Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
Concept
Predictability
Summary
Predictability is the degree to which a correct prediction or forecast of a system's state can be made, either qualitatively or quantitatively.
Causal determinism has a strong relationship with predictability. Perfect predictability implies strict determinism, but lack of predictability does not necessarily imply lack of determinism. Limitations on predictability could be caused by factors such as a lack of information or excessive complexity.
In experimental physics, there are always observational errors determining variables such as positions and velocities. So perfect prediction is practically impossible. Moreover, in modern quantum mechanics, Werner Heisenberg's indeterminacy principle puts limits on the accuracy with which such quantities can be known. So such perfect predictability is also theoretically impossible.
Laplace's demon is a supreme intelligence who could completely predict the one possible future given the Newtonian dynamical laws of classical physics and perfect knowledge of the positions and velocities of all the particles in the world. In other words, if it were possible to have every piece of data on every atom in the universe from the beginning of time, it would be possible to predict the behavior of every atom into the future. Laplace's determinism is usually thought to be based on his mechanics, but he could not prove mathematically that mechanics is deterministic. Rather, his determinism is based on general philosophical principles, specifically on the principle of sufficient reason and the law of continuity.
Although the second law of thermodynamics can determine the equilibrium state that a system will evolve to, and steady states in dissipative systems can sometimes be predicted, there exists no general rule to predict the time evolution of systems distanced from equilibrium, e.g. chaotic systems, if they do not approach an equilibrium state. Their predictability usually deteriorates with time and to quantify predictability, the rate of divergence of system trajectories in phase space can be measured (Kolmogorov–Sinai entropy, Lyapunov exponents).
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related courses (1)
MGT-641(c): Technology and Public Policy - (c) Technology, intellectual property and innovation policy
The class will provide information about what STI support tools exist and why, will explain the rationales and best practices for STI policy intervention and will provide with a sound understanding of
Related lectures (3)
Chaos and Sensitivity in Double Pendulum
Delves into chaos and sensitivity in the double pendulum system, exploring unpredictability and exponential divergence of trajectories.
Nonlinear Dynamics and Complex Systems
Covers chaotic behavior in complex systems, with applications in various fields and a historical overview of major developments in chaos theory.
Related publications (14)
Social-Transmotion: Promptable Human Trajectory Prediction
Alexandre Massoud Alahi, Yang Gao, Kaouther Messaoud Ben Amor, Saeed Saadatnejad
Accurate human trajectory prediction is crucial for applications such as autonomous vehicles, robotics, and surveillance systems. Yet, existing models often fail to fully leverage the non-verbal social cues human subconsciously communicate when navigating ...
2024Related concepts (6)
Self-organization
Self-organization, also called spontaneous order in the social sciences, is a process where some form of overall order arises from local interactions between parts of an initially disordered system. The process can be spontaneous when sufficient energy is available, not needing control by any external agent. It is often triggered by seemingly random fluctuations, amplified by positive feedback. The resulting organization is wholly decentralized, distributed over all the components of the system.
Logistic map
The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often referred to as an archetypal example of how complex, chaotic behaviour can arise from very simple nonlinear dynamical equations. The map was popularized in a 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation written down by Pierre François Verhulst. Mathematically, the logistic map is written where xn is a number between zero and one, which represents the ratio of existing population to the maximum possible population.
Butterfly effect
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state. The term is closely associated with the work of mathematician and meteorologist Edward Norton Lorenz. He noted that the butterfly effect is derived from the metaphorical example of the details of a tornado (the exact time of formation, the exact path taken) being influenced by minor perturbations such as a distant butterfly flapping its wings several weeks earlier.