85: Paths
| Paths |
 Title text: It's true, I think about this all the time. |
Explanation
This comic centers around the consideration what shortest path is available to a person travelling by foot. Cueball has to travel a rectangular distance, which (I believe) is part over pavement and part over some other material not really meant to tread on (grass, sand or granite). When Cueball goes to follow the pavement, he has to walk for 60 seconds. But when he traverses using the non-walkable material, he can cut up to 26% of his time. So, he thinks every time he has to travel this rectangle, which is a very human question. Would you rather walk the straight path, or be kind of illegal (to some standards) and use the non-walkable material in your way?
Transcript
- [Blueprint of a campus. Two buildings in the upper and lower left corners, respectively, and a rectangular lawn. A road encloses the lawn, another road traverses horizontally through the center of the lawn. The character is in the lower left and the upper right corner, where it says "my apartment".]
- [Dashed line 1, from the lower-left along the road to the top-left corner, then to the top-right corner] 60 seconds
- [Dashed line 2, from the lower-left along the road up to the center crossroads, then diagonally over the lawn to the top-right corner] 48 seconds (80%)
- [Dashed line 3, diagonally from the lower-left to the top-right corner] 44.7 seconds (74%)
- My apartment
- 1=t
- 2=(t*(1+√2))/3
- 3=(t*√5)/3
- When I'm walking, I worry a lot about the efficiency of my path.
add a comment!Discussion
An example of this problem would be if there is a drowning swimmer 100 meters offshore, you are 300 meters from the point on the shoreline closest to the swimmer, and you can run at 15mph and swim at 2mph, how far do you run along the shoreline before going into the water to get to the swimmer as quickly as possible?
The fact that Randall shows two different paths over the "grass" makes me think that he was thinking more along the line of obsessively optimizing his path rather than about whether it might be acceptable or not to walk over the grass. -- mwburden 70.91.188.49 21:23, 13 December 2012 (UTC)
