Translation as in space travel. I cannot find this term in any of the SF glossaries I have checked. Perhaps, I haven't look for it where I should. I was wondering whether this travel system appears in other stories and if so if it maintains its general meaning. In The Madness Season, Translation is defined as follows: Spoiler: "Translation" according to Friedman in TMS

'Translation' in The Madness Season or 'folding space' in Dune. It's the same idea. That through advanced mathematics and some exotic tech that can apply that mathematics, two non-local points in the space-time continuum can be brought together. When I was at university, one of my courses was on a topic called Metric Spaces. Essentially, a metric space was a definition for a mathematical set, where the members in the set were defined by distance in relation to each other, and where three or four conditions had to be met. If those conditions held, then the function was a metric space. So, mathematically, using these different sets, you could construct entire universes that were completely distinct from the one in which we exist. The first time I really 'got' the idea, I was blown away...and the first thing that came to my mind was the disembodied pink brain Krang from Teenage Mutant Ninja Turtles who came from Dimension X. I realised that what I was looking at on paper with these different metric spaces were effectively different universes. And I felt some level of glee at having a glimmer of understanding of what a Dimension X might mean. I think this whole idea of 'Translation' in the novel is just some fancy descriptions for stating that they Tyr have managed to apply something like this mathematical trick (which is theoretically true and consistent) onto the laws of nature. So, the Tyr can leave one universe (or a metric space) and enter another one, where the rules of distance are different, and travel within that universe/metric space (or not at all, depending on what the rules are), and then come back to the first universe at a different location, perhaps instantaneously or with the passing of very small increments of time. When you 'translate' an object in mathematics, you move it some measurable distance from one location (say, on a two or three dimensional xyz-grid) to another exactly as it is. The object is not rotated, not inverted, not mirrored, not changed in any way. I guess Friedman is using that term in the same way. All this fantasy/magic with hyperspace or underspace or whateverspace is just the application of these metric space mathematical ideas. I liked the explanation in Dune the best. It was intuitively one of the simplest. Just fold space so that two different point coincide into one, so you really do travel instantly at any point in the galaxy or potentially the universe. I also liked Zindell's intuitive explanation in Neverness.

Let me see whether I've got this metric thingy right. So, points belonging to the same parameter are actually a single point. Like the imaginary line, one could draw after piercing different sheets of paper with a long needle? Then, by folding the paper in a specific way, one could choose by which hole to enter and by which one to leave? And hence without consuming time/space in the process. This brought back some memories of when I took technical drawing and my teacher used to look up me in despair...

This sounds like the class of SF devices that work on the conceit that a certain class of mathematics or understanding of math allows some sort of transport. Reynold's cryo-arithmetic engines, MacLeod's kraken piloted hyperspace ships and the navigators of Dune replacing the previous computers are all examples, but they aren't all FTL. The difference between "translating" as FTL vs. hyperspace travel and wormholes is largely handwaving. You can say that you are "becoming tachyons" or that you are "entering hyperspace", but really the only difference is the explanation about what the FTL environment is and how fast it (apparently) works. They could be said to be the other FTL option from "warp", where you stay in the standard universe but change the rules here. The only other distinct system I can think of is the Infinite Improbability Drive, which could be said to be a type of quantum device that makes you "happen" to come into existence somewhere else.