On 08 Jun 2015, at 03:30, Bruce Kellett wrote:
LizR wrote:
On 6 June 2015 at 11:26, Bruce Kellett <bhkell...@optusnet.com.au <mailto:bhkell...@optusnet.com.au
>> wrote:
LizR wrote:
This is true if events have an existence apart from maths.
However, that is still being debated. Tegmark's "mathematical
universe hypothesis" suggests that time and events are
emergent
from an underlying timeless mathematical structure.
To take something that is (hopefully) less contentious, the
block universe of special relativity already suggests
something
similar to this. In relativity, all chains of events are
embedded in a space-time manifold, and hence causation comes
down to how world-lines are arranged within this structure.
This is not true. Causality is still a fundamental consideration
in
SR, and that carries over into the basic structure of quantum
field
theory. Even within the block universe model, the light cone
structure of spacetime is fundamental. The light cone encapsulates
the fundamental insight of SR that causal influences cannot
propagate faster than the speed of light -- the light cone is the
limiting extent of causal structure. The laws of physics
consistent
with this structure in SR and beyond are have a (local) Lorentz
symmetry, which preserves the causal structure between different
Lorentz frames. The distinction between time-like and space-like
separations of events is aa fundamental tenet of physical law.
None of this contradicts what I said. All I am concerned with is
that SR indicates that events are embedded in a 4D continuum.
Describing how they're embedded doesn't change that.
You started with Tegmark's idea that time and events are emergent
from an underlying timeless mathematical structure.
Something proved to be the case, well before, in the case we assume
computationalism. In that case, there is no more choice in the matter.
tegmark assumption becomes (well was already before) a theorem of
computationalist cognitive science.
My point was that in order for time to emerge from a block universe
certain structure was necessary --
Well, this is doirectly false with comp, in the sense that all you
need is the emulation of a brain of a person believing in time, and
those exists all in the block mindscape constituted in a tiny part of
arithmetic.
we need a 4-dim manifold with a local Lorentzian metric, and
physical events must be arranged with a particular structure on this
manifold -- they cannot just be arranged at haphazard. So the way
events are embedded is in fact crucial.
Yes, but that occurs easily, as we need only the brain emulation. The
problem is that we get too much aberrant dreams, and thus an inflation
of possibilities. But the math parts shows that self-reference put the
eaxct constraints required to have a measure on the consistent
continuations, even a quantum one.
The question is then whether this 4 dimensional manifold with a
local Lorentzian metric exists in arithmetic?
It does not have to exist in arithmetic, it needs to be recoverable
from the FPI in arithmetic.
It might exist in arithmetic, and not have the right measure. it might
also not exist in arithmetic, but recoverable from the FPI. or both
case can be true: it exists in arithmetic, and is recoverable from the
FPI. In that case the measure would be computable, and I doubt this is
possible, but fundamentally, it is an open problem. of course,
approximation of it exists in arithmetic. Arithmetic contains all
simulations of all physical phenomena, with 0, 1, 2, 3, 4, ...
100^100, ... decimals exact.
If not, there is no possibility for a time variable in arithmetic
per se, and consequently nothing can 'emerge' from arithmetic, since
emergence is a temporal concept.
We need only the "dital time" to get the digital brain emulation, to
get the arithmetical mindscape. If a physical time emerges or not
remains to be seen. Note that S4Grz1 and X1* logic already brought a
subjective time.
Note that it is important to distinguish between structures that can
be described mathematically and the structure of arithmetic or
mathematics themselves.
Yes. Quite important. Even after the reversal, although physics is
made purely arithmetical, it is only through machine's psychology and
theology that this happens, and the science physics are explained to
be different from the mathematical science. For example mathematical
(arithmetical) existence is some thing like ExP(x), but physical
existence is [2]<2>Ex [2]<2>P(x). Physics remains untouched by comp.,
except it is put on logico-arithmetical grounds. What change is
physicalism in metaphysics. It becomes testable, and false if comp is
true.
Bruno
Bruce
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