 ...Schmidhuber:03gm,Schmidhuber:04gmhtml.^{1}
 Or `Goedel machine', to
avoid the Umlaut. But
`Godel machine' would not be quite correct.
Not to be confused with what Penrose
calls, in a different context,
`Gödel's putative theoremproving machine' [30]!
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 ... machine^{2}

Turing reformulated Gödel's unprovability results in terms
of Turing machines (TMs) [56] which
subsequently became the most widely used abstract model of
computation. It is wellknown that there are universal
TMs that in a certain sense can emulate any other TM or any
other known computer. Gödel's integerbased formal language
can be used to describe any universal TM, and vice versa.
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 ...
etc.^{3}
 We see that certain parts of the
current may not be directly observable without changing
the observable itself.
Sometimes, however, axioms and previous observations will allow
the Gödel machine to deduce timedependent storage contents that
are not directly observable.
For instance, by analyzing the code being executed through
instruction
pointer IP in the example above, the value of IP at
certain times may be predictable (or postdictable, after the
fact). The values of other variables at given times,
however, may not be deducible at all.
Such limits of selfobservability
are reminiscent of Heisenberg's celebrated
uncertainty principle [12],
which states that certain physical measurements are necessarily
imprecise, since the measuring process affects the measured
quantity.
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