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This is a blog on why we believe and do what we do, why we pretend otherwise, how we might do better, and what our descendants might do, if they don't all die.
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Back in 2008 Eliezer Yudkowsky blogged here with me, and over several months we debated his concept of “AI foom.” In 2011 we debated the subject in person. Yudkowsky’s research institute has now put those blog posts and a transcript of that debate together in a free book: The Hanson-Yudkowsky AI-Foom Debate.
Added 6Sept: Bryan Caplan weighs in.
Debate Is Now Book
"Doesn't that contradict your earlier claim:"
Well, a process that changes infinitely fast is a bit like an infinite density in time...
"I think what you're saying is that physical continuity (nonquantization of time or space) implies that infinitisimal time spans exist."
Yes, but even if infinitesimal time spans exist that does not have to mean any physical process works in infinitesimal time steps.
"I think assuming continuity implies actual infinitesimal time spans create Zeno's paradox"
Or processes just take an infinite number of infinitesimal steps at a time.
This reminds me of an Isaac Asimov short story where people have discovered how to travel to alternative universes. They reckon there are an infinite number of them so people start claiming alternative Earths for themselves and they expect to never encounter an alternative humanity. Than one day they do because the alternative Earths with humans on them are a fraction of all the worlds: the probability of meeting them is actually finite. Perhaps nature solves Zeno's paradox in a similar way.
you're definitely not going to get infinitely many worlds without allowing for a type of infinity within every world.
Doesn't that contradict your earlier claim:
"It depends on whether you believe states can change over infinitesimal timespans."
I think what you're saying is that physical continuity (nonquantization of time or space) implies that infinitisimal time spans exist. (I think assuming continuity implies actual infinitesimal time spans create Zeno's paradox - http://tinyurl.com/b9kn4tb )