Re: Orthogonal (fwd)

Forwarded message:

> Date: Sun, 26 Oct 1997 16:33:58 -0800
> From: Kent Crispin <kent@bywater.songbird.com>
> Subject: Re: Orthogonal

> The first context where I am aware of this use of the term orthogonal
> is from language design -- it was promoted by Niklaus Wirth and other
> purists, with languages like Pascal, Modula, CLU, and so on.  Larry
> Wall's "perl" language, with its slogan "there's more than one way to
> do it", is a direct revolt against the language purists.
> 
> The basic idea is that a computer language should have the minimum
> number of constructs necessary to span the intended application.  So
> for example, you don't provide hyperbolic trig functions, because the
> user can implement them using simpler math functions.  On the other
> hand, you do supply commonly used math functions that would otherwise
> require iterative algorithms.
> 
> I do believe the use of the term this way was inspired by the 
> notion of a 'basis' in a vector space -- a set of orthogonal
> vectors that span the space, ideally, unit vectors.

Can you better define the term 'basis'?

I can see the union 'build complicated things out of basic building blocks'
and the use of Occam's Razor (I'm as lazy as any other programmer) but fail
to see how this maps to anything relating to the concept of orthogonal.
Which clearly doesn't have any inherent minimalist cast.


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On Sun, Oct 26, 1997 at 06:42:14PM -0600, Jim Choate wrote:
> > I do believe the use of the term this way was inspired by the 
> > notion of a 'basis' in a vector space -- a set of orthogonal
> > vectors that span the space, ideally, unit vectors.
> 
> Can you better define the term 'basis'?

This is basic linear algebra:

V a vector space -- the set of all (s1,s2,s3,...,sn), where si is an
element of the set of reals.  A set of vectors {v1,v2,...,vm} in V is
linearly independent if there is no set of scalars {c1,c2,...,cm} with
at least one non-zero element such that sum(ci*vi) == 0.  A set of
vectors S spans a vector space V iff every element of V can be expressed
as a linear combination of the elements of S.   Finally, a basis for 
V is a linearly independent set of vectors in V that spans V.  A 
space is finite dimensioned if it has a finite set for a basis.  The 
standard basis (or natural basis) for a vector space of dimension n 
is th set of vectors

(1,0,0,...0)
(0,1,0,...0)
(0,0,1,...0)

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An entity claiming to be Jim Choate wrote:

: I can see the union 'build complicated things out of basic building blocks'
: and the use of Occam's Razor (I'm as lazy as any other programmer) but fail
: to see how this maps to anything relating to the concept of orthogonal.
: Which clearly doesn't have any inherent minimalist cast.
: 

Minimalism is merely a by-product of orthogonality.  A language is considered
orthogonal if builtin functions do not provide overlapping functionality.
So the term orthogonal probably refers to the fact that there is no
point of intersection in the functionality of the language (or system, as
the thread started out).

And I will not argue about vector spaces until I get bookshelves and actually
dig my Linear Algebra texts out of the boxes around my apartment.

Mark

- -- 
[] Mark Rogaski                   "That which does not kill me
[] wendigo@pobox.com                 only makes me stranger."

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