Parameter

A parameter comes from ancient words meaning "beside" and "measure." It is any feature that helps us describe or sort out a certain system, like an event, project, object, or situation. Parameters are important because they help us understand a system or judge how well it is doing.

Parameters have special meanings in different areas of study, such as mathematics, computer programming, engineering, statistics, logic, and linguistics. They are also used in more general ways, like when we talk about the rules or limits of a test or a game.

Modelization

Main article: Modelization

When we use math to describe a system, the numbers that define the system are called parameters. For example, in studying how things move, we might use the weight, size, or how thick or thin something is as parameters.

There are different ways to pick these numbers. For example, when looking at how something moves on a big round shape like Earth, we can use angles to show where it is, or we can use distances from a known place. These choices help us understand movement better, whether it's over a big area or a smaller one.

Mathematical functions

Mathematical functions often have inputs called arguments. But they can also have something called parameters. Parameters are special values that help define a group of related functions.

For example, a quadratic function can be written as f(x) = ax² + bx + c. Here, x is the argument, but a, b, and c are parameters. These parameters decide which specific quadratic function we are using. We can also use parameters in the name of a function, like log_b(x), where b is a parameter showing which base logarithm we are using.

Sometimes, whether a symbol is a parameter or an argument changes how the function works. For example, in the falling factorial power n^k_, if k is a parameter, it creates a polynomial function of n. But if n is the parameter, it does not create a polynomial function of k.

Parameters are also used in mathematical models to describe relationships between measurable quantities. They help explain how different parts of a system are connected. In geometry, parameters can describe curves, like how the unit circle can be shown using a parameter t. In statistics, parameters help us understand and estimate properties of groups based on samples.

Computer programming

In computer programming, we talk about two ideas called parameters and arguments—or more formally, a formal parameter and an actual parameter.

For example, in a function like

y = f(x) = x + 2,

x is the formal parameter of the function.

When we use the function with a number, like

f(3): or, y = f(3) = 3 + 2 = 5,

the number 3 is the actual parameter for the function; it’s the value we put in place of the formal parameter.

These ideas are explored more deeply in functional programming and related fields like lambda calculus and combinatory logic. Different programming languages use slightly different words for these concepts; for example, C uses the terms as described here, while Eiffel follows an alternative convention.

Artificial intelligence

In artificial intelligence, a model helps guess what might happen next. Parameters in a model are like special numbers that decide how important different pieces of information are. These numbers help the computer learn and understand information better.

Engineering

In engineering, the word parameter can mean a single thing that is measured. But this use is not always the same — sometimes, engineers use the word channel for a measured thing and keep parameter for the setup details about that channel.

Generally, properties describe what a system is like, while parameters are special mixes of these properties that help us understand how the system will act. Properties can have many different sizes or types, but parameters usually do not, or they relate to time.

Environmental science

In environmental science, especially in chemistry and microbiology, a parameter helps us describe a specific chemical or tiny living thing by giving it a value. This value might show how much of something is there, like a concentration. It can also be a simple yes-or-no answer, a statistical result like a 95 percentile value, or sometimes even a subjective opinion.

Linguistics

In the study of language, a parameter is like a simple on-off switch. It is used in a special idea called Universal Grammar, which helps us understand the basic rules that all languages follow. This switch helps explain why languages can be similar but also different in small ways.

Logic

In logic, some people use the word "parameters" to talk about special parts of a rule or idea that can change. These parts are called parameters when they are used in a certain way. Other parts inside the rule are called variables. This helps when we change one part of the rule for another, making sure we don’t mix up the parts that should stay the same and those that can change. Most people, though, just call all these changing parts "variables" and then sort them into two groups: free variables and bound variables.

Music

Main article: Musical parameter

In music, a parameter is a part that can be changed on its own. Common parameters include pitch, loudness, duration, and timbre. These ideas are especially important in a type of music called serial music, where each part follows a certain pattern. Some musicians have questioned using the word "parameter" this way, but it is still used often in music and when making recordings.