Bruno Marchal wrote:
> Le 25-avr.-06, à 17:37, Tom Caylor a écrit :
> >
> > In fact, "closed system" and "meta element" seem to be contradictory.
> Not necessarily. It could depend of what you mean exactly by "closed".
> Closure for the diagonalization procedure is the key. Diagonalization
> is the key of the "heart of the matter". I will come back on this
> later.

Closed system (Principia Cybernetica): An isolated system having no
interaction with an environment.  A system whose behavior is entirely
explainable from within, a system without input...

Mathematically, a closed system contains its boundary, or it contains
its limit points.  In other words, anything expressable with the given
axioms/language is itself a member the system.

> > And, back to the original question, "closed system" and "erasing
> > information" seem to be contradictory.
> Why?

I'm at an impasse with myself in trying to explain my intuition
further.  Meanwhile I'm studying up on diagonalization, waiting for
your "heart of the matter" (which I take as just a pun and not
referring to physical matter, heaven forbid).

Speaking of "impasse with myself" and diagonalization, a thought
occurred to me that an instruction that "erases information", like a
Turing machine "goto" statement (e.g. Wei Dai's "go to the beginning of
the tape" instruction) seems to be a *self-referential* instruction.
Maybe this has something to do with the original question and (I
maintain) the need for a meta viewpoint, or an open system, to
understand it.


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