I feel it’s a missed opportunity to exclude the ice cream sales and drowning deaths correlation, but that’s just me. I like the maximal time route goes up, though.
It does: Light does not follow the path of minimal distance between two points, but the path of minimal time. This is called Fermat’s principle.
Because water has a higher refraction index than air, light is slower in it and therefore takes a longer time to travel through it. Thus, it takes less time to take a longer path that spends more time in the air.
Fun fact: The underlying law of this principle is the principle of least action. This is the most basic law of nature we know of and can be used to derive all of physics.
The probably of the path it takes is the sum of all possible paths. Richard Feynman uses this exact swimmer in the water example during ok if his lectures.
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.
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 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.
I couldn’t tell what I was looking at until I searched for an explanation. All I could see was a person falling into some water past a floating ice cream stall. It’s supposed to be a beach:
I was more like: but if he choses the alternative paths, he doesn’t get the ice cream - that doesn’t make sense! Then I understood our priorities differ.
As an Aussie, I don’t see why that is unusual. You use your feet. But if it’s only two icecreams, then you hold them both in one hand and swim with the other one. All I can say about this one though is that this is a very flat beach: Waves would ruin the icecream pretty bloody fast.
Swimming with something that can’t get wet is not unheard of here. I sometimes swim a book over to somewhere to read, or a phone to a good place for a photo too.
See, that IS completely unheard of here! If it’s not supposed to be wet, we wouldn’t dream of swimming with it!
I don’t know if it’s because you guys are born excellent swimmers like Norwegians are with skiing, but I don’t know ANYONE who wouldn’t assume that swimming with something invariably means getting it wet 😄
I’m not positive but it might be due to the steps the Lemm.ee admin is taking to combat the CSAM uploads that have been happening and prevent the server’s administration team from being liable for potentially harmful and illegal images being hosted on their server.
