Q3.46: Describe in your own words the meaning of a model?
Can you think of examples of how models are used to describe
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)?