Sunday, February 24, 2008

Damn you Rubik's Cube!

In an attempt to enrich my life with activities and skills with a higher level of sophistication than the average human, I decided I was going to solve the Rubik’s cube. The choice to do so actually fell into my lap. I won a Rubik’s cube at a Matlab seminar for answering a question. Up until then I hadn’t thought about the cube for several years.

I, like the majority of you, had put the Rubik’s cube on a pedestal: The impossible puzzle cube that only the super intelligent had a chance to solve. I’m sure anyone who has tried and failed would compare it to the accursed cube from Hellraiser! Since my intellectual achievements would suggest myself being a bit sharper than the average person I was compelled to give it a shot.

Aside: The Rubik’s cube is sometimes referred to as the Genius cube (or the Professor’s cube for larger ones). Let’s consider what it really means to be a genius. Typically we associate geniuses with high IQ’s. But is the IQ test really a good measurement? The original IQ test was completely wrong. It calculated a person’s “mental age” then divided it by their actual age. I believe that our mental capacity is a limit cycle and therefore becomes saturated at some point. If we live by the adage “you can’t teach an old dog new tricks,” then let’s say our mental capacity peaks between 25-35. For some people it probably remains consistent from then on out, at least till they reach extreme old age…or no longer use it and therefore lose it. For others I would imagine it declines somewhat as age increases. One thing is constant though; a person’s actual age is always increasing. Therefore their IQ would be continually decreasing. More updated IQ tests are probably better. They use a standardization model which approximately matches a Gaussian distribution where an IQ of 100 is considered the average. I hate to reference an encyclopedia, but to my dismay Wikipedia has a pretty complete synopsis of the IQ. I’m still pretty skeptical of any IQ test, because it’s too subjective (see the Wikipedia section on composite score and IQ factors). For instance, person can improve their IQ by studying! If IQ is a measure of aptitude, that alone is a fundamental flaw and should be enough to discredit it as a real measure of aptitude. I consider intellectual aptitude is an inherent ability to obtain, process, and store mental stimulus; more like an intellectual capacity or prowess. It seems that an IQ test can be likened to a weightlifter. His strength increases the more he uses the muscle. To me, the IQ test is a measure of instantaneous mental ability while it should be a measure of maximum capacity and therefore does not change in time. I acknowledge that, like a muscle, working a person’s mind will unlock greater abilities and should be a life’s pursuit for everyone.

Anyway it doesn’t really matter. For lack of a better understanding of the human mind, we use the IQ test. So what is a genius then? This site (http://wilderdom.com/intelligence/IQWhatScoresMean.html) is about on track with other sources that break down IQ into labels. Basically, it follows over the total distribution

· Over 140 - Genius or near genius

· 120 - 140 - Very superior intelligence

· 110 - 119 - Superior intelligence

· 90 - 109 - Normal or average intelligence

· 80 - 89 - Dullness

· 70 - 79 - Borderline deficiency

· Under 70 - Definite feeble-mindedness

For high IQs

  • 115-124 - Above average (e.g., university students)
  • 125-134 - Gifted (e.g., post-graduate students)
  • 135-144 - Highly gifted (e.g., intellectuals)
  • 145-154 - Genius (e.g., professors)
  • 155-164 - Genius (e.g., Nobel Prize winners)
  • 165-179 - High genius
  • 180-200 - Highest genius
  • >200 - "Unmeasurable genius"

According to the Gaussian distribution approximately 0.25% of the population is at an IQ of over 140. In the U.S. that equates to 752850 people (US pop as of July 2007, 301,139,947 X 0.0025=752850). That’s bullshit. If that statistic is correct, then according to the state testing done on me when I was in school, I’m in that group. However, I am absolutely NOT a genius and I’ll confidently say neither are you! A Gaussian distribution suggests that there is a smaller probability of a random sample falling closer to the tails than the middle. This implies that it’s more and more difficult to fall higher on the tail the closer to the limit you get. This could mean that the jump in capacity between an IQ of 115-124 is much less than the jump between 155-164. I can MAYBE find the 0.25% plausible, but the definition of genius needs to be seriously reconsidered especially if the increase in one point becomes harder to obtain and more significant at the extremes. I might suggest starting the genius IQ's at 160 or so.

So what was the point of that long aside about IQ? I know for a fact that you don’t have to be a genius to solve a Rubik’s cube. In fact, I’m pretty sure that given enough time and patience a monkey could be trained to solve it.

When I first decided to solve it, I decided that there must be a systematic method. I presumed that you could solve the cube a layer at a time. I also expected that certain patterns of rotation (algorithms) would result in a predictable fashion. Sadly, I did get stuck and found some instruction on youtube

http://www.youtube.com/watch?v=HsQIoPyfQzM

http://www.youtube.com/watch?v=IW_BBp3FPMQ

He gives a pretty good description of an idealized solution. It’s not perfect since it is idealized. Either way, I was right on all my presumptions. I feel confident that given a little more patience, I could have discovered all but the very last algorithm on my own. That one is less intuitive, but perhaps… I added a little more description to solve some of the problems that our friend Dan skipped. Follow his nomenclature for the commands.

