This post was completely rewritten on July 17th, 2015, 6:10 AM. Comments before that are not necessarily relevant.
Assume that our minds really do work the way Unification tells us: what we are experiencing is actually the sum total of every possible universe which produces them. Some universes have more 'measure' than others, and that is typically the stable ones; we do not experience chaos. I think this makes a great deal of sense- if our minds really are patterns of information I do not see why a physical world should have a monopoly on it.
Now to prove that we live in a Big World. The logic is simple- why would something finite exist? If we're going to reason that some fundamental law causes everything to exist, I don't see why that law restricts itself to this universe and nothing else. Why would it stop? It is, arguably, simply the nature of things for an infinite multiverse to exist.
I'm pretty terrible at math, so please try to forgive me if this sounds wrong. Take the 'density' of physical universes where you exist- the measure, if you will- and call it j. Then take the measure of universes where you are simulated and call it p. So, the question become is j greater than p? You might be thinking yes, but remember that it doesn't only have to be one simulation per universe. According to our Big World model there is a universe out there in which all processing power (or a significant portion) as been turned into simulations of you.
So we take the amount of minds being simulated per universe and call that x. Then the real question becomes if j > px. What sort of universe is common enough and contains enough minds to overcome j? If you say that approximately 10^60 simulated human minds could fit in it (a reasonable guess for this universe) but that such universes are five trillion times rarer than the universe we live in, than it's clear that our own 'physical' measure is hopelessly lower than our simulated measure.
Should we worry about this? It would seem highly probable that in most universes where I am being simulated I once existed in, or humans did, since the odds of randomly stumbling upon me in Mind Space seem unlikely enough to ignore. Presumably they are either AIs gone wrong or someone trying to grab some of my measure, for whatever reason.
As way of protecting measure, pretty much all of our postsingularity universes would divide up the matter of the universe for each person living, create as many simulations as possible of them from birth, and allow them to go through the Singularity. I expect that my ultimate form is a single me, not knowing if he is simulated or not, with billions of perfect simulations of himself across our universe, all reasoning the same way (he would be told this by the AI, since there isn't any more reason for secrecy). This, I think, would be able to guard my measure against nefarious or bizarre universes in which I am simulated. It cannot just simulate the last few moments of my life because those other universes might try to grab younger versions of me. So if we take j to be safe measure rather than physical measure, and p to be unsafe or alien, it becomes jx > px, which I think is quite reasonable.
I do not think of this as some kind of solipsist nightmare; the whole point of this is to simulate the 'real' you, the one that really existed, and part of your measure is, after all, always interacting in a real universe. I would suggest that by any philosophical standard the simulations could be ignored, with the value of your life being the same as ever.
We have additional evidence for BB, that is idea of eternal fluctuation of vacuum after heat death, which may give us very strong prior. Basically if there is 10 power 100 BBs for each real mind it will override the evidence by non randomness of our environment. (Bostrom wrote about similar logic in Presumptuous philosopher.) What I wanted to say that efforts to disprove BB existence by relying on BB ability to distinguish chaotic and non chaotic environments are themselves looks like circular logic)))
I agree that sapient beings are more probable because they have many more internal states. But it also means that you and I are in the middle of IQ distribution in the universe, that is no superintelligence exists anywhere. This is grim. It is like DA for intelligence and it means that high intelligence post-humans are impossible. It may still allow some kind of mechanical superintelligence, which uses completely different thinking procedures and lack qualia.
Basically, the main meta difference between your and mine positions is that you want to return the world to normal, and I want it to be strange and exploite its strangeness. :))
You long example is in fact about aliens who created DA for themselves. My idea was that you may use mediocracy logic for any reference class, from which you randomly chosen, and you could belong to several such classes simultaneously. But the class of observers who knows about DA, is special class because it will appear in any alien specie, and in any thought experiment. This class include such observers from all possible species and so we may speak about their distribution in the universe. Also such class is smallest and imply soonest Doom in DA. Even Carter who created DA in 1983 knew it, and as he was the only one at the moment in this class, he felt himself in danger.
In your example you also have a subclass of aliens who knows all that, and it will exist not for long. It will be killed by meteorite in several months. )) Its subclass is smaller and its time duration is smaller. But result is the same - extinction.
How? The proportion of chaotic minds to orderly minds will never change. Even if there are infinite BBs in the future, it doesn't alter how likely it is that the 'heat death' model is simply mistaken, and that some infinite source of computing is found for us to use.
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