There is another counter argument, not just saying we're not typical observers, but there's a counter argument that says I am more likely to be in one of the two scenarios. The self-clampling assumption makes it seem as if you could have been born into any universe at all. That cancels out the probability shift that the Doomsday argument says we should make in favor of there being fewer.
Human civilization is only a few thousand years old (depending on how we count). So if civilization will ultimately last for millions of years, it could be considered surprising that we’ve found ourselves so early in history. Should we therefore predict that human civilization will probably disappear within a few thousand years? This “Doomsday Argument” shares a family resemblance to ideas used by many professional cosmologists to judge whether a model of the universe is natural or not. Philosopher Nick Bostrom is the world’s expert on these kinds of anthropic arguments. We talk through them, leading to the biggest doozy of them all: the idea that our perceived reality might be a computer simulation being run by enormously more powerful beings.
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Nick Bostrom received his Ph.D. in philosophy from the London School of Economics. He also has bachelor’s degrees in philosophy, mathematics, logic, and artificial intelligence from the University of Gothenburg, an M.A. in philosophy and physics from the University of Stockholm, and an M.Sc. in computational neuroscience from King’s College London. He is currently a Professor of Applied Ethics at the University of Oxford, Director of the Oxford Future of Humanity Institute, and Director of the Oxford Martin Programme on the Impacts of Future Technology. He is the author of Anthropic Bias: Selection Effects in Science and Philosophy and Superintelligence: Paths, Dangers, Strategies.
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