Function (biology)

A biological function is the reason some object or process occurred in a system that evolved through a process of selection or natural selection. Thus, function refers forward from the object or process, along some chain of causation, to the goal or success. Compare this to the mechanism of the object or process, which looks backward along some chain of causation, explaining how the feature occurred.

A functional characteristic is known as an adaptation, and the research strategy for investigating whether a character is adaptive is known as adaptationism. Although an assumption that a character is functional may be fruitful as a research method, some characteristics of organisms are non-functional, and may simply be emergent phenomena arising as a side effect of functional systems (see Spandrel (biology)). They may also have a reduced function or lost function entirely over time due to changing conditions, in which case they are said to be vestigial.

The correlation of form (also referred to as structure) and function is one of the central themes in biology. However, knowing the structure of something does not necessarily reveal its function. To illustrate the point, an enzymologist discovering an unknown enzyme would be highly unlikely to identify its function with only structural information. It is also possible for different structures to carry out the same function. Teeth and the gizzard of a bird highlight this point: both grind up food, serving the same function in terms of digestion.

Function

Function may refer to:

Math, computing and engineering

Music

Other uses

See also

Ξ function

In mathematics, the Ξ function (named for the Greek letter Ξ or Xi) may refer to:

Minkowski's question mark function

In mathematics, the Minkowski question mark function (or the slippery devil's staircase), denoted by ?(x), is a function possessing various unusual fractal properties, defined by Hermann Minkowski (1904, pages 171–172). It maps quadratic irrationals to rational numbers on the unit interval, via an expression relating the continued fraction expansions of the quadratics to the binary expansions of the rationals, given by Arnaud Denjoy in 1938. In addition, it maps rational numbers to dyadic rationals, as can be seen by a recursive definition closely related to the Stern–Brocot tree.

Definition

If is the continued fraction representation of an irrational number x, then

whereas:

If is a continued fraction representation of a rational number x, then

Intuitive explanation

To get some intuition for the definition above, consider the different ways of interpreting an infinite string of bits beginning with 0 as a real number in [0,1]. One obvious way to interpret such a string is to place a binary point after the first 0 and read the string as a binary expansion: thus, for instance, the string 001001001001001001001001... represents the binary number 0.010010010010..., or 2/7. Another interpretation views a string as the continued fraction [0; a₁, a₂, … ], where the integers a_i are the run lengths in a run-length encoding of the string. The same example string 001001001001001001001001... then corresponds to [0; 2, 1, 2, 1, 2, 1, …] = √3 − 1/2. If the string ends in an infinitely long run of the same bit, we ignore it and terminate the representation; this is suggested by the formal "identity":