2821: Path Minimization

2023-08-29T12:13:20Z

Xkcdrw: Added a refractive index reference

{{comic
| number = 2821
| date = August 28, 2023
| title = Path Minimization
| image = path_minimization_2x.png
| imagesize = 562x559px
| noexpand = true
| titletext = Of course you get an ice cream cone for the swimmer too! You're not a monster.
}}

==Explanation==
{{incomplete|Created by WAITING AN HOUR BEFORE SWIMMING - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

In this comic, it appears that Cueball, standing on shore, is observing a swimmer who is possibly (but not obviously) in distress. The comic illustrates five potential paths that can be taken to reach the swimmer, each with a different reason to make them viable, in the manner of demonstrating different optimal strategies that can be chosen. The described paths are indicative of the path light takes between materials with different refractive indices.

The first path is an angle away from Cueball, straight to the swimmer, which allows for the minimum possible distance to be traveled, some on land and the remainder in the water.

The second path travels more obliquely from Cueball to the water and then at a sharper angle to the swimmer. This path would take the shortest amount of time, presuming that Cueball would move faster on land (covering more of the distance) and slower through the water (but less distance). The exact angles would depend on how much faster Cueball is on land than in the water. Note that this is the path light will take through mediums with different refractive indices.

The third path travels at a far more oblique angle to the water such that the subsequent swimming path is entirely perpendicular to the shoreline, adding to the amount of time spent on land in order to minimize the time spent swimming. Depending on one's swimming ability versus running ability, this could be the safest path to take.

The fourth path travels nearly parallel to the beach. In fact moving slightly ''away'' from the swimmer but towards an intermediate goal: an ice cream stand. After that, the path turns and aims straight towards the swimmer, as all the others eventually do (although it is not made clear at this point if Cueball will be eating, or just carrying, an ice cream even whilst swimming).

The fifth and final path, barely visible directly above Cueball, is labeled as the path that ''maximizes'' time. This path, presumably, travels around the entire world, likely stopping for many, ''many'' rest breaks. It should be noted that, by the definition given, it is theoretically possible to stretch the maximum time taken out forever by simply walking away and never returning.

You could also fulfil the criteria of reaching the target in finite, but arbitrarily long, time by following a {{w|random walk}}(+swim) or even follow a {{w|space-filling curve}} carefully chosen to be the maximally finite scenario. Or you could simply choose any path, and stop for an arbitrarily long time, or travel at a speed approaching zero. In the comic, however, a requirement for simplicity of path may dictate the use of the opposing {{w|great-circle distance}}, or a variation with maximum swim-time without ''undue'' time-wasting detours, and assume equal speeds of travel on all routes.

The title text adds the stipulation, to the ice-cream path, that you also carry an ice-cream to the target swimmer to 'justify' that choice of route. But how this squares with the reason to rendezvous with the swimmer, or the manner in which this would further complicate the swimming stage, goes unsaid. But it makes it clear that ''not'' doing this isn't considered socially permissable, whether or not he had stopped to eat an ice-cream of his own beforehand.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:Path that minimizes distance [A straight line from beach cueball to ocean cueball, bearing about 135]
:Path that minimizes time [A line from beach cueball to the waterline closer to horizontal, bearing about 120, then angling towards ocean cueball, bearing about 150]
:Path that minimizes swimming [A line from beach cueball to the waterline closest to ocean cueball, bearing about 115, then angling toward ocean cueball, bearing 180]
:Path that minimizes time until you get ice cream [A line from beach cueball to an ice cream stand manned by Ponytail, bearing about 90, then angling toward ocean cueball, bearing about 190]
:Path that maximizes time [A line from beach cueball away from the shore, bearing 0, fading and disappearing at the top of the panel, and reappearing at the bottom of the panel directly below ocean cueball]

{{comic discussion}}

[[Category:Food]]
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Ponytail]]
[[Category:Multiple Cueballs]]

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2821: Path Minimization