Q3.47: In this unit we have used a very simple model: an ant wandering back and forth with steps of equal length taken at equal time intervals. Yet this simple model describes many processes in the real world. How can this be, since our model is so simple? Very similar results are predicted by more complicated models that add more randomness: steps of random length, steps in random directions, steps that take place randomly in time. It turns out that the predictions of these more complicated models are similar to ours as long as our model reflects the average step length, average time between steps, and average distance from the starting point. Often in science a simple, easily understood model makes good predictions about the more complicated real world.

Q3.48: Does changing the number of steps the random walk takes effect the relation between "mean squared distance'' and "step number''? Does it change the "average distance'' from the origin?

Q3.49: Why would we care about being able to relate "mean squared distance'' and "step number''? What does this tell us? Hint: think in terms of "predicting''.

Q3.50: Can you think of examples from nature where particles may move around in a random way? List examples from nature where the random motion is biased. Can you list some of the possible sources of the bias (e.g., draft air currents would bias the smell of the open ammonia bottle)?