The answers usually ring back as "the maximum you could reach" or "something you push to get closer and closer to". The climbers might blurt out "15d!" And then they list examples - speed limits, rules (limit 5 per person), world records (sub-2 hour marathon). I then follow up with, "Ok, let's take your definitions, and say a limit is the maximum value a person or thing could reach. Does whether or not you actually reach the limit change its value?"
Mathematically speaking - no, it doesn't. Whether a limit is "realized" or simply approached closer and closer, it's value remains the same. This is because limits "exist" as a quantifiable idea. They are specific, measurable, yet intangible. And while there are many lessons to be learned from Sharma and Gullich, this notion of a limit from Newton and Leibniz is as foundational in deriving fulfillment as it is deriving functions.
Two legends whose approaches to limits changed the world.
Process.
A lot of math boils down to taking an input, applying a process, and then getting an output. Climbing parallels this quite well.
- Input a goal, route, number, trip, etc.
- Apply training, tactics, psychology, etc.
- Do or don't reach the desired output.
A lot of people won't "vibe" with this. I understand it is an oversimplification to condense someone's entire life focus/love into a 3-step scientific method. Climbing can be such an organic thing, influenced by hundreds of ethereal variables - relationships, weather, mood, and mental health, to name a few.
My aim here isn't to give a formula. My aim is to highlight the satisfaction one could have from understanding projecting the same way we understand limits mathematically. When I am projecting a route, my process always begins with uncertainty. If I am certain I can do a route from the beginning, it is not at my limit. It usually takes a few days to even think I could do it. That is the first shift, and it's pretty exciting. It's the first nip at the dangling carrot. The second shift usually comes between 2 weeks and 2 seasons/years/life-crises later. And this one is sometimes AS, IF NOT MORE, spectacular of a feeling than sending. This shift is the breakthrough moment when something indicates you can do the route. It's no longer a thought, it's simply and certainly attainable. You've put in a sufficient amount of time, training, tactics, sacrifice (and self-loathing?) to reach a point where the send is a possible outcome.
People think that things like training, effort, and devotion are supposed to increase your odds of success on a route. They believe they start the projecting process with a 100-sided "send die". With every tie-in, they roll the die, fall, and the number of sides on the die decreases. The more they try, the fewer sides there are. After some weeks, it's a 20-sided die. In other words, odds of sending increase.
If we assume your project is at your limit, this is a faulty view. You're not starting with any odds of sending. For many, many days, there is no die to roll, or if there is, it's got infinitely many sides (aka a sphere, and will never land). You have no chance. If you had a chance to send in the first couple of weeks, you wouldn't be climbing at your limit.
What we are actually training and sacrificing for is a probability of sending to even exist. This is the feeling. This is the moment after weeks/months/seasons of effort when you have a go where all of a sudden, you are hit with the rush of possibility. You had the "freshness" in the last crux. The razor felt big for the first time. You held the swing to its apex. You actually got something back at that joke of a rest. It's all circumstantial, but there is something which indicates now, you get to roll the die. Now, your chances are nonzero.
In my experience, this is a very exact moment in every project. The reason this feeling is so powerful and often more gratifying than the moment I send, is that it often takes me MUCH longer to get to this point, than to go from this point to sending. For example, my proudest achievement in climbing is sending Southern Comfort Right, a hard 14a at my home crag in Alabama. I spent 3 seasons trying this route, and on my third year, I spent ~2 months trying to link the 4th bolt to the top. Once I had done this, I knew I was capable of sending, and sure enough, I did send just a few sessions later.
If you skip to around 2:57, you'll see me stick the move I fell on for 3 years. This is from the 4th bolt, not the ground, but it's the "moment" I knew I was finally capable. Keep sound on and you'll hear me say "I'm so happy" between breaths and smiles...again, this link was 3 years in the making.
While this anecdote is one of "success", there are a few routes I've felt this sensation of possibility with, yet left without the send. This brings me back to the notion of a limit I mentioned earlier. Mathematically speaking, a limit is the value a function approaches as your input approaches a value. In the context of climbing/projecting, a limit is perhaps the goal, number, route, etc. that you are CAPABLE of reaching, but whether or not you actually reach it is moot.
I understand as well, if not better, than most that sending is not moot. Sending matters. Sending is exhilarating. Sending marks tangible progression. When we give nearly everything and don't send, it hurts. We feel robbed, unworthy, and inferior. However, if there is any solace to be found in this mathematical nerd-jargon of a blog post, it's that equating what we are capable of doing with what we actually do does hold value. To feel capable is fulfilling. It's not the desired outcome, but it is infinitely close. And mathematically speaking, that is no different.
