Reflections on Rat Fest ’25

See here. Lucas had asked:

Can you say more about why we need correspondence to make sense of the concept of self-similarity? I don't see why. And it seems to me that self-similarity is all we need to make sense of the universality of computation.

My response below. For others reading this, Erik has also since started a dedicated discussion on the topic of correspondence: https://veritula.com/discussions/is-correspondence-true-in-cr

The FoR glossary entry on self-similarity from chapter 4 reads:

self-similarity Some parts of physical reality (such as symbols, pictures or human thoughts) resemble other parts. The resemblance may be concrete, as when the images in a planetarium resemble the night sky; more importantly, it may be abstract, as when a statement in quantum theory printed in a book correctly explains an aspect of the structure of the multiverse.

The way I read that, it means the images in the planetarium correspond to the night sky. Otherwise we wouldn’t consider them similar.

From chapter 6, on the universality of computation and how “various parts of reality can resemble one another”:

The set of all behaviours and responses of that one object exactly mirrors the set of all behaviours and responses of all other physically possible objects and processes.

That means there is one-to-one correspondence between the behaviors and responses of the first object and those of all the other objects. This is basically another way to describe the self-similarity property of the universe.

From chapter 10, in the context of mathematics (italics mine):

… the physical behaviour of the symbols corresponds to the behaviour of the abstractions they denote.

(The same is true of the physical parts of a Turing machine harnessing the self-similarity property of the universe to correspond to other physical objects.)

From chapter 14, in the context of the creation of scientific knowledge (which, AFAIK, DD views as increasing correspondence):

The creation of useful knowledge by science … must be understood as the emergence of the self-similarity that is mandated by a principle of physics, the Turing principle.

It’s been ages since I read FoR so I’m relying on word searches in the ebook but it’s full of these links between self-similarity and correspondence.