Sample question and response

A reader asked “Why did the chicken cross the road?”

It is well known that this is a hard question to analyze rigorously.  However, by starting with the 1-dimensional chicken diffusion equation

\[ \frac{\partial^2\chi}{\partial x^2} + \frac{1}{4\sqrt{\pi}}\frac{\partial \chi}{\partial t} \approx 0, \]

where \(\chi\) is the local density of chickens, we may arrive at the answer, “Because it wanted to get to the other side (to a first order approximation).”