FOM: Comments regarding the Friedman's "Degenerative Cloning"
Wlodzimierz Holsztynski
wlod at westpole.com
Wed May 9 19:31:26 EDT 2001
NOTATION:
\< -- less or equal
>/ -- greater or equal
=/= -- not equal
N -- the set of natural numbers, N := {1 2 ...}
==========================================
I feel privileged to witness the progress
of Friedman's work on his "Degenerative
Cloning" and hope to see the "ultimate"
version soon.
If I may, I'd like to suggest "cabinet
of babushkas" for the "set of disjoint circles".
The standard notion would be a "forest", i.e.
a partially ordered set (X \<) such that
for arbitrary a b c \in X if c \< a and
c \< b then a \< b or b \< a. Thus
cabinets of babushkas are really forests but
in the context of cloning and when we think
about objects containg other objects, babushkas
appeal to me much more.
I also have two natural generalizations
of cabinets of babushkas. They allow
to carry the same cloning (and dying) processes.
These generalisations are not terribly exciting
but they make things more flexible, possibly
there is a seed of a special algebra.
I didn't want to make my letter too long
but if there is an interest in such generalisations
I'll present them (I would be honored if Dr Friedman
liked them enough to incorporate them in his work).
Best regards,
Wlodzimierz Holsztynski
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