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Re: The limit of all computations
by Stephen P. King
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On 5/20/2012 1:03 PM, Quentin Anciaux wrote:
Dear Quentin,
OK, but what exactly is it that operates the transition from one state to the next? What is the connecting function(s)? This is what theories of time try to explain.
Sure, it is a form of invariant or fixed point on a collection of transformations. But I invite you to look into exactly what is known about how these invariants exist and what are their requirements. For example, in the Brouwer fixed point theorem there is the requirement that there exist a closed, convex and compact set of points, a function transforming them and a means to evaluate the functions. If the conditions are met then the theorem predicts that a function f(x)=x exists.
When we say that "physical world is the thing that is stable in the majority of computations that compute your current conscious moment", we are effectively saying that the physical world is much like that x such that f(x) = x. The computations are the functions transforming the states. They are actions, not entities. Additionally we have to account for all possible versions of "your current conscious moment" since whoever "your" is referring to is not a set of only one member, thus we have to have an explanation that applies to all possible observers (aka entities with the capacity of having a "current conscious moment").
What purpose would the "primitive physical universe" serve? Here I agree 100% with Bruno. His result proves that there cannot be "a primitive physical universe". My argument with Bruno is over the ontological status of numbers. He claims that they are ontologically primitive and I claim that they cannot be.
We can define "objective" to be that which is invariant with respect to transformations on the collection of content of all possible conscious entities can observe *and* communicate to each other. In other words, the "objective universe" is what which we can all agree upon as existing. We do not need to think that it is somehow "independent of us". It is sufficient to say that it is dependent on all of us and not dependent on any one of us. This way of thinking applies to computational universality as well: a computation is universal iff can be run on any functionally equivalent physical system such that it does not depend on any one physical configuration.
And what defines the computations? Do definitions just appear by fiat?
How many paths exist in the continuum that you are considering here? Each path would be equivalent to a computation in your thinking, no? Are the paths capable of being smoothly transformed into each other? If so, then the continuum has a certain topological property known as "simply connected". There are situations that involve computations that show that this topological condition cannot be satisfied. The concurrency problem is one of these situations.
I agree, but this does not make time any less "real".
I am OK with circularity if and only if one is consistent with the set theory and logic that is required. This is a well studied area in mathematics...
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2012/5/20 Stephen P. King <stephenk1@...>
On 5/20/2012 6:06 AM, Quentin Anciaux wrote:Hi Quentin,
In Bruno's theory, the physical world is not computed by an algorithm, the physical world is the limit of all computations going throught your current state... what is computable is your current state, an infinity of computations goes through it. So I don't see the problem here, the UD is not an algorithm which computes the physical world 4D or whatever.
Quentin
Maybe you can answer some questions. These might be badly composed so feel free to "fix" them. ;-)
1) If my "current state" is equivalent to a 4-manifold and the "next" state is also, what is connecting the two? Markov's proof tells us that it is not a algorithm. So what is it?
Any computations going through your current state has a next state. You don't have *a* next state but many next state, any state is always computed by an infinity of computation.
Dear Quentin,
OK, but what exactly is it that operates the transition from one state to the next? What is the connecting function(s)? This is what theories of time try to explain.
2) Is there another equivalent set of words for "the physical world is the limit of all computations going through your current state"?
The physical world is the thing that is stable in the majority of computations that compute your current conscious moment, if computationalism is true (if consciousness is turing emulable).
Sure, it is a form of invariant or fixed point on a collection of transformations. But I invite you to look into exactly what is known about how these invariants exist and what are their requirements. For example, in the Brouwer fixed point theorem there is the requirement that there exist a closed, convex and compact set of points, a function transforming them and a means to evaluate the functions. If the conditions are met then the theorem predicts that a function f(x)=x exists.
When we say that "physical world is the thing that is stable in the majority of computations that compute your current conscious moment", we are effectively saying that the physical world is much like that x such that f(x) = x. The computations are the functions transforming the states. They are actions, not entities. Additionally we have to account for all possible versions of "your current conscious moment" since whoever "your" is referring to is not a set of only one member, thus we have to have an explanation that applies to all possible observers (aka entities with the capacity of having a "current conscious moment").
3) Is there at least one physical system running the computations?
No, if the UDA is correct... well technically there still could be a primitive physical universe, but you could not use it to correctly predict your next moment, nor what you see, and you would not be able to know what it is (because all of what is accessible to you is in the computations that support you, still if computationalism is true).
What purpose would the "primitive physical universe" serve? Here I agree 100% with Bruno. His result proves that there cannot be "a primitive physical universe". My argument with Bruno is over the ontological status of numbers. He claims that they are ontologically primitive and I claim that they cannot be.
Is the "physical universe" a purely subjective appearance/experience for each conscious entity?
It is subjective in the sense that it can be only known subjectively. It is objective as the thing that each conscious entity can observe.
We can define "objective" to be that which is invariant with respect to transformations on the collection of content of all possible conscious entities can observe *and* communicate to each other. In other words, the "objective universe" is what which we can all agree upon as existing. We do not need to think that it is somehow "independent of us". It is sufficient to say that it is dependent on all of us and not dependent on any one of us. This way of thinking applies to computational universality as well: a computation is universal iff can be run on any functionally equivalent physical system such that it does not depend on any one physical configuration.
What is it that shifts from one state to the next?
The computations.
And what defines the computations? Do definitions just appear by fiat?
4) What is the cardinality of "all computations"?
N0 ? and if we take that to contains oracle program, even the continuum.
How many paths exist in the continuum that you are considering here? Each path would be equivalent to a computation in your thinking, no? Are the paths capable of being smoothly transformed into each other? If so, then the continuum has a certain topological property known as "simply connected". There are situations that involve computations that show that this topological condition cannot be satisfied. The concurrency problem is one of these situations.
5) Is the totality of what exists static and timeless and are all of the subsets of that totality static and timeless as well?
Time is an internal thing of existence, time is related to an observer.
I agree, but this does not make time any less "real".
We are OK with a circular reasoning? Succesion of states => succession of events => succession of states => ...
6) Does all "succession of events" emerge only from the well ordering of Natural numbers?
Succession of events emerge from the succession of states, of what is needed to compute you, it does not have to be related to the ordering of natural numbers.
Quentin
I am OK with circularity if and only if one is consistent with the set theory and logic that is required. This is a well studied area in mathematics...
-- Onward! Stephen "Nature, to be commanded, must be obeyed." ~ Francis Bacon--
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