Orthogonality

[4] The Ancient Greek ὀρθογώνιον (orthogṓnion) and Classical Latin orthogonium originally denoted a rectangle.

[6] In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity to the linear algebra of bilinear forms.

Many works by painters such as Piet Mondrian and Burgoyne Diller are noted for their exclusive use of "orthogonal lines" — not, however, with reference to perspective, but rather referring to lines that are straight and exclusively horizontal or vertical, forming right angles where they intersect.

For example, an essay of the Thyssen-Bornemisza Museum states that "Mondrian [...] dedicated his entire oeuvre to the investigation of the balance between orthogonal lines and primary colours.

[9] This usage was introduced by Van Wijngaarden in the design of Algol 68: The number of independent primitive concepts has been minimized in order that the language be easy to describe, to learn, and to implement.

On the other hand, these concepts have been applied “orthogonally” in order to maximize the expressive power of the language while trying to avoid deleterious superfluities.

Typically this is achieved through the separation of concerns and encapsulation, and it is essential for feasible and compact designs of complex systems.

The emergent behavior of a system consisting of components should be controlled strictly by formal definitions of its logic and not by side effects resulting from poor integration, i.e., non-orthogonal design of modules and interfaces.

Orthogonality reduces testing and development time because it is easier to verify designs that neither cause side effects nor depend on them.

An orthogonal instruction set uniquely encodes all combinations of registers and addressing modes.

One such scheme is time-division multiple access (TDMA), where the orthogonal basis functions are nonoverlapping rectangular pulses ("time slots").

Well known examples include (a, g, and n) versions of 802.11 Wi-Fi; WiMAX; ITU-T G.hn, DVB-T, the terrestrial digital TV broadcast system used in most of the world outside North America; and DMT (Discrete Multi Tone), the standard form of ADSL.

so that the subcarriers are orthogonal to each other, meaning that crosstalk between the subchannels is eliminated and intercarrier guard bands are not required.

One econometric formalism that is alternative to the maximum likelihood framework, the Generalized Method of Moments, relies on orthogonality conditions.

In particular, the Ordinary Least Squares estimator may be easily derived from an orthogonality condition between the explanatory variables and model residuals.

[14] In organic synthesis, orthogonal protection is a strategy allowing the deprotection of functional groups independently of each other.

In philosophy, two topics, authors, or pieces of writing are said to be "orthogonal" to each other when they do not substantively cover what could be considered potentially overlapping or competing claims.

Thus, texts in philosophy can either support and complement one another, they can offer competing explanations or systems, or they can be orthogonal to each other in cases where the scope, content, and purpose of the pieces of writing are entirely unrelated.

[28] In the ancient Chinese board game Go a player can capture the stones of an opponent by occupying all orthogonally adjacent points.

The cartridge senses the motion of the stylus following the groove in two orthogonal directions: 45 degrees from vertical to either side.