Mathematical absurdities

So right now I'm thinking about the summation of divergent sums. What do I mean by that? Well, say I wanted to add up some numbers:

1+2+3+...+N

That should give me some answer, right? e.g., if N=4 then I'd have

1+2+3+4=10.

Not so bad, right? In fact, it's not hard to show (if you are good at math) that you can find the general answer

1+2+3+...+N=N*(N+1)/2

Which works for the above example because 4*(4+1)/2=10.

Obviously, the higher you count, the bigger the answer is going to be, right? But what if I wanted to never stop... in other words, what if I wanted to count all the way to infinity. "Ha ha!" you say! Such an idea is absurd! But No! You can do it! And the answer is... -1/12. That's right - I said negative one-twelfth. I know! It sounds dumb. But mathematicians and physicists have a way of doing it so that that's what you get. It's called analytic continuation of the Riemann Zeta Function. (by the way, Wikipedia is my best friend) And they use it in all seriousness! It's a majorly important part of string theory. And before you let this turn you off of string theory, it is also the method by which one calculates a completely standard, uncontroversial, physically tested (and true) phenomenon called the Casimir Effect. And this Riemann guy was a seriously important, revered mathematician of the 19th century, and his function is apparently one of the most important objects in pure mathematics.

Anyway, this is just what I've been thinking about lately. Now you know. And knowing...

Kudu sausage looks like turds

The Powers that Be

It's interesting when things happen here to remind me that I am actually living in a (first world city in a) fairly third world country.

Due to foreseen (but somehow incompetently overlooked by the government) increases in the economy of South Africa since '94, the demand for electricity has skyrocketed. So much so, in fact, that the supply created by the electricity company, Eskom, is really no longer sufficient. So we've been having daily "load shedding" at random points during the day. Suddenly, the electricity will just go off for two hours at a time, and they are basically cycling this effect across the city. What's worse is that they're hilariously inconsistent in telling the public when it's going to happen. I've heard rumors that this is not supposed to last - that by next week they should stop the load shedding, but I have a hard time seeing how that's possible. I guess they're using this stoppage time to store up more electricity... but the problem is only going to get worse as time goes on.

Obviously people are pissed off, most vociferously, businesses - I've heard reports of millions to billions of dollars already having been lost. The stupidest thing is that, like I said before, Eskom knew this was going to happen for the past 15 years, and they apparently kept telling the government about it, but really to no avail. So they didn't do anything until 10 freaking years later, when they finally told Eskom in 2004 to go ahead and build another power station. But that obviously takes years to do, and it sounds like it'll be at LEAST five years until it's completed, during which time demand will continue to grow, and the whole deal will just get more screwed up.

The one thing it has taught me, though, over the past week - having a laptop is a major advantage over a desktop, since the battery will keep the power cuts from destroying my system...

USA, I'm ok!

Well, I'm back from vacation in Cleveland and NYC. Had a great time, but it is also nice to be back. Here are some pictures of Christmas 2007.


Here's Alex and Kristen's stockings before (and after) Xmas


Kristen and Squee, in front of the Krismas tree



Laurence the anime character


My African present to Scott and Dad. I thought it was cool

If I owned a business

These would be my motivational posters