ArticleslgStudy

mathematics

Predictability

Predictability is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Predictability rather than just read about it. In short: Predictability is the degree to which a correct prediction or forecast of a system's state can be made, either qualitatively or quantitatively. Predictability and causality Causal determinism has a strong relationship with predictability.

Key takeaways

  • Predictability belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Predictability to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Predictability from memory before moving on to harder problems.

Reference excerpt

Predictability is the degree to which a correct prediction or forecast of a system's state can be made, either qualitatively or quantitatively.

Predictability and causality 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 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.

In statistical physics 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).

In mathematics In stochastic analysis a random process is a predictable process if it is possible to know the next state from the present time. The branch of mathematics known as Chaos Theory focuses on the behavior of systems that are highly sensitive to initial conditions. It suggests that a small change in an initial condition can completely alter the progression of a system. This phenomenon is known as the butterfly effect, which claims that a butterfly flapping its wings in Brazil can cause a tornado in Texas. The nature of chaos theory suggests that the predictability of any system is limited because it is impossible to know all of the minutiae of a system at the present time. In principle, the deterministic systems that chaos theory attempts to analyze can be predicted, but uncertainty in a forecast increases exponentially with elapsed time. As documented in, three major kinds of butterfly effects within Lorenz studies include: the sensitive dependence on initial conditions, the ability of a tiny perturbation to create an organized circulation at large distances, and the hypothetical role of small-scale processes in contributing to finite predictability. The three kinds of butterfly effects are not exactly the same.

In human–computer interaction In the study of human–computer interaction, predictability is the property to forecast the consequences of a user action given the current state of the system. A contemporary example of human-computer interaction manifests in the development of computer vision algorithms for collision-avoidance software in self-driving cars. Researchers at NVIDIA Corporation, Princeton University, and other institutions are leveraging deep learning to teach computers to anticipate subsequent road scenarios based on visual information about current and previous states. Another example of human-computer interaction are computer simulations meant to predict human behavior based on algorithms. For example, MIT has recently developed an incredibly accurate algorithm to predict the behavior of humans. When tested against television shows, the algorithm was able to predict with great accuracy the subsequent actions of characters. Algorithms and computer simulations like these show great promise for the future of artificial intelligence.

In human sentence processing

Linguistic prediction is a phenomenon in psycholinguistics occurring whenever information about a word or other linguistic unit is activated before that unit is actually encountered. Evidence from eyetracking, event-related potentials, and other experimental methods indicates that in addition to integrating each subsequent word into the context formed by previously encountered words, language users may, under certain conditions, try to predict upcoming words. Predictability has been shown to affect both text and speech processing, as well as speech production. Further, predictability has been shown to have an effect on syntactic, semantic and pragmatic comprehension.

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Predictability

Start with the simplest possible case. Write down what Predictability claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Predictability before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Predictability ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Predictability

In research
Predictability appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Predictability in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Predictability is common in secondary-school and first-year university syllabi. It links to neighbouring topics Prediction, Statistical mechanics, so understanding it makes those chapters shorter.
In everyday life
Look for Predictability outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Predictability in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Predictability means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Predictability out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Predictability in simple terms?

Predictability is the degree to which a correct prediction or forecast of a system's state can be made, either qualitatively or quantitatively. Predictability and causality Causal determinism has a strong relationship with predictability.

Why does Predictability matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Predictability?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Predictability.

Tags

  • Prediction
  • Statistical mechanics

Keep exploring