Orthogonality

In mathematics, orthogonality is the relation of two lines at right angles to one another (perpendicularity), and the generalization of this relation into n dimensions; and to a variety of mathematical relations thought of as describing non-overlapping, uncorrelated, or independent objects of some kind.

The concept of orthogonality has been broadly generalized in mathematics, science, and engineering, especially since the beginning of the 16th century. Much of the generalizing has taken place in the areas of mathematical functions, calculus and linear algebra.

Etymology

The word comes from the Greek ὀρθός (orthos), meaning "upright", and γωνία (gonia), meaning "angle". The ancient Greek ὀρθογώνιον orthogōnion (< ὀρθός orthos 'upright' + γωνία gōnia 'angle') and classical Latin orthogonium originally denoted a rectangle. Later, they came to mean a right triangle. In the 12th century, the post-classical Latin word orthogonalis came to mean a right angle or something related to a right angle.

Orthogonal (novel)

Orthogonal is a science fiction trilogy by Australian author Greg Egan taking place in a universe where, rather than three dimensions of space and one of time, there are four fundamentally identical dimensions.

Technically, the space-time of the universe portrayed in the novels has a positive-definite Riemannian metric, rather than a pseudo-Riemannian metric, which is the kind that describes our own universe.

The first novel of the trilogy, The Clockwork Rocket, was published in 2011, the second, The Eternal Flame, in 2012, and the third, The Arrows of Time, in 2013.

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