Here is my favorite quote from Rumsfeld "Going to war without France is like going to play golf without an accordian."

One of my previous posts dealt with the optimization of multivariable functions. I was applying it to social economics, but this is actually a problem that I have spent a great deal of time thinking about in its more general context since it is at the very heart of modern science and engineering. The reason that one cares so much about the extrema of a functions is because those states usually represent stable configurations of the system. This is of course most readily apparent in chemistry and physics since the extrema of the energy correlate with the structure of atoms and molecules. Let's say that we have a function F of N continuous variables. How can we find the extrema of such a function? When one is talking about single variable analytic functions, the answer is simply to set the derivative of that function equal to zero and solve. That is of course not possible in multivariable functions (except for the case of separable functions which I talked about in my previous post), and that is what leads us to optimization theory.
The first thought that might come to one's mind is that you can just evaluate the function at every point in its space and simply pick out the point that has the greatest of least value. This is called complete enumeration, and it is the most computationally intensive alternative... so much so that it is never done except for very limited cases of very few variable with defined constraints on the values that those variables can take.
The next approach that comes to mind is to start at a point and follow the gradients around that point. If you let such a simulation run long enough, the hope is that it will eventually happen upon the extrema and get stuck there. One way to think of this is a bowling ball being rolled around in the Grand Canyon. The ball will follow the potential gradients around it until it gets to the lowest point accessible to it. This is not a bad method except for the fact that it is notorious for missing extrema. Obviously if you start the simulation at one point, and the true extrema is separated from that point by a massive potential barrier, then you will never find that point. This brings up a recurring point in these methods, which is that one never has a guarantee of finding anything, since that would require complete enumeration. Still, the gradient method is very useful in situations where you want to investigate a specific region of the space to determine what the extrema in that region is.
Alright, I have to go to class now... more on this later

So, I was at the gas station, and I was talking to some construction workers there, and one of them put it best..."f&*% France F#$% Germany F*^@ Russia and F(*$ China. I don't understand how anyone will still be able to oppose the war after watching the video of the people in Basra and Baghdad taking to the streets and cheering for the U.S. troops. That is the most solid indicator that this is something that they have wanted for some time. The blood of some innocent Iraqis may be on our hands, but that blood pales in comparison to the blood on the old Iraqi leadership's hands. As for all the rest of the Arabs who are watching is disbelief and disgust as the Iraqis celebrate, the only reason I can see for that is that they have never tasted freedom. The Iranian government must be shaking in their boots at this very moment.

So, I was looking at some of the old pictures I have on my computer, and I found this one. I am posting this for all those people who are against the war and think that we don't have a right to free the people of Iraq. This is possibly one of the bravest men in history, and a testament to man's desire to be free.
For those who were too young to remember this, it is Tiananmen Square, 1989.

What I don't understand is what it means to be under "friendly fire." Call me silly, but if someone is firing a gun at me, that is the definition of unfriendly.

You know who is my favorite personality of the war... Mohammed Saeed al-Sahaf, the Iraqi information minister. He is like a two year old who just learned how to say no. We need to hire this guy to work for us. I can just see him on Wolf Blitzer...

Blitzer : "So Mr. al-Sahaf, corporations are reporting record losses and analysts are saying that we are headed to the worst recession ever."
al-Sahaf : "No, that is not true, the accountants are imperialist war-mongers who will be destroyed."
Blitzer : "I have heard rumors that many of the major financial institutions are on the verge of collapse."
al-Sahaf : "No, that is not true, you are an imperialist war-monger who will be destroyed."

I bet if someone were to go interview this guy when he is in prison after the war, he would still deny everything. It is a good thing that we get unbiased reporting that is free of the kind of propaganda that could mask the complexities and devastation of war.