Traditional Leading and Maximum Entropy

Many climbers have told me that they are fascinated about this aspect of climbing: Climbing experience strikingly reflects real life, which makes them look at their lives more closely in different perspectives and grow due to this self-retrospection. I can relate to that. I have learned a great deal from being so intimate with the challenge, being face-to-face with my fear. After climbing, I often feel so alive; I get closer to my inner image. Climbing makes us pound on what we have experienced throughout our lives.

I find another direction applies as well. Many things I learned from an academic setting allow me to analyze rock climbing in a systematic way. Through comparative study, I digest things better and have the ability to integrate loose ends. I believe that all different schools of philosophy come from the same origin and point to the same destination. Therefore, I especially enjoy finding similarities between two disciplines, in a way to verify my hypothesis. For example, I found that traditional leading and maximum entropy (ME) machine learning (ML) have striking similarities. More interestingly, ME is my favorite ML model and trad leading is my favorite form of climbing.

Before I go into what the concept of an ME model is. I should talk briefly about the term “entropy.” I think the term “entropy” derives from physics; in computer science terminology we use entropy to measure information, and people can use them interchangeably. The higher the entropy is, the more information we have. The way to determine entropy depends on the probabilities of possible outcome of an event we are interested in. For example, say the event we are interested in is whether the sun will rise from the east. Since the sun always rise from the east, the possibility of sun rising from the east is one. We have zero entropy for this case. We have zero entropy for something absolutely certain; no more information to gain. However, if the event we are interested is the outcome of tossing a coin, then we have some entropy because at a fair toss, both heads and tails have 50% chance to appear.

Many things can affect the outcome of an event. How you are going to place your hands, your feet; how fatigued you currently are; whether you can find a good stance within the next few moves; how many climbing skills you have equipped etc. They all contribute to whether you are going to send a route or not. The outcome can also be described in a smaller scale: for example, whether you will pull through a roof or not.

A good model should be able to explain the past and predict the future. An ME model processes all the past events include all the known outcomes of an event and the values of corresponding parameters which affect the outcome. Taking existing constraints into consideration, this ME model therefore tells you the possibility of each single possible outcome of an event; and this set of possibilities maximizes the entropy, in other words, it maximizes the information we get.

The neat thing about an ME model is that it makes no presumptions. Everything it needs is collected objectively – constraints, past events, and values of parameters associated with past events. There is one somewhat subjective part here: you have to decide which parameters you think will affect the outcome. In rock climbing language, constraints can mean the rock type, the rock features which allow only certain moves etc; parameters can mean the place you are going to hold on, the way you are going to proceed the move, the distance to the next good stance etc.

Besides that it gives me the most freedom, another reason I love trad leading is that I have to think a whole lot. My mind has to constantly work when I am climbing. I think; therefore I am. I train my mind as an ME model – given different sets of possible sequence moving on rocks, I project the success rate, the fun level, and the risk. In order to get as accurate as possible predictions, I have to know very well what my body can do and what my body cannot do at every specific moment. We rock climbers are risk takers, but we take calculated risk, and this is the way I calculate my risk.