B3D-Chapter 7

Irene Klein

Reading through Chapter 7, I was familiar with the term "configuration spaces" but I was unable to find a concrete definition. Overall, I was most intrigued by the way one can describe a movement using different dimensionalities. For instance, when moving an arm, one moves it(physically) in three space. However, on p. 135 the book talks about the arm having six dimensions, not including the wrist. It seems to all depend on the measurements one decides to use. Since an arm can be described both in three dimensions and six, depending on the dimensionality, is the 3-D view like a projection of a hypercube in 3 space?

It seems that in this chapter, we are talking about a different type of dimensionality than in previous chapters. In previous chapters we were talking about spatial dimension. Now we seem to be talking about graphical or numerical dimensionality. Every object discussed in the chapter is able to be described in 4 or more dimensions, yet they exist in only three dimensions. But do they exist in more?

Prof. Banchoff's Response