LessWrong 2.0 Reader

Basically, this shows that every term in a standard Bayesian inference, including the prior ratio, can be re-cast as a likelihood term in a setting where you start off unsure about what words mean, and have a flat prior over which set of words is true.

If the possible meanings of your words are a continuous one-dimensional variable x, a flat prior over x will not be a flat prior if you change variables to y = f(y) for an arbitrary bijection f, and the construction would be sneaking in a specific choice of function f.

Say the words are utterances about the probability of a coin falling heads, why should the flat prior be over the probability p, instead of over the log-odds log(p/(1-p)) ?

I'm curious what disagree votes mean here. Are people disagreeing with my first sentence? Or that the particular questions I asked are useful to consider? Or, like, the vibes of the post?

In deep meditation people become disconnected from reality

Only metaphorically, not really disconnected.  In truth, in deep meditation, the conscious attention is not focused on physical perceptions, but that mind is still contained in and part of the same reality.

This may be the primary crux of my disagreement with the post.  People are part of reality, not just connected to it.  Dualism is false, there is no non-physical part of being.  The thing that has experiences, thoughts, and qualia is a bounded segment of the universe, not a thing separate or separable from it.

Is this just the thing where evidence is theory-laden? Like, for example, how the evidentiary value of the WHO report on the question of COVID origins depends on how likely one thinks it is that people would effectively cover up a lab leak?

To be clear, this is an equivalent way of looking at normal prior-ful inference, and doesn't actually solve any practical problem you might have. I mostly see it as a demonstration of how you can shove everything into stuff that gets expressed as likelihood functions.

Why wouldn't this construction work over a continuous space?

Do you want me to spoil it for you, do you want me to drop a hint, or do you want to puzzle it out yourself? It's a beautiful little puzzle and very satisfying to solve.

Presumably in deep meditation people become disconnected from reality.

Yes it is easy to forget something if it does become a part of your personality. So a new bad thing is easier to forget.

I don't see how this helps. You can have a 1:1 prior over the question you're interested in (like U1), however, to compute the likelihood ratios, it seems you would need a joint prior over everything of interest (including LL and E). There are specific cases where you can get a likelihood ratio without a joint prior (such as, likelihood of seeing some coin flips conditional on coin biases) but this doesn't seem like a case where this is feasible.