Recently, CIP noticed that our mountains were missing and wondered if "the simulation we live in had glitched, wiping out all those pixels". But later he came up with the explanation that "violent winds had stirred enough of our desert dust to obscure everything further away".

Obviously, Occam's razor suggests to go with his first explanation, which only needs one simple software glitch, while the second assumes the somewhat coordinated movement of gazillions of molecules, which seems quite unlikely.

Of course, an even sharper razor suggests that CIP is not real at all and the blog about his opinions is in fact written by one of Google's AI bots - in other words fake news.

Meanwhile, in comments to Scott A., people wondered about clouds, because "if you’re a cloud, there’s a fairly high chance that you’re living inside a 5-day forecast weather simulation."

But I am not so sure about that.

How can a Google AI bot be really sure of anything?

### multiple choice

If you select an answer to this question at random from the 5 choices below (*), what is the probability that you will be correct?

A: 20%

B: 40%

C: 0%

D: 20%

E: none of the above

(*) uniform probability distribution, "none of the above" includes "the question makes no sense"

added later: It is important that A and D are both 20% for the paradox to work. But assume that we change D to e.g. 30%, this would significantly change the puzzle; but would it be less paradoxical?

A: 20%

B: 40%

C: 0%

D: 20%

E: none of the above

(*) uniform probability distribution, "none of the above" includes "the question makes no sense"

added later: It is important that A and D are both 20% for the paradox to work. But assume that we change D to e.g. 30%, this would significantly change the puzzle; but would it be less paradoxical?

### too many worlds

In the following I shall use W0, W1, ... to denote different possible worlds; with "possible" I mean "compatible with physics as we know it".

In other words, each Wi corresponds to a particular 4-geometry and matter content.

Let me assume that "physics as we know it" does allow the creation of baby universes; see also this.

In the following I will use [Wb] to denote a world which created Wb as a baby universe; obviously many different worlds would be able to create the same world Wb and I leave it up to you if [] picks a particular one or represents all of them (it does not really matter for the argument I am trying to make).

We can then generalize this notation so that [Wa, Wb, ...] denotes a world which creates several baby universes Wa, Wb, ... and

[[Wc]] denotes a world which creates a baby universe which then creates Wc as its baby universe. And so on and so forth.

If you read my previous blog post, then you already know where I am going with this:

Let us assume that we can count all possible worlds in the set S = {W1, W2, W3, ...}.

It is then clear that every subset {W1, {W2, W3}} etc. corresponds to a possible world [W1, [W2, W3]] etc. etc.

so it immediately follows that S cannot be countable, because the powerset of S has higher cardinality than S itself.

It actually follows that S is not a proper set imho.

So how can a believer of the many worlds interpretation define a wavefunction of the universe over all possible worlds?

There is a different way to arrive at the same conclusion: If one considers a path integral Z over all 4-geometries (after some necessary but currently little understood regularization 8-) as the wavefunction of the universe, then the assumption of "baby universes" is equivalent to a sum over 'not simply connected' 4-manifolds; but this sum Z does not really exist, due to Goedel's theorem.

Notice that the problem does not go away even if we keep the 'not simply connected' 4-geometries (quasi)classical and only consider the quantum matter to trigger the creation of baby universes (or not).

In other words, each Wi corresponds to a particular 4-geometry and matter content.

Let me assume that "physics as we know it" does allow the creation of baby universes; see also this.

In the following I will use [Wb] to denote a world which created Wb as a baby universe; obviously many different worlds would be able to create the same world Wb and I leave it up to you if [] picks a particular one or represents all of them (it does not really matter for the argument I am trying to make).

We can then generalize this notation so that [Wa, Wb, ...] denotes a world which creates several baby universes Wa, Wb, ... and

[[Wc]] denotes a world which creates a baby universe which then creates Wc as its baby universe. And so on and so forth.

If you read my previous blog post, then you already know where I am going with this:

Let us assume that we can count all possible worlds in the set S = {W1, W2, W3, ...}.

It is then clear that every subset {W1, {W2, W3}} etc. corresponds to a possible world [W1, [W2, W3]] etc. etc.

so it immediately follows that S cannot be countable, because the powerset of S has higher cardinality than S itself.

It actually follows that S is not a proper set imho.

So how can a believer of the many worlds interpretation define a wavefunction of the universe over all possible worlds?

There is a different way to arrive at the same conclusion: If one considers a path integral Z over all 4-geometries (after some necessary but currently little understood regularization 8-) as the wavefunction of the universe, then the assumption of "baby universes" is equivalent to a sum over 'not simply connected' 4-manifolds; but this sum Z does not really exist, due to Goedel's theorem.

Notice that the problem does not go away even if we keep the 'not simply connected' 4-geometries (quasi)classical and only consider the quantum matter to trigger the creation of baby universes (or not).

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