Right angles escaped geometry and now describe Wi-Fi, DNA and vinyl records
Orthogonal started life as a Greek word for a rectangle. Today mathematicians use it for vectors that meet at right angles, but engineers, chemists, statisticians and philosophers have borrowed it to mean something broader: two things that do not interfere with each other at all.
The roots are the Ancient Greek for upright and angle. The Greek orthogonion and Latin orthogonium first named a rectangle, later a right triangle, and by the 12th century orthogonalis referred to a right angle. In mathematics the idea generalises perpendicularity. Perpendicular is usually kept for lines and planes crossing at right angles, while orthogonal stretches to vectors, curves and abstract spaces. In quantum mechanics, two eigenstates with different eigenvalues are automatically orthogonal.
Engineers took the notion of independence and ran with it. Adriaan van Wijngaarden introduced orthogonal language design with Algol 68, meaning a small set of features that combine freely with predictable results. A processor instruction set counts as orthogonal when any instruction can use any register in any addressing mode. In system design, an orthogonal component can be changed without side effects rippling elsewhere, which shortens testing. Wireless technology relies on orthogonal frequency-division multiplexing, spacing subcarriers precisely so they do not interfere; it underpins versions of 802.11 Wi-Fi and the terrestrial digital television used across most of the world outside North America.
A stereo vinyl record is a literal case. Its V-shaped groove has walls at 90 degrees, each carrying one channel, and the cartridge reads motion in two directions 45 degrees either side of vertical. In chemistry, orthogonal pairs interact only with their partners: in DNA, cytosine pairs with guanine and adenine with thymine, but the cross combinations are strongly disfavoured. Statisticians call uncorrelated explanatory variables orthogonal, since their effects can then be estimated separately or together with the same result.
The word has spread even further. Painters such as Piet Mondrian and Burgoyne Diller worked almost entirely in orthogonal lines, strictly horizontal and vertical. In chess it means along the same rank or file, and in Go stones are captured by filling every orthogonally adjacent point. Philosophers call two texts orthogonal when their subjects simply do not overlap.
Source: Orthogonality
