The discussion continues from last week and ends here.

The last description (made in Part 6) leads to an important observation. So far, I’ve discussed and illustrated the *projection* and the *unfolding* of various “cubes” into lower dimensions. But what happens if a higher-dimensional cube is simply inserted into a lower dimension so it *intersects* that dimension? Say, for example, we insert a 3-D cube into a 2-D space (a plane). Assuming it is inserted “square-on” rather than at an angle, what we see in the plane is a single square. This is illustrated in Figure 6.

In an analogous way, a 4-D hypercube can be inserted into a 3-D space. Unfortunately, we can’t draw a diagram that shows a 4-D cube intersecting a 3-D space. However, a person living in this 3-D space would see a 3-D cube just like in Heinlein’s fictitious story from Part 1 (assuming, again, that it intersects “square-on”).

At this point we can evaluate whether higher-dimensional thinking is useful for understanding difficult doctrines of the Bible. Beginning with a two-dimensional universe, imagine that a person living in this universe encounters the projection of a 3-D cube as seen in Figure 1. A 3-D person looking down on this world from the perspective of three dimensions will immediately describe it as the projection of a 3-D cube in his world, and will recognize that the various angles are right angles (90 degrees). On the other hand, the 2-D person will see two squares (cubes in his world) connected by some lines. If the 3-D person somehow communicates with the 2-D person (say via a written message), and states that all the angles are right angles, the 2-D person will disagree. Such a claim contradicts his measurements.

On the other hand, if the 2-D person realizes (after reading a book about higher dimensionality by some guy named Hugh Ross) that his object is the *projection* of a 3-D cube from a dimension beyond his experience, then he will acknowledge that such a claim about right angles can, in fact, be true. But the 2-D person must first believe in the existence of higher dimensions.

Figure 6: Intersection of a cube and a plane

By analogy, a person living in a three-dimensional universe may encounter descriptions or explanations of phenomena that cannot be correct based on the reasoning processes he normally applies. The only conclusion would be that they are invalid or incoherent. However, it may also be true that an appeal to higher dimensions can possibly resolve the problem, but again, this requires the belief that such higher dimensions exist. When it comes to doctrines such as the Trinity, higher-dimensional reasoning has helped some people resolve the difficulty. However, we must remind ourselves that a revealed doctrine about the nature of the God of the cosmos is ultimately beyond—but not against—reason.

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