Gleaning the Cube

I’ve become obsessed with remembering how to solve this damn Rubik’s Cube.

I use the white cross method, and I’m able to get the top and middle sections solved with relative ease. It’s the bottom that’s been kicking my butt.

The white cross method is a series of algorithms that start with solving for the edge cubies on the white side (forming a white plus sign or cross), then solving the white corner cubies, then solving the four middle edges.

This is where it breaks down for me. When flipped over, with the white center on the bottom and the yellow center on the top, there are three basic configurations you look for. From any of those three configurations, there are a series of algorithms that can be run to get to another interim step.

The goal here is to solve the yellow edges, then finish with the yellow corners. Voila, it’s solved!

However, it’s not so easy.

(This is about to get pretty numbers-heavy, so feel free to bail at this point. I won’t judge you.)

There are 26 physical cubies (as they’re called), but there are 54 individual cubie faces exposed – nine each of white, green, blue, orange, yellow and red.

Let me do the math for you. If you call the current state of the cube it’s configuration, then there are more than 43,250,000,000,000,000,000 possible configurations. That’s 43 quintillion 250 quadrillion. That’s a huge number. And only one of those 43 quintillion possible configurations is the “solved” configuration.

Someone much smarter than I am figured out that there is a one in 43 trillion chance – that’s 1/43,000,000,000,000 – that you’ll “accidentally” solve the puzzle.

In 1974, when the Hungarian professor of architecture Erno Rubik invented his Hungarian Magic Cube, the story goes that he developed the puzzle as a way to demonstrate to his students how to build a structure with multiple moving parts without the structure falling apart. He didn’t realize that he’d created a puzzle until the first time he scrambled it then tried to restore it to its original state.

One account I read stated that it took Rubik a full month of testing, developing nomenclature, and logging test algorithms before he discovered a solution. But to be sure, his original solution is just one of many.

The Rubik’s Cube – or the solution to it, anyway – falls into the category of Group Theory. When considered as a whole, or in subparts, the groups of algorithms that comprise any given solution allow the puzzle solver to successfully solve the puzzle.

With much more than 43 quintillion possible configurations, it came as a huge surprise to me that the God Number for the Rubik’s Cube is 20. The God Number, or the minimax value, is the least number of moves (algorithms) that an omniscient being would need to solve the given puzzle from any configuration. The upside of this is that it makes competitive speed cubing, as it’s called, much less mysterious. With the potential of being able to solve any given configuration in twenty moves or less, it’s just a matter of memorizing the various algorithms and practicing for hours on end. Much like learning tennis or guitar or cooking, it’s an acquired skill involving much practice and hours of determination to improve.

Just as interesting to me is the search by mathematicians for the Devil’s Number, or Satan’s Number. Whereas the God Number involves the minimum number it would take to solve any configuration just once, the Devil’s Number is concerned with determining the minimum number of algorithmic moves it would take to solve every one of the 43,250,000,000,000,000,000 different configurations. I know for certain that it’s a number between 43 quintillion and 865,000,000,000,000,000,000 (43 quintillion times 20), but anything beyond that I have to leave to someone with a more powerful computer than my Mac.

Whew, that’s a lot of numbers! I think I need a nap. But first I’m going to try to solve this last corner cubie…

(Credit for much of this goes to the SYSK podcast on Rubik’s Cubes and the geniuses that inhabit the math side of Wikipedia…)

Perfect Endings

There are no perfect endings.

It’s surprising to me, actually, how many of the songs that are in my current playlist have to do with endings.

I ordinarily have just one working playlist. When I grow tired or bored of it, rather than just create a new one, I’ll delete it and start over fresh. It can be anything from a mood change to hearing an old song that I forgot about to just being discontented with my current soundtrack, but it doesn’t take much for me to blow everything up and start fresh.

I don’t ordinarily have themed playlists, at least not beyond “current faves” or something equally trivial. So it came as a bit of a shock when I played a number of songs in a row that dealt with endings…

and if it’s over, just remember what I told you

it was bound to happen so just keep, movin’ on

there’s no perfect endings…

I enjoy a little Straylight Run now and then, and The Perfect Ending is one of my favorites. Formed as a side project by two members of the alt band Talking Back Sunday, they tend towards more moody, contemplative pop. Great for early morning drives to work in the early morning light.

…for once I’m at peace with myself

I’ve been burdened with blame, trapped in the past for too long

I’m movin’ on

I go through my country phases now and again, but Rascal Flatts is about as country as I get these days (see what I did there?). I enjoy the country-pop sound of Rascal Flatts – having grown up on ELO, Chicago, and the like, there’s a certain appeal for me in the straightforward love ballad. I’m Movin’ On fits the bill nicely.

…I’ll be the one if you want me to

anywhere I would have followed you

say something, I’m giving up on you…ˆ

A know very little about A Great Big World beyond the fact that they never should have let Christina Aguilera within fifty miles of this song. Their “solo” version of Say Something is stunning in it’s simplicity, and is a mainstay of my “mellow” playlists. Plus, it’s super easy to play on the piano, making it a mainstay of my piano setlist on the rare occasions I abandon my guitar for my keyboard on a gig.

