Topology and Creation

Topology and Creation

Mathematical topology sheds some light on the different forms of animals seen in the creation. We can imagine a space E of possible environments and a set of n body plans. Each body plan i has some efficiency Fi(e) in environment e. The Creator would, in our simple human approximation of His thinking, choose the body plan i maximizing Fi(e) for a creature that is to live in environment e. Thus each body plan i has a region Ri in which it is the optimum choice. Within this region Ri, all created organisms will be highly similar. However, when one crosses outside of this region, suddenly the chosen body plan will change drastically, because another Fj(e) will be optimal.

Let's consider what happens within a region Ri. Suppose e1 and e2 are two environments in this region, and suppose there is a continuous path from e1 to e2 in the region Ri. As we travel along this path from e1 to e2, the optimum creature will change gradually, but within the same general body plan. This gradual change from one creature to another is like a ``continuous deformation'' in topology by which one structure can be changed into another. For example, we can imagine a mouse being gradually deformed into a bat. The limbs will change their shapes to some extent, the forefingers will become very long and distorted, skin will grow between the bones, but the basic body plan will stay the same. There will still be the same number of fingers on each forepaw, and the structure of the bones will be similar. However, this will not be due to common descent, but rather to the mathematical properties of a continuous deformation.

We can consider that the Creator chose a finite set {e1,e2,e3, ..., ek} of environments that closely approximated all of the environments that would occur on earth. Then the creatures made would be those that would optimize their efficiency on each of these environments. So we will not see all of the steps in the deformation from a mouse to a bat illustrated in created life. But in some cases, many of the steps along a path from e1 to e2 may correspond to created organisms, leading to sequences that can be mistaken for evolutionary progressions. However, since there were only a finite number of created organisms, there will be gaps between the organisms in these sequences, gaps that cannot be filled in.