I think a lot of this post can be boiled down to “Computationalism does not scale down well, and thus it’s not generally useful to try to capture all the information that is reasonably non-independent of other information, even if it’s philosophically correct to be a computationalist.”
And yeah, this is extremely unsurprising: Even theoretically correct models/philosophies can often be intractable to actually implement, so you have to look for approximations or use a different theory, even if not philosophically/mathematically justified in the limit.
And yeah, trying to have a prior over all conceivable computations is ridiculously intractable, especially if we want the computational model to be very expressive/general like these computational models, with abstracts. primarily due to the fact that it can express almost everything in theory (ignore their physical plausibility for now, because this isn’t intended to show we can actually build these):
This paper describes a type of infinitary computer (a hypercomputer) capable of computing truth in initial levels of the set theoretic universe, V. The proper class of such hypercomputers is called a universal hypercomputer. There are two basic variants of hypercomputer: a serial hypercomputer and a parallel hypercomputer. The set of computable functions of the two variants is identical but the parallel hypercomputer is in general faster than a serial hypercomputer (as measured by an ordinal complexity measure). Insights into set theory using information theory and a universal hypercomputer are possible, and it is argued that the Generalised Continuum Hypothesis can be regarded as a information-theoretic principle, which follows from an information minimisation principle.
Due to common misconceptions about the Church-Turing thesis, it has been widely assumed that the Turing machine provides an upper bound on what is computable. This is not so. The new field of hypercomputation studies models of computation that can compute more than the Turing machine and addresses their implications. In this report, I survey much of the work that has been done on hypercomputation, explaining how such non-classical models fit into the classical theory of computation and comparing their relative powers. I also examine the physical requirements for such machines to be constructible and the kinds of hypercomputation that may be possible within the universe. Finally, I show how the possibility of hypercomputation weakens the impact of Godel’s Incompleteness Theorem and Chaitin’s discovery of ‘randomness’ within arithmetic.
So yes, it is ridiculously intractable to focus on the class of all computational experiences ever, as well as their non-independent information.
So my guess is you’re looking for a tractable model of the agent-like structure problem while still being very general, but willing to put restrictions on it’s generality.
So my guess is you’re looking for a tractable model of the agent-like structure problem while still being very general, but willing to put restrictions on it’s generality.
Is that right?
I think everyone is doing that, my point is more about what the appropriate notion of approximation is. Most people think the appropriate notion of approximation is something like KL-divergence, and I’ve discovered that to be false and that information-based definitions of “approximation” don’t work.
I think a lot of this post can be boiled down to “Computationalism does not scale down well, and thus it’s not generally useful to try to capture all the information that is reasonably non-independent of other information, even if it’s philosophically correct to be a computationalist.”
And yeah, this is extremely unsurprising: Even theoretically correct models/philosophies can often be intractable to actually implement, so you have to look for approximations or use a different theory, even if not philosophically/mathematically justified in the limit.
And yeah, trying to have a prior over all conceivable computations is ridiculously intractable, especially if we want the computational model to be very expressive/general like these computational models, with abstracts. primarily due to the fact that it can express almost everything in theory (ignore their physical plausibility for now, because this isn’t intended to show we can actually build these):
https://arxiv.org/abs/1806.08747
https://www.semanticscholar.org/paper/The-many-forms-of-hypercomputation-Ord/2e1acfc8fce8ef6701a2c8a5d53f59b4fdacab3a
https://arxiv.org/abs/math/0209332
So yes, it is ridiculously intractable to focus on the class of all computational experiences ever, as well as their non-independent information.
So my guess is you’re looking for a tractable model of the agent-like structure problem while still being very general, but willing to put restrictions on it’s generality.
Is that right?
I think everyone is doing that, my point is more about what the appropriate notion of approximation is. Most people think the appropriate notion of approximation is something like KL-divergence, and I’ve discovered that to be false and that information-based definitions of “approximation” don’t work.