JBlack

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So much the worse for the controversy and philosophical questions. If anything, the name is the problem. People get wrong ideas from it, and so I prefer to talk in terms of decoherence rather than "many worlds". There's only one world, it's just more complex than it appears and decoherence gives part of an explanation for why it appears simpler than it is.

Reinforcement learning doesn't guarantee anything about how a system generalizes out of distribution. There are plenty of other things that the system can generalize to that are neither the physical sensor output nor human values. Separately from this, there is no necessary connection between understanding human values and acting in accordance with human values. So there are still plenty of failure modes.

This doesn't look like a bet. It looks like a service for which you charge €3500 and 3+ months of the customer's time, but will refund €2000 of that if they don't think you lived up to your claims.

This is an interesting discussion of the scenario in some depth, but with a one-line conclusion that is completely unsupported by any of the preceding discussion.

The data rate of optical information through human optic nerves to the brain have variously been estimated at about 1-10 megabits per second, which is two or three orders of magnitude smaller than the estimate here. Likewise the bottleneck on tactile sensory information is in the tactile nerves, not the receptors. I don't know about the taste receptors, but I very much doubt that distinct information from every receptor goes into the brain.

While the volume of training data is still likely larger than for current LLMs, I don't think the ratio is anywhere near so large as the conclusion states. A quadrillion "tokens" per year is an extremely loose upper bound, not a lower bound.

I think this example omits the most important features of the Sleeping Beauty problem. It's just a standard update with much less indexical uncertainty and no ambiguity about how to conduct a "fair" bet when one participant may have to make the same bet a second time with their memory erased.

Answer by JBlackMay 18, 202350

The model here is not a very good one in one important respect: opening the door twice in quick succession does not cost anywhere near twice as much as opening it once.

When you leave open the door, the colder air falls out the bottom and drags more warm air in past the contents, raising their temperature quite rapidly. While there is some additional turbulent mixing in the airflow around the initially moving door, it is not really significant compared with the overall downward convection flow inside the fridge. The flowing air cools and falls out the bottom continuously.

When you close it again, the airflow quickly reduces to almost nothing as the air stratifies by temperature - the coldest air is no longer free to flow out. The rate of heat transfer into the food reduces substantially. Eventually the air cools via the refrigerated walls and starts cooling the contents back to an equilibrium temperature, though this takes quite a few minutes.

So in terms of the important thing - temperature of the contents - you're better off opening it each time as an open door heats the contents much faster than a closed one even with the same warm air in it.

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 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.

A Solomonoff hypothesis can be any computable model that predicts the sequence, including any model that also happens to predict a larger reality if queried in that way. There are always infinitely many such "large world" models that are compatible with the input sequence up to any given point, and all of them are assigned nonzero probability.

It is possible that there may be a simpler model that predicts the same sequence and does not model the existence of any other reality in any meaningful sense, but I suspect that a general universe model plus a fixed-size "you are here" will in a universe with computable rules remain pretty close to optimal.

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