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Rh times these objections can be fairly well met, so that a final conclusion as to the applicability of the theory is reached with difficulty. Further, it is clear that there is usually but a single solution for a problem so that if it is solved at all it will be solved in the same way and given time enough some one is by the law of accident sure to hit upon it. But the greatest difficulty with the theory of independent invention is found in the observed distribution, for this tends to be continuous over certain areas, instead of intermittent, as would be the case if due to accident, unless we assume a greater age for New World culture than other facts warrant. Also, we have historical examples of diffusion, as, for example, the Ghost Dance religion, the Peyote Cult, the Grass Dance ceremonies, the Spanish horse culture, etc., and scarcely one of the contrary kind. In these historic cases, the phenomena came under direct observation so that there can not be the least doubt as to diffusion, or borrowing by one social group from another. The most satisfactory conclusion, then, seems to be that while there is reason to believe that different social groups will ultimately solve many of their problems in the same way, they are far more likely to borrow the solutions of their neighbors, which arrangement gives the initial solution a very great advantage. Hence, when there is continuity of distribution we may posit a single origin, or locality, from which the trait has been diffused, until we can find evidence to the contrary.

The most modern advocate of the diffusion theory is Graebner, who is disposed to the extreme view that independent invention is practically impossible and that all similarities, however widely separated, are to be considered as having single origins. Such extreme views are always harmful, for they set up a mere formula according to which problems are solved deductively, whereas the true and safe method of science is to proceed empirically. The ideal method is to treat each case according to its own data and not to assume diffusion from a single locality until we have some good, specific reasons for so doing.

There is, however, still another theory to account for similarities in culture—an hypothesis first advocated by