I've thought about memes and eigenvectors in great depth now -- and I'm
sure it's the closest analogy I have yet stumbled across in linear
algebra. Here goes:
An eigenvector x is a vector with the property that
T(x) = c*x
Where T is the function and c is a scalar (usually called "lambda", but
since I can't get that symbol here...)
Anyway, the key thing to realize here is that these vectors are the perfect
representation of memes -- vectors such that they are only changed in
*importance* as they get mapped from one area into the next.
Additionally, they have another property that I think makes a lot of sense
-- an eigenvector is only an eignevector for a particular linear mapping --
that is, it is a property of the *function* not of the vector space. What
this means is that it's not the vector space that makes an eigenvector do
what it does, but rather the function -- or in memetic terms, it's not the
idea, it's the brain that replicates.
Brodie's "buttons", then, are properties of our internal functions fA and
fi that all people share -- sex, food, danger: these are all ideas which
people pass on to others *unchanged*. This works becuase all of our minds
are similar at this basic level -- we all respond in the same way to these
stimula. Think about an alien -- would he respond the same way to an
advertisement containing sex? I doubt it. This shows that memes are
dependent on the function.
Now in linear algebra, we go on to develop a method of *finding* the
eigenvectors of a linear map -- and in certain cases, enough of them can be
found such that *any* vector can be represented as a linear combination of
eigenvectors of the linear map, which in our case would basically mean that
it would be possible to express *any* idea as a meme-complex! However,
there are many linear maps for which not enough eignevectors can be found
to acomplish this -- and I think these best represent our minds.
However, even in that case it is usually possible to find entire sub-spaces
of eignevectors of the function -- meaning that entire sets of ideas have
the meme's ability to simply "by-pass" our critical thinking skills and map
straight into our ideo-sphere's. I think we should call the dimension of
the eigenvector subspace of our function fi our "advertising vunerablity
coefficient" and the dimension of the subspace of our function fA our
"brainwashing vunerability coefficient"
One unfortunate consequence of this entire thing is that usually
eigenvectors only have meaning for a function which maps from a vectorspace
to itself -- otherwise what does it mean to say that
T(x) = c*x ? I think the only way we can really get over this stumbling
block is if we say (at the very least) that
dimension (E{m}) = dimension (I{m}) = dimension (A{m})
Which on an intutive level doesn't make much sense. I think we can still
say that
E{m} > I{m} > A{m}
by ensuring that there are plenty of zeros in the Vx and Rx values.
ERiC