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Date: Fri, 16 Dec 2005 13:41:59 -0800
From: Brandon Wirick <brandon@yrick.com>
To: lojban-list@lojban.org
Subject: [lojban] Re: A Proposed Explanation of {gunma}
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> Someday I need to find out what is the meaning in
> Lojban speak of "orthogonal;"  I don't get "at
> right angle to" even as a metaphor (or rather it
> makes sense as at least two conflicting metaphors
> and I don't see enough usage to figure which is
> intended).

Orthogonality is a concept from linear algebra that describes a
condition among vectors in an inner-product space that have
inner-products of zero. In Euclidean space, orthogonality manifests as
right angles, but it can also apply to sets of polynomials that have
interesting but hard to visualize relationships. A zero inner product
means that a projection of one vector in the direction of the other is
zero; when one vector is scaled, its projection in the direction of
the other doesn't change, because it's zero. The metaphor is usually
extended to sets of adjustable things that don't affect each other
when they are adjusted.


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