Re: [lojban] Re: A Proposed Explanation of {gunma}

[John E Clifford <clifford-j@sbcglobal.net>]

--- Brandon Wirick <brandon@yrick.com> wrote:

> > 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.

I.e., a xorxes says "are independent."  Thanks. 
I am not sure that there was such a thing as
linear algebra when last I took maths but I am
sure it wasn't in my classes.  No wonder the
metaphor was obscure to me.