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Old 2017-12-12, 06:06   #34
axn
 
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Originally Posted by MooMoo2 View Post
Coerced guesses will not be allowed (for example, a dictator cannot round up a whole bunch of slaves and force them to submit guesses to the wizard). A proof is not required, but the wizard will not say whether a person's guess has already been submitted before by someone else from another part of the world. The torture is designed to be as long and painful as possible before death, and nothing but the victim's head will be given to his/her closest friend or family member.
If preventing guesses was your intention, just rate-limit any submission (say 1 per day) instead of taking this rather macabre route.
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Old 2017-12-12, 06:30   #35
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It is the first part the difficult one, To get to 1885 or so. Once you arrive into the late 19th century technology you could conceivably be there in 25-75 years.

But there is a big problem. Turing, Newton, Einstein, Cauchy, Galois, Leonardo, Dirichlet, Jean de la Vallée-Poussin, Gauss, Euclid, Fermat, Cantor, Leibniz Ramanujan, Euler etc. will all be dead and one thing is to know the underlying mathematical theory more or less well and a totally different one is to create a thinker.

Last fiddled with by rudy235 on 2017-12-12 at 06:32
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Old 2017-12-12, 09:00   #36
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That's a best-case scenario, so add another 130 years for delays due to war, pandemics, etc.
90% of people would die on the first day without social media, Facebook, Twitter, Instagram.
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Old 2017-12-12, 09:50   #37
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What about the other life forms? Today we have domestic animals and plants which humans rely upon to live. Would those animals and plants also be reverted to 200,000BC states of evolution? Would they all need to be re-domesticated all over again? If so then I suspect it would take ~202,017 years to get back to where we were. I see no reason to think it would all suddenly be easier the second time around. Knowledge of today is not anything like knowledge from 202,017 years ago, we would have to relearn old survival knowledge from scratch. All our fancy modern knowledge would be useless in the world of 200,000BC and lost after a few generations.

Maybe this entire scenario already happened 202,017 years ago!
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Old 2017-12-12, 11:38   #38
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...
Maybe this entire scenario already happened 202,017 years ago!
Maybe MooMoo is the wizard, taunting us before the storm ;)
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Old 2017-12-12, 16:32   #39
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I still maintain that threats of torture, no matter how dire, would not deter guessing -- assuming enough members of the surviving remnant population want to restore the status quo ante. I cannot, however, discount the possibility that, within a fairly short time, the surviving remnant will be so small, and so focused on the basics of surviving, that thoughts of their prior existence will largely be pushed aside. And, once any thoughts of modern life have passed from living memory, the very concept of "restoring" it will in a very real sense be lost. I mean, how do you "restore" to someone something they have never had?

I also cannot discount the idea that the surviving remnant will reject the wizard's offer, and decide to rebuild modernity through their own efforts. This actually seems to me to be the most likely reaction. Why should they believe a magical wizard willing to subject humanity to such a profound trauma would honor a promise to humanity? This approach would probably involve first devising ways to write down the knowledge in peoples' heads before it is lost -- in particular, the knowledge of written languages.

Even so, it is certainly conceivable that part of the the surviving remnant will remain absolutely devoted to the idea of restoring all that was taken. To such devotees, threats of torture, no matter how dire, would be no deterrent.

As another historical example, I point to Japan. From the early 17th Century to the middle of the 19th Century, Christianity was outlawed in Japan. For most of that time, Japan secluded itself from the rest of the world. Christians were persecuted with a thoroughness that would have left Nero in awe. If you were caught practicing Christianity, your whole family could be wiped out in a very unpleasant manner, such as being crucified, or thrown, one by one, into an active mud volcano. Yet, when Japan's seclusion was finally ended, it was found that "hidden Christians" had continued practicing their faith for almost two and a half centuries.

