What do you get when you combine an ancient Chinese math problem, Bamboo, Zen Koan, and the Pythagorean Theorem? Enlightenment, baby!
Given that Samurai Strength is a fork (in hacker terms) of Rinzai Zen, I’m quite fond of the practice of Kouan (Koan) study. However, it is something that can be so easily misused, and made into something silly, nonsensical, an exercise is pointless paradox. That is rather sad considering the profound usefulness of “taking your mind to task”, and forcing it to deal with a problem that appears to be impossible when first encountered, and obvious once understood.
Math to the rescue!
Zen in the Art of Mathematics
I once had a mathematics professor (with whom I took a couple of years of advanced analysis courses) who described learning mathematics as the following.
Imagine yourself stumbling around in a dark room for years, feeling the objects with your hands and mapping in your mind what the room must look like. You become quite confident in your beliefs about how the room must look. You are convinced, after all, you’ve had years of feeling this room out, literally.
Then, suddenly, by accident, you flip on the light switch! Finally, and despite all of your feeling, you can SEE the room as it really looks. Some of what you believed was true. Most of it wasn’t. This realization — this turning on of the lights — was instantaneous, revelatory, a moment of enlightenment in the most literal (and in the most metaphorical) sense of that word.
His definition of your path through mathematical study sounds remarkably like the descriptions of Zen Enlightenment. And I have often found the parallels to be astounding.
The Goal Is Not The Answer (Literally & Figuratively)
Beginners to mathematics often think of it as a “right answer/wrong answer” field, that the POINT is getting the right answer. Nothing could be further from the truth, and this attitude is a sure sign shared by people with the least understanding of mathematics, and why it is important.
These answer-seekers are quite prone to quickly looking up their coveted answers in the back of the book immediately (or in today’s world, googling them!). Don’t worry, unlike many of your math teachers, I won’t chide you for that. Because to do so would be to make the same mistake of placing the ANSWER as the most important thing. It isn’t.
The answer is like any other goal: it isn’t the point.
The process of finding the answer, the process of working out the solution, the underlying methodology of solution-finding, is like the journey. And as we all (should) know, life is about the journey.
The Chinese Bamboo Problem
Given all of that fancy stuff, lets dive into our first Mu Math ^{1} problem. It is … damned old. The ancient Chinese were doing some really cool stuff at around the same time the Greeks were. And what’s cool is the number of parallels (puns intended). The following problem comes from around 250 BC.
The Problem
Imagine a single stalk of bamboo standing straight up. It is 10 feet long. Now imagine it breaks, but at the break-point, the top section is still hanging on by a thread. The tip of the stalk now has fallen over and is touching the ground, but remember that at the break point, the bottom section of the bamboo and the top section on still attached.
The tip of the top piece, which is on the ground, is 3 feet from the base of the bamboo.
QUESTION: How long is the remaining bamboo from base to break point?
Solution
You can either attempt to solve this on your own (suggested!), or dive right into the solution below. Either way, the point is not the answer. The point is for you to take out some paper, and write this solution out, and recount it to yourself. Think on it. Meditate on it. Understand WHY it is true, so that you’ll have gained knowledge that helps you solve OTHER problems in the future, not just this singular problem.
Notice that, because the bamboo is still attached at the break point & because it is touching the ground, we have a triangle. More over, because the bamboo bottom was sticking straight up, we have a RIGHT TRIANGLE with a 90 degree angle formed from the ground and the base piece.
This means we can use our good-ole trusty Pythagorean Theorem to solve it.
PYTHAGOREAN THEOREM: , where is the (the side across from the right angle)
Let’s call the base to the break part of the bamboo, side .
Let’s call the ground, side .
And let’s call the broken-off piece of the bamboo (the one that is going from the break-point to the ground), the hypotenuse, or side .
What other info do we have?
We know that the ORIGINAL Bamboo stalk (pre-break) was a whopping 10 feet tall. So…
We now have all that we need to solve this problem. Given that we know that side , we can rewrite the Pythagorean Theorem as:
or
And since we also know that , we can rewrite it again as
Now, it’s plug-n-chug time!
which implies (I will use the logic symbol for from now on):
So we know that our hypotenuse is 5.45 feet long! What does THAT tell us about how long the remaining piece of bamboo is? Everything!
Remember that the remaining piece, side , was equal to , so we have
There’s our answer: The remaining stalk of bamboo is 4.55 feet long.
Lesson
Who cares about the answer. Really! The length of some random imaginary stalk of bamboo is hardly worth remembering. Think about the broader implications.
- Geometry is a nice model.
- Pythagoras wasn’t no slouch.
- The Chinese didn’t know who Pythagoras was, but they DID know his theorem
- What does that say about it being HIS theorem?
- Was it an invention, or a discovery?
- If it was a discovery, does that make Math like Archaeology and mathematicians like Indiana Jones?
Now go lift something heavy,
Nick Horton
Footnotes
- The word Mu in Japanese (Wu in Chinese) means on its surface “does not have” or “not” or “nothing”, but it goes far deeper than that in practice, particularly in the practice of Zen, where it holds a near-central place in study. You can think of it as The Void, as space, as eternity, as infinity, as zero, as the empty set, or in the terminology of The Never Ending Story, as The Nothing! ↩