The BCS is better than the playoffs when it comes to determining a “true” national champion this year.

To put it in the simplest terms, a playoff would have meant that LSU would have had to play even more games to win the championship. People forget this when arguing for a playoff. Each additional game is a chance for LSU to lose what almost everyone agrees they deserve.

Let’s see what 4- and 8-team playoffs would have meant mathematically.

Hypothetical Numbers #1: Let’s be incredibly generous and say LSU is so good, they would beat any top 8 team 90% of the time.
Under the BCS, LSU would have a 90% chance to be crowned national champions.
In a 4-team playoff, it drops to 81%.
In an 8-team playoff, that drops again to 72%.

Hypothetical Numbers #2: Something a bit closer to reality, but still generous: LSU would beat Alabama 60% of the time, OK St 70% of the time, and the rest of the top 8 80% of the time.

Under the BCS, LSU has a 60% chance or 70% chance to be crowned national champions (depending on who ends up #2).

The math for the playoff systems is more difficult. In a 4-team system, LSU would be playing #4 then the winner of Alabama vs OK St. The chance of LSU winning the championship is somewhere between 48% and 56%. While the exact number depends on the odds of Alabama vs. OK St., it’s not much better than a coin flip.

In an 8-team system, obviously, it’s even worse. If LSU gets lucky and doesn’t have to play #2 or #3, they would have only a 51% chance to win all 3 games. The odds are somewhere between 38% and 51%, depending on the odds of #2 and #3 making it to the national title game.

I’m well aware playoff proponents will argue that the playoffs are better anyway because things are decided “on the field”. And that’s fine, as long as they are aware of what they are getting. There are simply too few games played during the football season to have a high degree of confidence that a “true” national champion was crowned, whatever the system.

Math and religion. Oh how long I’ve wanted a post that combines these two topics.

Anyway, some Bible skeptics like to criticize the Bible for claiming that pi is equal to 3 based on this reference:

(1 Ki 7:23 NIV) He made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits to measure around it.

The circular object is 30 cubits in circumference and 10 cubits in diameter. Thus the Bible says pi = 3, LOL. Right?

Well, it’s not LOL, and it doesn’t take some of the odd gymnastics Biblical apologists use to see why.

It’s all about significant digits. The concept of significant digits helps us determine how precise a number is and how precise we can expect any calculations to be.

For a real-world example, let’s say you’re driving to Houston, desperate to visit me. You see one of those signs that says “Houston 100″, indicating the city is 100 kilometers away. (Yes, I know it’s miles and feet in the US. I want to use metric. Hrmph.)

Imagine you step out of your car and stand by the sign. Then you take a step 1 meter backwards away from Houston. You wouldn’t say “I’m 100.001 km away from Houston now!” Why?

The sign has a precision to the nearest km. We can’t tell whether the sign is actually 100.1 km, 99.729 km, or somewhere in between. There’s a limit to how precise we can be.

Let’s go back to the Bible passage. The dimensions are 30 cubits and 10 cubits, both numbers with only one significant digit. Without any further information on the measurements’ precision, calculations can only be expected to be precise to one significant digit.

30 / 10 = 3. Pi to one significant digit is 3. The Biblical figure for pi is as accurate as it can possibly be given the measurements. Nothing to see here. There are enough questions about the Bible not to dwell on a non-issue.

It’s said that we dream every night, but simply don’t remember them. I don’t know how true that is, but last night I had two dreams that I could easily recall. Whether that’s because of going to bed 2 hours earlier than normal, or reading the Tel’aran’rhiod chapter in the Dragon Reborn (it’s about a World of Dreams), who knows.

Anyway, here they are:

Dream #1

In a classroom, there were about 25 of us listening to a lecture by Martin Gardner, who was well-known for his recreational mathematics writing.

The topic had something to do with finding certain types of solids that could have integral values for their sides, akin to finding integral solutions to the Pythagorean equation. At some juncture, I pointed out some error he made while using an irregular solid as an example. He thanked me and I felt rather proud (even though the error was trivial).

During the lecture, somehow I realized it was February 1979, so I must have traveled back in time.

Despite not knowing what Gardner looked like, in the dream he basically looked like himself without the glasses. And maybe a bit more hair.

After the lecture, most the students gathered in a circle and started chatting. I had a suspicion that some of them were also time travelers, but didn’t want to tip off non-time travelers in case that had dire consequences. So I simply asked if anyone else was a “Traveler” (about 8 or 10 people raised their hands).

