Knowing vs Understanding
Do you remember math class in high school? Do you recall what this even means? 4!
4! is four factorial, or 4x3x2x1, multiplying the number by every positive integer less than it. 4!=24 A longer example would be 6!, 6x5x4x3x2x1=720. An interesting concept in math, but rarely used in the average persons life. A couple of weeks ago Julie and I came across a math puzzle video on Youtube which reminded us that the factorial function exists as part of one of the solutions.
While watching the solutions, it was explained that 0!=1. Intuitively this did not make sense to us. If a factorial is the product of all positive integers less than or equal to the number, and zero has no positive numbers less than it, how could this equal anything at all, except perhaps equal zero?
A google search produced the following explanation:
"Factorial of a number in mathematics is the product of all the positive numbers less than or equal to a number. But there are no positive values less than zero so the data set cannot be arranged which counts as the possible combination of how data can be arranged (it cannot). Thus, 0! = 1."
After reading this statement a dozen or so times, it sort of makes sense, but I still don't quite understand why this is true or how it works. But that isn't important. What's important is that this statement drew my attention to the difference between knowing something, and understanding something. I "know" that 0!=1, but I don't understand why, and I can't explain it to anyone else.
In climbing, the difference between knowing something and understanding something can be critical. Knowing how to lead belay is a great skill to have. But understanding how a rope system works, the intricacies of a belay system, and the interactions of the different components in that system is the difference between a mediocre belayer and a belayer who will make good moment-to-moment decisions and ultimately avoid accidents much more confidently.
In my position as a climbing instructor and gym employee I come across many climbers who seem to know how to belay, but fail to understand the fundamental concepts behind the rope system. I see errors that, to my trained eye, seem basic. Too much slack out while the climber is close to the ground, belayers standing very far away from the wall unable to give a soft catch, not holding the brake rope at all times; these seemingly beginner mistakes are consistently made by experienced climbers who fail to understand their task and the consequences of their complacency.
I urge all of my students, and anyone else reading, to not only learn from your experiences, but to seek understanding. Absorb new information, process and consider it, and strive to understand things well enough to make good decisions based on what you've learned. Your life may depend on it.
Let's go climbing.
