Date: Sun, 05 Sep 1999 10:13:16 -0700
From: Bill Spight <bspight@pacbell.net>
Subject: Re: Context as transformation rules
To: memetics@mmu.ac.uk
Dear James,
<<
i1 --t1-> m1 --t2-> m2 --t3-> i2
Now, in a case of genuine replication:
i2 = i1 and hence
t3 = -(t1 + t2)
because the total amount of transformation must be zero (otherwise i1
wouldn't exactly equal i2).
If this is reminding you of vector arithmetic, it was meant to. In fact, in the 3-transformation case you can construct a 'triangle of vectors' of sorts. The t1, t2, and t3 arrows are the sides of the triangle. The i1, m1, m2, and i2 forms are the points of the triangle (i1 and i2 are the same point because of the i1=i2 restriction).
>>
Very nice! <s>
If you can establish a group structure for the transformations, that would be great.
I do have a question about equivalence classes. If, for all contexts, given forms i1, i2, and m, there exist transformations t1 and t2 such that
i1 -t1-> m and
i2 -t2-> m
do i1 and i2 belong to the same equivalence class?
What I am getting at here is the question of how we equate i-forms. With genes we can look at the DNA. At present we cannot do anything similar for i-forms of memes, and the prospects for doing so do not look good.
(BTW, I think that the answer to my question is no. We have to restrict possible transformations, I think.)
Best regards,
Bill
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