What Would Pythagoras Do?
"Just ask for directions, honey" "Sssssh! I'm trying to remember my cosine laws!"
There’s a weird psychological phenomenon that humans exhibit regarding cognitive mapping — or how we instinctively choose how to move from Point A to Point B. Apparently we aren’t very good at it.
In fact, in a 1995 UC Berkeley study [pdf], one experiment showed that only 16% of subjects traveled the same walking path from A to B as B to A.
This doesn’t make sense, but I can’t help but find myself doing the exact same thing every single day! I take one route to the coffee machine, and a different route back to my desk. I take one route to work, and a slightly different route back home. It is entirely subconscious, but I’m mentally satisfied that my decisions are appropriately the fastest routes in both cases.
But clearly I’m wrong; both routes can’t be the fastest. Unless they’re equal, but that’s highly unlikely.
Perhaps human brains are easily tricked into thinking a certain route is faster over another. Didn’t we pay attention in high-school geometry?
Here’s a simple but tricky test:
You have to walk a grid from the upper-left corner to the lower-right corner, moving around the large white boxes. You may choose one of the 5 colored zig-zag paths to take. Which path would you instinctively choose? What if you were traveling the other direction? Be honest.
Which path is fastest? Note that some paths overlap along the borders. (Click to make it bigger)
Once you’ve made your gut decision, try to figure out which path is actually the fastest – you might surprise yourself.
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11:13 AM on September 30th, 2009
I’d like to say that I’d take the blue path in both directions…
But clearly it’s exactly the same distance as any of the other paths given that there is no diagonal travel on _any_ of them and the x and y translations are the same.
I’ll admit that the orange path has some allure… from the corner of it you can see both start and end without interruption, which seems like a desirable situation from a predator/trap avoidance perspective.
I guess that’s part of it… it’s not just speed we’re worried about, as humans. We like to feel like we’re in control.
Lets hypothesize two paths between A and B. One of them has a bunch of narrow winding streets near A, and the other has a bunch of narrow winding streets near B. When traveling, I think I’d prefer to defer the windy streets part of my trip until the end, generally speaking. It gives me a better feeling driving on wide straight streets, so I’d probably instinctively choose that path initially. Perhaps after traveling that particular route a number of times I’d get used to it and would end up just taking whichever was fastest… I not sure I can accurately predict my future behavior in this case.
12:01 PM on September 30th, 2009
I have the exact same response, Nato.
While all paths are equal, my gut reaction is to take the blue path for both directions.
And I can’t explain it, but the orange path is indeed alluring.
Try this: Flip the picture upside down. For me, the orange path becomes MORE desirable than blue.
8:47 AM on October 1st, 2009
I think blue is the popular choice because it is easy to overlook the fact that we are supposed to never walk diagonally. We are indoctrined with “the shortest distance between two points is a straight line”, and (if you squint) the blue line appears to be closest to straight.
Also, in real life the A->B path is different from B-> path for many other reasons: left turns can harder than right turns, you don’t want to get caught ogling the new receptionist twice, you want to minimize disrupting the people working at those desks in the office, you walk faster with an empty coffee mug than a full one, etc.
10:35 AM on October 7th, 2009
Also, when driving traffic is a huge factor, and often varies along different roads in the morning vs the afternoon so, both routes can in fact be fastest. Gotta watch those assumptions