I'm sure this talk will be of interest, even if most of the ideas that he talks about will be familiar to readers here.
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In this talk David Deutsch discusses "the most important discovery in human history"; how humanity moved beyond a few hundred thousand years of complete ignorance about the universe. Deutsch attempts to be specific about what led to this change - he concludes that it is the insistence that an explanation be 'hard to vary'.
Whilst a 'hard to vary' explanation is functionally the same as a, more commonly known, Occam's Razor explanation (since fewer parameters necessarily make a fit harder to vary) the slightly different emphasis might be a useful pedagogical tool. A 'hard to vary' explanation will perhaps lead more naturally to questions about strong predictions and falsifiability than Occam's razor. It also seems harder to misunderstand. As we know, Occam's razor suffers because of the difference between actual complexity and linguistic complexity, so an explanation like "it's magic" can appear to be simple. Magic might appear simple, but it will never appear 'hard to vary', so students of rationality would have one less pitfall awaiting them.
Deutsch also touches on what constitutes understanding and knowledge and cautions us not to trust predictions that are purely of an extrapolated empirical nature as there is no true understanding contained there.
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If you haven't already read Deutsch's book "The Fabric of Reality" I'd highly recommend that as well.
I agree that there's nothing new to people who have been on Overcoming Bias and Less Wrong for a few years (hence the cautionary statement at the start of the post) but I do think it's important that we don't forget that there are new people arriving all the time.
Not everyone would consider "the conjunction fallacy and how each detail makes your explanation less plausible" a standard point. We shouldn't make this site inaccessible to those people. Credit where it's due - Deutsch does a nice job of presenting this in a way that most people can understand.
I don't think his way of explaining it is any easier for a newcomer. It doesn't make sense unless and until you already have a firm grasp of the basis for Occam's razor. And if you know how to justify Occam's razor, you already understand why adding details penalizes the explanation's probability.
Furthermore, his idea can't be summarized as "good explanations are hard to vary". It's more like, "good explanations are hard to vary while preserving their predictions".
I do appreciate that you added a summary.