Determinism: Difference between revisions

Revision as of 20:15, 2 December 2015

by Areeba Abid

Determinism is the idea that if all the net forces acting on a system are known, the behavior of the system can be calculate using iterative prediction to determine its state at any given time.

The Main Idea

Newton's laws allow us to predict the motion of an object if we know the initial position, initial momentum, and forces acting on the object. Using iterative prediction, we can calculate where the object will be at any given time in the future. If this idea is extrapolated to all objects in the universe, it would seem that we could predict the future of the entire universe if we only knew the initial conditions (the starting positions and momentums, and forces being applied) of each object. From a scientific standpoint, this means that the future state of the universe should theoretically be able to be determined by scientists using simple physics. This idea has been taken even further in a philosophical context to argue that humans do not have free will, because the atoms that make up our bodies simply continue to move in the paths we would expect based on their initial conditions.

Practical Limitations

While the idea of determinism seems straightforward at first, there are actually complicated reasons that we cannot precisely predict the future of small, simple systems, much less the entire universe.

One practical limitation is the fact that initial conditions can only be measured as accurately as our instruments allow, and after a few time steps, small inaccuracies build on each other. This means that over time, our model of the system and our predictions of its future state stray farther and farther away from the actual future state of the system. This is why iterative prediction is usually only used over small periods of time.

Another practical limitation is that we must necessarily simplify systems to be able to model and calculate them. It is impossible to account for every interaction within and outside a system, since every single particle in the universe interacts with every single other particle in the universe, resulting in an unthinkable number of calculations that would need to be done to accurately account for the net forces on a system. This introduces error that limits the long term accuracy of any calculations that we can carry out.

Chaos

Determinism and chaos are related, almost opposite concepts. Chaos results in systems that are extremely sensitive to initial conditions. This means that tiny changes in initial conditions quickly lead to dramatic differences in behavior. Any system that exhibits chaos presents a challenge to deterministic theory because the future behavior of a system is so difficult to predict and varies wildly based on miniscule, imperceptible differences in initial conditions, demonstrating in an extreme way the practical limitations that hinder deterministic calculations.

For an example of a chaotic system, consider a game of pool. The blue and yellow paths are the result of very similar forces on the cue ball, but the outcomes are not similar. Slight changes in the force applied to the ball result in a wildly different outcome seconds later.

A Mathematical Model

For a deeper understanding of the mathematical equations relevant to determinism, see iterative prediction.

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

Weather Systems

Be sure to show all steps in your solution and include diagrams whenever possible

Simple

Middling

Difficult

Connectedness

How is this topic connected to something that you are interested in?
How is it connected to your major?
Is there an interesting industrial application?

History

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

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 ===A Mathematical Model===
-What are the mathematical equations that allow us to model this topic.  For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.
+For a deeper understanding of the mathematical equations relevant to determinism, see [[iterative prediction]].
 ===A Computational Model===