I notice that "erasure of information" on a goto instruction occurs
only for goto instructions which send the Turing machine to an
instruction already executed.  Thus the self-reference is a reference
to the *past* self of the Turing machine, which in a sense is the only
self the Turing machine knows.


Tom Caylor wrote:
> 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.
> Tom

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