Anyone who reads my resume knows, I have a Bachelor of Mathematics from the 
University of Minnesota, Institute of Technology.

I used to joke that I went to M.I.T. - well, the MINNESOTA Institute of 
Technology anyway, not the Massachusetts one :-) I ended up going sort of 
sideways into computers - but it turns out I like that better.

Anyway, I did pick up a few interesting things during my rather brief life 
as a Mathematician that I think real people might find interesting.

So today I'd like to talk about "The Random Walk". (This used to be called 
"The Drunken Walk", but that's not politically correct any more :-)

It goes like this - we have a poor drunk at a lamp post and he starts to 
wander off into the night. Because he's drunk he staggers about going random 
distances in random directions - constantly changing - because he's drunk. 
The question is what will happen?

Now I think common sense says he will wander off into the distance until he 
falls off the edge of the earth or something.

But Probability Theory says NO! - he will keep coming back to the lamp post.

Why? Well, in Math if you have a problem that's hard to solve you throw that 
one out and solve one that's easy to solve.

So let's look at the one dimensional case first. Remember the old number 
line from High School Math? You have zero in the middle and plus 1, 2 ,3, 
... off to the right and minus 1, 2, 3, ... off to the left.

We'll start at zero and flip a coin. Every time we get heads, we'll move one 
number to the right and every time we get tails, we'll move one number to 
the left.

I think you can see that since the odds are fifty-fifty, you'll get about 
the same number of heads as tails - so after a gazillion flips you'll still 
be about at zero. They all cancel out.

This holds true in two dimensions as well. Our poor drunk is as likely to 
move in an easterly direction as a westerly one, as likely to move in a 
northerly direction as southerly one and so on, and so after hours of 
wandering about randomly, he will still be near the lamp post.

So that brings us to the ultimate question of all Advanced Mathematics - "So 
how does this help me balance my checkbook?"

Well, okay, it doesn't really, but think about this philosophically.

Basically, Probability Theory is saying that we're all a bunch of "Even 
Stevens".

Lots of things in life seem to be totally random and unpredictable. Some 
good, some bad. Some really good, some really bad.

This is saying, that if life knocks you into a bad place, just hold on 
because random chance will knock you back again.

No matter how bad things may seem - just hold on - you'll come back to 0,0 
and even be positive eventually.

It has to - it's Mathematics :-)

So just stay drunk and keep walking.
(No wait - not that drunk part :-)


And especially - Stay Jazzed!
--Tom Swezey