The idea that what happens at every moment has specific precedents has deep roots in human thinking and shapes profoundly the development of every individual. It predates science in that this idea appeared in human societies as a fundamental way to predict events by relating what happened before to what is likely to happen in the future. Searching for such relations fills the history of human communities since prehistoric times, finding its maximal expression in the sophisticated predictions of seasonal weather patterns in agricultural and fishing societies.
In historical times, these fundamental relations resulted in the idea that there is a clear relation between events described as “cause and effect”, whereby every event has a previous cause and nothing which occurs afterwards can have any effect on what precedes it. This idea has become a philosophical view known as ‘determinism’. Aristotle more than 2000 years ago distinguished different forms of causation including material cause, formal cause, efficient cause, and final cause1.
However, some philosophers of the British Empiricism school pointed out that this relation is not a property of the universe but is fundamentally due to a very human cognitive process which tends to associate phenomena in time, by custom and mental habits.2
Studies relevant to the attribution of cause and effect indicate that the interval between an event and another is exemplified by a ball hitting another and the other ball start moving. To be regarded by human observers as causally linked, the interval between discrete physical events needs to be between 70-140 ms.3
Despite philosophical arguments on the nature of the universe as being deterministic or otherwise, in the experimental sciences, the search for causes requires finding preceding conditions which are necessary and sufficient for a given phenomenon to occur. Classic experimental research tries to establish which factors are essential for a phenomenon to occur. To identify a unique factor as necessary, all the other factors need to be kept experimentally as constant as possible. Where this is attainable, by creating controlled experimental conditions, a clear dependence of a phenomenon on some factor can be established. There has been a clear distinction between the idea of causation and correlation. While indeed correlation does not mean causation, finding that two or more events are correlated do help in organising appropriate behaviour in a meaningful and hopefully effective way and is part of the ongoing ‘test of reality’ in real life. In more complex systems, where multiple preceding factors are not controlled, the identification of ‘causal’ factors is much harder.
The discovery of critical factors that make events predictable, and often controllable, has generated extraordinary results. Much of modern technology and science is the result of the application of this principle, which can be described as deterministic causality, synonymous with predictability. Thanks to this conceptual frame, planes do fly, infectious diseases can be prevented and often cured, buildings and bridges usually stand up, we can talk to each other by telephone, communicate via internet and so on.
However, phenomena in the natural world seldom fit the rule of one cause-one effect. There are many reasons for this. The first is that more than single factor underlies natural events since most observed ‘events’ are preceded by multiple events. The second reason is that the apparently equal causes can result in different effects. This is because causal relations are most often non-linear. To appreciate the importance of non-linear relations we need to summarise its history to become modern physics of non-linear dynamics whereby small changes can lead to large changes.
Modern thinking in physics was developed by Galileo Galilei in the early 1600s when he realised that we do not need to ask for the cause of a state of motion if the motion is uniform, any more than it is necessary to ask the reason for a state of rest. The problem was to understand the causes of changes in motion (ie changes in velocity and/or direction) which requires identifying the instantaneous changes in the velocity of a body. This requirement led to the introduction of the concept of infinitesimal quantities leading to instantaneous values of speed and acceleration thanks to the birth of calculus with differentiation and integration by Newton and Leibniz4 . The motion of a body under the influence of gravity could be represented with equations in which a derivative (instantaneous change) is one of the unknown parameters in a set of differential equations. A problem of dynamics could then be expressed in the form of such a set of differential equations. The instantaneous state of each of the bodies in a system could be described by its position, velocity and acceleration (respectively, the first and second derivatives of the position) with the body regarded as a point. A set of forces that vary with distance gives the precise acceleration of a body at each point; the accelerations then bring about changes in the distances separating the bodies and therefore change the set of forces acting in successive instants.5
Following a synthesis by Newton, a complete description of nature according to the laws of motion was possible and simply required the description of the initial position and velocity of individual bodies subject to the force of gravity. The world according to this view behaves like a giant mechanical clock in which every movement in the past, present, or future are determined and thus computable by solving the appropriate equations. The basic characteristics of mechanical trajectories are lawfulness, determinism, and time reversibility.
Pierre-Simon Laplace at the beginning of the 19th century in his “Systeme du Monde” and following the ideas of Buffon6 suggested that all physico-chemical phenomena were due to the actions of forces which included the force of gravity, electric and magnetic forces. Laplace summarised this view in his classical statement: “Consider an intelligence which, at any instant, could have a knowledge of all forces controlling nature together with the momentary conditions of all the entities of which nature consists. If this intelligence were powerful enough to submit all this data to analysis it would be able to embrace in a single formula the movements of the largest bodies in the universe and those of the lightest atoms; for it nothing would be uncertain; the future and the past would be equally present to its eyes”7
William Rowan Hamilton (1805-1865) simplified the descriptions of motion by developing a single function related to the total energy of a system. Thus, a system described by a Hamiltonian equation implies a system which has no loss of energy8. One can conceive an abstract space of many dimensions with one dimension for each of the coordinates describing a physical system comprising of a certain number of particles. This is the space of the dynamic systems suitable to describe the universe as being comparable to a giant clockwork mechanism.
This wishful idea was soon to prove far too idealised to be applicable. It assumed too many concepts which simply could not be established in principle.9 The idea of a clockwork universe with immutable ‘laws’ as designed by a supreme being and predetermined in all its details was to be abandoned. But before this simplistic universe could be abandoned, new conceptual and mathematical tools had to be developed.
- Aristotle: Physics II, 3, and Metaphysics V, 2. ↩︎
- John Locke (1680): An Essay Concerning Human Understanding; David Hume (1748): An Enquiry Concerning Human Understanding ↩︎
- György Buzsáki (2011): Rhythms of the Brain, Oxford University press. https://www.oup.com.au/books/others/9780199828234-rhythms-of-the-brain ↩︎
- https://en.wikipedia.org/wiki/Gottfried_Wilhelm_Leibniz; https://en.wikipedia.org/wiki/Isaac_Newton ↩︎
- https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion ↩︎
- Georges-Louis Leclerc, Comte de Buffon: https://en.wikipedia.org/wiki/Histoire_Naturelle ↩︎
- Pierre-Simon Laplace (1814): Essai philosophique sur les probabilites; English version (1819): A Philosophical Essay on Probabilities; Dover, New York (1951) / New translation, Springer-Verlag, New York (2011). ↩︎
- Hamiltonian mechanics has a close relationship with geometry and serves as a link between classical mechanics and quantum mechanics. https://en.wikipedia.org/wiki/William_Rowan_Hamilton ↩︎
- Percy Bridgman (1927): The Logic of Modern Physics. Click here to download a PDF. ↩︎