Preface

This preface is a brief note to those intending to read Visualizing 4-space. Visualizing 4-space is one of the many vivid and dynamic topics written for the purpose of being read in Thinking 4-D. As one can tell by its title, the particular topic covered by the material presented in Visualizing 4-space is a topic centered around discussion of the fourth dimension. Visualizing 4-space is, however, not the only topic in Thinking 4-D to address the fourth dimension. The fourth dimension is also discussed in the Thinking 4-D topic Visualizing the Hypersphere. What relationship, if any, exists between the material associated with these two topics?

What must first be made clear is that Visualizing 4-space was the first of the two topics to be written. Visualizing the Hypersphere came afterward. The relationship that exists between these two topics is a time-related relationship. Because Visualizing 4-space came before Visualizing the Hypersphere, Visualizing the Hypersphere can by its own nature be considered to be a continuation of the concepts presented in Visualizing 4-space, taking over where Visualizing 4-space left off. Therefore, some concepts found in Visualizing the Hypersphere have their origin in Visualizing 4-space. Of those concepts having origin in Visualizing 4-space, you may find that they are explained much more clearly in Visualizing the Hypersphere. This is, quite simply, because the passage of time brought about greater familiarity with these concepts.

Which discussion on the fourth dimension, in conclusion, should be read first? Well, what makes Visualizing the Hypersphere appear to be the "better" topic on the fourth dimension is that it not only covers all vital concepts presented in Visualizing 4-space, but, as stated, does a better job of it. Visualizing the Hypersphere is "better" in the sense that the explanation of the fourth dimension it provides is much more thorough and complete. Yet some crucial concepts exist in Visualizing 4-space that are not covered in Visualizing the Hypersphere, making Visualizing 4-space of value. It is for these reasons we should consider Visualizing 4-space and Visualizing the Hypersphere to each serve their own designated purpose. Because each discussion on the fourth dimension is equally worthy of being read, the order in which they are to be read is a matter of personal choice.