There are two kinds of people in the world, those who enjoy mathematics and those who don’t. What is interesting is that even those who enjoy mathematics don’t quite agree on how should mathematics be taught. On one side there are people like the famous mathematician John Conway who would carry fruits and vegetables to the classroom to teach students about geometry and curvature while on the other side there are people like the famous computer scientist Dijkstra who insist that right from the start, students should learn rigorous abstract concepts. My own belief is that majority of people develop appreciation for mathematics only through specific examples and that it takes a level of expertise before which one may start appreciating rigorous mathematics. I belong to the first category of people who think that playing games, looking at bicycle tracks and thinking of real life situations is a much better way of getting introduction to mathematics.
Saw on a T-shirt in the canteen today 🙂
This is what your heart does when it pushes blood around your body, what some electrical circuits do as they charge and discharge and cell division too, likely does that. What I am talking about is “relaxation oscilations”.
Remember the normal heartbeat patterns where you see a spike followed by very little activity and then a spike again? That is an example of relaxation oscillations. A number of chemical, mechanical and hybrid systems are known to exhibit such oscillations. They crop up in control problems too as we shall see.
In many systems that are controlled, the basic mechanism is this. If the system is going to stop, the control puts energy into it, to keep it going. On the other hand, if the system is taking too much energy, the control reduces it.
Think about it in terms of the hert. If it tries to stop, the body is designed to keep it going and if its potential is going too high the body is designed to bring it back to normal too. So what we get is known as the phenomena of nonlinear damping. In such oscillations, for small value of oscillations variable, the damping is large and negative. For large variable value the damping is large and positive to reduce the oscillations. This finally gives the blip like oscillations that we see in the heart. A textbook example for an interested student is the Van der Pol system.
Essentially nonlinearity rocks.