So I don't think threats of even the worst kind of torture would deter guessing. The idea of simply going through the odd numbers greater than 274207281 - 1 is one I hadn't thought of. The density of primes around 2p - 1 is about 1/(p*log(2)), indicating a "average" gap of about 1.4*p. According to the Wagstaff Conjecture, the "average" gap between one exponent p giving a Mersenne prime and the next is about .47*p. Since the density of primes around p is about 1/ln(p), it seems reasonably likely that it will take fewer guesses to turn up the next Mersenne prime than to turn up the next prime after 274207281 - 1. Of course, sieving out by small primes would eliminate a lot of odd numbers greater than 274207281 - 1 as candidates, but it would take a lot of sieving to offset a factor of log(74207281).
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Old 2017-12-12, 16:42   #40
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Originally Posted by axn View Post
If preventing guesses was your intention, just rate-limit any submission (say 1 per day) instead of taking this rather macabre route.
Without any way of long-distance communication, this wouldn't really make sense.

For instance, let's say that some group comes up with a reasonable guess, say 2^75753169-1. One of the people in that group is willing to suffer and die for the cause, but is unable to do so. The wizard simply says, "Nope, some fisherman off Australia went looking for food and got stung by a jellyfish earlier today. He guessed an exponent right before he died, so humanity has used up their guess of the day." The poor fisherman had little mathematical knowledge, so his guess was something that had no chance of being prime, like 2^100000000-1.

Each day, something similar happens, and reasonable guesses rarely, if ever, get submitted. Is that what we really want?
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Old 2017-12-12, 17:00   #41
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Quote:
Originally Posted by Dr Sardonicus View Post
Of course, sieving out by small primes would eliminate a lot of odd numbers greater than 274207281 - 1 as candidates, but it would take a lot of sieving to offset a factor of log(74207281).
Not a lot. Sieving by p < 26250 is sufficient. And it is very easy -- you can use SoE.

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Without any way of long-distance communication, this wouldn't really make sense.
Sure. But presumably the wizard will facilitate the coordination. After all, he's "testing" humanity, so he should run the "test center". There is nothing to lose for the wizard, If someone has genuinely found a prime, they should be able to convince others that they have the goods. But humanity cannot simply guess their way out of this with this protocol.
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Old 2017-12-12, 17:19   #42
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What about the other life forms? Today we have domestic animals and plants which humans rely upon to live. Would those animals and plants also be reverted to 200,000BC states of evolution? Would they all need to be re-domesticated all over again? If so then I suspect it would take ~202,017 years to get back to where we were. I see no reason to think it would all suddenly be easier the second time around.
Can we shortcut our way through this and bring back something resembling 5000 BC without having to re-domesticate any life forms? If so, that would shorten the timeline by at least an order of magnitude.

Quote:
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Maybe this entire scenario already happened 202,017 years ago!
If it did, would you accept the wizard's offer to replace what we have now with the man-made objects we had in 200,001 BC? The technology they had was advanced enough to discover M74207281, but other than that, you don't know anything about them.

Also, do you think most of humanity would accept? I think that almost everyone in first-world countries would reject the offer, but there would be plenty of people in underdeveloped parts of the world that would take the chance.
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Old 2017-12-13, 04:39   #43
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I think you and retina underestimate what the most knowledgeable humans are capable of doing even if you ignore the average person (and I think you guys underestimate the average person too).
I am with Dubslow here. You all underestimate humanity, and generally, life. I have seen the people around me doing wonders from thin air, and I am very optimistic about the outcome. I am still reading from this post (#8) forward (man! you posted 4 pages about this creep already??? ) but my guess, without seeing your arguments forward, will be like less than 10 years. Maybe 5. I could almost make a "project plan" for it... Haha, yeah, I know, the best project manager it the guy who believes that nine pregnant women can deliver a baby in one month, but yet.... centuries? C'mon!
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Old 2017-12-13, 06:53   #44
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Originally Posted by LaurV View Post
I am with Dubslow here. You all underestimate humanity, and generally, life. I have seen the people around me doing wonders from thin air, and I am very optimistic about the outcome. I am still reading from this post (#8) forward (man! you posted 4 pages about this creep already??? ) but my guess, without seeing your arguments forward, will be like less than 10 years. Maybe 5. I could almost make a "project plan" for it... Haha, yeah, I know, the best project manager it the guy who believes that nine pregnant women can deliver a baby in one month, but yet.... centuries? C'mon!
I think that's an order of magnitude too optimistic...
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