May 22, 2003

Initial Conditions

Well the little go-round I just had with html and my browser is as good a place to start as any. Bear with me as I go into a bit of detail about how my browser (Internet Explorer, you might use Netscape or any one of a number of other options but I think they all do the same basic thing). The browser does a number of things to make pages load faster. One of the things it does is that the first time it downloads a picture, it makes a temporary copy of that picture and stores it deep in your hard drive. Everytime you look at a picture on a web page, your browser looks to see if it already has a copy of that picture. If it does then it uses the copy on your hard drive rather than downloading it again - this makes pages load faster. It keeps track of pictures by their names.

Now my problem is that I often diddle with pictures as I go along but leave their names the same. Many times I have beaten my head against the wall trying to figure out why the changes I have made in the picture don't show up on my web pages. The reason is that I change the original and I change the web page version, but I forget to tell my browser to update its copy so it continues to use the copy of the initial version that it has stored on my hard drive.

The point here is that the browser initializes itself and then proceeds happily and I forget that the browser has this initial condition and beat my head against the wall.

Initial conditions are just that - they are the place that a system or a process starts from. They are the parameters of a model at the point that the model begins to run. In a baseball game, the initial conditions include the number and skills of the players available to play each position, the starting pitcher, the batting order, the umpiring staff, the size of the crowd, the weather and the score. As the game progresses each of these parameters can change and the details of how the game develops will be influenced by those changes. Changes in some parameters are more influential than others (pitcher vs crowd size).

Initial conditions have to do with time and answer the question "What is the state of the system of interest at the beginning of the time period of interest?" In the baseball example above, the period of interest was implicitly a single game. If I were interested in the history of a team or league, the parameters I choose to follow and specify as a starting point would likely be different. They would certainly include the management, the home town, and the ball park.

Begin Aside
Exercise for the reader: In the context of a single game, is the ball park an initial condition?
End Aside

Thus one person's initial conditions are another's intermediate state. In the context of weather, today's weather is an intermediate value in yesterdays 5-day forecast, but is the initial condition for today's 5-day forecast. Similarly the political state of an institution or nation provides initial conditions for the development of policy solutions.

Consider the activities of the EPA. Christie Todd-Whitman's initial conditions included US participation in the Kyoto protocol and she advanced from that condition. Unfortunately rate of change of that parameter was very high and negative. Her initial conditions also included much stronger political pressure to roll back environmental regulations that she had championed as Governor of New Jersey. Todd-Whitman's resignation changes the state of the EPA and will be part of the initial conditions that her successor inherits.