Disproving the SIA disproves the Fine-Tuning Argument and Boltzmann-brain-based arguments

My worst post on LW of all time is Boltzmann brains, like Doomsday, require no explaining. It's currently sitting at -18, which I think would be fair if my argument presented was mistaken. However, no one has of yet has shown me where my argument goes wrong.

So, I'm back at it again -- this time with variant examples to use, and gunning after the Fine-Tuning Argument as well as Boltzmann brains.

The SIA says that theories of the universe that predict more people we might be should be proportionally more likely. The FTA says that our universe is so unlikely that we need God to explain how we came to be in such an unlikely spot. The idea of Boltzmann brains tries to say that this unlikeliness is vastly even more unlikely, barring some sort of Godlike explanation.

Lorenzo Elijah, PhD explains here:

A Boltzmann brain is a pocket of low-entropy order that emerges due to quantum fluctuations in an otherwise high-entropy environment. Just imagine what scientists describe as the heat-death of our universe. In that scenario, all the stars and planets have decayed into atoms. The universe is just an ocean of particles without form or structure. Physicists theorise that if this state persists for long enough, then eventually these particles will randomly arrange themselves into all sorts of structures for brief instances of time. Many of these structures will be structurally identical to human brains arbitrarily similar to yours. Since your entire mental experience supervenes on the particular configuration your brain is in right now, that means there might be observers with qualitatively identical experiences to yours popping in and out of existence. These observers would obviously be in skeptical scenarios because all of their memories and immediate sense perceptions would be false. They wouldn’t actually be petting a dog or subscribing to my blog—First Principles. They would just be Boltzmann brains created mere moments before, only to perish the moment after.Now here’s the danger of Boltzmann brains. Because they are mere pockets of low entropy, they are overwhelmingly more likely than real people like you and me.

Putting some terms on this:

• P(Atheism) = P(God) = 1/2
• P(I’m not-Boltzman | God) = 1
• P(I’m not-Boltzmann | Atheism) = 1/N, extremely small
• P(Atheism | I’m not-Boltzmann) = extremely small, via Bayes’ Theorem

There’s two problems with this. First, I don’t know if we can condition on “I’m not-Boltzmann” because I have no idea if I’m a Boltzmann brain or not. (If you’re certain you’re not a Boltzmann brain yourself, please let me know how you came to that conclusion.) (Also I’d like to note that the possibility of being a Boltzmann brain doesn’t bother me in the slightest because that possibility doesn’t actually change anything about my preferences and therefore my behavior.)

The bigger problem is that this sequence of assumptions depends on either SSA or SIA style of reasoning.

Lorenzo Elijah continues:

the multiverse hypothesis has no solution to the Boltzmann brain problem. And since we should rule out any hypothesis with a Boltzmann brain problem, we have no choice but to accept a design hypothesis to account for fine-tuning.So, is that it? Is it just over for naturalists? Not quite. There is an escape hatch, but I don’t recommend it. If one wants to avoid the theistic conclusion, the best way would be to deny the Bayesian epistemology that undergirds these arguments.

I will endeavor to show there’s no Bayesian violation here.

The God, the angel, and M.C. Escher

Two examples should be all that we need to disentangle Bayes from Boltzmann.

First, imagine God is chatting with you, an angel, about how to create the multiverse. He has two plans. In Plan A, 99 out of 100 universes will end up running on Euclidean geometry. In Plan B, 99 out of 100 universes would run on Escheresque geometry.

Waterfall, by M.C. Escher

God says He’ll flip a coin to choose which plan to go with, then He’ll give you the corporeal form you’ve always wanted to experience and make you wake up in a random universe. You wake up on Earth. Do you believe the coin is 100x more likely to have resulted in Plan A?

Next, let’s say you’re no longer an angel, but now a human physicist and prophet. Visiting you in a dream, God explains that all universes in the multiverse are either Euclidean or Escheresque, and is in the middle of saying…

“in fact, currently there are 100 universes. 99 out of these 100 universes are E-”

…when he gets cut off by Lucifer starting another war in the Middle East. He says He’ll be back in five minutes. Given that Earth is Euclidean, during those five minutes, should you believe that a primarily-Euclidean multiverse is 100x more likely than a primarily-Escheresque multiverse?

More to the point: Do you believe these two questions are essentially identical?

(They’re not.)

If you say yes to both of these questions, then you are forced to either accept the SSA and the Doomsday Argument or the SIA and the Presumptuous Philosopher, both of which are absurd. Furthermore, the SIA leads to a contradiction for infinite-sized realities, as I proved here.

Thankfully, there’s an alternative. We can be good Bayesians and answer “yes” to the first question…

• P(mostly Escheresque multiverse) = 1/2
• P(angel becomes Euclidean | mostly Escheresque multiverse) = 1/100
• P(mostly Escheresque universe | angel becomes Euclidean) = P(A | M)*P(M)/P(A) = 1/100*(1/2)/(1/2) = 1/100

…and “no” to the second:

• P(mostly Escheresque multiverse) = 1/2
• P(Earth is Euclidean | mostly Escheresque multiverse) = 1
• P(mostly Escheresque universe | Earth is Euclidean) = P(E | M)*P(M)/P(E) = 1*(1/2)/(1) = 1/2

Of course, a rationalist should try to avoid assigning probabilities of perfectly zero or one—but for the math to work out, you have to assume identity functions with perfect certainty. E.g., P(2pac still lives) = P(2pac still lives).

The part that trips people up, in this case, is defining “Earth”.

• In the mostly Euclidean universe, “Earth” is an ambiguous pointer to any one of God’s 99 Euclidean universes.
• In the mostly Escheresque universe, “Earth” is defined as the 1 and only Euclidean universe. We shouldn’t use probability to describe the “chance” that Earth is Euclidean; we should use the identity function.

This makes “Earth” a fundamentally different kind of pointer than the “angel” from the first example:

• In the mostly Euclidean universe, “angel” refers to the one who was speaking with God.
• In the mostly Escheresque universe, “angel” refers to the one who was speaking with God.

When the angel wakes up, it learns something new as it finds itself within a Euclidean body. This observation connects two different properties (“angel” && “Euclidean incorporation”).

Earth, on the other hand, could never have “woken” itself up into an Escheresque universe, because Earth was by definition always Euclidean (“Earth” → “Euclidean universe”).

We can’t make any assumptions about Earth’s place in the multiversal cosmos because we don’t know anything about how Earth may or may not have been randomly “drawn” from any kind of array of possibilities (unlike with the angel). All we can say is that the Earth has Earth’s properties, because the Earth is the Earth, and the Earth being the Earth doesn’t tell us anything about universes outside of Earth’s. And that’s the essence of the Self-Identity Non-assumption (whose abbreviation I picked out of a dry sense of humor, not any allegiance to Satanism), the alternative to both SSA and SIA that leads to neither of their absurd conclusions.

All the information about our universe, inside our universe, tells us nothing about the properties of outer universes—including their preponderance. I know it’s unintuitive, but Earth could be unique, a jewel that’s literally 1 out of 10^52, and that still wouldn’t create any “unlikeliness” that metaphysical theories must address. If you’re still struggling with that unintuitiveness, then please allow me to suggest revisiting the Bayesian postulates above; it’s how I get un-confused, any time I start to get mixed up: Double check the assumed priors and prior likelihoods.