I think what avturchin is getting at is that when you say “there is a 1⁄3 chance your memory is false and a 1⁄3 chance you are the original”, you’re implicitly conditioning only on “being one of the N total clones”, ignoring the extra information “do you remember the last split” which provides a lot of useful information. That is, if each clone fully conditioned on the information available to them, you’d get 0-.5-.5 as subjective probabilities due to your step 2.
If that’s not what you’re going for, it seems like maybe the probability you’re calculating is “probability that, given you’re randomly (uniformly) assigned to be one of the N people, you’re the original”. But then that’s obviously 1/N regardless of memory shenanigans.
If you think this is not what you’re saying, then I’m confused.
The idea of reducing hypotheses to bitstrings (ie, programs to be run on a universal Turing machine) actually helped me a lot in understanding something about science that hindisght had previously cheapened for me. Looking back on the founding of quantum mechanics, it’s easy to say “right, they should have abandoned their idea of particles existing as point objects with definite position and adopted the concept and language of probability distributions, rather than assuming a particle really exists and is just ‘hidden’ by the wavefunction.” But the scientists of the day had a programming language in their heads where “particle” was a basic object and probability was something complicated that you had to build up—the optimization process of science had arrived at a local maximum in the landscape of possible languages to describe the world.
I realize this is a pretty simple insight, but I’m glad the article gave me a way to better understand this.