Grids are facing the challenge of moving from batch systems to interactive computing. In the 70s, standalone computer systems have met this challenge, and this was the starting point of pervasive computing. Meeting this challenge will allow grids to be the infrastructure for ambient intelligence and ubiquitous computing. This paper shows that EGEE, the largest world grid, does not yet provide the services required for interactive computing, but that it is amenable to this evolution through relatively modest middleware evolution. A case study on medical image analysis exemplifies the particular needs of ultra-short jobs.