Let us assume that the end of the universe will be consistent with the Big Crunch for the rest of our story, simply the 'event' which is most easily described as the inverse to the Big Bang, the universe contracting into a singularity. Let us also assume that you have, by billions of years worth of advancements in science, remained alive. The end is near, the temperature of space is already several hundred degrees and climbing. Despite our advancements, we are unable to know what exactly will result from the event as we have no prior examples. However, we were aware that, for quite some time, our universe was shrinking. With the forewarning to prepare we created a spaceship capable of exiting the universe entirely, however by the time it has acquired enough power to make such an escape, you have been rendered the last living intelligence in the universe. Therefore humanity has given you command of the spacecraft you're currently inhabiting, given complete freedom, but only two possibilities, with four plausible outcomes.

Option 1: You can choose to remain in the universe, eventually the laws of physics dictate your craft will be unable to resist gravitational forces, the heat, and radiation, you will be consumed as everyone else already has into the event.

O1 Outcome 1: With all matter from which the current universe began being restored into singularity, this universe is repeated. How many times you are consumed and how many times the event has happened in unknowable, but likely approaches infinity. No one will ever know that this is happening. But everyone dies repeatedly, yet everyone always come back to live repeatedly. Death ceases permanence. Yet with repetition comes the destruction of free will, every time you will choose death, and every time this universe will repeat.

O1 Outcome 2: Due to the true randomness in quantum mechanics a completely new universe is created from the old, possibly one with altered properties of physics and thus uninhabitable. Or just slightly off, potentially spawning new intelligent creatures. Whatever the case, the cycle of destruction and creation goes on. You give life yet will never be brought back to experience it.

Option 2: Using the power the spacecraft has gathered you decide to initiate the escape process to leave the universe, hoping to ride out the event.

O2 Outcome 1: You escape and ride out the Big Crunch, returning after the Big Bang. Unlikely as it is, you may find new life in this new universe but with less mass the Big Bang is different, thus humans will in almost all certainly be gone forever, except for you. With a near infinite lifespan you're able to repeat this escape process multiple times. You prove free will by changing the universe's loop and escaping existentialism, but by that same decision you garuntee the dead who may have lived again will continue as pre-universe history.

02 Outcome 2: For whatever reason, the space craft doesn't actually work, the world outside the universe is instant death, maybe the space craft runs out of power before the Big Bang can reoccur. Whatever the reason, you die, with new parameters for the start and end of the universe, your death is permanent, and no one else will have life repeated.

The end question is simple, assuming a 50/50 chance of each outcome occurring per option. What is the best command and why.

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1.2 is (probably?) an illusion. A universe of finite total energy and finite size should  be subject to the quantum mechanical version of the Poincare Recurrence Theorem. After some number of cycles it would return arbitrarily close to its previous Big Bang starting state. Might require vast amounts of time, but still.

This leaves me with 1.1, a guarantee that only this single universe will ever exist, or a coin toss between 2.1 and 2.2, which guarantee a wide variety of different universes ever existing, whether I'm in them or not. I choose 2. 

Note: 2.2 results in a new universe with less mass than the old one. After enough cycles, the universe may get light enough to no longer end in a big crunch, opening up the possibility of a universe that doesn't end, which may enable unbounded maximum entropy and something like Dyson's Eternal Intelligence. Meanwhile, 2.1 may enable me to start out as a Type IV civilization and engineer (if not on the next cycle, then on a later one) something like an Omega Point scenario.

Additional note: any infinite time series in a quantum world is going to branch off to include, for example, all possible Boltzmann brains infinitely many times. So "I" will recur anyway. What's the minimum duration I need to exist in order to count? Because knowing I'll recur in 1.1 and 1.2 for infinitely many disjointed lifespans, or knowing I'll recur in 2.1 and 2.2 for infinitely many disjointed moments, maybe would affect my choice  the same way?

I would like to remind people how Big Bang works. It happens everywhere. Therefore a "big Bang in reverse" will also shrink into everywhere. Words like "escape" should be read in the sense of "plane shift" rather than "translate". Warp drives and orion drives would be fundamentally useless for this task but since we are positing "unknown future tech" it does something relevant . These things don't work that there would be a special priviledged superduper black hole somewhere and empty flat space outside of that.

The claim of "destruction of free will" in O1.1 seems to me also a standard confusion about free will which is incorrect. If we run you multiple times in identical circumstances and you always produce a particual choice then it makes sense to label that option "your choice". If we run you multiple times and you produce different resolves then what you happen to present is not connected to who you are so it is not an expression of "you".

Also "world outside the universe" is pretty much a contradiciton in terms. Sometimes in some ontologies "universe" descripes a kind if time line or a particular 4d slice (and there are 5d or other exotic things which these 4d slices can be a part of). But "universe" also has the meaning of "all that exists" like the Marvel Cinematic Universe contains multiple timelines, multiple planets and all kinds of stuff (rather than just a one linear collecition of celestial bodies). Even in the strawman "super duper blackhole + flat space" picture the "flat space" is not outside the universe (ie the universe is not just the matter content of the universe).

In outcome 2.1 it should be possible to kickstart a different intelligent race which could be immensely valuable. If humans can't happen exactly, just ("just") picking a lifesupporting planet and trying to crashland on that so that your bacteria will survive the crash could give life a couple of billions of years of headstart in the new configuration.

If we run you multiple times and you produce different resolves then what you happen to present is not connected to who you are so it is not an expression of “you”.

That itself is a standard confusion.

A torn decision is one in which your beliefs and desires are in conflict, and approximately balanced so.that there is no course of action which is is.overwhelmingly aligned with them. A form of indeterminism under which an internal coin toss occurs to settle a torn decision, has the property that you cannot make a choice that is fundamentally against your wishes. It might seem that a "random" choice would be one that had nothing to with your reasons and desires, since that is s plausible interpretation of "random", but an internal coin toss is not random in that sense -- the options chosen between come from you, are part of you

One can choose to use a mixed strategy. The "internal coin" need not be truly random. The point however is that an agent that takes an action is succesfully using their will. If you put in yourself into a situation knowing what you will choose that doesn't take choice away from you. And the other way around losing knowledge of what you will choose doesn't "grant" you free will.

The “internal coin” need not be truly random.

But if it is, agency is not removed, despite your argument .

The point however is that an agent that takes an action is succesfully using their will. If you put in yourself into a situation knowing what you will choose

If there is only one thing you can choose, as a result of determinism, then you lack freedom of choice in the libertarian sense. Whether you know what you will choose is not very relevant.

That did make me hone my intuitions. I appear to have implicitly assumed that causing will have a single effect. But I would actually be somewhat fine with multiple mutually exclusive effects as long as there is "effection structure" (which I am less sure what it even means). But having the options open because "missing implementation" is not fine. If your plan is "2. ???? 3. PROFIT" it is not a plan at all.

The choice of what options are permissible is clearly an agentic choice. But I have a hard time swallowing that a truly random step could be a part of a things "character". If rain conditions on whether I will take a umbrella with me, its the athmosphere which is a not-me that is deciding between those scenarios (I can only decide that I am going to sensibly monitor the rain). The coin flip if it is not pseudorandom I would be unsure but lean on that it is not part of the strategicing or decision process. Yet at the same time it feels like a bit of my body could have such flakey character, which could on principle be part of the cognitiive machinery. Feels like it needs to be noised and can't make for a structural part for the actual function of it.