions. We can deal with 54 equaling six hundred twenty-five or calculate with any other number of dimensions; mathematics itself doesn't have to relate to the physical world.
Is there actually such a thing as four-dimensional reality? Before we say no, I want to bring up a tale written by Rev. Edwin A. Abbot over one hundred years ago called Flatland. I came across it in a series called The World of Mathematics published about fifty years ago, a very good set of books worth looking at if you can find it.
Flatland is a sad little story told by a two-dimensional being who lives in a two-dimensional world like our flat piece of paper. All of the people's bodies have the different shapes pictured below. The higher the class they're in, the more equal sides they have. The soldiers and lowly workers are triangles with two equal sides. The people in the middle class are triangles with three equal sides. Professional people are squares (we can relate) or with more than four sides, and the narrator of the story is a square. The author, Rev. Abbot, tells us a little too much about himself and his times in this story.
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