…and if you were to ask me, after all we’ve been through

do you still believe in magic? yes, I do

yes I do, of course I do…

It wouldn’t be a mellow playlist without at least a couple of Coldplay songs, and this tune, written in the midst of a divorce, always surprises and impresses me with it’s hopeful ending. After the crushing lonliness and defeat, Chris Martin reveals in Magic that he is still able to see the light at the end of the tunnel, still able to believe in the magic of love even as it dies in his own life.

I am ready to be new again

I’m ready to hear you say

who I am is quite enough

Not an “endings” song per se, but still an upbeat alt-rocker in the same vein as the other songs in this list. New Again by Taking Back Sunday puts a nice endcap on things – after all the teeth-gnashing and navel-gazing of the previous songs, New Again strikes a hopeful chord, reveling in the fact that I know I’m good enough, I’m just waiting for you to admit it, too. It’s a nice counterpoint to Say Something, in which the singer admits defeat; here, the singer isn’t giving up, and is determined to see things through to the bitter end.


There is nothing more jarring than waking up to the truth.

Granted, truth can be an extremely subjective thing in this context. Can’t that be said about all truths, though? We take it for granted that the sun will rise in the morning, but we can’t know it for certain. We can make the assumption, based upon past experience, that the sun will rise, but we don’t – we can’t – know it until it actually happens.

But what if we lived in denial of this fact? What if we’d spent the last ten years telling ourselves that it wasn’t the sun that was rising, but it was actually something else? An enormous flaming chariot, for instance, ridden across the sky every day by Helios, as the Greeks believed?

And then came the morning that you arose from bed, looked out across the plains at the horizon, and suddenly you saw the sun for what it was – middle-sized star? And you also realized that the rotation of the planet every 23 hours, 56 minutes and 4 seconds was what caused the sun to rise, and not some mythical, fiery figure riding his flaming chariot across the sky?

To wake up to a truth of this magnitude can really mess with your day, let alone your week, month, or life. Maybe you’ve always suspected it. Maybe it never made sense. But it was always so much easier to believe the lie you told yourself, because the alternative was/is unpleasant.

Still, denial is a powerful ally. It is so much easier to maintain the status quo, to tell yourself that you’re better off not knowing the truth, than to accept yourself, and your situation, for what it is, good or bad. Knowing the truth, and not accepting it, is cowardice, pure and simple. It is living a lie, and that is worse than the alternative.

Self-esteem – value and self-worth – can only be fully, truthfully realized when the truth is accepted and dealt with.


Self-esteem can be a tricky thing.

We’re all born with self-esteem, but somewhere along the way, it gets systematically beaten out of us – sometimes literally, sometimes figuratively, sometimes both. Some people learn to deal with this at an early age, and adopt a façade of being well-adjusted, a fake air of confidence. Most of us, though, learn to deal with it in other ways – acting out, or adopting a self-deprecating sense of humor, or any of a dozen other ways of masking the pain.

Life can seem so difficult sometimes. Pride (or a lack thereof) convinces us that either we deserve more, or that we’re getting precisely what we deserve. It’s easy to look at the suffering of others and think to oneself, “Well, at least I don’t have it THAT badly!” But this is a false dichotomy – we all suffer individually, in our own little island of existence, and to varying degrees. Starving children in Africa, tortured citizens of Hong Kong or the Middle East, or victims of unspeakable crimes right here in the United States have no real bearing on the individual suffering we each experience.

Psychologists use the term “self-esteem” to describe an individual’s sense of value or self-worth. Abraham Maslow, in his Hierarchy of Needs, makes the case the we all need both esteem (or respect) from others as well as inner (self-) esteem. People who suffer from low self-esteem often find themselves in self-destructive situations or relationships. These situations become a self-fulfilling prophecy, validating one’s own low sense of self.

Although genetics play a role in it, most psychologists believe that self-esteem is shaped by one’s own environment. Allowing oneself to continue to exist in an abusive relationship – in fact, seeking out these relationships in the first place, whether consciously or unconsciously – is one of the hallmarks of low self-esteem. It is a hard habit to break, this vicious cycle of believing you get what you deserve, then being abused (either physically or emotionally) and believing you deserve to be treated in the manner.

How best to break this cycle, this merry-go-round of pain and suffering. There are many different strategies proposed by many different psychologists and therapists, but most all of them have one thing in common – it is best to rip the band-aid off rather than to continue to exist in the situation, hoping it will get better.

Sometimes, sadly, this is not always possible – at least not immediately. Certainly, if an individual is in imminent physical danger, getting out of the situation is (and should be) the main priority. But in cases of emotional abuse, the situation is not always cut-and-dried, not always so black-and-white. It may even be the case that no abuse is intended; it may be a matter of simple miscommunication. So many people are afraid of the unknown that they would rather live with the devil they know than take a chance with the devil they don’t know.

In the absence of the ability or opportunity to leave, the first step is to try to set definitive boundaries with the other party. Try to have an adult conversation with them concerning your wants and needs. Often, it is merely a matter of miscommunication between the two parties. However, if and when it becomes evident that there is (and can be) no common ground, it is time to start to think about moving on, to start preparing for the end of the relationship.

I don’t have the answer. I wish I did. Or maybe I do, and I am just too afraid of the devil I don’t know.