"Tim Rhodes" <proftim@speakeasy.org> wrote:
> Eric, tell me more about subspaces. I have a feeling your
> theoretical mathmatics is a bit fresher than mine.
Actually, I'm currently learning about subspaces, so let's hope so!
To quote the book: A subset W of a vector space V is a subspace of V if and
only if the following conditions hold:
a) (x + y) is an element of W if x, y are elements of W
(the "closure" property -- why I think a subspace might actually
*define* a meme-complex, or even "world-view")
b) cx is an element of W if x an element and c is an element of the field
(so the weight of a meme does not affect it's involvement in the
meme-complex)
c) W has a zero vector. (??? Any ideas on what the "zero" meme might be?
"Faith"? "Apathy"?)
We may not need this last requirement in memetics???
Actually, I think the idea of a zero meme is very fertile -- what kind of
meme is present in all meme-complexes? What does "zero" mean in memetics?
There are a few other concepts I think should also be thought about -- the
null space is one.
The null space is the set of ideas which a function sends to "zero" -- for
our purposes, I think intrepreting this as "the set of ideas which the
function ignores" would work. Infact, the dimension of the null space
might tell us the "dogmatism" coefficient of the function!
How about the "range" of a function? (range is the area which the function
maps into) The dimension of the range of fA would represent the *size* of
your meme-scape (or memory). This would be the kind of thing we would all
like to increase -- more knowledge. The dimension of the range of fi would
be the "open mindedness" coefficient -- "vision" in classical CoV?
I think we've got some really good ideas to work with here!
ERiC