I actually documented and completed this task on accident, Here's how...

A little while ago one of the gentlemen that I work with got himself a Rubik's Cube to help kill the boring mid day hours. I’m sure everyone has seen one of these at somepoint in their life. My grandparents had one and I never paid it much attention. They are always sort of around. Perhaps egged on by my boredom I found myself picking it up and just tinkering a little but. At first just a twist here and there, then more and more. After a few maddening days filled with twisting and wrestling, turning and unturning trying to make it all come together, I was defeated. I got frustrated and turned to the internets to devise a proper strategy to go about getting it done. That is to say I didn’t want to know exactly move for move how to solve it, just a basic explaination of how to move one section of the cube from say the lower left of one side to the upper right corner on the next side. During the course of this investigation I came across the article on them in Wikipedia. I was startled to read:

“In fact, there are (8! × 38) × (12! × 212) = 519,024,039,293,878,272,000 (about 519 quintillion on the short scale) possible arrangements of the pieces that make up the Cube, but only one in twelve of these are actually reachable. This is because there is no sequence of moves that will swap a single pair or rotate a single corner or edge cube. Thus there are twelve possible sets of reachable configurations, sometimes called "universes" or "orbits", into which the Cube can be placed by dismantling and reassembling it.” - http://en.wikipedia.org/wiki/Rubik's_Cube

Holy SH*T!!! 519 Quintillion!!! How big is that, my brain doesn’t even understand?!? 519 billion billion. What does that mean?!?! Even if only one in twelve is a reachable state, that makes 43.25 quintillion actually achievable configurations.

Since my feeble, puny, pathetic brain couldn’t actually believe or understand what type of a number that represented I begin to think of other really large numbers of things that I could figure out to try and give it some context. And so, I began taking notes.

I began by wondering how the Rubik’s cube number compared to the number of millimeters between the earth and the sun. That work can be seen across the bottom of the white board. I knew that it takes light 8.31 minutes to get to earth, and that the speed of light is 299,792458 meter per second. Following that through, I found the sun to be a disappointingly small 149 trillion millimeters from the earth.

I know that sounds like a large number, but lets review the number of zeros involved
519,000,000,000,000,000,000
149,000,000,000,000

Six zeros is a very big difference. The number of combinations on a Rubik’s cube is a million times greater than the distance from the earth to the sun in millimeters!?! HAVE I GONE COMPETELY INSANE!?! IT”S A 3X3X3 FRICKING CUBE!!! What can be that big?

Undaunted I set out in search of larger numbers. Now I admit at this point my calculations get much more approximate, but I feel that for the purposes of approaching the correct orders of magnitude they are close enough. My mind began to wander towards bigger questions… How many grains of sand are there on the earth? A quick search yielded a few websites which began to approach the question in an appropriate way. This seems like the right idea:
http://www.hawaii.edu/suremath/jsand.html
I accept these numbers again only as approximations but I agree somewhere near 7.5 quintillion grains of sand on the earth seems plausible. That is 7.5 x 10^18 or 7.5 billion billion. Impressive yes, but 100 times smaller than the number of all possible Rubik’s cube combinations, and five times smaller than the number of actually achievable (without dismantling and reassembling) configurations. Rubik wins again, no wonder I couldn’t solve the damn thing. So my quest for yet larger numbers continued, note taking all the while so I could compare these numbers side by side as I was trying to figure them out.
After sand I inevitably became curious about the number of stars in the universe. Google helped me out again. They essentially said we have approximately 400 billion stars in the Milky Way galaxy, with at least 40 billion galaxies.
http://answers.google.com/answers/threadview?id=539329
Debate over this obviously gets heated amongst internet trolls, I don’t really care, I feel safe in assuming we land somewhere near 600 quintillion stars in the universe. That is almost 100 for every grain of sand, but relatively not that much larger than the number of combinations possible on the Rubik’s cube. Very impressive for a small little stupid toy.
Feeling pretty good with myself for finding something at least in the same ballpark as the massive Rubik’s number I felt that I had certainly given myself the type of perspective that I had been looking for. But perhaps intoxicated with the sweet sweet liquor of knowledge I decided not to let my note taking stop just because I had found something equal to the cube. I had to find something larger. And I am happy to tell all of you that I found a number twice as large or perhaps even larger than all of the ones I have mentioned so far. My notes show the number of molecules comprising the earth to be near 1.1 x 10^44 I can’t reconstruct my exact sources on this, but I found this link which places the number even higher, somewhere near 1x10^50 for the number of atoms in the earth
http://education.jlab.org/qa/mathatom_05.html

The Rubik’s cube remains the largest discreet number that I think I have ever contemplated, but the others are very impressive to me as well. Anyway, the point is I took notes. I hope you all learned something, I know I did. Dare to ask the stupid questions, and take notes!

Here is one more link for those who can’t get enough Rubik.
http://web.usna.navy.mil/~wdj/rubik_nts.htm

To be honest with you fine people of the sf0 community, I still don’t feel satisfied, I am thinking about taking some more notes right now before your very eyes. Yes, I am opening my web browser in another window. I have more to say.

The Earth is ~ 4,500,000,000 years old (4.5 Billion (wikipedia says so))
That is ~1,642,500,000,000 days old (1.64 Trillion)
Or ~39,420,000,000,000 hours old (39 Trillion)
A.K.A ~2,365,200,000,000,000 minutes old (2.36 Quadrillion)
And ~141,912,000,000,000,000 seconds old (141 Quadrillion)
THAT MEANS IF YOU DID ONE RUBIK’S CUBE COMBINATION EVERY SECOND SINCE THE EARTH CAME INTO EXISTENCE, YOU WOULD NOW BE ~1/3657th of the way to doing all of the “possible arrangements”, and ~1/305 of the way if you don’t plan to take your cube apart and only do the “reachable” configurations.

If you started doing ONE combination PER SECOND when the universe began
13.7 billion years
5,000,500,000,000 days (5 trillion)
7,200,720,000,000,000 minutes (7.2 quadrillion)
432,043,200,000,000,000 seconds
You still wouldn’t have gotten the cube into every “possible arrangement”
So amazing for such a little cube! I still don’t believe it. I hope I am just bad at math. Next time you see one of these take a moment to appreciate its possibilities, and

Take Notes.