Mathematics of Mountaineering – Boulder Weekly

I bet Sir Isaac Newton wasn’t a mountaineer, but mountaineers share ties with the great mathematician and physicist. For example, he discovered gravity, a subject of extreme interest to those of us who hope to avoid its effects.

We also share a broader view of the quantitative side of life. The status of mountaineering as a STEM activity is underrated, but consider this: we have seven peaks and fourteen 8,000 meter peaks. Colorado has 53 14ers. Each state with 100 mountains has a list of the top 100 mountains. We quantify crucial movements, track numerical grade and class systems, and use measures such as topographic prominence to determine whether a mountain even is a mountain. We develop simple equations like calculating elevation gain per hour or complex ones like Colorado author and climber Gerry Roach’s “Efferculty” R Point system. Wrap your head around this and you’ll be able to levitate yourself with sheer mental power, saving wear and tear on your boots.

An additional factor in our misunderstanding of the central role of mathematics in mountaineering is our difficulty in grasping what mathematics is. As Dr. William Bricken notes in his Emblematic mathematics, it’s not pages of long division worksheets, it’s actually a “visual and experiential” activity. This is exactly how mountaineers apply it in the hills: how many feet higher is the summit? How long before this storm blasts us with lightning? What lift takes us out of this frightening whiteness? Using this expanded definition, we peak-baggers should lend a hand. We are honorary applied mathematicians.

To help me analyze this quantitative data that we are struggling with, I bought a tower from my mountaineering friends and asked this question: “Of all the calculations you use in mountaineering, which one do you find the most matter?”

The big winner was “the crux,” since that rating determines whether a team even has the skills to reach the top. But the issue struck a chord, spanning multiple nights, forcing me to buy so many tours that my son’s meager legacy was in jeopardy.

In these weighty deliberations, we have categorized quantitative considerations into three rough categories:

  1. Schedule numbers: Basic numbers, often developed by looking at maps and guidebooks. In this category, think about weight (especially weight through the crux), distance, total elevation gain and gain per mile, time, and amount of daylight available. You also need to consider the human element – how big is a team (such as an ideal three/four when traversing a crevasse field) and how fit do participants need to be ? A critical element in forming a team is the “Knucklehead rapport” – the rapport between questionable personalities and solid mountaineering citizens. If this number exceeds 1:2, you risk the disintegration of the team before reaching the trailhead.
  2. Ascension Day Numbers: The point where planning theory meets and is pulverized by practice. Are you climbing fast enough to get up and down before your loved ones call for mountain help? How long can your heart beat at an accelerated rate before bursting into your chest? How many mosquitoes can coexist in a cubic inch of air? A particularly granular example is my patented step counting process for measuring elevation gain – on steep inclines, 150 steps = 100 feet. I’ve counted millions of steps since performing this mental trick distracted me from the amount of pain I’m in.
  3. Useless glory numbers: Vital numbers by which we construct our self-image as mountaineers, boast to our peers and stun non-climbers. What is the most feet you have climbed in one day? What is, according to the rating, the most difficult summit you have reached? These are numbers that allow us to track our growth as climbers and demonstrate the often surprising feats of which we are capable. They let us into the “Hey, I’m a mountain climber” club. However, never forget the ‘useless’ in ‘useless glory’. Normal people don’t understand or care about these numbers. Quote them too often in mixed company and you won’t get any more party invites.

I admit that recognizing how much mathematics permeates mountaineering surprised me at first. Like most of us, I entered the wilderness in search of beauty and that overwhelming awe that raw nature inspires. To quote Emerson, “Have mountains. . . any other meaning than that which we consciously give them when we employ them as emblems of our thoughts? Mountaineering incorporates a lot of math, but at best it should lead beyond rote calculation to the ineffable, to a feeling outside of words and numbers. Undeniably, mountaineers who are too focused on reaching their objectives end up confronting this equation: obsessive concentration on the peak X = – [aesthetic appreciation] +- [spiritual transcendence].

And not all characteristics of a community that insists on calculating its achievements are pretty. Mountaineers are known to be competitive, neglectful of relationships, and reckless when pursuing goals. Hunting lists can turn sublime experiences into work. Two peaks before finishing the prestigious Bulger List, my friend Jon Karpoff sometimes sighs with relief, imagining the day when he will be “freed from the tyranny of the Bulgers”. He looks forward to a big party once these last two peaks complete his feat, but the peaks themselves? Maybe not so much. . .

My personal concerns are much more prosaic. I wonder how many miles I’ve traveled, counting my steps, watching my breathing, and skirting wonders. A unicorn may have frolicked, ridden by Bigfoot and followed by yetis throwing lupins, while I walked grimly, eyes downcast on my boots.

So I weighed the scales a bit before finally giving in and appreciating the predominance of mathematics in mountaineering. Emerson might disagree, but we could do worse than run after milestones through the great mountain ranges of the world. As Robert Browning says, “A man’s reach should exceed his reach, or what good is a paradise?”

Climber and psychologist Malcolm Bass notes that mountaineering engages our major psychological systems, creating attachments within teams, leveling our emotions, and providing “a sense of direction, purpose, and growth.” My peak journal provides me with more than good memories, it tells me what I’m ready to face next. All of these numbers help us set ambitious but achievable goals and serve as tangible manifestations of the motivations that make mountaineering so addictive.

As with all scientifically based research, I hope this article will provide the foundation for further exploration. For example, how does navigation technology change our ability to solve problems? Kids, there was an unimaginable time when people navigated by compasses and lines on a paper map. Using these abstractions, they created mental terrain models that often contradicted what their senses were telling them. What is lost when a GPS eliminates this tension between our rational and experiential selves?

Exploring this subject requires deeper thought than you will ever get from me, so here are two additional areas of practical importance:

First of all, since my main contribution to mountaineering is an ability to endure unnecessary suffering, I would appreciate the development of “The Index of Suffering so that I can foresee in what inhuman state I will return home.

At the same time, the mountaineering community calls for the creation of “The satisfaction index”, an algorithm incorporating elements such as weather, views, Knucklehead ratio, insects per inch of exposed skin, rock or snow condition, amount of terror and number of beers on ice in the car.

I leave it to my fellow mathematicians to take this critical research forward.

  • While I take full responsibility for the quality of the jokes above, I would like to thank my friends Dave Cunningham, Jon Karpoff and Joe Duggan for helping to deepen the content of this article.

Malcolm Bass’s comments on the psychology of climbers were extremely helpful in developing my understanding of why climbers climb. Unfortunately, Mr. Bass suffered a serious stroke last spring. His family and friends started the Move Mountains for Malcolm GoFundMe