I think we can say more: it seems probable that the bulk of any computation will take place in the domain of navigation. Thus, I think we can say with absolute certainty that the whole class of FTL drives relies on math that is known to be solvable in polynomial time. We could arrive any time between 5 minutes and 10 53 years from now, so don't wait up." - ≠P Space trucker "I'm hauling 20 tons of frozen bananas to Alpha Centauri. If the math for a jump isn't known to be " in P," people wouldn't rely on FTL as primary transportation. And nobody who is fleeing from combat would consider that device to be their best chance of escape they probably wouldn't even turn it on. But we wouldn't put one of those in every single spaceship. ![]() If we had a machine today that could take us to the stars at faster-than-light speed, but it had the same time complexity as cracking AES, we might actually build a few of them and turn them on, because even though the likelihood of near-term success is low, the potential payoff is enormous. cracking AES-256), it seems self-evident that nobody would actually put these systems into a multitude of vessels if it was reasonably likely that very many FTL transits would fail to compute within a reasonable timeframe. the halting problem), or not solvable within a useful time (e.g. However, I think we can reasonably exclude a lot of territory.įor one: while there may be a huge class of problems that are either literally unsolvable by computers (e.g. It's obviously impossible to evaluate the time-complexity of a set of problems if I don't specify those problems. Second, let's talk about some constraints. I only care about the time required by the math. ![]() Presumably, the math can be performed whether or not the drives are ready you could even do the math just for fun, and not actually execute the transit once you have the solution. It's often the case that the FTL system must "warm up" (or "cool down" from the previous transit), and that takes time too, but these are always presented as orthogonal concerns. in Star Trek, the computer monitors the warp field and propulsion system to make continuous adjustments), it doesn't impact departure or arrival in any way that we see.Īlso, I am talking about the math only. And if there is any math that must be performed during the transit (e.g. This is true whether the transit is instantaneous (as in BSG) or not (as in SW). But this is the putative justification, and indeed it sometimes gets mentioned by characters.Īnother thing that's almost universally true is that there is no complementary calculation for how to shut down the FTL I don't think I've ever seen something like that. Of course, this isn't why writers do it: they do it because it's a low-effort way to manufacture a ticking clock when you want suspense. if your destination is something in motion, like a planet or star, you can't calculate its position without also specifying a time.Īnd so the most straightforward approach is to read the current values from the environment. It must be performed immediately prior to the FTL transit.Įven without knowing the engineering particulars, there are a couple of obvious reasons why this might be the case: some of the terms in the equations depend on the point of departure, or are time-sensitive, i.e. Whether you're talking about Star Wars' hyperdrive, or Battlestar Galactica's FTL, or probably any of a dozen less well-known variants, the calculation cannot be prepared in advance. ![]() What I propose instead is to enumerate some observable characteristics that are common to a variety of popular fictional FTL systems, and then to reason about their time complexity.įirst, let's talk about the observed characteristics of the FTL systems I have in mind. The obvious challenge here is that we don't have FTL, and I'm not going to describe a specific system and ask you to analyze it. Of course, I'm aware that there are problems that would take more time (and energy) to solve than exists in the universe. For someone fleeing for their life, this is effectively "infinite time." video transcoding, defeating some forms of cryptography.
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