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…)

PSA – The Dangers of DHMO

I usually reserve this space for amusing anecdotes about my life or nifty little nuggets of trivia that I’ve come across, but this is serious stuff and needs to be disseminated to anyone who can read so they can be forewarned about the dangers of DHMO.

Dihydrogen monoxide (DHMO) can act as both (either) an acid or a base – it is amphiprotic. It can be found in solid, liquid, and gaseous forms.  Its pH is 7, higher than any other acid known to man. It is both tasteless and odorless.

Extensive research has shown that water bottles stored on grocery store shelves for more than a month contain extremely high levels of DHMO. This applies to both plastic and glass bottles.

Starbucks (as well as most all coffee shops) use thermally agitated dihydrogen monoxide in all of its coffee-based beverages. DHMO is known to cause severe burns when it comes in contact with the skin, and once DHMO comes into contact with skin, it cannot be washed off.

Large U.S. manufacturers routinely dump vast quantities of DHMO in our lakes, rivers and streams – and it never biodegrades.  Research has shown that dihydrogen monoxide is deliberately sprayed on organic crops in the U.S.

Scariest of all for parents: If you give your children juice boxes, you should know that each juice box contains more dihydrogen monoxide than an ounce of methamphetamine.

Breathing in too much DHMO can lead to certain death. In fact, the sad truth is that 100% of people who come in contact with dihydrogen monoxide eventually die.

Please be sure to check all labels – don’t mistakenly ingest this dangerous compound, lest you meet a horrible fate! Dihydrogen monoxide is not to be trifled with. If you’re the political activist sort, please write your Congressperson and/or Representative and let them know that you fully support a ban on any products containing this harmful chemical.

It’s up to us to be the change in the world we want to see!

Is that a supercomputer in your pocket, or are you just glad to see me?

While listening to a podcast about the Simulation Hypothesis Argument, I ran across an interesting set of numbers.

To start, by way of comparison, the human brain can process anywhere from 38 thousand trillion (3.8 x 10^16) to one billion billion (1 X 10^18) processes per second, depending upon whom you ask. Those are pretty big numbers:



Per second. It’s breathtaking, and truly amazing.

By contrast, in 1985 the Cray 2 supercomputer came online at the NASA Ames Research Center in Mountain View, CA. If you took a small automobile and stood it up on its end, you’d get a general idea of the size of this supercomputer. Certainly not the room-spanning computers of the 1950’s and 1960’s, but not a small machine, either.

This state-of-the-art supercomputer could run 200,000,000 processes per second, and it was replaced within three years by the Cray Y-MP.

That’s 200 million. Not human brain-type processing, but pretty spectacular, nonetheless.

Just over thirty years later, Apple Computer released a supercomputer that could run 600,000,000,000 – that’s 600 billion, with a ‘b’ – processes per second. That’s a processing increase of 3,000%.

30 years. 3,000%. Astounding.

And the name of the supercomputer Apple released, this computational powerhouse that out-processed a thirty-year-old supercomputer by a factor of 3,000? You may have one in your pocket – you certainly own something similar, if not the precise model itself.

Apple called it the iPhone X.

Fast (and Furious) Food

Although I still eat way too much fast food – I’m a lazy “cook,” sue me – I find most of it gross and unpalatable. It’s more of a convenience than anything. This, of course, does NOT include the Frenchie sandwich at Jimmie John’s…mmmm, love me some Frenchies!

Here are a few of my favorite fast food (and fast food-related) facts:

Fried Chicken  Wild fowl were domesticated about 9,000 years ago in China and the Middle East. It made it’s way to Egypt, where you can see chicken represented in many hieroglyphs. It was also used to feed the slaves who built the pyramids.

Eventually making it’s way to Britain via Greece, it is believed that fried chicken was introduced to the U.S. by Scottish settlers (or invaders, if you prefer). These were pan-fried birds; the South were the first to fry them up in vats of hot oil.

In the late 1920’s or early 1930’s, Harlan Sanders opened a restaurant in Corbin, Kentucky to sell his secret recipe fried chicken. The restaurant bombed out, but Sanders soon hit upon a brilliant strategy. He hit the road, selling his recipe and the rights to use his trademarked phrase “Kentucky Fried Chicken” in exchange for a nickel for every piece of chicken sold.

