On 5/20/2012 8:08 PM, meekerdb wrote:
On 5/20/2012 4:13 PM, Stephen P. King wrote:
On 5/20/2012 4:39 PM, meekerdb wrote:
On 5/20/2012 1:31 PM, Stephen P. King wrote:
My point is that for there to exist an a priori given string of
numbers that is equivalent our universe there must exist a
computation of the homomorphies between all possible 4-manifolds.
Because otherwise the amazing precision of the mathematical
models based on the assumption of, among other things, that physical
systems exist in space-time that is equivalent to a 4-manifold. The
mathematical reasoning involved is much like a hugeJenga tower
<http://en.wikipedia.org/wiki/Jenga#Tallest_tower>; pull the wrong
piece out and it collapses.
Markov theorem tells us that no such homomorphy exists,
No, it tells there is no algorithm for deciding such homomorphy
*that works for all possible 4-manifolds*. If our universe-now has
a particular topology and our universe-next has a particular
topology, there in nothing in Markov's theorem that says that an
algorithm can't determine that. It just says that same algorithm
can't work for *every pair*.
I agree with your point that Markov's theorem does not disallow
the existence of some particular algorithm that can compute the
relation between some particular pair of 4-manifolds. Please
understand that this moves us out of considering universal algorithms
and into specific algorithms. This difference is very important. It
is the difference between the class of universal algorithms and a
particular algorithm that is the computation of some particular
function. The non-existence of the general algorithm implies the
non-existence of an a priori structure of relations between the
I am making an ontological argument against the idea that there
exists an a priori given structure that *is* the computation of the
Universe. This is my argument against Platonism.
therefore our universe cannot be considered to be the result of a
computation in the Turing universal sense.
Sure it can. Even if your interpretation of Markov's theorem were
correct our universe could, for example, always have the same topology,
No, it cannot. If there does not exist a general algorithm that
can compute the homomorphy relations between all 4-manifolds then
what is the result of such cannot exit either.
The result is an exhaustive classification of compact 4-mainifolds.
The absence of such a classification neither prevents nor entails the
existence of the manifolds.
But you fail to see that without the means to define the manifolds,
there is nothing to distinguish a manifold from a fruitloop from a pink
unicorn from a ..... Absent the means to distinguish properties there is
no such thing as definite properties.
We cannot talk coherently within computational methods about "a
topology" when such cannot be specified in advance. Algorithms are
recursively enumerable functions. That means that you must specify
their code in advance, otherwise your are not really talking about
computations; you are talking about some imaginary things created by
imaginary entities in imaginary places that do imaginary acts; hence
my previous references to Pink Unicorns.
Let me put this in other words. If you cannot build the equipment
needed to mix, bake and decorate the cake then you cannot eat it.
You can have the equipment mix, bake, decorate and eat a cake without
having the equipment to mix, bake, decorate, and eat all possible cakes.
My analogy failed to demonstrate its intended idea, it seems. Let me
rephrase. Do cakes exist as cakes if it is impossible to mix, bake and
decorate them? Do they just magically appear out of nothing? No. Neither
does meaningfulness and the definiteness of properties.
We cannot have a coherent ontological theory that assumes something
that can only exist as the result of some process and that same
ontological theory prohibits the process from occurring.
or it could evolve only through topologies that were computable from
one another? Where does it say our universe must have all possible
The alternative is to consider that the computation of the
homomorphies is an ongoing process, not one that is "already existing
in Platonia as a string of numbers" or anything equivalent. I would
even say that time_is_ the computation of the homomorphies. Time
exists because everything cannot happen simultaneously.
We must say that the universe has all possible topologies unless
we can specify reasons why it does not.
I don't fee any compulsion to say that. In any case, this universe
does not have all possible topologies.
Why do not see that as surprising? We experience one particular
universe, having one particular set of properties. How does this happen?
What picked it out of the hat?
If you want to hypothesize a multiverse that includes universes with
all possible topologies then there will be no *single* algorithm that
can classify all of them. But this is just the same as there is no
algorithm which can tell you which of the UD programs will halt.
Indeed! It is exactly the same! The point is that since there is
nothing that can computationally "pick the winner out of the hat" then
how is it that we experience precisely that winner? Maybe the selection
process is not a computation in the Platonic sense at all. Maybe it is a
real computation running on all possible physical systems in all
possible universes for all time.
I am trying to get you to see the difference between structures
that are assumed to exist by fiat and structures that are the result of
ongoing processes. This is debate that has been going on since
Democritus <http://plato.stanford.edu/entries/democritus/> and
Heraclitus <http://plato.stanford.edu/entries/heraclitus/> stepped into
the Academy. Can you guess what ontology I am championing?
That is what goes into defining meaningfulness. When you define that
X is Y, you are also defining all not-X to equal not-Y, no?
No. Unless your simply defining X to be identical with Y, a mere
semantic renaming, then a definition is something like X:=Y|Zx. And
it is not the case that ~X=~Y.
When you start talking about a collection then you have to define
what are its members. Absent the specification or ability to specify
the members of a collection, what can you say of the collection?
This universe is defined ostensively.
Interesting word: Ostensively
"Represented or appearing as such..." It implies a subject to whom
the representations or appearances have meaningful content. Who plays
that role in your thinking?
What is the a priori constraint on the Universe? Why this one and
not some other? Is the limit of all computations not a computation?
How did this happen?
No attempts to even comment on these?
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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