As a geometry teacher, I like to keep a Rubik’s Cube in my room. The students usually seem to think it’s a way for me to show off (my average time is about two minutes… not championship level, but fast enough to be impressive). But I’ve come to see the cube as a metaphor for mathematics, and for approaching life’s problems.
Most people see a scrambled cube and get overwhelmed. I see student after student use unproductive strategies. They’ll get all nine of the red faces aligned and think they’ve solved a side, even if the nine cubes aren’t in the right orientation. They’ll then attack a different color, getting frustrated when the first side returns to chaos.
In the cube, in mathematics, and in life, we want things to be in order, but we struggle to see the way to that point. Here are some lessons I’ve learned from the cube that apply to solving any complex life problem.
Lesson 1: It is easier to create chaos than to create order.
Few people can solve a Rubik’s cube.
Meanwhile, anyone can scramble a cube, anyone at all. It takes no special skill or knowledge. And it can be done quickly: A dozen or so turns is sufficient to scramble a standard cube to the point that only the most skilled of solvers can reconstruct the moves.
We, humans, are good at creating messes. Entropy is the natural state of things: Chaos erodes away at order with little influence from us, but even so, we excel at helping entropy. Even our naïve attempts to create order in the cube tend to create more chaos.
We prefer order; there is something soothing in a solved cube. For me, it is almost compulsive to solve any scrambled cube I come across. But creating order comes from focused, deliberate effort; creating chaos comes naturally.
Lesson 2: Approaching order sometimes involves creating more chaos.
The first phase of the algorithm I use for solving the Rubik’s cube involves picking a color side and solving it. The next phase is to solve the middle layer. This is impossible to do without temporarily “scrambling” the top layer. There is an order in this disruption: It’s really a process of moving the finished work out of the way. But to observers, it looks like I’m destroying my previous work.
Major housecleaning ventures involve moving things out of the way, often into bigger, messier piles. It’s possible to accomplish small cleaning tasks by starting at one point and systematically moving through the area to be cleaned, but larger tasks often entail the creation of additional mess in order to move to the goal of proper order.
We talking large tasks, we can get frustrated if the work we’ve already done has to be temporarily dismantled, but steps backward are often necessarily to move forward with integrity.
Lesson 3: You cannot resolve chaos all at once. Pick your battles.
The speed demons who solve the cubes in a matter of seconds may well see how to coalesce the entire chaos at once, but for most of us, slow and steady wins the race. The main strategy I’ve seen in guide after guide for solving the cube is: Solve one side. Then solve the middle. Then solve the corners, then the last four side pieces (or vice versa).
When I see students approach the cube, I tend to most often see a holistic approach: How can I solve everything at once? If you’ve decided to solve red first, solve red first. Let orange get as messy as it gets, because it doesn’t matter yet. We’ll get to orange eventually.
Likewise in life: Don’t try to solve everything all at once. If you’re tackling the issue of racism, don’t go after every act of racism all at once. Pick your battles, and focus.
Lesson 4: In a truly random world, specific chaos is as likely as specific order. Chaos is easier because there are more ways to be chaotic.
Of all the lessons here, this is the one I struggle the most to understand.
This is easier to see with a deck of cards. A fully sorted deck, A-K, sorted by suit is just as likely a configuration as any other specific shuffling. So why can we generally not expect such a thing? Because there are only a handful of “fully sorted” configurations (twenty-four, to be exact), out of about 1068 possible configurations.
So while any specific ordering is no more likely than any other, there are lots more ways for a deck to be “shuffled” than for it to be in “order.” At the same time, we want order, but if someone shuffled a deck and gave it to us in the same order that it comes out of the box, we would accuse them of cheating.
Jordan Ellenberg addresses this at length in “How Not to Be Wrong,” in which he also discusses how mathematical thinking can be applied to much more in life than “just math.”
We want order, but we literally stack the deck against ourselves when evaluating randomness. Expecting chaos gets in the way of us achieving the order we so crave.
Lesson 5: To the uninitiated, systematic applications of complex patterns look like magic.
My students marvel at how quickly I can solve the cube. I’m at a stage now where I can solve portions without looking, which confuses them.
I’m not doing anything special, and I’m not cheating. I’ve been solving the cube for three decades, and I know what I’m doing. There was a time when it was a mystery to me, too.
Any chaos can be brought to order with the right strategy. Some strategies are more complicated than others, and outside observers won’t necessarily see the strategies you’re using. They may even mock you. However, the efficacy of a strategy is not in how it looks to outsiders, but in whether it works.
More by author Paul Hartzer here on The Good Men Project:
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In a fair world, the right to offend others comes with the obligation to suffer offense.
It’s not enough to just starting out handing out hugs and ice cream and forgetting about the past.
Photo credit: Flickr/Doug Aghassi