> > No program can determine its hardware. This is a consequence of the
> > Church
> > Turing thesis. The particular machine at the lowest level has no
> > (from the program's perspective).
> If that is true, we can show that CT must be false, because we *can*
> a "meta-program" that has access to (part of) its own hardware (which
> is intuitively computable - we can even implement it on a computer).
It's false, the program *can't* know that the hardware it has access to is
the *real* hardware and not a simulated hardware. The program has only
access to hardware through IO, and it can't tell (as never ever) from that
interface if what's outside is the *real* outside or simulated outside.
Yes that is true. If anything it is true because the hardware is not even
clearly determined at the base level (quantum uncertainty).
I should have expressed myself more accurately and written " "hardware" " or
"relative 'hardware'". We can define a (meta-)programs that have access to
their "hardware" in the sense of knowing what they are running on relative
to some notion of "hardware". They cannot be emulated using universal turing
machines (in general - in specific instances, where the hardware is fixed on
the right level, they might be). They can be simulated, though, but in this
case the simulation may be incorrect in the given context and we have to put
it into the right context to see what it is actually emulating (not the
meta-program itself, just its behaviour relative to some other context).
We can also define an infinite hierarchy of meta-meta-....-programs (n
metas) to show that there is no universal notion of computation at all.
There is always a notion of computation that is more powerful than the
current one, because it can reflect more deeply upon its own "hardware".
See my post concerning meta-programs for further details.
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