On 2/2/2013 6:19 AM, Telmo Menezes wrote:
On Mon, Jan 28, 2013 at 2:13 AM, Stephen P. King
<[email protected] <mailto:[email protected]>> wrote:
On 1/27/2013 6:54 PM, Telmo Menezes wrote:
On Mon, Jan 28, 2013 at 12:40 AM, Stephen P. King
<[email protected] <mailto:[email protected]>> wrote:
On 1/27/2013 6:07 PM, Telmo Menezes wrote:
Dear Bruno and Stephen,
On Sun, Jan 27, 2013 at 6:27 PM, Stephen P. King
<[email protected] <mailto:[email protected]>> wrote:
On 1/27/2013 7:19 AM, Bruno Marchal wrote:
The big bang remains awkward with computationalism.
It suggest a long and deep computations is going
through our state, but comp suggest that the big
bang is not the beginning.
Dear Bruno,
I think that comp plus some finite limit on
resources = Big Bang per observer.
Couldn't the Big Bang just be the simplest possible state?
Hi Telmo,
Yes, if I can add "...that a collection of observers can
agree upon" but that this simplest possible state is uniquely
in the past for all observers (that can communicate with each
other) should not be just postulated to be the case. It
demands an explanation.
It's uniquely in the past for all complex observers
Hi Telmo,
I would partition up "all possible observers" into mutually
communicating sets. Not all observers can communicate with each
other and it is mutual communication that, I believe, contains the
complexity of one's universe.
That makes sense to me.
Hi Telmo,
Can you see that this requirement even works if there are an
infinite number of 'observers'?
Basically my reasoning follows Wheeler's /It from Bit/ idea.
because:
- It cannot contain a complex observer
How do we know this? We are, after all, speculating about what
we can only infer about given what we observe now.
Isn't it just a tautology? I don't know how to justify it any further.
It's like saying that an empty glass does not contain water.
Yes, it is a bit tautological but non-negligible because it sets up
the contra-factual basis for what is. That *is* is the complement of
what *is not*. Since the number of things that 'didn't happen' is,
generally infinite, we can see how events are somehow sieved or selected
from many. This leads to the idea that an observation is a selective
action, a map from many to one. Classical physics seems to claim that
only one event follows from a previous single event, but this kind of
reasoning fails when we try to make sense of QM. I am working out a
logical strategy...
- It is so simple that it is coherent with any history
Simplicity alone does not induce consistency, AFAIK...
I'm thinking in the following terms: imagine a CA which has an initial
state where a single cell is on. For any super-complex state that you
find down the line, the initial simple step is always a consistent
predecessor.
I generally do not like CA models as they presuppose a fixed set of
possible outcomes or rule - which then requires an explanation as to how
that rule is selected, and it assumes an absolute time or, equivalently,
global synchrony of the transition events. I start with a pair of
physical events and their duals (propositional algebras) and work out
the mappings between them as Vaughan Pratt describes in his /Rational
Mechanics and Natural Mathematics/ paper. One can then set up chains of
such and more complex lattices to obtain space-time toy models.
That doesn't mean it's the beginning, just that it's a likely
predecessor to any other state.
> The word "predecessor' worries me, it assumes some way to
determine causality even when measurements are impossible. Sure,
we can just stipulate monotonicity of states, but what
> would be the gain?
I mean predecessor in the sense that there are plausible
sequences of transformations that it's at the root of. These
transformations include world branching, of course.
I am playing around with the possibility that monotonicity
should not be assumed. After all, observables in QM are complex
valued and the real numbers that QM predicts (as probabilities of
outcomes) only obtain when a basis is chosen and a squaring
operation is performed. Basically, that *is* is not something that
has any particular ordering to it. Here I am going against the
arguments of many people, including Julian Barbour.
Ok, this also makes sense to me. But can you accept that there is
quantifiable similarity between states?
Sure, there must be to have any thing like continuity and
transitions of event to event and state to state. My point is that we
should never assume a measure of similarity that cannot be physically
implemented. It one's idea of a measure requires an infinite task to be
performed, one should have a pretty good reason why it is being
promoted! If it is impossible to measure some quantity, then it cannot
be taken to be knowable. We can cheat a bit and use equivalence classes
and so form to reason abstractly about things, but all of the results
are mere concepts and should not be promoted to being 'real' in the same
sense that a physical object is 'real'.
In this case we can still build a state graph from which we can
extract timelines without requiring ordering.
Sure, but there must be some relation between events that is
equivalent to a greater than or equal to (or less than of equal to, of
the logical equivalent such as A implies B, or A necessitates B, ...)
for the state graph to be relatable to timelines unambiguously.
The more complex a state is, the smaller the number of
states that it is likely to be a predecessor of.
Sure, what measure of complexity do you like? There are
many and if we allow physical laws to vary, infinitely so...
I like the Blum and Kolmogorov measures, but they are still
weak...
I had Kolmogorv in mind and it's the best I can offer. I agree,
it's still week and that's a bummer.
Maybe we should drop the desiderata of a measure and focus on
the locality of observers and its requirements.
I don't think I understand what you mean here.
Why start off with statistics? Why not start of with a simple
relation between a pair of objects and then work out a combinatorial
model. We can work out the statistics after we have figured out a model
of the system.
--
Onward!
Stephen
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