Our expectation is that knowledge follows a diffusion process through geographic, institutional and technological spaces. Thus, researchers that are “nearby” along each of these dimensions would be particularly likely to benefit disproportionately in the time period immediately after the antecedent innovation occurs. We expect, however, that this “localization effect” will tend to fade over time, so that eventually the probability of an antecedent benefiting a remote descendant may be no lower than the probability of benefiting one nearby.

Thus localization and the fading of localization are phenomena that derive from the relationship between two inventions or inventors. But these relational phenomena are intrinsically tied up with the attributes of the antecedent and descendant themselves. A particular inventor (or group of inventors) may just be good at picking up and implementing others’ ideas quickly, and others may be good at disseminating or spreading the implications of their research, or may produce research which is systematically more “fruitful” in stimulating others. The probability that a particular group will benefit from some other group (and the changes over time of this probability) will therefore be determined jointly by the properties of each group, and the properties of the relationship between the groups.
In addition to diffusing outward over time, bits of knowledge also become obsolete. Thus, though the probability that a given inventor will know of a given antecedent increases as the time lag between them grows, the probability that the antecedent will actually be helpful declines, on average. The combination of diffusion and obsolescence processes may cause the probability of using a given antecedent to first rise and then fall with elapsed time.