parameter

This is the name a function declares in advance, before anyone calls it. Programmers who want to be exact call it a formal parameter. They keep argument for the value that fills it at run time: in a greeting function, name is the parameter and "Ada" is the argument. Everyday speech often blurs the pair, which is where the loose "value passed in" use comes from.

The experimenter's dial is set once per run and turned between runs. The word joins Greek para-, "beside", and metron, "measure", and reached English through French paramètre. Fix the parameter and you have one curve or one trial. Change it and you have the next, so a family of cases hangs on it. That sets it apart from the variables that move within a single run, and from the property-describing sense.

Science's workhorse sense usually comes with a qualifier naming the property, as in cohesion parameters and solubility parameters. Charles M. Hansen uses these to characterize surfaces. A parameter in this sense is often something to be found rather than set, as when researchers estimate an unknown parameter and the error in that estimate. That reverses the held-constant sense, where the value is chosen in advance.

In machine learning the word has become a yardstick of size, and models are described by how many parameters they hold. The Guardian in 2020 called GPT-2's 1.5bn parameters "a mere" figure. Unlike the experimenter's fixed setting, no one chooses these values; training adjusts them. Public discussion tracks the count rather than any single value.

A statistician's parameter is a fact about the whole population, not about the sample in hand. The true share of voters backing a candidate is a parameter, and the figure a poll reports is only an estimate of it. Keeping the two apart is the point of the term. A parameter is usually unknown, and much of statistics exists to bracket it, as a confidence interval does.

In the looser programming use, parameter simply means whatever value gets passed in. Careful writers prefer argument or actual parameter here and keep the bare word for the declared placeholder. In casual talk, such as reading a parameter from the command line, the loose use does no harm. In documentation or teaching, the stricter pairing avoids confusion.

In geometry the parameter is a length rather than a setting: a line segment fixed by a conic and a chosen diameter or abscissa. Taken along the principal axis, it has a name of its own, the latus rectum. Readers of geometry texts will often find that term used where this one could stand. The two name the same quantity when the diameter in question is the principal axis.

Crystallographers use the word for proportion rather than size. What matters is how the three axes compare with one another, not how long any one of them is. The position of each plane follows from that ratio, so a mineralogist can locate a crystal's faces from it. Compare the species' fundamental ratio, which fixes one standard proportion for a whole mineral species.

Here the axial ratio becomes an identity card. Each crystal species has one fundamental set of proportions, so quartz and calcite can be told apart by it. The plane-locating ratio works within a single crystal, while this one belongs to the species as a whole. It is a property of the kind of mineral, not of any one specimen.

Algebraists drop "uniformizing" once the setting is clear and speak simply of the parameter, or of a chosen parameter t. It is an element that generates the unique maximal ideal of a discrete valuation ring. Other elements can then be expanded as power series in it, and an element's order is measured against it.