This intriguing question was posed to us by a high school student. My initial reaction to this question is to post a link to Heidi Klum. More productively, I'd like to try to present some ideas for thinking about models and what they look like.
To a scientist, a model is a way of representing an idea about how the world (or some part of it) works. In many ways, a model is just a way of expressing an hypothesis or a set of hypotheses. How a particular scientist thinks or the audience they're addressing to will dictate what the model looks like.
For me, I like to start with a conceptual model, usually represented as a drawing. For example, here's a diagram I use to explain how temperature and chlorophyll influence copepod growth and reproduction:
The circle at the left represents an egg. The red arrows show the path that the egg takes to become an adult copepod. The arrows are colored red to suggest that how long it takes to go through these stages depends on temperature. The long arrow at the top represents reproduction (adults making eggs). The number of eggs produced depends on the amount of food available. Since this particular copepod eats mostly phytoplankton, the arrow is colored green. These graphical models are very useful for helping think through a problem. My notebooks are filled with less attractive versions of these, and most days, there is some version written on my whiteboard with colored markers.
While conceptual models and diagrams are the most common models in science, when most scientists speak of models, they mean a mathematical models. The advantage of mathematical models is that they force the modeler to be very precise about how the components fit together. They also can be used to make predictions that can be compared to data. The disadvantage is that they require mathematical training to understand. Some mathematical models are relatively simple and can be written on a few sheets of paper. Other models are more complicated, and this is where computers come in. Here's a snapshot of some computer code that represents copepod growth and reproduction:
This code is written in a language called "C". The code is then given to a computer program called a compiler that turns the code into the language of 1's and 0's that the computer recognizes. We then push a button and wait while the program runs. The program produces a series of output files. To view the results, we have to load these files into Matlab and plot them in various ways.
This is probably my favorite step--part science, part engineering, part art. Pretty, in it's own way, but no Heidi Klum.
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