ROW 1

Fi U Li Ui Cross-right spot wrong orientation

Ri Di | R D Corner-directly below the correct corner

ROW 2

Ui Li U L | U F Ui Fi 2nd layer-moving from top to the left

U R Ui Ri | Ui Fi U F 2nd layer-moving from top to the right

ROW 3

"L" in top left corner If you dont have an "L" just pick a corner and begin

F R U Ri Ui Fi

This gives the "line"

Repeat to get the Cross

once in the cross line up 2 middles with the right sides

IF they are next to each other

put one away from you and one in your right hand

then do

This lines up all the middle pieces on the sides

R U Ri U | R U U Ri never need to do more than twice ?CHANGE ORIENTATION to get the previous description?

rotate u to get all the middles on the sides finished

IF the they are opposite each other, put one facing and one away then do

R U Ri U | R U U Ri

then like normal

R U Ri U | R U U Ri (U)

now with the CROSS and the middle pieces lined up

find the corner that has the correct colors, but not the correct orientation

put it in the bottom right corner an do

U R Ui Li U Ri Ui L repeat if necessary, but always keep the same orientation

IF none are in the correct corner, do it with any wrong in the bottom right corner

once the corner pieces are in the right place, but the wrong orientation,

put it in the bottom right corner and do

Ri Di | R D

rotate ONLY the top until another unsolved cube is in the bottom right and repeat

Really, all you have to memorize is about 5 algorithms. The rest are intuitive or closely related to another. I would suggest that it is just as important to observe how a block is replaced as it is to observe how a block is moves. That will help make the solution much more intuitive. It took me about 1 day to go from zero to being able to solve any cube. There are much more advanced solution than the one provided here. I can solve any cube in around 5 minutes with these instructions. More advanced solutions will decrease the time.

When it’s all said and done, I was extremely disappointed that the solution is so systematic. Absolutely no thought is needed once a person has memorized the algorithms. I really can’t express my dismay enough. I had sought this project as a way to increase my sophistication. How can I not be disappointed when I learned that the ominous Rubik’s cube is, at its heart, rudimentary child’s play?

and now, a deep thought
-How much the Rubik's cube is like life, daunting at the start, but trivial at the end.

5 comments:

E.Jacob said...

I think part of your disagreement with the IQ test lies in your personal definition of intelligence. There are varying definitions of the word.

•(intelligence) the ability to learn or understand or to deal with new or trying situations

•(intelligence) the ability to apply knowledge to manipulate one's environment or to think abstractly as measured by objective criteria

•(intellect) revealing or reflecting good judgment or sound thought

•(intellect) having or indicating a high or satisfactory degree of mental capacity

Some of these definitions seem to correlate with your line of reasoning – “I consider intellectual aptitude is an inherent ability to obtain, process, and store mental stimulus; more like an intellectual capacity or prowess.” However some of the definitions sway from that and describe things which certainly can change in more than just time and age, but with practice.

Additionally, the inherent ability to obtain, process and store metal stimulus can be altered by practice. Practicing problem solving and other reasoning skills work the brain and physically change the brain. Thus the intellect does change with practice and your IQ should reflect that.

Just as a side note, I agree that the old test were in error and that your age should have nothing to do with your intelligence. In fact, since your age is just a moderately irrelevant measure of your distance traveled around the sun it is not directly correlated to the aging process anyways. However, you invoke the adage that old dogs cannot be taught new tricks. This has little to do with the strength of a person’s mind at old age and more to do with their stubbornness. Though, it is typical that the best work done in one’s academic career is in their 30’s, so your argument still stands.

As far as the Rubik’s cube goes, you did look up how to solve it instead of fighting through it by applying your intellect. So, although it is not a signifier of genius, it is still pretty hard to solve on your own, but then again, I have never solved one.

Josh said...

Thanks for the comment. I agree with it completely. I realized that while i was formulating this topic, that my definition of intelligence my be purely my own. I was a little worried because of it, but i felt that in the end my idea was reasonable.

In regards to your last paragraph. It is undoubtedly difficult to solve the cube on your own. However, I believe i mentioned that the only non intuitive part was the final set of rotations. The rest could be worked out within a few weeks or a few months depending on the level of diligence and adherence to the scientific method. I've said this to you directly that i dont feel my 3d perception is all that great (a possible mark of genius). Up until the last step i think i can get by with simply observing initial and final positions of specific pieces. The last one is simply unnatural without better spatial abilities.

Regardless, i assumed and had hoped that once i knew a couple tricks or a general method, each solution would stress my abilities. I was wrong.

Michael Vincent said...

After you're done with that, try the bigger ones, 5x5 cubes are fun

Steven said...

I just got to the same place as you did (two years ago!): When you know how, it's always just easy.

However, there are still some fun options:
o Try and do the first layer corners and middle layer at the same time
o Learn some extra moves - needing to do moves I already know "backwards" is a little bit brain flexing
o Use a different solving strategy - If you know the right corner translating tricks then try doing all the middle pieces first, and then the corners is a 3D challenge

My next project is to lose the cube for a few years and then come back and see if I can still remember it :-)

Anonymous said...

The genius of the Rubik's is in speedcubing.

Check out Feliks Zemdegs, who holds the WR for a 3x3x3 single at 6.24s. As in, six seconds.

Whilst memorising algorithms is a large part, and effectively when you move onto more advanced methods the number of algorithms simply increases (57 OLL + 21 PLL; 350+ ZBLL), the concept of double slot F2L (first two layers) and LL (last layer) recognition and execution time is where "IQ" comes in. Spacial awareness, memory and reaction time are required, and whilst I've learnt all OLL + PLL algs, I'm still at a PB of 16.xx when others who know the same algs are nearing the 10s mark.