39 KiB
How would you munchkin this: a device that answers yes or no questions
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Author: u/None *
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URL: https://www.reddit.com/r/rational/comments/3nrq2j/how_would_you_munchkin_this_a_device_that_answers/
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Score: 10
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Created: 2015-10-06T23:04:14
Post:
Somehow you have come across a simple-looking 8.5x11" piece of paper with a remarkable property: if you write down a yes/no question at the top of the page and put it out of sight for an hour, then the next time you glance at it you will see the answer written in elegant cursive below your query. An additional hour later all writing is erased from the page and you can ask something again. You must print your question legibly, no smaller than what would normally correspond to a 12 point font.
The piece of paper will not predict the future. It will not tell you which stocks will rise or fall tomorrow. It will, however, answer any question about the present or the past, provided the question itself is well-defined.
When your question is insufficiently precise, you will see a slanted question mark appear beneath your query in response. "Is Fermat's last theorem true?" produces such a question mark. By contrast "Does Fermat's last theorem follow from the ZFC axioms?" produces a "Yes." It seems that the paper has some background knowledge and does not need an explanation of what Fermat's last theorem is or what the ZFC axioms are.
Asking "Has my girlfriend cheated on me?" produces a question mark. The paper does not have care to parse the (culturally dependent) context of "cheating." On the other hand, if you ask whether your girlfriend has engaged in certain acts and provide anatomical descriptions, you will have your answer.
It seems as if there is no fact about the past or present the paper does not know. Direct questions ("What are you?") produce only question marks in response. So do questions without a yes/no answer.
You would not decline riches and fame, but you'd really like to use this thing to do something meaningful for humanity. What do you do?
Edit: some words.
Comments:
u/ArgentStonecutter [+20] Emergency Mustelid Hologram (an hour later)
Binary search Path To Immortality.
u/None [+3] (8 hours later)
As a hypothetical, imagine that someone in Ancient Greece had this piece of paper. Could that person use it to advance the state of scientific knowledge to 20th century level within their lifetime via binary search?
I'm not so sure. It seems that certain conceptual leaps are necessary to even ask the right questions. For example, to even conceive of relativity theory one has to be able to imagine time as "just another dimension" not altogether different from the three spatial dimensions. I believe even something as basic as the use of coordinates was foreign to ancient Greeks and introduced by Descartes.
u/TheAtomicOption [+2] (16 hours later)
That would also be my goal, but I'm not sure we could get all the way there given the time constraints others are talking about, but it would definitely get you some really really great to have information about where to look.
I'd probably start by categorically ruling out things that, while most rational people dismiss them, would completely change the game if they existed. I'd ask about magic, the supernatural, and perhaps spend one question on technologically advanced aliens. Hopefully it wouldn't take long to rule out things like lich-dom and then you could go back to the difficult task of asking specific enough questions to get answers that advance science.
u/Endovior [+1] (2 days later)
I imagine asking about 'magical' or 'supernatural' phenomena would produce a lot of question marks. Exactly how would you specify such a request? Sufficiently analyzed magic is just science, after all, and nothing that's possible in the real world is actually 'supernatural'.
u/TheAtomicOption [+1] (2 days later)
Yea, it depends on how distinct the questions have to be. There's a lot of imprecision in the description of what the paper can understand vs what it can't interpret.
u/TheAtomicOption [+2] (16 hours later)
Precision for direct immortality questions would be difficult. Does having your name "immortalized" in history (or a headstone) count?
I think I would start by looking for small molecules to cure various conditions. I'd start with diseases that are currently sucking up all the research funding, but aren't producing very fast advances, for example Alzheimer's: "have one or more molecules existed that would, at some correct dosage, cure greater than 80% of Alzheimer's patients without killing them?"
If you get a yes then you find it with
"For the molecules referenced by the question asked at [first question's date/times]. Is the k-th character of the IUPAC name for the molecule with the shortest IUPAC name numeric?"
You'd know you had the complete name when you asked about the next character and got a ?.
Now you just have to ask about dosage per kilo and/or administration methods and hardest of all, get the FDA to trust the paper enough to skip clinical trails for things discovered by precise use of the paper.
u/Geminii27 [+2] (7 hours later)
Even assuming you are awake 24/7 or can have a printer print new questions on it every two hours, that's only 12 questions per day. That may not be nearly enough to discover the precise parameters of even one path in a lifetime.
You could use it to discover if anyone has already accidentally stumbled on the path, and eventually get a name and location for them. If you're blindly sweeping for the path, though, you could be there a very long time.
u/GrumpySummoner [+1] (10 hours later)
Investigate if it's possible to decrease the time it takes the machine to formulate answers first. Then focus on immortality.
u/leplen [+15] (2 hours later)
Having flawless information looks pretty similar to predicting the near future. Humans already make all sorts of predictions of the future without knowing it.
