In the mathematical sense, the identity element of a set with a binary
associative operation defined on it is the most boring element in the set,
i.e., if you perform the specified operation on an element 'a' and the
identity element, you'll get 'a' out. (An example of an identity element
is the number '1' in the multiplication of real numbers:
1 * a = a;
another is tbe number '0' in the addition of real numbers: 0 + a = a.)
When I first created this site (1994 or so, I think), I was living by myself for the first time, and had a lot of time to think about myself, probe the darker corners of my psyche, and generally reflect on what sort of person I was and what sort of person I wanted to be. That, plus the fact that there was just the one (note the connection to the mathematics above) sentient resident of my apartment (although my cat and I might have differed on exactly which one of the two of us that it was) led to the pun that you've just been overintroduced to. (The place I'd moved out of, which had been named the Continuum, was rechristened the Semi-Group, which is a set with an associative operation that does not have an identity...otherwise it would be at least a monoid.)
As I am now living with Megan, my personal choice would have been to rename our webpages "The Primal Space" and "The Dual Space", in another strained mathematical-paranomasiacal attempt to play off our theme of compl{i,e}mentarity. However, Megan has not warmed to this notion. . .ah, well.
If Megan and I ever end up forming a combined household with certain others of my friends, I will lobby mightily to get the place (and possibly our collective Web presence, if any) known as "N-Space". (Or perhaps "X-Space" if one of my friends ever does something sufficiently rigorous with the bizarre notion of continuous dimensional change that I came up with sometime in 1998. And you thought fractals were weird...)
Last modified 9 August 2000