hypervolume love

# hypervolume

## Definitions

• noun geometry A volume in more than three dimensions.

hyper- +‎ volume

## Examples

• In the case of hypersolids there are rules for computing the volume of the boundary or of portions of the boundary, and for computing the hypervolume, that is, the magnitude of that portion of four-space inclosed.

• In fact, some evolutionary algorithms may indeed be stuck to a particular hypervolume but that is a feature by design, not a limitation of evolutionary algorithms and in fact, in evolution it seems that gene duplication is a major contributor to innovation.

• They don't assume a designer or observer necessarily, only that there is a hypervolume of possibility that can be resolved to a solution by some method.

• Remember how ID proponents used to argue that evolutionary theory could not explain ‘creativity’ as “evolutionary algorithms are stuck to a particular hypervolume”?

• Furthermore, the fitness function explicitly targets the Steiner solution within that hypervolume—and the program simply follows the fitness function to find the answer.

• All together, there are about 7*1024+10 = 7*1034 possible organisms in the “hypervolume” - a large number indeed.

• All this encoding places the program in the hypervolume of networks and the Steiner problem.

• Here are two physical realizations of such networks - just two members of untold billions from the “hypervolume” of possible solutions.

• This is representative of the typical “organism on the street,” selected randomly from the vast hypervolume of solutions.

• If the connections in the Genetic Algorithm are physically represented by wooden sticks of various lengths, and the nodes are physically represented by bolts that can be used to connect the sticks at their ends, then the “hypervolume” of possible solutions includes any and all arrangements of sticks, provided that the bolts used to connect the sticks have one of the five fixed positions, or any allowed “variable” position.