A possible solution is to not pick out. Generate all possible minds (with some realistic constrains), and let them all live their lives. 

If we have enough computational resources to run billions of slightly different versions of Archimedes, then we create billions of virtual habitats for them, and let them be.

One of them will be the Archimedes. We don't know which one, but at least we succeeded in bringing him back. 

While our current understanding of physics is predictably-wrong, it has no particular reason to be wrong in a way that is convenient for us.^[1]

Meanwhile, more refined versions of some of the methods described here seem perhaps doable in principle, with sufficient technology. 

You can make difficult things happen by trying hard at them. You can't violate the laws of physics by trying harder.

1. ^{^}

   Out of the many things that might be wrong about the current picture, impossibility of time travel is also one of the things I'd least expect to get overturned.

I agree. We still don't know how 85% the Universe works (dark matter), and our main physics frameworks don't play well with each other. It means, there is still a lot of undiscovered physics. 

What we see as physically impossible today could become a mundane engineering problem in a few decades. Such transitions from impossible to mundane have already happened a few times (e.g. transmutation of elements).

Some kind of time travel, or at least time scanning (Option 3) seems the best option.

Love your subreddit (but I don’t like Reddit much and I almost never use it).

I think we should not assume that our current understanding of physics is complete, as there are known gaps and major contradictions, and no unifying theory yet.

Thus, there is some chance that future discoveries will allow us to do things that are currently considered impossible. Not only computationally impossible but also physically impossible (like it was "physically impossible" to slow down time, until we discovered relativity).

The hypothetical future capabilities may or may not include ways to retrieve arbitrary information from the distant past (like the chronoscope of science fiction), and may or may not include ways to do astronomical-scale calculations in finite time (like enumerating 10^10^10 possible minds). 

While I agree with you that much of the described speculations are currently not in the realm of possibility, I think it's worth exploring them. Perhaps there is a chance. 

I think it makes sense to resurrect him anyway. We don't know what exactly he has disliked in resurrection, and he didn't know what the future humanity can offer. 

It's safe to assume that only people with a severe mental illness choose to die. This is true in any circumstances, regardless of how tragic they are. 

So, if there is no mental illness in play, and Aleister understands what exactly he is losing, he may choose to die again.

In the future where we can do technological resurrections of distant ancestors, the field of psychiatry will certainly be advanced enough to cure all or almost all suicidal patients (in many cases, the cause is as banal as a minor biochemical deficiency). Thus, such deaths will (almost) never happen. 

The space of Jupiter-brains is indescribably immensely larger than that of human brains. A human brain almost certainly has fewer than 10^10^20 distinguishable configurations, while a Jupiter-brain probably has more than 10^10^40 configurations. Don't let the fact that the number at the top is only twice the other fool you, these numbers are incredibly different in magnitude.

The fraction of Jupiter-brain configurations delayed due to exploring the space of all possible human brains first is less than 0.000000...(10^40 zeroes)...0001%. So don't worry about the waste of computing power.

Of course, both are utterly impractical to explore. With a computer the size of the observable universe that explores 10^100 configurations per second, it will take 10^10^20 seconds to explore just the human brain configurations. It will also take 10^10^20 years, because on these scales the change in the exponent between seconds and years is so small that it would require more decimal places than is worth typing. For that matter, the ratio in computing power between a universe-sized supercomputer and an abacus is likewise irrelevant.

People saying things like "just simulate all possible brains" are making implicit assumptions that can't be supported in anything we've observed of the universe.

I think he would still very much like to not die in the conventional sense.

I agree, the technological resurrection idea should not be used as a reassurance in own immortality. It is much better to avoid dying than to rely on such speculations. 

Recreating past human minds would be a cosmic waste in my opinion, why explore the space of current human minds when you can explore the space of jupiter-brains?

Why not both? We could save the 100+ billion lives awaiting resurrection, and then explore the space of jupiter-brains. Saving lives is not a waste of resources.

Excellent questions! 

Are we interested in Archimedes mind from any specific point in time or just at any point in his life?

One possible solution is to resurrect the oldest version of the person, but before the onset of any irreversible brain damage. For example, we bring back the version of Archimedes from some minutes before his murder by a Roman soldier. But for many patients, the timing will be tricky to decide (e.g. slowly progressing Alzheimer). 

The state of the minds we're generating in our search.  Are we generating minds whose state is that of a mind that has experienced one billion years of torture?  Is that bad?  Stopping torture is good, no?

I agree, such states of mind should be excluded, if possible. At least because they're unrealistic, and thus are unnecessary increasing the search space. 

How many minds will be generated that did not want to be resurrected?

If we use the method #2, many trillions of such minds will be generated. I think, in most cases, we can repair the will to live without a deep modification of the mind. But I don't know how to handle the remaining cases. The least we can do is to give them a choice: do you want to exist or not? We gave them the second chance, and they should decide if they want to use it.

can we generate a mind without "running" it?  If we can generate a mind, and the mind isn't running, are we OK with generating the tortured mind if we can inspect it in a not-running state?

