There are many kinds of dynamics. Some are complicated, others are not. To try and understand this better, we can take a vector field that depends on just one parameter, and let this parameter change slowly. This shows that the dynamics, under influence of this parameter, is sometimes simple and then, without warning, becomes very complicated. We see bifurcations happening.
The dependence on initial conditions for the future of a system can look discouraging. However, there is a positive and constructive approach. In fact, this Lorenz’ real message, but it is not that well known by the general public.
In 1963, Edward Lorenz (1917-2008), studied convection in the Earth’s atmosphere. As the Navier-Stokes equations that describe fluid dynamics are very difficult to solve, he simplified them drastically. The model he obtained probably has little to do with what really happens in the atmosphere. Read More
At the end of the 17th century, Gottfried Wilhelm Leibniz (1646-1716) and Isaac Newton (1643-1727), independently one from the other, invented a brilliant mathematical tool: infinitesimal calculus or differential and integral calculus. Read More