Help with sets

[Lawrence D'Oliveiro]

In message <mailman.1606.1286889135.29448.python-list at python.org>, D'Arcy 
J.M. Cain wrote:

> On Tue, 12 Oct 2010 23:34 +1300
> Lawrence D'Oliveiro <ldo at geek-central.gen.new_zealand> wrote:
>
>>> Symmetry is always a tricky balance in programming languages.
>> 
>> Is that what we used to call “orthogonality”?
> 
> No, orthogonality is something else.  "Orthogonal" means "perpendicular
> to."

The appropriate meaning is ‘being able to combine independently” (as in the 
orthogonal decomposition of a Fourier transform). An example of contemporary 
usage, from the “Revised Report on the Algorithmic Language ALGOL 68” (1974, 
I think):

    0.1.2 Orthogonal design
    The number of independent primitive concepts has been minimized in
    order that the language be easy to describe, to learn, and to implement.
    On the other hand, these concepts have been applied “orthogonally” in
    order to maximize the expressive power of the language while trying to
    avoid deleterious superfluities.

So “orthogonality” has to do with use of minimum number of primitive 
components (operators, object types) in a maximum number of meaningful 
combinations.