## Little Gödel

One day, little Gödel went to class. For whatever reason—perhaps, an unhappy love affair or a bad hangover—little Gödel’s teacher did not feel like teaching. Instead, he instructed the class to sum all of the integers to one hundred, that is, to calculate $\sum_{i=1}^{100}$.

The teacher correctly expected most of the class to do what I now consider the most inefficient method of performing this operation; they started as follows:

$1+2 = 3\\
3 + 3 = 6\\
4 + 6 = 10\\
...$

At about this point, little Gödel walks up to his school master and writes 5025 on the chalk board and proclaims, “I’m done!” Perplexed by the rapidity with which little Gödel solved this problem, the instructor inquires him to “show his work”.

Little Gödel goes on to illustrate that while thinking about the problem he realized that
$100 + 0 = 100\\
99 + 1 = 100\\
98 + 2 = 100\\
97 + 3 = 100\\
...\\
51 + 49 = 100$

“This means we have $50*100$ or $\frac{1}{2}n*n$ 100’s to sum. But summing the same number over and over is multiplication, that’s easy! However we can’t add 50 to anything–there is no other number between 0 and $n$ that hasn’t been used which will sum to 100. Therefore, at the end of our multiplying spree we must add 50 or $\frac{1}{2}n$.

Therefore, the sum must be $\frac{1}{2}n * n + \frac{1}{2}n$.” He quickly simplifies this equation to
$\sum_{i=1}^{n} = \frac{n^2 + n}{2}$

We all learned something that day! Too bad about the teacher, though.

## Closing the Interstate dangerous?

The state has long has the ability to “close” the interstate. Normally, this just implies that the weather makes any travel dangerous and if you go out and get stuck you’ll be fined heavily for going out after you’ve been warned.

Recently several gates have been installed on on-ramps in the Siouxland area which can be closed to physically bar access to the Interstate.

Those who would go out when the Interstate is closed will still go out if the gates are closed. However, now they are forced to take secondary roads which are arguably more dangerous than the interstate in adverse weather due to narrowness of the lanes, and that two-way traffic is mixed on the same road.

On the interstate, when you’re alone, you can putz along in the middle of two lanes going slow and you have nearly 20 feet of road on either side of you.

I don’t agree that installing gates is a solution.

## Windows 7 pop-under?

I can’t believe this. I left my desk an hour ago to work on other things while Microsoft Office chugged on this re-activation thing. It had hung at 90% indefinitely. Clicking the close “X”, confirm my request to cancel, and it still hangs.

It’s here I realize a glowing icon in the task bar. Clicking it reveals, “Do you want allow the following program to make changes to this computer?”

I suddenly miss the days when notifications were displayed in a manner that caused you to, well, notice them.

## You can now include media in your posts…

Thanks to anarchy media player.

From the visual editor you may click the “A” for anarchy and paste in the URL for your media.