By 1964, the year 1) I was born, and 2) Colonel Sanders sold his franchising business, there were 600 restaurants nationwide. As of 2014 (the most recent number I could find), there were almost 19,000 franchises around the world. That’s a lot of chicken!

Fast Food Stats  When it comes to fast food, there are a number of common ingredients. Here are a few I found interesting:

1. The most common fast food meat: Chicken. This isn’t by volume (that would be beef), but rather by number of menu items. McDonald’s, for instance, offers almost as many chicken options as burger options. And on average, fast food joints tend to offer more chicken options than beef options – when was the last time you had ground beef on your Caesar salad, for example?

2. The most common fast food spice: Salt.  There is sodium chloride even in things you wouldn’t expect – shakes and ice cream sundaes, for example. It is used in different combinations to add or enhance flavor to a myriad of items. One slice of the American cheese you’d find on a Big Mac contains 250mg of NaCl, making it one of the saltier options available. And that doesn’t take into account all the salt you may dump on your fries.

3. The most common color additive: Caramel.  While Red No. 40 is the most widely used food coloring in the world, fast food places seem to love their caramel coloring. Part of the psychology of eating is that for something to taste good, it must look good, and a nice, rich caramel tone seems to serve the industry pretty well.

Photographer: Greg DuPree, Food Stylist: Emily Neighbors Hall.

Tacos  Before the 1950’s, you would be hard-pressed to find a taco anywhere at any restaurant in the U.S. That’s when a restaurant owner in Southern California noticed the migrant Mexican workers packing tortillas in their lunches, and stuffing them with meats and vegetables from home.

Deciding that might be a good item to add to his menu, he began offering tortillas folded in half and stuffed with food he thought his customers might like – ground beef, lettuce, tomatoes, shredded cheese.

One problem in ran into pretty quickly was that flour tortillas didn’t keep for very long, so he couldn’t keep a very large supply of them at any one time. He solved this by shaping and deep frying the tortillas – thereby creating the first hard shell tacos.

This menu item went over so well that he opened a restaurant in 1962 devoted entirely to serving this new menu item.

His name? Glen Bell.

As of last year (2018), there were over 7,000 Taco Bells in 27 different countries. By state, California, then Texas, then Florida have the most restaurants. There is even a Taco Bell in Mexico…well, sort of. It’s actually in Tijuana. Close enough, right?

Mid-Year’s Day Resolutions

It’s been nearly four months since I’ve written anything, so I thought this would be a good opportunity to bring you up to speed on what I’ve been doing.

On July 1, I decided – a Mid-Year Day’s Resolution, if you will – to accomplish two things.

  1. Learn something new every day.
  2. Learn a new skill by the end of the year.

Number 1 is going very well. I’ve subscribed to a couple of very good email newsletters, and I’ve become immersed in the world of podcasts. Stuff You Should Know, hosted by Josh Clark and Chuck Bryant, is a particular favorite. Alex Williams’ Ephemeral is another podcast I’ve really enjoyed. The End of the World with Josh Clark, hosted by Josh Clark (duh!), is highly recommended (by me) as well.

When I can’t listen, or don’t have the time to devote 30-60 minutes to a podcast, short articles on the interwebs have become my go-to means of enrichment and entertainment. Google News, How Stuff Works, and Mental Floss all have permanent bookmarks in my phone’s browser.

I’ve given number 2 some thought, and I think I’m leaning towards learning to play tennis. Since I’ve done so well with golf – someone really needs to come up with a sarcasm font – I thought I’d give tennis a try. The worst that could happen is that I suck as badly at tennis as I do at golf, but I’ll be in better shape at least, right? RIGHT?!?!

Oh, who am I kidding? The worst that can happen is probably having a heart attack on the court as I’m lunging to return a well-placed cross-court smash from my opponent.

So, over the course of the remainder of the year, I hope to be able to share something new with you almost every day, whether it’s a status update on my tennis lessons or some seemingly insignificant-yet-interesting bit of trivia, like why golf balls have dimples or why you couldn’t get a taco in the U.S. until the mid-1950’s.

We’ll probably also get into my irrational fear of microscopic black holes – thanks, Josh Clark – but that’s another post for another day.


Here’s one from the Learn Something New Every Day file…

One of my New Year’s resolutions that quickly fell by the wayside was to learn and use a new word every day.

I’m not sure if it’s because I’m lazy, or no one got me a word-a-day calendar for Christmas, or some combination of the two, but by the end of the first week of January, this particular resolution was toast.