I think a mind who is not experiencing any suffering is not increasing the total suffering. For example, a cryonics patient who is still in liquid nitrogen - can't suffer, because their neurons are not firing. Same for a digital mind who is not running (e.g. just a static file on a HDD, doing nothing).

If we're just generating possible minds, how many will say "Yo, I'm Archimedes!" but actually have no relation to our historical Archimedes? 

There will be many trillions of such minds. I see two possible solutions: 1) we use some smart filtering to avoid generating unrealistic Archimedes, 2) we generate all Archimedes, real or fake, and just let them live their lives. 

Thank you! Will read it. 

Another work of fiction on the topic is a science fiction novel by Philip José Farmer called "To Your Scattered Bodies Go".

Speaking about fiction, the method #2 could create minds indistinguishable from the minds of some fictional characters. 

For example, one of the generated minds could believe that his name is Harry James Potter-Evans-Verres. He could have the right personality, and vivid memories of all the relevant events from the HPMOR. It will be quite a shock to learn that you're nothing but a fictional character reconstructed from a Harry Potter fanfic by some galaxy-scale posthuman machine. 

Although I'm pretty sure Harry would support such a project.

For example, the Archimedes' work called On Sphere-Making is lost. We only know about its existence through references by other authors. 

If our goal is to recover On Sphere-Making, we could try to reconstruct it from all the preserved information about it (the Method 2), using the references, historical data, a systematic search across all ancient parchments etc. 

But if we have the tech that could directly retrieve information from the past (Method 3), we could just copy On Sphere-Making from the first manuscript. 

My reasoning was as follows.

The typical book page contains about 3k chars (including spaces). 

If we encode each char in UTF-8 (8 bit), a 200-pages book will contain about 5*10^6 bits (about 600 KiB).

Thus, to generate all 200-pages books, we must generate all binary numbers of the length 5*10^6 .

There are 2^(5*10^6) such numbers, or about 10^10^6.

There are at most 10^82 atoms in the universe. If we replace each atom with a (classical) computer, and split the work among them, each of the computers will need to generate 10^(10^6 - 82) books.

If each computer is generating one example per femtosecond (10^-15 sec), it will take them roughly 10^10^6 sec to finish the job.

It's much much longer than the time before the last black hole evaporates (10^114 sec).

And this is only the generation. We also need to write the books down somewhere, which will require some additional time per book, and a hell lot of storage.

I suspect that the entire task can be done dramatically faster on quantum computers. But I'm not knowledgeable enough in the topic to predict the speedup. Can they do it in 1 sec? In 10^10^3 sec? No idea.

We could also massively speed up the whole thing if we limit it to realistic books, and not just strings of random characters. E.g. use only the relevant parts of UTF-8.

The estimate is based on my (ridiculously primitive) 20th-century understanding of computing. How will people think about such tasks in 1000 years is beyond my comprehension (as it was beyond comprehension 70 years ago to measure stuff in petabytes and petaFLOPS).

You're right, the goal is to bring the Archimedes back to life, not just some similar mind. 

We humans are changing all the time. My mind from 1 year ago is different from my current mind (say, the difference is X percent). So, if you resurrect me, and the difference is less than X, then I don't have to worry about the difference.

I also agree with you on time travel. If it's possible, then it will be the best solution. Just mind-upload the person from the past, before they die. 

I don't advocate for nonconsensual mind changes (edited the post to make it clear).

Can we possibly agree that mind control is not OK?

Imagine that your friend has a severe depression (e.g. caused by their gut microbiome), to the point of attempting suicide.

You have a medication that fixes their gut microbiome, curing their depression, with no side effects.

In such a situation, is it OK to ask your friend to take the medication? (with a proper medical consent etc).

If your friend takes the medication and thanks to it doesn't have suicidal thoughts anymore, is it right to call the whole situation a "mind control by Jbash"? 

Can't a person even die without being harassed by busybodies?

Paramedics don't abandon a patient because the patient committed suicide. They're trying to save his/her life regardless. And they're doing the right thing.

In a world where you can create whoever you want and fully resurrect people no matter when they died, life ethics will be drastically different from our own. People would kill themselves in spectacular ways just for fun, as today they would practice extreme sports (just to cite Prime Intellect).

As per our assumptions, Archimedes 2.0 is the Archimedes, the 3rd-century BC Greek thinker who was temporary dead but who will be alive again.

(in exactly the same sense, as some of the today's clinically-dead patients will be alive, thanks to the modern medical tech).  

Thus, the plan is not just create some minds similar to Archimedes, but to save the life of Archimedes himself. 

I see resurrecting a long-dead person as morally equal to saving a contemporary who is in grave danger.