B3D Chapter 1 Summary

The first chapter of B3D is entitled "Introducing Dimensions" and serves as a starting point for those readers who have little or no understanding of the concept of higher dimensions.

Not too surprisingly, Edwin Abbott Abbott's book Flatland is mentioned on the first page of the first chapter.  The idea that objects of different dimensions could interact with other dimensions was (and still is) quite revolutionary.  Also, Abbott's ability to break the ideas down into simple dimensional analogies made the book easy to read.  This, added to Abbott's keen satirical writing style, allowed Flatland to be appreciated on not only a scientific level but also from a literary perspective.

After the discussion on Flatland, the definition of the word dimension and the concept of dimensions as coordinates are both explained.  With so many different uses of the word dimension, it is important to understand the different contexts in which it is used.  In this way, it helps to realize the wide range in which the term dimension can be used.  In many cases, the use of coordinates to describe a position in a specific dimension is useful for seeing the overall picture.  This also allows for a dimension-to-dimension comparison of various types of information and helps to understand the various relationships from one dimension to the next.

Also, the topics of dimensional progressions and visualization technology are discussed.  With the concept of dimensional progression, the use of analogy is used to guess at what goes on at higher dimensions.  One such example is that of a 4-dimensional cube, known as a hypercube, whose many properties can be inferred from the progressions in the first three dimensions.  Next, the history of visualization technology is chronicled from the telescope to the microscope to the X-ray.  And the future of this field looks to hold many new discoveries for us, with the help of computer graphics.

Finally, with respect to possible exercies at the end of the chapter, because the first chapter is a basic primer for most readers, there might not be that much to develop in this case.  One type of exercise, though, might be to ask the reader to infer a formula (such as we did in class) for figuring the edges (and other measurable items) on objects in various dimensions.  In this way, the reader could get a better understanding of the geometrical progression from one dimension to another.