To thrive in this frenetic world, certain cognitive tendencies are useful: to embrace novelty, to absorb a wide variety of information, to generate new ideas. The possibility that such characteristics might be associated with A.D.H.D. was first examined in the 1990s. The educational psychologist Bonnie Cramond, for example, tested a group of children in Louisiana who had been determined to have A.D.H.D. and found that an astonishingly high number — 32 percent — did well enough to qualify for an elite creative scholars program in the Louisiana schools.

It is now possible to explain Professor Cramond’s results at the neural level. While there is no single brain structure or system responsible for A.D.H.D. (and some believe the term encompasses more than a single syndrome), one cause seems to be a disruption of the brain’s dopamine system. One consequence of that disruption is a lessening of what is called “cognitive inhibition.” The human brain has a system of filters to sort through all the possible associations, notions and urges that the brain generates, allowing only the most promising ones to pass into conscious awareness. That’s why if you are planning a trip to Europe, you think about flying there, but not swimming.

But odd and unlikely associations can be valuable. When such associations survive filtering, they can result in constructive ideas that wouldn’t otherwise have been thought of. For example, when researchers apply a technique known as transcranial stimulation to interfere with key structures in the filtering system, people become more imaginative and inventive, and more insightful as problem solvers.

Individuals with A.D.H.D. naturally have less stringent filters. This can make them more distractible but also more creative. Such individuals may also adapt well to frequent change and thus make for good explorers. Jews whose ancestors migrated north to Rome and Germany from what is now Israel and the Palestinian territories show a higher proportion of the A.D.H.D. gene variant than those Jews whose ancestors migrated a shorter distance south to Ethiopia and Yemen. In fact, scientists have found that the farther a group’s ancestors migrated, the higher the prevalence of the gene variant in that population.