uoahelperg t1_iwfqwj3 wrote
Reply to comment by testsubject_127 in Emergence as the conversion of information: a unifying theory | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences by antichain
I’d also like a dumbed down version.
From what I read it looks like the author is saying that information can change between a subset and a larger set leading to it processing inputs more or less efficiently.
If I understood the logic gate portion correctly it seems as simple as saying 1+1+1+1+1 isn’t quite the same as saying 5 because to do 5+1 you just do two steps and to do 1+1+1+1+1+1 you do a bunch of steps lol, but I am probably missing something.
Ed: also that when you add variability to it, for some things the smaller scale is not as consistent as the larger scale or vice versa, and the idea is that there’s different optimal scales to look at different things to get the most useful information.
Ripheus23 t1_iwg14v3 wrote
Think of the Lévy hierarchy in set theory, or higher-order logic more generally. Arithmetic and proof structures recursed over a first-order base can have surprisingly new characteristics, like you can prove different things in different ways as you go up, e.g. the well-ordering lemma can be used to derive the axiom of choice but not vice versa. Or in one family of intuitionistic logic the choice axiom allows deriving the law of excluded middle.
Subtly different structural inputs with substantially different outputs of content.
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