On 11/7/2012 8:18 PM, Craig Weinberg wrote:
On Wednesday, November 7, 2012 6:50:03 PM UTC-5, Stephen Paul King wrote:
On 11/7/2012 10:24 AM, Craig Weinberg wrote:
On Wednesday, November 7, 2012 8:19:03 AM UTC-5, Stephen Paul
King wrote:
On 11/7/2012 7:42 AM, Craig Weinberg wrote:
> Can anyone explain why geometry/topology would exist in a
comp universe?
> --
Hi Craig,
So far it seems that there is only a singular set of
countable
recursive functions (or equivalent) and thus a single Boolean
algebra
for the Universal Machine. If the BA (of the Universal number or
Machine) has an infinite number of propositions, how could it
be divided
up into finite Boolean subalgebras BA_i, where each of them
has a
mutually consistent set of propositions?
Additionally, how is 'time' defined by comp such that
transformations of topologies can be considered.
It occurs to me that computation can only occur where topological
position is borrowed from the physical, spacetime presence of
persistent bodies. Sense and static realism must exist a priori
to computation.
Craig
Hi Craig,
Yes, the set of equivalent computations (equivalent in the
sense of all are capable of generating the 1p content) can only
occur if there is a topological position. This position is
"borrowed" from the space-time that a set of persistent logics
have in common. Remember, one Boolean algebra has many different
but equivalent Stone spaces as its dual and each Stone space has
as it dual many equivalent Boolean algebras. I am using the
concept of an equivalence class. A space-time is a Stone space
that has some evolution, so it is a sequence of Stone spaces. A
computation is the evolution of a Boolean algebra or,
equivalently, a sequence of Boolean algebras. S3nse is the 1p
content/static realism of every Boolean algebra/Stone space pair -
like a snapshot of an experience.
What must be understood is that there is an (at least)
uncountable infinity of these dual pairs and only a finite number
of them can have a Boolean algebra (equivalence class) between
then, so this gives the illusion of a finite universe of physical
stuff for almost any finite subset of dual pairs.
--
As far as falsifying comp though, is there any reason for Boolean
algebra in and of itself to present itself as a Stone dual? Why have
any new ontological presentation of equivalence at all from a pure
arithmetic motive?
Craig
Hi Craig,
Comp is not false, IMHO, it is just looked as through a very
limited window. It's notion of truth is what occurs in the limit of an
infinite number of mutually agreeing observers. 1+1=2 has no counter
example in a world that is Boolean Representable, thus it is universally
true. This does not imply that all mathematical truths are so simple to
prove via a method of plurality of agreement. Motl wrote something on
this today:
http://motls.blogspot.com/2012/11/when-truths-dont-commute-inconsistent.htm
"When truths don't commute. Inconsistent histories.
When the uncertainty principle is being presented, people usually -- if
not always -- talk about the position and the momentum or analogous
dimensionful quantities. That leads most people to either ignore the
principle completely or think that it describes just some technicality
about the accuracy of apparatuses.
However, most people don't change their idea what the information is and
how it behaves. They believe that there exists some sharp objective
information, after all. Nevertheless, these ideas are incompatible with
the uncertainty principle. Let me explain why the uncertainty principle
applies to the truth, too."
Please read the read at his website
--
Onward!
Stephen
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