The Displacement Problem

Dembski (2002a) asserts that the displacement problem is, in fact, the core of his thesis. At a close inspection, however, it becomes clear that the displacement problem is irrelevant to real-life situations. Recall that he defines it as "the problem of finding a given target. . . displaced to the new problem of finding the information j capable of locating that target. Our original problem was finding a certain target within phase space. Our new problem is finding a certain j within the information-resource space J" (Dembski 2002b, 203). As he explains, "the fitness function is of course the additional information that turns the blind search to a constrained search" (202). Hence, the information-resource space J is meant by Dembski as a space of (possibly along with other sources of information) all possible fitness functions.

According to Dembski, the information-resource space J is "in practice . . . much bigger and much less tractable than the original phase space" (203). Hence, the original problem has been displaced to a much more intractable problem. To solve the new problem, he insists, the specified complexity must be injected by intelligence. In summary, his displacement problem means that the space of all possible fitness functions has to be searched to determine the fitness function for the problem at hand.

Dembski gives us no reason to assume that the information-resource space is much larger and much less tractable than the original phase space. In fact, there seem to be no such reasons. The information-resource space can be larger, about the same size, or smaller than the phase space. Dembski provides an example of a search for a treasure buried on an island (204). Instead of a search all over the island (whose topography constitutes the phase space), the search may be displaced to a worldwide search for a map of the island, wherein the location of the treasure is indicated. Now the information-resource space is the entire globe, which is immensely larger than the island in question.

This example can easily be reversed since it could happen as well that finding the map in question is much easier than finding the treasure itself without a map. Indeed, if it is known that the map is hidden in a certain building in a certain city, the information-resource space becomes the specific building and is much smaller and much more tractable than the original phase space (which was the entire island). But regardless of which space is larger and less tractable, and regardless of the very existence or absence of the displacement problem, it is irrelevant for a real-life optimization search. Here is why.

To start a search, a black-box algorithm needs no information about the fitness function. To continue the search, an algorithm needs information from the fitness function, but no search of the space of all possible fitness functions is needed. In the course of a search, the algorithm extracts the necessary information from the landscape it is exploring. The fitness landscape is always given and automatically supplies sufficient information to continue and complete the search.

Consider Dawkins's WEASEL algorithm. It explores the available phrases and selects from them, using the comparison of the intermediate phrases with the target. The fitness function has, in this case, built-in information necessary to perform the comparison. This fitness function is given to the search algorithm; to provide this information to the algorithm, no search of a space of all possible fitness functions is needed and therefore is not performed.

The same is true for natural evolutionary algorithms. The evolutionary algorithms, both designed by intelligence and occurring spontaneously, deal with given, specific fitness functions and have no need to search the information-resource space. Dembski's displacement problem is a phantom.

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