Reasons to Believe

"What’s All This Higher Dimensionality Stuff?", Part 5 of 7

For many years science fiction writers have used the so-called “fifth dimension” (a fourth spatial dimension) to serve as a platform for telling fascinating stories.

The discussion here continues from last week, Part 4.

The 3-D cube in Figure 1 (of Part 4) demonstrates the idea of the projection of an object from a higher dimension to a lower dimension. The object as drawn is not, in fact, a 3-D cube, but the projection of such a cube into two dimensions. Even so, the reader immediately identifies it as a picture of a 3-D cube. Another way of displaying a higher-dimensional object in a lower dimension is by unfolding it into a lower dimension.

Unfolding a square into one dimension
Figure 2: Unfolding of a square into one dimension

The unfolding of a 2-D object, a square, into one dimension is demonstrated in two stages in Figure 2. The unfolding of a 3-D cube into two dimensions is shown in Figure 3. The latter is obviously what results when a cardboard box is flattened.

Unfolded cube in two dimensions
Figure 3: Unfolded cube in two dimensions

An interesting feature of multidimensional geometry can be seen using the succession of “cubes” in Figure 1. Notice first that the 1-D cube can be generated by sliding the 0-D cube in a direction, or dimension, at right angles to itself. The beginning position defines one end of the line; the sliding action sweeps out the line; and the final position defines the other end of the line. This process is more easily seen when using the 1-D cube to generate a 2-D cube, or square. The beginning position of the line defines one side of the square; each end of the line sweeps out two sides of the square; and the final position of the line forms the fourth side of the square. Figure 4 demonstrates these two examples.

Generating higher-dimensional "cubes" by sliding lower dimensional "cubes"
Figure 4: Generating higher-dimensional “cubes” by sliding lower dimensional “cubes”

Hang in there. There’s a point to all this. We’ll continue next week.

 


Part 1 | Part 2 | Part 3 | Part 4 | Part 5 | Part 6 | Part 7

 

Subjects: Bible Difficulties, String Theory

Dr. David Rogstad

Dr. Dave Rogstad received his PhD in physics from Caltech and worked over 30 years for NASA’s Jet Propulsion Laboratory. Though now retired, Dave continues to serve as an RTB board member and participates regularly in several RTB podcasts.