You need to distinguish between world models—which can include any number of entities no matter how complex or useless—with the predictions made by those models. The predictions are sequences (more correctly, probability distributions over sequences). The models are not.

A world model could, for example, include hypothesized general rules for a universe, together with a specification of 13.7 billion years of history, that there exists a particular observer with specific details of some particular sensory apparatus, and that the sequence is based on the signal from that sensory apparatus. The actual distribution of sequences predicted by this model at some given time may be {0->0.9, 1->0.1}, corresponding to the observer having just been activated and most likely starting with a 0 bit.

The probability assigned by Solomonoff induction to this model is not zero. It is very small since this is a very complex model requiring a lot of bits to specify, but not zero. It may never be zero—that would depend upon the details of the predictions and the observations.

I suspect that the paradigm of computation one chooses plays an important role here. The paradigm of a deterministic Turing machine leads to what I described in the post—one dimensional sequences and guaranteed solipsism. The paradigm of a a nondeterministic Turing machine allows for multi-dimensional sequences. I will edit the post to reflect on this.

Solomonoff induction is about computable models that produce conditional probabilities for an input symbol (which can represent anything at all) given a previous sequence of input symbols. The models are initially weighted by representational complexity, and for any given input sequence are further weighted by the probability assigned to the observed sequence.

The distinction between deterministic and non-deterministic Turing machines is not relevant since the same functions are computable by both. The distinction I’m making is between models and input. They are not the same thing. This part of your post

[...] world models which are one-dimensional sequences of states where every state has precisely one successor [...]

Confuses the two. The input is a sequence of states. World-models are any computable structure at all that provide predictions as output. Not even the predictions are sequences of states—they’re conditional probabilities for next input given previous input, and so can be viewed as a distribution over all finite sequences.

You need to distinguish between world models—which can include any number of entities no matter how complex or useless—with the predictions made by those models. The

predictionsare sequences (more correctly, probability distributions over sequences). Themodelsare not.A world model could, for example, include hypothesized general rules for a universe, together with a specification of 13.7 billion years of history, that there exists a particular observer with specific details of some particular sensory apparatus, and that the sequence is based on the signal from that sensory apparatus. The actual distribution of

sequencespredicted by this model at some given time may be {0->0.9, 1->0.1}, corresponding to the observer having just been activated and most likely starting with a 0 bit.The probability assigned by Solomonoff induction to this model

is not zero. It is very small since this is a very complex model requiring a lot of bits to specify, but not zero. It mayneverbe zero—that would depend upon the details of the predictions and the observations.I suspect that the paradigm of computation one chooses plays an important role here. The paradigm of a deterministic Turing machine leads to what I described in the post—one dimensional sequences and guaranteed solipsism. The paradigm of a a nondeterministic Turing machine allows for multi-dimensional sequences. I will edit the post to reflect on this.

Solomonoff induction is about computable models that produce conditional probabilities for an input symbol (which can represent anything at all) given a previous sequence of input symbols. The models are initially weighted by representational complexity, and for any given input sequence are further weighted by the probability assigned to the observed sequence.

The distinction between deterministic and non-deterministic Turing machines is not relevant since the same functions are computable by both. The distinction I’m making is between

modelsandinput. They are not the same thing. This part of your postConfuses the two. The

inputis a sequence of states. World-models are any computable structure at all that providepredictionsas output. Not even the predictions are sequences of states—they’re conditional probabilities for next input given previous input, and so can be viewed as a distribution over all finite sequences.