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In geometry, means "perpendicular to." In integral calculus and Fourier analysis, a set of functions is orthogonal over an interval if and only if the integral of the product of any two of the functions is zero when the functions are different and nonzero when the functions are the same.

(computing:) By analogy with the mathematical meanings of the term, features are said to be orthogonal when they combine gracefully and in an expected manner, even if seemingly wholly unrelated.

For instance, the UN*X shells will let you use ls -t and head to let you find your 10 newest files, even though I doubt any of Bourne, Ritchie and that lot thought of this specific functionality.

In linear algebra, a matrix is orthogonal if each row is perpendicular to every other row. This can be brute force tested by taking the dot product of every pair distinct rows, and ensuring that the result is zero in each case. Some orthogonal matrices:

[ 1 0 0 0 ] [ -2 4 0 ] [ 3-2i 13 ]
[ 0 1 0 0 ] [ 2 -1 0 ] [ 3+2i -1 ]
[ 0 0 1 0 ] [ 0 0 3 ]
[ 0 0 0 1 ]

Two vectors u,v in a Euclidean vector space V are orthogonal iff I(u,v)=0, where I is the inner product associated with V.
In R^n, using the standard inner product or "dot product", (a1, a2,...,an) and (b1,b2,...,bn) are orthoganal if a1*b1+a2*b2+...+an*bn=0.
orphaned i-node = O = OS

[from mathematics] Mutually independent; well separated; sometimes, irrelevant to. Used in a generalization of its mathematical meaning to describe sets of primitives or capabilities that, like a vector basis in geometry, span the entire `capability space' of the system and are in some sense non-overlapping or mutually independent. For example, in architectures such as the PDP-11 or VAX where all or nearly all registers can be used interchangeably in any role with respect to any instruction, the register set is said to be orthogonal. Or, in logic, the set of operators `not' and `or' is orthogonal, but the set `nand', `or', and `not' is not (because any one of these can be expressed in terms of the others). Also used in comments on human discourse: "This may be orthogonal to the discussion, but...."

--The Jargon File version 4.3.1, ed. ESR, autonoded by rescdsk.

The Orthogonal series is a sci-fi trilogy by Greg Egan, composed of The Clockwork Rocket, The Eternal Flame, and The Arrows of Time. It is an example of how you can simultaneously be hard sci-fi and violate the laws of physics.

Let's talk about geometry. The Pythagorean theorem tells you a² + b² = c², relating two possible paths you can take through space. Taking a different path increases the distance you need to travel.

Note I said space. What about paths through time? Well, as it turns out, the Pythagorean theorem for time is a² - b² = c². That is, taking a "longer" path reduces time. If you've ever heard of how travelling near the speed of light causes your personal time to be shorter, this is the formalization of why.

What does this have to with a sci-fi novel? Simple.

What if Pythagorean theorem for time was a² + b² = c², just like space? Orthogonal is about such a universe.

This changes physics. There's no universal speed limit. Different wavelengths of light travel at different speeds. Emitting photons causes your energy to increase. And that's only the beginning.

Orthogonal is an exploration of an alternate world. The plot is lacking, but the joy comes from the world. Go read it.

Or*thog"o*nal (?), a. [Cf. F. orthogonal.]

Right-angled; rectangular; as, an orthogonal intersection of one curve with another.

Orthogonal projection. See under Orthographic.

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