Question

[Kairos]

Gödel's first incompleteness theorem first appeared as "Theorem VI" in Gödel's 1931 paper "On Formally Undecidable Propositions of Principia Mathematica and Related Systems I". The hypotheses of the theorem were improved shortly thereafter by J. Barkley Rosser (1936) using Rosser's trick. The resulting theorem (incorporating Rosser's improvement) may be paraphrased in English as follows, where "formal system" includes the assumption that the system is effectively generated.

First Incompleteness Theorem: "Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F." (Raatikainen 2015)

The unprovable statement GF referred to by the theorem is often referred to as "the Gödel sentence" for the system F. The proof constructs a particular Gödel sentence for the system F, but there are infinitely many statements in the language of the system that share the same properties, such as the conjunction of the Gödel sentence and any logically valid sentence.

Each effectively generated system has its own Gödel sentence. It is possible to define a larger system F’ that contains the whole of F plus GF as an additional axiom. This will not result in a complete system, because Gödel's theorem will also apply to F’, and thus F’ also cannot be complete. In this case, GF is indeed a theorem in F’, because it is an axiom. Because GF states only that it is not provable in F, no contradiction is presented by its provability within F’. However, because the incompleteness theorem applies to F’, there will be a new Gödel statement GF′ for F’, showing that F’ is also incomplete. GF′ will differ from GF in that GF′ will refer to F’, rather than F.

Your universe simulation, theoretically speaking, is a formal system like F. Because you are simulating a universe and that therefore includes rules for things like arithmetic and logic, it is possible to make statements that reach outside of your simulation, referring to the real universe.

This problem happens because a simulation by it's very nature is a formulated system of logical statements and rules. Once you create a system, you open yourself up to this problem. All simulations of sufficient complexity can infer at least some of the computational rules of the real universe from inside the simulation. The real universe just is. It's not a system of rules that excludes other rules. Do you kind of grok what I am telling you? It's alright if you don't. LOTS of people don't get this shit, especially physicists who don't listen to anybody else and refuse to disabuse themselves of the belief that they are the fundamental science.

 

[samzeman]

It's possible you guys aren't considering procedural generation. We are never going to reach a galaxy outside of our own, most likely, and so we can only see them up to a certain resolution. It's possible they only exist up to that resolution. So it's really only systems we can see in detail that have to be fleshed out, and any new ones we look at can be generated on the spot algorithmically. It's a combination of rendering only what we are looking at and only generating things once we look at them for the first time. Like Minecraft. Though I do expect that citing Minecraft might detract from the legitimacy of my point

I'm just saying, there are ways we save computing power that can apply to this universe too. They don't have to actually generate and simulate 6 quintillion or however many planets, just like Minecraft doesn't generate 32 million^2 blocks the second you make a world, or it would take like, a few hours to generate one and the lag from simulating all of that would make it unplayable.

The universe might be a little exponential but it's also exponentially empty and low-res as you go further out. Light diffuses over distance, so there is a maximum visual distance, and our sensors can only get so sensitive, which would be the resolution limit of our vision as a species. We can barely move any distance on an intergalactic scale, so it's unlikely we'll get close to any of the background setpeices. It could also be like a skybox, where it's just footage of a bunch of events that barely affect us and that we cannot affect.

 

[Scarecrow]

Question for you. Why is it that when people do physical time travel they do not materialize in outer space. After all, the earth is moving.

Because one parallel jumps out of the normal time and physics law and enter into a like dimensional...?

 

[dimension-1hacker]

Your universe simulation, theoretically speaking, is a formal system like F. Because you are simulating a universe and that therefore includes rules for things like arithmetic and logic, it is possible to make statements that reach outside of your simulation, referring to the real universe.

This problem happens because a simulation by it's very nature is a formulated system of logical statements and rules. Once you create a system, you open yourself up to this problem. All simulations of sufficient complexity can infer at least some of the computational rules of the real universe from inside the simulation. The real universe just is. It's not a system of rules that excludes other rules. Do you kind of grok what I am telling you? It's alright if you don't. LOTS of people don't get this shit, especially physicists who don't listen to anybody else and refuse to disabuse themselves of the belief that they are the fundamental science.

Your universe simulation, theoretically speaking, is a formal system like F. Because you are simulating a universe and that therefore includes rules for things like arithmetic and logic, it is possible to make statements that reach outside of your simulation, referring to the real universe.

This problem happens because a simulation by it's very nature is a formulated system of logical statements and rules. Once you create a system, you open yourself up to this problem. All simulations of sufficient complexity can infer at least some of the computational rules of the real universe from inside the simulation. The real universe just is. It's not a system of rules that excludes other rules. Do you kind of grok what I am telling you? It's alright if you don't. LOTS of people don't get this shit, especially physicists who don't listen to anybody else and refuse to disabuse themselves of the belief that they are the fundamental science.

the sestem is derived from an outside sestem and so on therefor the same logic can be applied to a non simulated universe? does it depend on what is being simulated because logic is not based off matters shape or size, but something else inherent in matters properties?
a sestem can prove itself but doesn't understand itself is nothing more then a reactent to an input therefor not inherentle a conscious or software based sestem, just hardware? binare code be definition are two numbers be themselves therefore don't produce understanding of themselves.

 

[Angelface239]

Question for you. Why is it that when people do physical time travel they do not materialize in outer space. After all, the earth is moving.

Actually i dont know why.

 

[Snake Plissken]

I believe John Titor had the answer to that question..

 

[Angelface239]

I believe John Titor had the answer to that question..

Okay.