How Simple Mathematics Can Save College Football

I'm pulling out a post from I originally typed up when I first heard the Big 10 would have 12 teams and the Big 12 would have 10.  Of course when I first typed this I was not on twitter and had no real good way of sharing.  I've slightly updated it with some real nifty high tech graphics.

As a math teacher I feel it is my duty to help make sense of this whole Big 10 has 12 teams and Big 12 has 10 teams confusion. Obviously powers that be of these conferences want to make us think, or maybe they mean it when they say "student comes first in student-athelete." Possibly in an attempt to raise the bar in terms of mathematics.  For it to make sense that the Big 10 has 12 teams, they will have to move from the traditional numerical system (base 10) to to a slightly more complex system (base 12). Well complex for now, who knows this might just take off and change the whole way we think about numbers. Anyways here is how it works. We have long been familiar with the base 10 number system so much so that we do not even need to mention that we are in fact discussing numbers in base 10. Remember back in grade school when you would look at number blocks, and ten ones cubes could be traded in for a 1 stick of ten, and ten sticks of ten could be traded in for a large 10x10 square or 1 100 block.

If this is painful for you I'm sorry. Take two aspirin, a large glass of water and fight through it. (On second thought, to avoid any lawsuits here, please ignore that advice without first consulting with a licensed physician). Ok, so in base 12, it would work more like this, it would take 12 ones to trade in for one stick of 12, and 12 sticks of twelve would be traded in for one 12x12 block (or 1 block of 144), of course a major problem with this explanation is that it is explained using base 10 numbers.

So if we examine the number 10 in base 12 looking digit by digit (which of course the word digit is based on the number of digits we have on our hands - 10) we would find that 10 in base 12 equals 12 in base 10. That aught to be about as clear as mud. So hears hoping we can make it about as clear as a window on a Subaru in their commercials. The zero or the first digit from the right in the number 10 in base 12 means that there are zero "ones". And the one in the second place from the right (can't call it the tens place in base 12, think of it as the twelves place) means that we have 1 "12 stick" so our total value would be 1 "twelve" plus 0 "ones." Therefore 10 in base 12 equals does in fact equal 12 in base 10.

The marketing geniuses at the Big 10 can simply put it on cruise control in regards to their logo, just simply add a microscopically small 12 as a subscript to the 10 and call it a day, adding a subscript to the right of the number is the standard way of noting you are writing a number in a base other than 10.  (Of course they didn't there logo now pretty much looks like they are the Big 1, maybe I'm missing something subtle in their logo, like the had when the had 11 teams).

So, does the Big 12 have it just as easy now that they are down to 10 teams? Because after all, since 10 in base 12 equals 12 in base 10, then 10 in the Big 12 equals 12 in the Big 10, right? It would be far simpler to just end this post and say yes, but alas it is not that simple. Should the marketing geniuses at the Big 12 just add a microscopically small 10 in subscript to their logo, this would be an exercise in futility, there is no need to indicate 10 as base, as 10 is the base of our standard numerical system, and would therefore just indicate that 12 actually means 12, as the typical person over the age of four or five would understand it to mean. No they actually need to add a subscript of 8 to make it mathematically correct. Why's that? you say (and by you, I mean the only person on the planet that has read this far, thanks mom, and the one of you on the international space station as well, because I am quite certain that you understand number bases, and are probably a little board from the lack of human interaction up there). Well here is why, in base 8, the number 12 means that we have 2 in the ones place, and and 1 in the "eights" place. So the number 12 in base 8 means 1 "eight" plus 2 "ones" for a total of 10.

 So for this whole 10 in the Big 12 and 12 in the Big 10 thing to make sense all we need is for the Big 12 to move to base 8, and for the Big 10 to switch to base 12.  So that is how mathematics can save college football.  That and the SEC.

In my opinion, the Big 10 has made a far superior decision in it change of base. Purely from the perspective of uniform numbers, but I'll leave that for another post.