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Simulated Universe, suffers same problem as God.

Consider this:

Assuming that we are in a simulation of the ancestry of beings in another Universe, the question of the finite evolution of the Universe that those beings inhabits still subjects them to what we know about how the Universe is constructed no?

Would they not also be constrained by the forces of nature to design and build their simulation (us) and therefor aren't they also embedded and constrained as well.

Now, let's assume that they are a top level lifeform, meaning they themselves were NOT created as part of another Universes creation event...can we explore (either rigorously or by logic) whether or not this assertion is probable??

Is it possible that they are a top level being and in fact what is the likelihood of top level beings being the creators of our Universe.

I think if we accept the previous hypothesis, that all beings the simulated and the simulators are constrained by the limits of a common physics then we must conclude that if the variation of universal parameters that is supposed for universes in a multiverse is true that there is an infinite number of universal configurations. Not just ones conducive to the running of our "simulation" if that is what we are, or our top level Universe (if that is what we are).

If there is indeed an infinity of Universes...then the subset of Universes which have the conditions necessary to emerge top level beings that would then create Universes is itself infinite but still a smaller Infinity than the whole of the multiverse. If there is an infinite number of multiverses then the percentage of them that are top level Universes is itself *also infinite* leaving it as a certainty that they are NOT simulations.

The question is then, what is the probability that we are a simulation versus a top level Universe given the above.

Again, since the number of Universes with top level beings is infinite and the probability of their creating simulations is finite...then the probability that we are simulation is lower than if we are a top level universe (simply because the number of simulations must necessarily be a subset of the number of top level Universes *even if* that number is infinite).

Note it is no longer important to inquisite further, the answer is in the last line above:

"the probability that we are simulation is lower than if we are a top level universe"

How much lower? Well, since we already assumed that the number of Universes with beings that could even create a simulation is an infinite subset of all possible universes) and we also accepted that the percentage of these that actually created simulations of their ancestry are also an infinite subset...then across all the multiverse...the probability than any selected Universe is spawned via simulation dwindles to zero (since it always remains an infinite subset of Universes which themselves are an infinite subset of all possible Universes...those with and without creative beings).

So by a limit argument I conclude that we are likely NOT a simulation (I used a similar limit argument to conclude that we are also likely not the result of any God a few years ago) it would seem to be true in both cases from this intuitive argument comparing relative infinities no need to go into more rigorous analysis...I could be wrong but I've yet encountered a valid counter argument. Thoughts?


Matt Mahoney said…
First, "probability" is a mathematical model of belief, not of reality. It has a defined numeric value only when you can perform a large number of independent trials and count the outcomes. I assume that you cannot sample a large number of universes and test whether they are simulations. So really, you are talking about what you prefer to believe.

Second, you cannot compare infinite sets to deduce probabilities. What is the probability that an integer is a perfect square? 1, right, because the sets are the same size?

Third, you can't assume that we would only simulate our ancestors. We simulate all kinds of other things.

Fourth, you can't assume anything about the laws of physics in the universe simulating us. Space, time, and matter might be meaningless abstract concepts in their world, just like we simulate all kinds of abstract concepts.
Kearney said…
I can't wrap my mind around an infinite universe, although I try!
David said…
" I assume that you cannot sample a large number of universes and test whether they are simulations. So really, you are talking about what you prefer to believe."

-- Not when we are talking about a model which encapsulates all variations of what our reality could be like. In that case the model and the reality are one in the same...we have yet to select which sliver of the model fits our reality but that doesn't invalidate the use of mathematics to span that space. This is a silly is completely devoid of the admittance that we don't know which universe from the models infinite set is ours but guarantee that one of them is (since it spans all possible variations of all attributes that such a universe must possess).

The second is false, Cantor showed you can indeed compare probabilities between infinite sets. We've been doing so and getting finite results for over a century doing so to solve entire classes of problems which contain infinite values to agree with empirical results. Feynman used these methods in a novel way in quantum electrodynamics to solve a series of problems that plagued the Science called "renormalization". Using infinite values in relations is de regeur these days so I don't know where you are getting this view from.

The third point is irrelevant. Weather or not I assume we are only simulating or ancestors is independent of the outcome of if I did or not when comparing how probable it is that doing so would trigger the creation of other sentient entities.

Point four misses the entire point of multidimensional mathematics, all possible dimensional and energy and matter configurations are spanned by an multidimensional model. The level of abstraction is not set it is infinite (that's why mathematics makes such a good model for it) and thus allows it to be guaranteed to contain what ever configuration of spaces and attributes necessary to simulate any other type of universe (that's why it's called a multiverse in the first place). The abstract nature of many of these spaces and times to us is not relevant to our ability to use math a) to span them in their infinite multiplicity and b) compare the results of creation over the events of finite agents created within them.

Again, the infinites run away from one another and converge in a finite way.

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