Wednesday, February 27, 2008

The Nature Of Coincidence

Coincidence has always struck me as an interesting human observation. We find connections in things, some of which are there, and some of which are not. Either way, we enjoy connections. I find the concept of coincidence specifically interesting when put into the context of religion or superstition. Someone may associate a coincidence with an act of God, an answering of a prayer, or the result of a superstition or curse. Typically, if the observer is less swayed by the supernatural they may simply find the array of connections interesting. Now, for the most part this is a harmless occurrence, though, the perpetuation of a false belief in the context of mere coincidences could be harmful to ones long term development. By this I mean that continually believing that the root of a coincidence is something other than just a random improbable connection of events could limit ones imagination. This prevents you from looking beyond the resulting action and eliminates the need to look deeper. It is then that we may learn something new.

Let’s take an extreme example. Someone sees a rainbow. If they immediately account its creation to a higher being they may never think to study it closer. They would lose out on the opportunity to learn about the rainbow, thereby understanding that it is the result of an entire series of events. A rainbow is a fascinating event, photons reflecting and refracting slightly different at different wavelengths, splitting apart the spectrum. There are a myriad of physical processes which all play their role and create a rainbow. By immediately associating a coincidence to something more that a rare series of events we miss out on some of the hidden beauty in life. They say that ignorance is bliss, but in this case you must sacrifice a deep profound beauty which is evident in the multitude of subtle interactions for that bliss.

This problem is a result of the nature of coincidence, and maybe a little bit about how we act as humans. A coincidence may happen once in a while and it stands out among the normal. Thus, we notice it. Though, we don’t necessarily perceive the multitude of times in which things happen to be perfectly normal. Therefore, we do not have an appropriate perception of the rarity of the coincidence. This manifests itself in the context of belief. If we see coincidences often and presume them to be common we make it easier to account them to something greater than random, thereby invoking a connection between the connections. This can potentially create scenarios, and we do this often, where we see more in things than there really is.

This in no way discredits God or any belief for that matter, he might just as well be behind all the events which lead to a coincidence. What this does show is that humans are naturally predisposed towards believing in a superior force or being primarily due to a lack of understanding of probability. At least, that’s what I believe.

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 ( 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

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.


Fi U Li Ui Cross-right spot wrong orientation

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


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


"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.

Wednesday, February 20, 2008

Write Like No One's Reading

I was trying to think if that line made any sense. You should dance like no one is looking, and sing like no one is listening. I suppose you should write for yourself, like no one is reading. Now, doing that is all the easier when writing on an unknown blog.

I ran into Weldon Payne today. I good friend of mine and many others. He is a real writer. I told him that Josh (that is -=JR1=-, I hope I didn't spoil his alias) and I were writing on a blog and that I had one going for a while while I was in Germany. He said that he wished he had written more when he was younger, even 30 minutes 3 times a week. I enjoyed writing about my Germany adventures and now, taking his advice, I have chimed in on the blog.

The blog is supposedly going to have a more sophisticated tone, generally discussing topics in religion, politics, social observations and such. Unfortunately I don't have a clear topic to talk about right now. Although, I was just in the shower and since that is where I have discourses with myself and also where I think of things to write about - well... this is all I've got:

I checked my bank account today and I was happy to see that I got my tax return. In my current economic status, as quasi paid student, it was a pleasant bonus. Now this is mostly unrelated, but while I was in the shower I remembered a commercial for H&R block, or one of those tax places. They said that every year we, as a country, fail to receive over 1 billion dollars in tax returns. They play that up as a big deal. One whole billion dollars. It is a lot, until you remember that there are 300 million Americans. That is 33 bucks each. I bet a tax adviser is more than that.

On the other hand the US nation debt is $9,293,653,182,093.53 as I write. That is a bit more, it works out to about $30,000 a person. We could get a really good tax adviser for that. I actually wasn't trying to make a political statement there, but if there was one it is this: advertisers and politicians are stupid and manipulative.

Maybe next time I will write about something a bit deeper. Don't worry Mr. NoOne, I have ideas. -Eric

Monday, February 18, 2008

The Delusion of the BCS National Championship

I hesitate to make this the first post. The underlying theme of this blog is certainly not specifically sports related, but rather any random topic of intrigue, controversy, or other intellectual stimulation for reader and writer alike. This just happened to be something I've mulled over for awhile and which culminated about the same time as we formed this blog.

There is a huge controversy regarding the current BCS football system. Before I begin to elaborate, let me state that I’m definitely in favor of a playoff system. Currently there is something like 21 non BCS bowls and 5 official BCS bowls. Information regarding both can be found here or here Basically the non BCS games constitute teams that had alright seasons, but were most likely not conference powerhouses. BCS bowls loosely follow the following

Unless their champion is involved in the BCS National Championship game, the conference tie-ins are as follows:

  • Rose Bowl - Big Ten champ vs. Pac-10 champ
  • Fiesta Bowl - Big 12 champ
  • Orange Bowl - ACC champ
  • Sugar Bowl - SEC champ

The Big East champion takes one of the at-large spots remaining (Wikipedia).

