Chapter 12: The Church of the Fourth Dimension

 In this chapter the author took us through a story of an adventure into a church of four dimensions. In this church, an explanation of how a fourth dimension is possible is made. The sermon in the church covered the idea that four dimensions is possible and can be explained through the same logic that our three dimensional world is possible. After the dimensions are explained, the author takes us to a room with the pastor. The pastor demonstrates the idea of a fourth dimension by using magic tricks. Once of which is taking a piece of leather that has two slits in it but is connected at the end and braiding it. Another trick is taking a rubber band, placing it in the box, putting it under the table, and then revealing that the regular rubber band is now tied to another rubber band. Although both of these magic tricks can be done with slight-of-hand movements and logic, they do get the point across that a fourth dimension could be possible, and how it would work. The fourth dimension would make it possible to come into our third dimension at any point and exit it at any point.
  The Fourth Dimension Simply Explained by Henry P. Manning covered the topic of how a fourth dimension could be explained. One thing that I believe that Martin Gardner should have included within chapter twelve, is the explanation provided by Manning. This explanation was that one dimension could be described as a point extended outward from itself, and two dimension is that line extended outward from itself, three dimensions would be that plane extended outward from itself, and the cube that would be formed from that would be extended outward from itself to form a hypercube. This hypercube would represent the fourth dimension. I believe that this was a tremendous explanation that is easy to visualize. Something that I am happy that Gardner omitted from the chapter is the explanation of the triangles intersecting. The reason that I am happy that this was omitted from the chapter is because I feel that it was confusing, and would be difficult for many to understand.
  In Surfing Through Hyperspace by Clifford A. Pickover the three degrees of freedom (of our world) are explained. The three degrees of freedom describe the directions that something can move. In our three dimensional world, motion can happen in up and down, left and right, and forward and backward. What I liked was that Pickover gave the example of the fly. The reason that I wish that Gardner had included this example is that it makes a lot of sense and is a really good way to describe the limitations of three dimensions. It is explained that a fly could not move if placed in a box, so it would be in zero degrees of freedom. If the same fly was placed in a tube it would have one degree of freedom, forward and backward motion. This fly could have its wings removed and be allowed to walk along a flat (or curved) surface to demonstrate two degrees of freedom, forward and backward, left and right motion. A fly with its wings and not contained in a box that is the same size as it would have three degrees of freedom and would be able to use upward and downward, left and right, and forward and backward motion. I feel that this was very explanatory and easily visualized which would have added to the chapter in The Colossal Book of Mathematics. One thing that I feel was better left out of Gardner's book, was the whole story line. Although this chapter included a storyline, I feel like the story in Surfing Through Hyperspace included too many unimportant descriptions and got off track a lot.
  In Geometry of Four Dimensions by Henry P. Manning the definitions of a line, a plane, a hyperplane, and a space of four dimensions are given. The definitions are very clear, and assist in the understanding of the fourth dimension and how it is that a fourth dimension would exist. This fourth dimension would be a space made by five points that are not of the same hyperplane, but are collinear to two other points. The other descriptions are given before the description of a space of four dimensions and are very helpful. Something that I did not like was how Manning defined "a figure" among other words. I feel that it could prove confusing, and that he muddled his definitions. This, I feel, was better left out of Gardner's book.
  Overall, I feel that the chapter was good. The storyline helped keep the information easy to read, and created a good flow. This chapter seemed easy to read, but for a few of the concepts, it may have been necessary to reread a couple of times.