The answer is (1), except that that it's not the algorithm for
generating the laws of physics rather simply you, me, Bruno or whatever
other conscious entity at some particular state where they have some
conscious experience. Each different conscious experience is defined by
the action of some operator on a set of states. This defines a different
element for each different conscious experience.
The laws of physics are effective meta laws that describe the structure
of the multiverse. The laws of physics allow one to predict the
probability to experience certain experimental outcomes and this must
therefore already include any effects due to us having multiple copies
in various sectors of some Platonic multiverse.
Bruno has made some progress in deriving the laws of physics from such
ideas, but I'm not convinced at this moment that his approach is indeed
the correct path.
I've been thinking about a different approach, here one starts with
defining an observer moment as a fuzzy object defined by a mapping from
set of inputs to a set of outputs. The fuzzyness comes from the fact
that both sets have more than one element, so one cannot nail down
exactly what is observed, it has a finite width. On the other hand, the
range is not infinite, therefore the mapping is not clearly defined. The
larger you make the range of the mapping, the better defined the mapping
becomes but then the fuzzyness of what is observed increases.
Given any arbitrary observer moment defined by such an operator O, one
can construct a generator H such that:
exp(-i H t) = O E
where H acts on a larger space than O and then the exponentiation
results in the tensor product of O and another operator E that acts on
the extraneous degrees of freedom. The question is if there exists an H
that can be specified with just a few bits of information for some
generic O that needs to be specified using trillions of gigabytes of
information.
Saibal
On 26-08-2015 09:21, Peter Sas wrote:
Hi guys and girls,
I'm sure this question has already come up many times before, but it's
an important one, so I guess it can't do any harm to go over it again.
If the universe is thoroughly computational, what are the computations
'running' on? What I especially like to know is what options are
discussed in digital physics. So far I have encountered only the
following possibilities:
(1) Mathematical platonism: all natural numbers, and all mappings
between them (i.e. all algorithms), simply exist in 'Plato's heaven',
including those algorithms that compute our universe. The simple
non-spatiotemporal existence of those algorithms is enough to
'instantiate' a spatiotemporal world. This type of solution can be
found in Tipler, Tegmark and our own Bruno Marchal. Major problem: the
hard problem of consciousness.
(2) Simulation by an advanced civilization: Our universe is simulated
on a physical computer build by a superior intelligence. Nick Bolstrom
has explored this option and found it quite probable. I don't know
about that, but as a general approach to digital physics it fails. If
we want to understand the physical universe in terms of computation
then it is circular to postulate a physical hardware on which the
computations are running.
(3) Or perhaps it is not circular? This third option sees the physical
universe itself as a (quantum) computer (or cellular automaton)
computing its own future. Thus its present state is the input and the
temporally next state is the output. Isn't this how David Deutsch
approaches it? I am not very clear on this option. The major problem
seems to be that you have to presuppose an initial state of the
universe that itself is not the result of computation, just to avoid
an infinite regress. Or you accept the regress and say the universe
exists eternally (but this is problematic in light of the big bang).
But then you still have to explain why the universe exists eternally.
And then the explanation must still fall outside the computations
going on in the universe...
(4) The computations that yield our universe run on a platform that
exists somewhere else, in another dimension that is principally
inaccessible to us. Ed Fredkin has embraced this 'solution' and calls
this other dimension simply "the Other" which has a theological ring
to it. I don't like this option, but it seems to be the most
straightforward one.
Any thoughts or corrections? Are there some options I haven't
discussed.
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