It seems glaringly apparent that since the strength of any specific conference or the number of prominent teams therein can vary from year to year, the best teams may (and most likely) will not be playing for the glory of a BCS title. Take for instance the 2007 Big 12 conference. Missouri was for a short time ranked #1. All things considered, at the end of the regular season they were the highest ranked team in the nation. However, since they lost to another top 10 team (Oklahoma) in the Big 12 Championship game (an extra game played in the Big 12, SEC, and others that slip my mind), they lost their number one spot going into the bowl games. In fact they were removed entirely from any BCS bowl. They went on to an absolute victory against Arkansas in whatever diminished bowl they played in. Two things seem wrong here. First, how can a team who played 13 games (Missouri) be ousted from their spot in the national championship by a team who only played 12 (Ohio State). Especially since a win for Missouri in game 13 would have been inconsequential while a loss would (did) devastate a stellar season. This argument is spurred as much by suspicion of the accurateness of the rating system as it is for the need of a playoff format. Lets say there wasn’t a Big 12 championship game, then the 2007 season would have finished with Missouri, Oklahoma, and Kansas all in the top 8. Missouri would have been in the national championship game while Oklahoma would have snatched up the other BCS spot. Kansas, who was a #1 team for a brief time, would have been ousted from the BCS in the same fashion Missouri inevitably was. At the end of the regular season, both Missouri and Kansas had only one loss while Oklahoma had 2. Something seems inherently wrong with eliminating Kansas (or Missouri) from a BCS game. Ironically, Oklahoma lost their bowl game while Kansas and Missouri both won. Clearly, the Big 12 fostered 3 of the best teams in the nation while only 2 got to play in the big games. The same could be said for the SEC if LSU hadn’t won the extra game over Tennessee for the SEC championship. In that case Georgia would probably have been eliminated from a BCS game…or who knows, they might have been in the National Championship.

Second, what about teams from less competitive conferences that have shown potential for greatness. For example, as seen in 2006 in the miraculous win by Boise State over Oklahoma in the fiesta bowl, a WAC team finished a perfect season with a win over an established team. Of course Hawaii was unable to follow the following year as they got blown out by Georgia.

Even though I have my doubts as to the validity of the rating system, there is definitely a need for it. Clearly every D-IA team cannot be in a playoff. For this reason an assessment of the worthy teams must be made. For lack of a better system, I do not object to the current one. To amend the current computationally based rating system, I propose removing conference championship games from the rating system (and maybe the season). Also, team stats tallied into the ratings need to be those accumulated during regulation play; not the inflated stats that overtime provides. My proposal for the tournament system would add between 2 and 4 extra games for the top rated teams in the postseason. Here are two suggestions for an 8 or 10 team system based on the 2007/2008 season.

In this type of playoff, only the national champion can have the chance of a perfect season. Perhaps it’s only my perspective, and honestly I feel like it probably isn’t as decisive as I would like it to be, but it seems to promote a clearer national championship if there is only one undefeated team. If all conference championships are eliminated, then we are considering 4 games beyond the regular season at most. The season would need to end by the end of November. Finals for football players would be the first weekend following the first full week in December. That way the students have ample time to study. The first tournament game will be held the second weekend in December. I won’t say 100% since I don’t feel like looking up all possible weekends in the month of December, but I feel confident in saying that 2 weekends can host games during December. I feel it’s important for the students to have Christmas off. If for nothing else, it will give them an one to two weeks to recover from the bumps and bruises of the regular season. Games would start up New Years day. That day would host all the multitude of lesser bowls that are always held on New Years as well as some of the new BCS tournament games. The later of the BCS games would be held the second week of January as has been customary for the national championship in past few years. I’ve found it atrocious that Ohio State two years in a row played in the national championship after having such a long and unnecessary break. Take that from an LSU (and Tennessee…I have a Master’s of Science from UT, but a soft spot for LSU) fan. I wanted LSU to win hands down. As long as a Big 10 team sits that long, it’s always in question. It’s a glorified form of “icing the kicker.”

I don’t really understand the opposition from the NCAA or schools alike. The addition of more, not to mention post season, games will undoubtedly bring about more revenue and recruiting. The question seems obvious: why wouldn’t there be a playoff? It would pacify the fans, increase revenue, maintain the prestige of the BCS bowl games, give the students opportunity to heal and prepare for professional careers, all while making it possible for the most deserving teams to win a national championship regardless of the strength of their individual conference.

and now, a deep thought

-at what point will the players, coaches, and fans alike realize that their dreams for football greatness will always have an asterisk marking what could have been or should have been?