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The more likely our descendants are to be rich, long-lasting, and interested in simulating us, the more simulations of people like us we should expect there to be on average, relative to real people like us. And so the more we expect our descendants to be rich like this, the more we should expect that we are in fact living in a simulation [Bostom 2001].
I think that makes good sense. I think it's commonly accepted that our species will either never achieve a posthuman stage or posthumans will be very technologically advanced. If posthumans have the technology, resources, and desire to simulate us, they will.
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If we now suppose that human civilization lasts for ten thousand generations after the C-threshold, and has an average population of ten billion, there will be 1.0 x 1014 MD-streams, compared with 2 x 1012 original D-streams. With fifty simulated streams for every real stream, you have a one in fifty chance of actually being alive in the year 2002. On more optimistic scenarios, your predicament is even more precarious. If humankind has a long history – one million generations exist after the C-threshold, say, with constant or improving technology – and a larger average population during this period – a hundred billion, say – then we can expect a total of around 1.0 x 1017 MD-streams to occur, which would reduce your chances of being alive in 2002 to around one in fifty thousand! In this case, even if only one in a thousand people ever take a virtual reality trip back to 2002, the chances that you are really living in 2002 are still only one in fifty.
Basically, the more likely that posthumans are to run simulations more frequently, the higher the chance that we now live in a simulation.