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xkcd #2821: Path Minimization
(startrek.website)
Link to comic: https://xkcd.com/2821/
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this post was submitted on 29 Aug 2023
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Path that maximises time would be some kind of space-filling curve. Maybe it does that off panel?
Basically, yes. The path that maximises time goes around the world, so starts by going up off the top of the screen, and re-enters at the bottom.
Technically I think it could be a little longer by spiralling around the world several times, still reaching the target point despite going “in a straight line”. If we ignore the “straight line” restriction, which some of the other paths already do, then the sky’s the limit. Technically actually, the sky isn’t the limit, and the path could criss-cross over the whole planet first, and the air, and the whole galaxy, before reaching the destination as the last feasible space to arrive at. Personally I think that’s too complex for xkcd, if they are going for complex I’m sure they would have come up with something about paths through n-space and black-hole theory that is beyond my pay grade.
Xkcd good ;)
It’s the path that maximises time, not distance. Technically the path that maximises time could look the same as the path that minimises distance, they could just sit down and wait decades until a minute before they die of natural causes and then get up and head to the end, and that’s assuming that they need to arrive alive.
It would have to be a different panel but you could draw it as the whole screen being black except of the character and the destination.
If it's a space filling curve as Octoperson suggested, it wouldn't need to be big. Isn't a space filling curve infinite length if its offset is infinitesimal?
It's to do with light paths and diffraction. The time maximising path still hast to be a valid path.
path that maximizes time? just don't move. at all