Helping a little, old (rich) lady

One day, on the drive home from work, I witnessed an elderly lady in battered clothes struggling. Her wheelie basket, piled with laundry, had gotten stuck. In an unexpected and unprecendented pang of empathy, I stopped and offered assistance. Delighted to have me after, apparently, struggling for some time I was quickly able to pop the stuck wheel out of its prison (the sewer grate).

Preparing to leave, she stops me. “Before you leave, I have a reward to offer!”

She has my attention now. “I can give you 1,000,000 dollars or I can give you thirty daily payments starting today of one penny. I shall double each subsequent payment.”

To be kind, I offer the “lower” payment of a penny. I don’t need any old ladies millions of dollars. She gives me a penny and departs.

Sitting back in my office, I stop and think about what I’ve done. I realize that each day she pays me (for all thirty of them) I can expect 2^{day-1} cents. Considering it further, I begin to understand that the miracle of a doubling scheme such as this is that every subsequent day I will receive exactly one more cent than all the previous days combined.

A few weeks later, it now takes a rather large dump truck to deliver the little copper coins. Wondering how many dollars this all amounts to I quickly scribble on a pad of paper: \frac{2^{30}}{100} = \$10,737,418.

Just something to remember when you see an elderly lady in need.

I killed my workstation…

I cannot believe it. ~120 days uptime on my Slackware13.1-AMD64 system. I decided I needed to re-arrange my office. It was time for a change. Well, everything was nearly in place. When I went to slide my (running) PC back I accidentally touched the power switch on the rear after warning myself not to.

Evidently, 120 days of running leaves a lot of the file system in cache. It would not boot past lilo and I was ready for a change here, too. Booting to a live CD I backed up my /home/ and BFU’d the machine to FreeBSD 8.1-RELEASE. Last I tried it was a year ago, I’m interested to see if it or I have changed.

Sound (sp/dif)?
# kldload sound
# kldload snd_hda
# sysctl hw.snd.default_unit=2

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\\<br /> 3 + 3 = 6\\<br /> 4 + 6 = 10\\<br /> ...

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\\<br /> 99 + 1 = 100\\<br /> 98 + 2 = 100\\<br /> 97 + 3 = 100\\<br /> ...\\<br /> 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.