The full extent of the consequence of the non-linear dynamic nature of most natural phenomena, ie, the presence of non-linear elements in the differential equations that describe these phenomena, became clear in the 1960s by the observations of Edward Norton Lorenz. He was a meteorologist who was one of the first to use a computer to calculate the time course (trajectory) of some values of pressure and temperature of the atmosphere. He simulated the dynamics of the system with a set of three non-linear differential equations. When he re-ran the simulation with infinitesimal differences in the initial values because of the finite fractional numbers generated by the computer (ie, different initial conditions), he observed that the system evolved very differently every time. Small differences at the beginning led to totally different futures. This confirmed the idea of Poincaré who already had noted that small differences in the initial conditions could result in unpredictable consequences, The idea that small causes can result in disproportionate effects was then encapsulated by Lorenz’s famous ‘butterfly effect‘ according to which a beat of its wings in the Amazon may unleash a tornado in Texas1.
In summary, subsequent states of non-linear dynamic systems cannot be established with total certainty from a previous state.
1.4 The World is New at Every Moment
There is a further deeper reason for expecting the unpredictability of the future. In addition to the very high non-linear dependence of the initial conditions described above in most natural systems, even if all ‘initial conditions’ were known, their accuracy could not be more precise than the limit of confidence for knowing the momentum and the location of a particle in the system.
When we get down to the quantum level, there is a limit to how accurately you can measure the position and momentum of a particle, a problem known as the Uncertainty Principle of Werner Heisenberg2. When quantum level events interact with macroscopic structures, the universe becomes deterministic due to the ‘collapse of the wave function’. In other words, an uncertain fluctuation at a quantum level may give rise to a well determined macroscopic state which in turn would then proceed according to the non-linear dynamics of Chaos Theory.
Thus, in the real world, the precise initial conditions are not pre-determined. Despite the deterministic laws of the macroscopic world, according to Chaos Theory, the absolute predictability of the future is simply not possible. This means that the world no longer can be regarded as the giant clockwork of Laplace, with a completely predictable knowledge of the future given a knowledge of the past. This means that even the deterministic world does not have a predetermined future but is ‘new’ at every moment.
This idea was the basis of the book The Black Swan by Nassim Taleb3 according to whom attempts to predict the future of human affairs can be rendered utterly invalid by unexpected events in the future, which by their nature, cannot be predicted.
This does not imply that the expectation to understand new phenomena is impeded by this significant limitation. Within particular time domains, some periodic events are highly predictable. For example, duration of day and night are reasonably predictable for many years.
The illusion of absolute knowledge of the future states of the universe has been largely abandoned in science. Anybody still seeking it or being under the illusion of having found it is already outside the mainstream of scientific knowledge.
The loss of absolute determinism has another important consequence for human existence. It avoids the trap of the problem of determinism vs non-determinism of human actions. If complex physical events are not predictable because they are highly non-linear, it is no surprise that human behaviour, generated by a complex nervous system, may equally be unpredictable. I will discuss this under the ‘free will’ problem further down.
1.5 Order Out of Disorder
One of the main questions in physics has been how order, with some degree of stability, can possibly emerge from the chaotic nature of the universe. The answer came in second last half of last century with the discovery that transiently stable order can be created and maintained even in inorganic systems, apparently defeating the Second Law of Thermodynamics which states that a physical system evolves in time always by increasing the amount of disorder, in the form of random motion of atoms and molecules. To understand this better, we need to introduce the concepts of closed and open physical systems.
- Edward Lorenz (1964): The problem of deducing the climate from the governing equations. Tellus 16, 1–11. Click here to download the PDF; See also Lorenz (1995): The Essence of Chaos. University of Washington Press. ↩︎
- Heisenberg published several reports that included discussion of the Uncertainty Principle in 1927. One of them is available via NASA: The actual content of quantum theoretical kinematics and mechanics. Click here to download the PDF. ↩︎
- Nassim Nicholas Taleb (2007) The Black Swan – The Impact of the Highly Improbable, 2nd ed. Random House. ↩︎