Stock prices etc. are just a form of information, and any information advantage you have on the market can easily be translated into money. It's the ultimate in insider trading. Magic paper, is there a greater than 55% chance that Apple stock will increase by 2% in the next week? If I know whether a rumored merger is actually being discussed I have a huge advantage on the market. Magic paper, has the Fed decided to lower interest rates? Have G.E.'s earnings exceed the predicted value over the last quarter? This information is all known well before it's announced, and thus is well within the power of my notebook paper, but before it's publicly known, it's basically as good as gold.
Making lots of money ........ ✔
It also seems like it would be super useful for guiding research. Lots of long research projects have single bit answers at the end. Does P=NP? Is cold fusion possible? Can a superconductor stable at standard temperature and pressure be created using currently available technology?
Advancing science and human progress ........ ✔
And then of course my piece of paper is a halting oracle, and so I can specify an encoding and use it to output a binary representation of the answer to virtually any question. I'll need some knowledge to start with so I can ask good questions with short answers, but since I have plenty of money to hire researchers and I am hyper-efficient at directing research, paying people to come up with good compression algorithms for hard questions shouldn't be too difficult. Outputting the chemical formula of miracle materials like cancer cures and cheap water splitting catalysts seems particularly easy.
God-like power .............. ✔
u/Sagebrysh [+1] Rank 7 Pragmatist (5 hours later)
Magic paper, is there a greater than 55% chance that Apple stock will increase by 2% in the next week? If I know whether a rumored merger is actually being discussed I have a huge advantage on the market. Magic paper, has the Fed decided to lower interest rates? Have G.E.'s earnings exceed the predicted value over the last quarter? This information is all known well before it's announced, and thus is well within the power of my notebook paper, but before it's publicly known, it's basically as good as gold.
This seems like an amazing way to get arrested for insider trading.
u/Geminii27 [+6] (8 hours later)
How are they going to prove anything? Go live in the desert in a cave filled with psuedo-mystical trinkets and a solar cellphone. Get financial papers delivered; call in the trades. Any investigation will determine you take no calls and don't speak to anyone.
Not to mention that the paper can't predict future results perfectly; you're not going to have an uninterrupted string of successes.
u/Gurkenglas [+1] (19 hours later)
Apparently you had the insider information before you went there.
u/Endovior [+1] (2 days later)
Depends on how long you've been there. Insider information is typically time-sensitive, after all.
u/None [+1] (17 hours later)
Magic paper, is there a greater than 55% chance that Apple stock will increase by 2% in the next week?
It can't predict the future.
Magic paper, has the Fed decided to lower interest rates?
I don't think this will work. Magic paper have no information about that.
Have G.E.'s earnings exceed the predicted value over the last quarter?
And that information is public or private. In case it's private you still actually can access it.
It also seems like it would be super useful for guiding research.
Yes, it seems that you can easily half the time you need to research something specific.
I can specify an encoding and use it to output a binary representation of the answer to virtually any question
All you get is still one bit. You can't get it answer any in a form you need. I think it will answer NO to a question "Is there any form of question/s that can be used to get several bits of information out of you that are answers to a same question in a binary coded manner?" It can't store any information. You possible could add new information to a new question making a growing chain but paper has it's limits in a size of a question.
u/leplen [+2] (a day later)
You just ask questions of the following form: If I write the atomic number of the first element in the easiest to synthesize room temperature super conductor in binary, is the 2nd digit of that number a 1?
u/None [+1] (2 days later)
If I write
And if you don't?
in the easiest to synthesize
That's also is not at all strict mathematical way to define something. For paper easiest is not defined term.
u/Jiro_T [+1] (5 days later)
The magical clause here is "by my standards". The easiest way to synthesize by my standards.
Of course, the paper could conceivably interpret even that phrase strangely, but at that point you have the author using the vagueness in the scenario against you; no way to avoid that.
u/Psychobeans [+10] (28 minutes later)
It having knowledge of everything but lacking contextual clues seems incompatible. Either an entity knows everything or it doesn't. It would seem to me that it would know the answers to such questions, but be unable to give them for some reason.
I would begin by asking if it can answer questions about itself. Figuring out how the paper works (how it actually collects the information) could be even more valuable than the paper itself.
I would try to get more than yes or no answers out of it. For a question "X" I would ask "Is the first letter of the answer to "X" the letter 'a'?" and repeat for each letter.
What I would do next would depend on if the above works.
Edit: "Do you have a computational power limit?" and "Do you consume energy to function?" seem like highly important questions.
u/None [+1] (40 minutes later)
By the rules I have sketched out, you can only ask at most 12 questions a day (24 hours per day/2 hours per question) -- and you still need to sleep. Asking about the letters of the answer could get unwieldy very quickly.
