affine love

# affine

## Definitions

### from The American Heritage® Dictionary of the English Language, 4th Edition

• adj. Mathematics Of or relating to a transformation of coordinates that is equivalent to a linear transformation followed by a translation.
• adj. Mathematics Of or relating to the geometry of affine transformations.

• adj. Assigning finite values to finite quantities.
• adj. Describing a function expressible as (which is not linear, but is similar).
• adj. Of or pertaining to a transformation that maps parallel lines to parallel lines and finite points to finite points.
• adj. Having mutual affinity, of two materials.
• n. A relative by marriage.
• v. To refine.

### from the GNU version of the Collaborative International Dictionary of English

• transitive v. To refine.

### from The Century Dictionary and Cyclopedia

• Related; akin; affined.
• n. A relative by marriage; one akin.
• To refine. Holland.

• n. (anthropology) kin by marriage
• adj. (anthropology) related by marriage
• adj. (mathematics) of or pertaining to the geometry of affine transformations

## Etymologies

### from The American Heritage® Dictionary of the English Language, 4th Edition

French affin, closely related, from Old French; see affined.

## Examples

• We modeled the eating, lying, and standing dynamics of a cow using a piecewise affine dynamical system.

math

• We formulate a mathematical model for daily activities of a cow (eating, lying down, and stand - ing) in terms of a piecewise affine dynamical system.

math

• Thus, for example, the notions of Euclidean geometry are invariant under similarity transformations, those of affine geometry under affine transformations, and those of topology under bicontinuous transformations.

Logical Constants

• The axioms that Ketonen considers are those of projective and affine geometry, the former taken from Skolem's 1920 paper discussed in the first section above.

Chores

• Unlike proper length, this generalized affine length depends on some arbitrary choices (roughly speaking, the length will vary depending on the coordinates one chooses).

Singularities and Black Holes

• A maximal spacetime is singular if and only if it contains an inextendible path of finite generalized affine length.

Singularities and Black Holes

• The chief problem facing this definition of singularities is that the physical significance of generalized affine length is opaque, and thus it is unclear what the relevance of singularities, defined in this way, might be.

Singularities and Black Holes

• Thus the question of whether a path has a finite or infinite generalized affine length is a perfectly well-defined question, and that is all we'll need.

Singularities and Black Holes

• To say that a spacetime is singular then is to say that there is at least one maximally extended path that has a bounded (generalized affine) length.

Singularities and Black Holes

• This may involve 11-dimensions for the space directions for gauge potentials we measure as affine connections on the base spacetime.

Telekinesis and Quantum Field Theory