> But there are oh so many mathematical properties which I think we can use
> here -- you've defined sets in a space, but not used the concept of a
> BASIS, which I think would amount to "operating axioms".
>
> Additionally, the concept of a "subspace" I think would finally give us a
> handle on what a meme-complex is -- a certain subset of I{m} or A{m}
which
> is *closed*, meaning that the values VX and RX for that set are not
> functions of other, external memes; and that any combination of the memes
> in the subspace will result in more memes still *inside* that subspace
> (combining the ideas of "sin" and "redemption" in Christianity results in
> "grace", an idea still in the meme-complex).
>
> Additionally, is it possible to define the functions from these
subspaces?
> Can we decide whether these functions should/can be linear?
I'm not sure, but I would be surprised to find them linear, and as you say:
> Let me remind you that if we decide meme functions are *not* linear (as I
> think we must) the mathematics becomes much uglier...
I am not so sure we are at the point where we could even come close to
creating diffinative formulas for these relationships.
But we never will be if we don't start trying to think about it in those
terms now.
Eric, tell me more about subspaces. I have a feeling your theoretical
mathmatics is a bit fresher than mine.
-Prof. Tim