Bristol grinned suddenly. "Yes, dear," he said. He paused a moment to collect his thoughts. "First of all, you know that there are two coexistent universes or planes, with point-to-point correspondence, but that these planes are of very different size. For every one of the infinitude of points in our Universe—which we call for convenience the 'alpha' plane—there is a single corresponding point in the smaller or 'beta' plane."
Anne pursed her lips doubtfully. "If they match point for point, how can there be any difference in size?" she asked.
John searched his pockets. After a little difficulty, he produced an envelope and a pencil stub. On the back of the envelope, he drew two parallel lines, one about five inches long, and the other about double the length of the first.
"Actually," he said, "each of these line segments has an infinite number of points in it, but we'll ignore that. I'll just divide each one of these into ten equal parts." He did so, using short, neat cross-marks.
"Now I'll establish a one-to-one correspondence between these two segments, which we will call one-line universes, by connecting each of my dividing cross-marks on the short segment with the corresponding mark on the longer line. I'll use dotted lines as connectors. That makes eleven dotted lines. You see?"
Anne nodded. "That's plain enough. It reminds me of a venetian blind that has hung up on one side. Like ours in the living room last week that I couldn't fix, but had to wait until you came home."
"Yes," said John. "Now, let us call this longer line-segment an 'alpha' universe; an analogue of our own multi-dimensional 'alpha' universe. If I move my pencil along the line at one section a second like this, it takes me ten seconds to get to the other end. We will assume that this velocity of an inch a second is the fastest anything can go along the 'alpha' line. That is the velocity of light, therefore, in the 'alpha' plane—186,000 miles a second, in round numbers. No need to use decimals."