"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.
"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."[3]
"There is nothing mathematically implausible in that," I said.
"There is nothing implausible, yet to determine the exact distance from G to F is in most cases impossible. Unless the distances involved are of the proper ratio, say, 4 and 5, the line GF becomes an irrational number, of which it is impossible to find the exact value. Supposing the distance from E to F was one light-year and the distance from G to E, one year. Then GF would be the square root of one squared plus one squared, or the square root of two. Because we are dealing with such immense distances and because even the smallest decimal point of error might lead to disastrous results, we cannot attempt time travel unless we know the exact value of the square root of two, or any other irrational number."
As Trella finished speaking there was a coughing hum and the translator appeared in the room, containing the unharmed guinea pig and a copy of the Rihlon Gazette for Aug. 3rd, which was this day.
"Do you believe me?" she cried gleefully, waving the paper over her head.