The Math of Hiking

If you're like me, you've probably wondered at some point during a steep hike why the trail zigs and zags. Wouldn't it just be faster to go straight up the hill? Perhaps you've even tried to prove it, running through the woods, panting, getting scratched and poked by twigs while your hiking companions emerged unscathed and comfortable. Ok, maybe that one's just me.

Anyway, a new study has proven that yes, walking up a sufficiently steep hill via zigzags is more energetically efficient than going straight up. It's a pretty cool paper, but the coverage of the findings and the way they have been presented kind of bother me. So I found the article on sciencedaily.com, a pretty good site that showcases notable science stories each day. In a couple of hundred words, the article basically said the following: on a flat surface, the best route between two points is a straight line, but as you increase the slope, it eventually becomes better to go in a zigzag. Ok, thanks for that - seems pretty intuitive. I wanted to find out what the magical angle was at which the type of path should change. I didn't think this was asking too much - it's probably the most fundamental piece of data the study produced. A google search produced dozens of articles along the same lines, none of which gave any numbers. In fact, they were all pretty much the same: same quotes, same photos, many of the same paragraphs. In perusing some of the comments to the stories, the main sentiment was that this was pointless, that academics are wasting time and money by sitting in their ivory towers and proving common knowledge.

Finally, I found the actual journal article, which was surprisingly difficult. This brings up other questions about the effectiveness of the journal system as the center of academia if it's so difficult to access a widely-publicized paper, but that's a different rant. Anyway, the paper is surprisingly intense and interesting, complete with mathematical equations that were over my head and relatively far-reaching implications. And buried deep within the discussion section were the numbers I was seeking. Going uphill, it's more efficient to zig-zag on slopes above 7.4 degrees; downhill, the magic angle is 16.4 degrees. One potential implication could be for road construction; a properly designed mountain road could save time, gas, pollution, and reduce wear and tear on cars.

I think the point is that it's important to scientists to understand and communicate the implications of their work. Sure, math is fun for its own sake (to some people), but failing to address the purpose of the work just furthers the stereotype of out-of-touch academics. But I think most of the blame in this case falls on the journalists covering the story. I'd be surprised if they even read the paper; it's insulting that any peer-reviewed journal article that incorporates solid research and advanced math could be reduced to a single-sentence common sense platitude: zigzagging up slopes is better than not.