Parameter

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

Parameters mean different things in different areas of study, such as mathematics, computer programming, engineering, statistics, logic, and linguistics. They are also used in 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 something, the numbers that define it are called parameters. For example, when studying how things move, we might use the weight, size, or thickness of an object as parameters.

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

Mathematical functions

Mathematical functions often have inputs called arguments. 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 special numbers. They decide how important different pieces of information are. These numbers help the computer learn and understand better.

Engineering

In engineering, the word parameter can mean one thing that is measured. Sometimes, engineers use the word channel for the thing that is measured and use parameter for the setup details about that channel.

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

Environmental science

In environmental science, a parameter helps us describe something, like a chemical or a tiny living thing, by giving it a value. This value might show how much of something is there. It can also be a simple yes-or-no answer, a statistical result, or sometimes even an opinion.

Linguistics

In the study of language, a parameter is like a simple on-off switch. It is used in an idea called Universal Grammar. This helps us understand the basic rules that all languages follow. The switch explains 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 used in a certain way. Other parts inside the rule are called variables. This helps when we change one part of the rule, making sure we don’t mix up the parts that should stay the same and those that can change. Most people 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 by itself. Common parameters include pitch, loudness, duration, and timbre. These ideas are very important in a type of music called serial music, where each part follows a special pattern. Some musicians have wondered about using the word "parameter" like this, but it is still used a lot in music and recording.