Every problem in P is also in PSPACE, because fast algorithms just don’t have enough time to fill up much space in a computer’s memory. To prove that PSPACE is larger than P, researchers would have to show that for some problems in PSPACE, fast algorithms are categorically impossible. They hoped to prove that algorithms given a certain space budget can solve all the same problems as algorithms with a slightly larger time budget. A universal simulation can’t exploit the details of any specific problem, so it probably won’t save as much space as a specialized simulation. “This guy Hartmanis defined the time and space complexity classes,” he recalled thinking.