This article adapts a modification of Tamura's theoretical proposition and conducts a cross-country empirical investigation in an attempt to evaluate convergence on two different human capital proxies; namely enrollment rates and per capita researchers. The analysis considers three country groups at significantly different development levels: Advanced, developed and less developed countries. The hypothesis of convergence is rejected when alternative, to enrollment rates, approximations to human capital are used, merely implying the existence of a "convergence trap" for countries with significantly lower endowments of human capital. The results provide circumstantial evidence of within group convergence and between group divergences when enrollment in education is considered, but no convergence/divergence when research effort is considered. This last finding suggests the possibility of a "convergence trap", since initial human capital endowment could drive a process of worldwide polarization. (Contains 6 tables and 19 notes.)