> I consider it very brave (on this list) to actually put the definition of
> "meme" into one's own words.
Here was something I was working on last year in an attempt to understand
the dynamics of memes. (Its very long and dry and the lack of formating
makes it doubley so [for instance MEMEX should read MEME sub X], please
forgive)
-Prof. Tim
Memetic Vector Modeling
The quest for the mathematics of memes
by Professor Tim
"In (memetics) the goal is always to give an ironclad proof for some
unobvious statement. The very fact of the steps being linked together in
some ironclad way suggests that there may be a patterned structure binding
the statements together. This structure can best be exposed by finding a
new vocabulary--a stylized vocabulary, consisting of symbols-- suitable
only for expressing statements about (memes)."
Douglas R. Hofstadter from Godel, Escher, Bach (and transposed from number
theory onto the field of memetics)
Consider for a moment the seemingly elementary question of, "What is a
memetic vector?" As we are aware, a memetic vector simply anything which
selects memes from its environment, copies them, and re-introduces them
into its, or possibly another's, environment. The human mind is the
classic and timeless example of such a device. The role that a mind plays
in its meme-sphere can be seen as the blueprint for what it is to be a
memetic vector. But what does that mean? "A memetic vector selects memes
from its environment", but how? By what criteria? And what is its
environment? If we are to understand the transmission of memes with the
degree of accuracy necessary to make quantifiable predictions it is
imperative that we come to an understanding of the machine that is at work
in these transmissions, the memetic vector itself. What properties would
such a thing possess? What are its characteristics and machinations? And
can we create a model to express these qualities? More to the point, what
can we learn from the attempt? I think it is not at all inconceivable to
believe that we can, in fact, create a set of symbols and inter-relations
that will mirror the mannerisms of a memetic vector in regards to a given
set of memes. Such an attempt forms the basis of this extended rant.
Section #1:
Primary Provisional Definitions
Let us begin at the beginning, with some definitions. And what better
place to begin than with the meme itself. We will choose, within this
rant, to express any meme as follows,
MEMEX = the meme for "x" (previously expressed as <x>)
The nature of MEMEX , a sticking point in a great many discussions about
memetics, is as yet undefined. And, more to the point, need not be defined
in order for us to use it as part of a mathematical system. To be sure,
certain qualities of MEMEX will become apparent as we continue. But we
need not trouble ourselves overly with the question of what MEMEX is. It
is, in this case, a symbol and little else.
We can go on to define the following as well,
m = represents any given memetic vector.
This will be true for any vector, without regard to its nature. m therefore
could as easily represent an individual, a group of individuals, a culture,
or even a complex computer network that processes, selects, copies and
distributes information. Any and all of these, to the extent that they
function as a vector for the transmission of a meme or memes, can be
expressed as m.
Further the environment of m can be expressed as,
E{m} = the set of all MEMEX contained in the environment of the
vector m
Environment here can be defined as anything and indeed everything of a
memetic nature that comes in contact with the vector in question.
The contents of this set will, of course, change over time dependent on
the exposure of m to different sets of memes. And, as we shall see, a
certain subset of MEMEx can operate upon E{m} in such a way as to alter the
limits and extent of the set E{m}. This will also be true for the next
set, the memes internal to m.
I{m} = the set of memes that contains all MEMEX stored within the vector
m
Here it seems worthwhile to note that the value x in MEMEX, although it is
in truth a string, may be thought of numerically as well. If we first
imagine that the vector m has contained within it a catalog of all memes in
I{m} such that each MEMEX has a corresponding numeric value, such as: 1=
MEMEAARDVARK 2= MEMEBEAVER 3=MEMECAMEL , and so on (although the
particular order of this imagined listing need not be enumerated for our
purposes). It should, however, be understood in this context that any
numeric value assigned to a given MEMEX will be unique to m. That is to
say, for example, that what is represented by the term MEME1326 in I{mary}
may does not necessarily correspond to the MEME1326 in I{mark}. This is
not a problem for us for the moment though, since we will be working from
the viewpoint of a single vector and its internal relationships only. We
can feel free to address the protocols of translation between vectors
later, if and when the need arises.
It therefore becomes clear from this numeric understanding of MEMEX, that
we can also express I{m} using the following equation,
I{m} = MEME1+MEME2+MEME3+MEME4+...+MEMEN
n in this case, would be the total number of memes in I{m}. That is, the
number of memes stored internally within the vector m.
At this point you may also feel, quite rightly, that it seems improper to
give all memes within a vector the same weight. We know intuitively that
some memes will have a higher value within the meme-set of m than others,
while still other, stored memes will have little or no effect on the
functioning of the vector at all. Therefore it seems logical, and indeed
necessary, to assume that,
For every MEMEX in I{m} there is a corresponding value VX that represents
the importance placed on MEMEX for the given vector m
or
VX = the significance of MEMEX within I{m}
As we will see, understanding the nature of VX will lie at the heart of
modeling how a memetic vector functions and we will be returning to it
later in much more detail.
