He hurried on as Anne stirred and seemed about to speak. "But if I slide out from my starting point along a dotted line part way to the 'beta' universe--something which, for reasons I can't explain now, takes negligible time--watch what happens. If I still proceed at the rate of an inch a second in this inter-planar region, then, with the dotted lines all bunched closely together, after five seconds when I switch along another dotted line back to my original universe, I have gone almost the whole length of that longer line. Of course, this introduction of 'alpha' matter--my pencil point in this case--into the inter-planar region between the universes sets up enormous strains, so that after a certain length of time our spaceship is automatically rejected and returned to its own proper plane." "Could anybody in the littler universe use the same system?" John laughed. "If there were anybody in the 'beta' plane, I guess they could, although they would end up traveling slower than they would if they just stayed in their own plane. But there isn't anybody. The 'beta' plane is a constant level entropy universe--completely without life of its own. The entropy level, of course, is vastly higher than that of our own universe." Anne sat up. "I'll forgive you this time for bringing up that horrid word _entropy_, if you'll promise me not to do it again," she said. * * * * * John Shrugged his shoulders and smiled. "Now," he said, "if I want to get somewhere fast, I just start off in the right direction, and switch over toward 'beta.' When 'beta' throws me back, a light-year or so toward my destination, I just switch over again. You see, there is a great deal more difference in the sizes of Alpha universe and Beta universe than in the sizes of these alpha and beta line-segment analogues. Then I continue alternating back and forth until I get where I want to go. Establishing my correct velocity vector is complicated mathematically, but simple in practice, and is actually an aiming device, having nothing to do with how fast I go." He hesitated, groping for the right words. "In point of fact, you have to imagine that corresponding points in the two universes are moving rapidly past each other in all directions at once. I just have to select the right direction, or to convince the probability cloud that corresponds to my location in the 'alpha' universe that it is really a point near the 'beta' universe, going my way. That's a somewhat more confused way of looking at it than merely imagining that I continue to travel in the inter-planar region at the same velocity that I had in 'alpha,' but it's closer to a description of what the math says happens. I could make it clear if I could just use mathematics, but I doubt if the equations will mean much to you.