SAN FRANCISCO  It’s 1 p.m. on a Thursday and Dianne Bates, 40, juggles three screens. She listens to a few songs on her iPod, then taps out a quick e-mail on her iPhone and turns her attention to the high-definition television.

Just another day at the gym.

As Ms. Bates multitasks, she is also churning her legs in fast loops on an elliptical machine in a downtown fitness center. She is in good company. In gyms and elsewhere, people use phones and other electronic devices to get work done  and as a reliable antidote to boredom.

Cellphones, which in the last few years have become full-fledged computers with high-speed Internet connections, let people relieve the tedium of exercising, the grocery store line, stoplights or lulls in the dinner conversation.

The technology makes the tiniest windows of time entertaining, and potentially productive. But scientists point to an unanticipated side effect: when people keep their brains busy with digital input, they are forfeiting downtime that could allow them to better learn and remember information, or come up with new ideas.