For the moment, this convention, using VX as a term for the significance
of a meme, will allow us also to speak not only of the catalog of stored
memes internal to a vector, but likewise to construct an equation for the
belief system of the vector itself. If we suppose the active beliefs or
active memes working upon a vector are a function of the relationship
between the vector's stored memes and the value attached to them, it
becomes clear that by defining those active memes such that,
A{m} = is the set representing the belief system internal to m
it would follow that we could easily express A{m}, or what we commonly
refer to as the meme-set of m, in the following terms,
A{m}=MEME1*V1+MEME2*V2+...+MEMEN*VN
This is an important point and the distinction between active and inactive
or stored memes (A{m} and I{m} respectively) will hopefully enable us to
resolve some of the confusion surrounding the difference between exposure
to and infection with a meme or group of memes.
The question of whether A{m} is to be considered to be contained within
I{m} remains unanswered at this point. At first glance it would seem that
A{m} should be an independent set side-by-side with I{m}. But we must
remember that I{m} contains all memes stored by m. And this would seem to
indicate that the meme MEMEA{m} would also be found included in I{m}. Not
an entirely satisfying answer, since it has the potential to skirt along
the ragged edge of becoming an endlessly recursive system. But with any
luck, by looking at the relationships between E{m}, I{m}, and A{m} in
regards to MEMEX we will be able to shed some light on this question soon
enough.
These are just a very basic beginning definitions and it may seem that
countless number of terms will be needed at our disposal if we are to
accurately model the functioning of a memetic vector mathematically. This
may or may not be the case. But nevertheless we have made a good
beginning. We have a simple starting place. And from its familiar waters
we can launch our more detailed explorations into the realm of the memetic
vector, this internal structure, and its role in its environment.
Section #2:
E, I, A and Meme
So now, with a basic terminology in hand, let us look for a moment at how
a meme (MEMEX) makes its way from the larger environment (E{m}) into the
meme-set of the vector (A{m}). Or, more to the point, how it is that a
given meme floating haplessly in the vectors neighborhood becomes
incorporated within the belief system of that vector and what an
understanding of that process can tell us about the nature of memes and
memetic vectors generally.
First we will need to take a closer look at the set A{m}. In the previous
section we saw that the meme-set of m, A{m}, could be expressed as,
A{m} =MEME1*V1+MEME2*V2+...+MEMEN*VN
If we chose to define VX such that it corresponds to a value between 0 and
1 (or, in fact, between 0 and any positive number) where 0 signifies that
no importance or interest whatsoever is placed on MEMEX by m, then we see
that any MEMEX with a VX equal to 0, for all intents and purposes, falls
out of the equation for A{m}. Thus the set A{m} is reduced to and will
contain only those MEMEX that have a non-zero VX value. Here it finally
becomes obvious that A{m} is, not only, a subset of I{m}, but more
specifically the subset consisting only of those memes derived from I{m}
which have a positive VX value and are weighted within A{m} by virtue of
their significance to the vector m.
Likewise we will see that I{m} is itself contained within the set E{m} and
we would suspect that it may be derived from E{m} by using some, as yet
undefined, function. ( If you doubt this point, we need only remember that
the environment of vector m must include all the memes that are in contact
with the vector. And what closer contact can one imagine than those memes
stored within the very vector itself!) We can show this inter-relation in
the simplest terms as,
E{m} > I{m} > A{m}
If this seems like an oversimplification, you're right, it is. But simple
relationships do have their merit. Many problems in memetics arise when
people overlook this simple relationship and conclude, wrongly, that mere
exposure to a meme grants it a place in the vectors meme-set. As we saw,
the meme-set A{m} is derived from the internally stored memes I{m} by
virtue of a function. In this case that function, which we can call fA, is
defined by the relationship between MEMEX and VX for all values x within
I{m}.
Perhaps more to the point, it might do us some good to show the
relationship between beliefs, memories and the environment of a vector as a
series of functions. Taking what we already know, we can do this and by so
doing reveal a great deal about the hierarchies within a vector regarding
memes.
We may, for instance, characterize the operation of fA in this way:
For any x, fA[x] will be the results of weighing all included MEMEX
against their corresponding VX value.
Or, in a more formalized way,
A{m}= fA[ I{m}] and I{m}= fi[ E{m}]
where fi is the as yet undefined relationship between E{m} and I{m}. It
follows easily from this that,
A{m}= fA[ fi[ E{m}] ]
We now can envision a process whereby a meme-set is derived from the
environment by these functions, fA and fi. But what do we know of fi?
What are its qualities? How is it that an external meme becomes
internalized and what factors play a role in this process?
We can imagine a formula, perhaps similar to the one we used for
generating A{m}, may be at work in the internalization of MEMEX. So let us
create that formula first, and see if it will satisfy our needs. We can
then proceed to look at the details of the terms involved.
We might say that, for all MEMEX in E{m},
I{m}=MEME1R1+MEME2R2+...+MEMENRN
Here RX symbolizes the factor at work in selecting a MEMEX from the
environment to form I{m}, in much the same role that VX played in the
selecting of the set A{m}.
What then, will our intuitions tell us about the nature of our new, and as
of yet undefined, term RX?