I was speaking to the probability of life appearing in different parts of the (finite) ocean, so possibly I misunderstood what you were addressing. But since the reasoning should generalize:
I mean different sizes of infinity like these:
the set-of-all-sets is infinite, but the set-of-all-sets-including-that-set is one set larger, and so on
given an infinite length, 1⁄2 the length is still infinite, and so is 1⁄3 the length, but the 1⁄2 length is larger than the 1⁄3 length
an infinite tube of soap foam and an infinite rod of steel of the same diameter both contain infinitely many atoms, but there are more atoms in the steel, because it is much more dense
there are infinitely many numbers between 0 and 1. But there are twice as many numbers between 0 and 2.
More germane to the life example, if process 1 generates life at 1 per unit time, and process 2 generates life at 2 per unit time, as the arrow of time extends infinitely, both process 1 and 2 will generate life infinitely many times, but process 2 genesis is twice as large as process 1 genesis.
I’m not familiar enough with either SSA or SIA to apply them, and my grasp of anthropic reasoning is shaky in the extreme, but the idea of not rewarding population sizes baffles me. Do you have a preferred breakdown for this point I should check out, or will google serve me well enough?
If this claim is true, wouldn’t it also be true that a hypothesis in which life appears on every planet is more probable than a hypothesis in which life appears on every 10^40th planet?
If planets and stars lasted infinitely long, and were sufficiently constrained in their composition, then I would say yes. But this chain of reasoning ignores the local information we have about the problem. Returning to the primordial soup quote you were responding to, the argument is that what we know of thermodynamics doesn’t allow a causal mechanism to work. By contrast, the white-smoker vent hypothesis does allow a causal mechanism to work; therefore we should prefer it as the explanation for the origin of life (as we know it).
When I try running the intuition of your example of different frequencies of planetary genesis in reverse, and on primordial soup:
We should keep primordial soup on the table because a big world predicts this will still work an infinite number of times, then surely we must also keep a less-complex primordial soup (say, a primordial cocktail) on the table for the same reason; and then bare rock, with no soup at all; and then a complex cell springing into existence with no causal history; etc. This may be true, but doesn’t really seem helpful in terms of what to expect.
An alternative framing: would it be fair to say that under a big world, every prediction happens an infinite number of times? If I accept that all infinities should be treated the same, that still leaves us with the ability to compare the number of infinities, which should lead us to favor the hypotheses according to how many predictions they allow us to make.
Regarding the appearance of aliens, have you checked out the grabby aliens post yet? I recommend it.
If density/population size is so important, you may not like the conclusions you end up with! In particular, you probably end up concluding that this whole world is a simulation run on a different substrate, and that different substrate is infinite in extent and also extremely densely packed with life. I think...
SSA vs. SIA: I don’t have a favorite link, sorry. It’s been a while since I thought about this stuff. I remember liking Katja Grace’s posts on the subject, and Bostrom’s Anthropic Bias. Plus googling and the philosophy literature should work pretty well. Also some Stuart Armstrong posts but that’s more advanced.
Yeah, thinking about grabby aliens is the thing I need to know the probability number for. :)
I was speaking to the probability of life appearing in different parts of the (finite) ocean, so possibly I misunderstood what you were addressing. But since the reasoning should generalize:
I mean different sizes of infinity like these:
the set-of-all-sets is infinite, but the set-of-all-sets-including-that-set is one set larger, and so on
given an infinite length, 1⁄2 the length is still infinite, and so is 1⁄3 the length, but the 1⁄2 length is larger than the 1⁄3 length
an infinite tube of soap foam and an infinite rod of steel of the same diameter both contain infinitely many atoms, but there are more atoms in the steel, because it is much more dense
there are infinitely many numbers between 0 and 1. But there are twice as many numbers between 0 and 2.
More germane to the life example, if process 1 generates life at 1 per unit time, and process 2 generates life at 2 per unit time, as the arrow of time extends infinitely, both process 1 and 2 will generate life infinitely many times, but process 2 genesis is twice as large as process 1 genesis.
I’m not familiar enough with either SSA or SIA to apply them, and my grasp of anthropic reasoning is shaky in the extreme, but the idea of not rewarding population sizes baffles me. Do you have a preferred breakdown for this point I should check out, or will google serve me well enough?
If planets and stars lasted infinitely long, and were sufficiently constrained in their composition, then I would say yes. But this chain of reasoning ignores the local information we have about the problem. Returning to the primordial soup quote you were responding to, the argument is that what we know of thermodynamics doesn’t allow a causal mechanism to work. By contrast, the white-smoker vent hypothesis does allow a causal mechanism to work; therefore we should prefer it as the explanation for the origin of life (as we know it).
When I try running the intuition of your example of different frequencies of planetary genesis in reverse, and on primordial soup:
We should keep primordial soup on the table because a big world predicts this will still work an infinite number of times, then surely we must also keep a less-complex primordial soup (say, a primordial cocktail) on the table for the same reason; and then bare rock, with no soup at all; and then a complex cell springing into existence with no causal history; etc. This may be true, but doesn’t really seem helpful in terms of what to expect.
An alternative framing: would it be fair to say that under a big world, every prediction happens an infinite number of times? If I accept that all infinities should be treated the same, that still leaves us with the ability to compare the number of infinities, which should lead us to favor the hypotheses according to how many predictions they allow us to make.
Regarding the appearance of aliens, have you checked out the grabby aliens post yet? I recommend it.
If density/population size is so important, you may not like the conclusions you end up with! In particular, you probably end up concluding that this whole world is a simulation run on a different substrate, and that different substrate is infinite in extent and also extremely densely packed with life. I think...
SSA vs. SIA: I don’t have a favorite link, sorry. It’s been a while since I thought about this stuff. I remember liking Katja Grace’s posts on the subject, and Bostrom’s Anthropic Bias. Plus googling and the philosophy literature should work pretty well. Also some Stuart Armstrong posts but that’s more advanced.
Yeah, thinking about grabby aliens is the thing I need to know the probability number for. :)