Bill Haloupek <haloupekb@UWSTOUT.EDU> wrote:
> If by "intelligence" you mean innate mental ability, then I
> agree that intelligence and articulation are close to being
> orthogonal. I would add that thoughtfulness is also orthogonal
> to both intelligence and articulation.
I've often thought along similar lines -- although I don't think all of the
vectors like these are complectly orthogonal. Here's list of orthogonal
vectors:
intelligence -- the horsepower of your brain, the WAY a person thinks
creativity -- ability to come up with new knowledge
knowledge -- the base of information you are aware of -- hopefully
it *increases* with time.
articulation -- your ability to express what you know, or to
*COMMUNICATE* your creativity and knowledge to the
world. It's hard to communicate intelligence
directly, but since both creativity and knowledge
depend on it at least indirectly, and it does have
some effect on articulation, it can be "measured",
just not well.
Bill Haloupek <haloupekb@UWSTOUT.EDU> wrote:
> A meme, then,
> is something that tends to align nearby vectors?
If vectors are our minds, you are sort of right. I'll quote the book for
you:
A <I>meme</I> is a unit of information in a mind whose existence influences
events such that more copies of itself get created in other minds. --
Richard Brodie, _Virus of the Mind; the New Science of the Meme_
I think defining *minds* are functions and ideas as vectors (indeed, as the
vector space) makes more sense -- and it opens up the area of eigenvectors
or invariant functions to memetic analysis. Let me do a recap of what Tim
said, and the add where I think the linear algebra model of memetics should
go:
let E{m} be the vector space representing the ideo-environment
of host m
let A{m} be the vector space representing the ideo-awareness
of host m (m's *knowledge*)
let I{m} be the vector space representing the belief set
of host m (the ideas m believes in; acts upon; *communicates
to others*)
(it is worth noting that E{m} is infinite in theory, while both
A{m} and I{m} are finite, E{m}>A{m}>I{m})
Before we move on, I will also mention that Tims proposed us of scalars in
the above vector spaces to represent "importance". These scalars would
themselves be functions of time -- that is to say, the importance of ideas
changes to a host over time. For now, lets note that at any given time:
A{m} = x1*A1 + x2*A2 + ... + xn*An
for some scalars x1, ..., xn and some finite number of ideas
A1, ..., An. It's worth noting that any of the x's may be
equal to zero -- the person knows of the idea, but does not
think it important at all.
I{m} = b1*A1 + b2*A2 + ... + bn*An
for some scalars b1, ..., bn with bi <= xi for all i
(a person can't believe in it more than they think it
important, right?) Again, many more of these scalars
may also be zero. I used the same idea vectors becuase,
again, a person can't believe in something they don't know
about!
Then define two functions:
fi : E{m} --> I{m}
and
fA : I{m} --> A{m}
What exactly these function DO, other than map vectors into
the ideo-spaces, it really not known at this time.
(it's worth pointing out that the above functions are quite strange in that
they actuall are capable of expanding the space they map into. We might be
better to redefine the spaces as subsets of the ideo-universe to avoid
this, but I'll leave it as stands anyway. Tim's original functions
actually had A{m}= fA[ I{m}], and I'd be quite interested to hear WHY he
did this. It makes the function much more important -- the function
actually *creates* the space in his notation, rather than simply being a
map from one to the other.)
However, I can propose several possibilities.
First, I think that those functions actually control the scalars xi and bi
-- or that the dependance is mutual, if you like (we both control and are
controlled by our minds). Second, I say unto you that we can represent a
meme as an *eigenvector* of either or (preferably) both of these
functions.
Lets suppose their exists a "meme" Ak in E{m}.
Then fA(Ak) = (labmda1)*Ak
and fi((lambda1)*Ak) = (lamdba2)*(lambda1)*Ak
Resulting in the fact that a meme Ak moved from E{m} to I{m} with only a
change in importance. Now, of course, with Ak in I{m}, m will begin to act
upon and communicate Ak to others -- thus contunining the propagation
cycle. An especially virulent meme would have
lambda1 > 1 and
lambda2 > 1
so that the idea makes itself more important as it passes through the hosts
functions.
Of course, it goes without saying that most ideas are not memes -- most of
the things we here we "mutate" somewhat, so that, for some idea Aa
fA(Aa) = ca*Ab
where Ab is some slightly different idea. (I think it would be useful to
say that ideas which are numerically close to each other are related, so
that A123 is approximatly equal to A124)
As an aside, a meme-complex can then be viewed as a sort of eigenspace -- a
whole group of memes which propagate together, and define something like
"christianity" in the process.
ERiC