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 don't believe this should be asserted with the level of certainty you use. His explanation makes good intuitive sense to me, and I don't see why that must be overwhelmingly determined by preexisting understanding.
Then why didn't you realize that the bit about "while preserving their predictions" was an essential part of Deutsch's explanation and therefore include it in your summary of his idea?
If it was hard to see why you should have included that part, then it seems to me that Deutsch's approach doesn't clarify matters.