If you stereographically project the real numbers onto the unit circle and use the metric inherited from R^2, then in fact (2) is very close to infinity.

If you use the arctangent to project the positive reals onto a finite set, then again I would guess that (2) is very close to infinity.

There's an old joke...

Some psychologists do an experiment. They put a mathematician and a plumber on one side of a room, and a beautiful woman on the other side. They say, "You can cross half the remaining distance in the room as many times as you like." The mathematician sighs, "I'd never reach her!" The plumber shrugs and says, "You'd get close enough."

Either I don't get it, or you are misapplying a cached thought. Please explain to me where my reasoning is wrong (or perhaps where I misunderstand the problem)

It's not about the money this time - but the implications to utility are the same. The 'million dollars' in Newcomb's problem is allocated in the same way that life is allocated in this problem. In this problem the money is basically irrelevant because it is never part of Prometheus' decision. But existence in the world is part of the stakes.

The problem feels different to Newcomb's because the traditional problem was constructed to prompt the intuition 'but one boxers get the money!'. Then the intuition goes ahead and dredges up reasoning strategies (TDT for example) that are able to win the $1,000,000 rather than the the $1,000. But people's intuitions are notoriously baffled by anthropic like situations. No intuition "um, for some reason making the 'rational choice' is making me worse off" is prompted and so they merrily revert to CDT and fail.

Another way to look at that many people find helpful when considering standard Newcomb's it is that you don't know whether you are the actual person or the simulated person (or reasoning) that is occurring when Omega/Prometheus is allocating $1,000,000/life.

If consistent decision making strategy is applied for both Newcomb's and this problem then those who one box Newcomb's but two box in this problem are making the same intuitive mistake as those who think Quantum Suicide is a good idea based off MWI assumptions.

Then how come plate mail is listed with a higher encumbrance than chain mail in my D&D manual?

ETA: :-)

A prediction I made a while back, posted here for posterity. Rot13'd to avoid spoilers.

Fnagn Pynhf vf Avpubynf Synzry.

If anyone has made this prediction before, I'd love to see it discussed.

Pro: Posts like this get large numbers of upvotes, indicating that people want to see more of them.

Con: As SarahC points out below, however, when people start posting their opinions (which they will) things get ugly.

I'm somewhat on the fence, in that I (like many others) am insatiably curious about what would come out of such discussions, and believe that in the end either I or many other people will have a large number of incorrect beliefs rectified. On the other hand, I do not know if the community would recognizably survive such a discussion, so for now I'd say it's best to wait.

Including finding a spouse and baby-sitting co-op?

I think that Dungeons and Dragons fills this space in my life.

Tegmark cosmology implies not only that there is a universe which runs this one as a simulation, but that there are infinitely many such simulations.

I'm not sure that this is true. My understanding is that IF a universe which runs this one as a simulation is possible, THEN Tegmark cosmology implies that such a universe exists. But I'm not sure that such a universe is possible. After all, a universe which contains a perfect simulation of this one would need to be larger (in duration and/or size) than this one. But there is a largest possible finite simple group, so why not a largest possible universe? I am not confident enough of my understanding of the constraints applicable to universes to be confident that we are not already in the biggest one possible.

There is a spooky similarity between the Tegmark-inspired argument that we may live in a simulation and the Godel/St. Anselm-inspired argument that we were created by a Deity. Both draw their plausibility by jumping from the assertion that something (rather poorly characterized) is conceivable to the claim that that thing is possible. That strikes me as too big of a jump.

I contend that there is evidence for a god. Observation: Things tend to have causes. Observation: Agenty things are better at causing interesting things than non-agenty things. Observation: We find ourselves in a very interesting universe.

Those considerations are Bayesian evidence.

Your choice of wording here makes it obvious that you are aware of the counter-argument based on the Anthropic Principle. (Observation: uninteresting venues tend not to be populated by observers.) So, what is your real point?

You win. :-)