Imagine these factors didn’t work out for Earth, and it was yet another uninhabitable rock. We’d be standing on some distant shore, having the same conversation, wondering why Florpglorp-iii was so perfectly fine-tuned.
This is valid. Alice is doing the usual mistake of confusing P(One Particular Thing) with P(Any Thing from a Huge Set of Things) and Bob is right to correct her.
However, when we decrease the size of our Set of Things the difference between the two probabilities decreases. In the universe with billions of galaxies:
P(Life on at Least One Planet) is much much much higher than P(Life on One Particular Planet).
In the universe with only one galaxy the difference is not as dramatic. In the universe with only one solar system, with a few planets these probabilities become similar.
And so if Alice finds herself in such a universe it’s indeed rightfully surprising. As you’ve said yourself:
far more likely, you just get a few barren rocks circling a few billion times before their sun chars or consumes them.
On the other hand, if vast multiverse with many more planets exist then the difference between our two probabilities once again becomes high. So we would need to invoke multiverse to account for this kind of fine-tuning.
If the observer is distinct from Alice, absolutely. If the observer is Alice, nothing needs explaining in either case.
To put a bit of a crude metaphor on it, if you were to pick a random number uniformly between 0 and 1,000,000, and pre-commit to having a child on iff it’s equal to some value X—from the point of view of the child, the probability that the number was equal to X is 100%.
Apologies if there’s something more subtle with your answer that I’ve missed.
To put a bit of a crude metaphor on it, if you were to pick a random number uniformly between 0 and 1,000,000, and pre-commit to having a child on iff it’s equal to some value X—from the point of view of the child, the probability that the number was equal to X is 100%.
Conditional P(X|X) = 1.
However, unconditional P(X) = 1⁄1,000,000.
Just like you can still reason about unconditional probability of a fair coin even after observing an outcome of the toss, the child can still reason about unconditional probability of their existence even after observing that they exist. They can notice it’s very low, and therefore be rightfully surprised that they exist at all and update in favor of some hypothesis that would make their unconditional existence more likely.
This is valid. Alice is doing the usual mistake of confusing P(One Particular Thing) with P(Any Thing from a Huge Set of Things) and Bob is right to correct her.
However, when we decrease the size of our Set of Things the difference between the two probabilities decreases. In the universe with billions of galaxies:
P(Life on at Least One Planet) is much much much higher than P(Life on One Particular Planet).
In the universe with only one galaxy the difference is not as dramatic. In the universe with only one solar system, with a few planets these probabilities become similar.
And so if Alice finds herself in such a universe it’s indeed rightfully surprising. As you’ve said yourself:
On the other hand, if vast multiverse with many more planets exist then the difference between our two probabilities once again becomes high. So we would need to invoke multiverse to account for this kind of fine-tuning.
If the observer is distinct from Alice, absolutely. If the observer is Alice, nothing needs explaining in either case.
To put a bit of a crude metaphor on it, if you were to pick a random number uniformly between 0 and 1,000,000, and pre-commit to having a child on iff it’s equal to some value X—from the point of view of the child, the probability that the number was equal to X is 100%.
Apologies if there’s something more subtle with your answer that I’ve missed.
Conditional P(X|X) = 1.
However, unconditional P(X) = 1⁄1,000,000.
Just like you can still reason about unconditional probability of a fair coin even after observing an outcome of the toss, the child can still reason about unconditional probability of their existence even after observing that they exist. They can notice it’s very low, and therefore be rightfully surprised that they exist at all and update in favor of some hypothesis that would make their unconditional existence more likely.