By means of radio signals the exact location of every explored planet had been determined. It was therefore only a matter of mathematical calculation to find the target. There was some risk, of course, if a mathematical error were made in computing the range but considering the risks involved in ordinary methods of interstellar flight everything was in favor of the translator.
"The whole secret of the invention lies in locating the proper _Now_ in space-time," Trella explained.
"Of course," she said, "the _Now_ we experience on earth is not the same _Now_ that exists simultaneously on Rihlon, the second planet of Proxima Centaur. We are dealing with space-time, Fred. Time is a dimension, it stretches like a line through space. If we connect the _Now_ of the present with the _Now_ of ten minutes ago, we have a straight line, just as we would have a straight line if we connected any two points in the universe. The _Now_ of the present and the _Now_ ten minutes ago on Rihlon also would be a straight line, but it would not be the same straight line."
"But it would be parallel!" I exclaimed, beginning to see her point.
"Oh, so you _do_ know something about mathematics?"
"Of course! If you connect the _Nows_ of the present on both the earth and Rihlon, you have a straight line, perpendicular to the parallel time lines of both the earth and Rihlon. Why couldn't your invention be used for time travel? Couldn't you connect the present--_Now_ of Rihlon with any _Now_ in the time line of the earth--any _Now_ of the past or future?"
"The idea occurred to me, but it won't work," Trella replied. "There's a serious obstacle we can't overcome. In going backward or forward in time we do not travel in lines perpendicular to the parallel time lines of the earth and Rihlon--or for any other planet for that matter. But we travel like this--" Trella drew a figure on a piece of paper.
A G E B -------+----+------ \ | \ | \ | C \|F D ------------+-----
"The line AB represents the time line of the earth and the line CD represents the time line of any other planet X. The two lines are parallel. E represents the earth--_Now_, and F the _Now_ on planet X. A line connecting the two is perpendicular to both AB and CD. Supposing we should travel from F to a point G, a _Now_ in the earth's past. If we connect F and G we would have a right triangle GEF. The hypothenuse GF would be the square root of GE squared plus EF squared."