Someone also brought up World of Warcraft and talked about the first expansion. Not the actual first expansion, but some expansion invented in the dream, which had a Final Fantasy 5 Bomb pictured on the CD cover (?????)

Eventually, everyone packed up to leave. But I realized I didn’t know how to get back to my own time, and was hoping to tag along with the others. But they all left quickly and it took me FOREVER to pack. Fortunately, Gardner realized that I was a time traveler. He told me I just needed to keep going and I’d find the right guide, or something like that. I didn’t understand and tried to ask for clarification, but whenever I looked at him, he faded further into a brown mist and grew fainter. There was no choice but to move on.

Wandering through a hall, I couldn’t find the guide Gardner was talking about, and eventually wandered into a supermarket. I started to think about what would happen if I were stuck in this time period. My ATM card wouldn’t work. The cash I did have was from the 21st century, so that was bad. I thought about going to see my parents, which would include my dad in an afro. But I didn’t even know what state I was in, so that wasn’t an option.

Then I woke up.

Dream #2

If you don’t want to experience a somewhat disturbing mental image, please stop reading now.

Understand this is really for the 4 or 5 readers who are entertained by this kind of thing.

You probably aren’t one of them.

OK, I warned you.

The scene starts at the Griffins’ house. As in, the Griffin family from Family Guy. Lois and I start making out in the kitchen. Peter ambles by, and doesn’t seem to care in the least. Even so, I tell Lois we should go back to my place. Which is a house next door that we are teleported into.

From the inside, it seems to be a one-room log cabin with a bed and sparse furnishings. She climbs on top of me, and we start having sex. I look up, and Stewie is there in a blue diaper, yelling and all ticked off. I get up and tell Lois we really need to do this somewhere else, but she doesn’t seem aware of the danger.

Lois Griffin is so hot, she’s made me watch all of 6 episodes.

Does anyone know if there’s a difference between an antiderivative and an indefinite integral? I’ve always kinda thought they were the same thing, although I’ve heard some people have different definitions for them.

OK, so. It’s June. The Yankees are 1 game behind the Red Sox. And ESPN is asking whether you think the Yankees must beat the Red Sox tonight.

How can this possibly be a “must win”? Are the Yankees going to be eliminated from playoff contention? All of a sudden, they’re going to lose confidence and become a .500 team? It’s not like there are more than 90 games left in the season.

The most frightening part is that 44% say it’s a “must win”. I really hope they’re joking.

Hope you enjoyed June 11th’s Tour of Stupid.

Has this work week been particularly stressful or frustrating? I leave you with this pick-me-up for the weekend — at least you’re smarter than the guys in the following story:

The menu at the Coffee Garden at 900 East and 900 South in Salt Lake City has included a scrumptious selection of quiche for about 10 years.

The recipe calls for four fresh eggs for each quiche.

A Salt Lake County Health Department inspector paid a visit recently and pointed out that research by the Food and Drug Administration indicates that one in four eggs carries salmonella bacterium, so restaurants should never use more than three eggs when preparing quiche.

The manager on duty wondered aloud if simply throwing out three eggs from each dozen and using the remaining nine in four-egg-quiches would serve the same purpose.

The inspector wasn’t sure, but she said she would research it.

Source: Eggsacting Math

You are at a party with 22 other people.

1. Estimate what the chances are of at least two people at the party having the same birthday.

2. Now calculate it. (For simplicity, feel free to assume no one was born on Feb. 29)

Yes, I was surprised.

You know what I discovered?

e ^πi = -1 (that’s e ^ (pi * i) = -1 if it didn’t display properly for you)

How freaky is that? (Explanation here.)

For those of you who read The Daily WTF: obvious troll is obvious. (Yes, aware that annoying meme is annoying, deal with it.) I can’t believe how many people have taken commenter Top Cod3r seriously.

: I didn’t really have anything to say, except that we have a little Mr. E icon now for when I have an aside. And, uh, stay in school and don’t do drugs.

Today’s π day. March 14 is 3/14 and π is 3.14…. 3.1415926535 was as far as I cared to memorize, and even that was a waste of time.

This is a perfect day to share any π-related stories. My favorite is the day I learned about radians as an angle measurement and that a circle was 2π radians. 11th grade, I think. That had a profound effect on my future development as an adult.

Additional reading: piday.org is supposed to be the “official” π day site (at least, it’s the first site that showed up in Google).