Multiple scientific studies have pinpointed the length of time it takes to make something a habit, and the findings usually land somewhere in the three-week range – i.e. it takes about 21 days of repetition to make something a habit. My assumption is that this applies only to beneficial habits – I seem to have no difficulties whatsoever in adopting bad habits after just one or two repetitions.

Once you hit that 21-day mark, it becomes smooth sailing, and you’ve now adopted a (hopefully beneficial) habit. Your body (or mind, if it’s a mental habit) kicks into autopilot, and you begin to feel pangs of guilt immediately when you skip the activity.

Go to the gym a couple of times a week, for instance – or whenever you feel like it – and it becomes easy to rationalize not going. I’m busy, I’m tired, I’m not feeling that well – all of these become valid reasons to avoid said activity.

What you’re actually trying to do is train your body and/or mind to develop and engage in another automatic behavior, and we have a name for this: Automaticity. This is the state of committing a physical or mental activity to muscle memory.

One of the most commonly cited examples involves driving. If you commute to work, try to recall the exact route you took – pretty easy right? If you take the same route to work every day, or cycle through two or three different routes that are essentially similar, then it’s easy to recall how you got to work today.

Now, try to recall and describe in detail three different vehicles you encountered on your way to work today. A bit more difficult, correct? Unless you encountered something out of the ordinary – an accident or collision, a truck with a vibrant, unique wrap, or something else along those lines, chances are you can’t recall the details about any of the vehicles that were making the same journey as you, despite the fact that you most likely encountered dozens of vehicles on your trip this morning.

This is because you were driving on autopilot. Your body was engaged in an activity that it had already performed hundreds or thousands of times before – driving a car – freeing up your mind to address the issues that are really important to you. Are you going to be on time with all this traffic? Where are you going to eat for lunch? Will you be able to sneak out before 5pm today to try and beat the traffic home?

Automaticity is a useful tool, and it allows us to function in a more sophisticated social environment. Think about the last time you embarked on a long-distance road trip. Being aware of the dozens or hundreds of miles that were passing by, as they were passing by, would be agonizing, to say the least. Listening to music, playing word games with your fellow passengers, and planning your itinerary when you reach your destination are all activities your mind is able to engage in as your body engages in the rote function of piloting your vehicle down the highway.

There are other fascinating real-world applications to this as well. One study that I came across, by the social psychiatrist Robert Cialdini, discussed the level of compliance in individuals when presented with differing scenarios. In one of his studies, he presented his subjects with three different requests:

“I have five pages to copy, may I user your copier? I’m in a rush.”
“I have five pages to copy, may I use your copier?”
“I have five pages to copy, may I use your copier? I need to make copies.”

In the first instance, a valid need is being expressed – I’m in a hurry, can I use your copier? – and a full 94% of respondents replied in the affirmative. That is to say, they allowed the person to make their copies.

In the second instance, that percentage dropped to 60% – in other words, a lack of a valid reason increased the resistance within the group of respondents to allowing the person to complete their task.

Interestingly, in the third instance, compliance jumped back up to 93%, despite that fact that, although a reason was given, it was not a valid reason. The only difference between the second and third requests is the addition of the additional (meaningless) phrase. However, most respondents made no value judgments of what was said – they heard what they thought was a valid reason, and so complied with the request.

Further, when the request was made of something a little more substantial – in Cialdini’s study, for instance, the request was subsequently increased from five to twenty pages – disruption can occur, jerking the subject back to attention to focus on the situation at hand.

In the case of our copiers above, the percentages dropped to 40%, 25% and 25%, indicating that the subjects were now paying closer attention to the reasoning when asked to make substantially more copies – “because I need to make copies” was no longer considered a valid reason, as evidenced by the matching percentages for both options two and three.

Apply this to your drive to work as well. Did that guy in the maroon BWM with the IMRICH vanity plates just cut you off? Disruption has pulled you away from your internal reverie and drawn your focus back to the task of driving, and presented you with a series of choices. Do you honk and flip him off? Hit the gas and try to cut him off? Let it go? Whatever your choice, you are now fully focused on the situation unfolding before you.

Automaticity is a valuable, if unintentional, tool for dealing with the humdrum, repetitive tasks each of us needs to carry out without wasting valuable mental energies that can best be utilized elsewhere. Embrace this condition and learn to use it whenever you can – it will pay huge dividends in the end.