On 20 Mar 2012, at 03:42, Stephen P. King wrote:
How is the notion of space coded in numbers? People argue that
we can recover a notion of time from the well order of integers, but
what about spaces? How do we get those?
Stephen, here I suspect you are confusing comp with digital physics.
There are no reason that space (nor God, nor souls, ...) can be
encoded in numbers. On the contrary, arithmetic as seen by inside, and
taking the 1-indeterminacy into account ('course) is full of things
which will exists (from the machine's viewpoint) and which are not
encodable with numbers. This comes from standard mathematical logical
results. The 1-I is typical with that respect. defining it by "Bp & p"
leads to a knowledge logic which can be proved to be not
arithmetically definable, nor is truth, nor is sensible matter and
most qualia, nor is consciousness itself, and very plausibly, nor are
physical spaces and times.
The self-referential logics makes possible to "meta-formalize" them,
though, notably by those many typical things that the machine cannot
formalize, yet can know about.
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