As for your first point -- there is no logical incompatibility. You put certain sorts of questions to it, you get answers. You put other questions, you get nothing. You notice a pattern...
u/Psychobeans [+3] (52 minutes later)
I can cut the number of brute force questions required with a binary search. "Is the first letter of the answer to "X" in the first half of the English alphabet?"
I could cut even more by asking "Is the first vowel of the first word of the answer to "X" in the first half of the English alphabet?". Once I have the vowels of each word, figuring out the full answer should be easy, and I can narrow it down with more questions and end with "Does "Y" answer "X"?" to check my work. Sure, it will take a few days, but I don't need to ask it for literally every letter.
u/None [+3] (an hour later)
Indeed, I agree. But if you do the calculations, you should still find it quite difficult to obtain answers which are even moderately long.
For example: suppose an answer has 50 characters (i.e., about ten words). There are 26 letters in the English language plus space, which leads to 27^50 possibilities. Each question can cut down the space by a factor of 2 at most, so you will need at least log_2(27^50) questions; dividing this by, say, 7 questions a day, you get about 34 days.
You can probably do much better by making use of the redundancy of the English language, whose entropy is not that high, though your ability to use various error-correcting codes for this purpose is extremely limited by the fact that you need to fit the questions on an 8.5x11" piece of paper in 12 point font.
u/Psychobeans [+2] (an hour later)
Regardless, we've arrived at the fact that this object's rules can be circumvented, which is very useful to know. The next step is to obtain a full copy of the rules, if possible.
u/Sagebrysh [+2] Rank 7 Pragmatist (an hour later)
34 days isn't too bad, and I know if I had such a sheet of superpaper, I would definitely be alarm clocking it to get 24 answers out of it a day. 34 days for the rules, then binary search a path to immortality. That one might take a few years, but I'm patient, once I have immortality, I have all the time in the universe.
u/None [+4] (an hour later)
Just to clarify: 34 days is an upper bound on the time to get an answer to any well-defined question whose answer has 50 characters or fewer.
That is assuming 7 questions per day. If you get 12 questions out of it per day (e.g., by sleeping half hour every hour or some such thing), you can get it in less than 20 days.
Edit: Actually, thinking about it, you can ask whether the k'th bit of the LZ algorithm (essentially what zip uses to compress text) is 1 or 0. Using Shannon's famous estimate of 1.6 for the entropy of the English language, this lets you produce answers at a rate of about 0.31 characters per hour. This means you would need about 7 days to get a 50 character answer.
u/Sagebrysh [+2] Rank 7 Pragmatist (an hour later)
Right and I can reduce that with some of the methods listed above, which will let me get the ruleset. With the ruleset, my options significantly open up for metagaming it even more.
Then with the basics understood, we can move on to the whole path to immortality thing.
Other possible angles of attack would be to figure out how the paper works, and if its recreatable. Things like, what counts as 'observed' in the context of the paper? If I have a machine taking video of it, does it stop working? Or does it do something weird like retroactively erase the information when you look at the video? (which would be crazy and imply all sorts of weird new physics)
Does the answer show up in ink, pencil, human blood? Does it just use what you used to write the question?
u/None [+2] (an hour later)
The paper does not mind being recorded. It answers questions just as before, and the video shows the answers seemingly writing themselves about an hour after the question is written down.
I'm not sure what you mean by "ruleset." What would you ask it?
u/Sagebrysh [+2] Rank 7 Pragmatist (an hour later)
Oh boy now we're cooking with gas! Okay, well, if it doesn't mind being recorded, then we can start with some equipment to check for things like EM fields, temperature fluctuations in the paper, and other stuff I can't think of offhand. When a person writes something on paper with a writing implement, a small amount of friction (and thus heat) is generated at the contact point between the tool and the paper, look for things like that. Make sure there's not a tentacle belonging to some huge eldritch entity reaching in with its intangible limbs and and writing the answers.
As for what questions to ask, lets start with basics.
Use /u/pyschobeans approach with the following starter questions.
What are you?
How do you answer questions posed to you?
How were you created?
Who created you?
Why were you created?
That's just a few for starters.
u/Psychobeans [+3] (2 hours later)
We can assume by OP's answers that the paper is some form of conscious entity with (at least) full read access to the universe. The best course of action is to immediately destroy the paper, as we have no way of determining if the entity means harm to us. There is a high chance that it is a bound demon trying to escape, and that risk is not worth taking.
u/Norseman2 [+4] (15 hours later)
If it is a bound demon with full read access to the universe, then you've already lost.
We've already established that it has unspeakable computational capability. We could conceivably convert Chinese characters into a numeral system, using all the characters in the Kangxi Dictionary, in order, as numerals in a base-49,030 numeral system which we henceforth call the Kangxi Numeral system. We could then ask "When converting the following number, X, from the Kangxi numeral system into the base-10 Arabic numeral system, is the digit '7' the last digit in the smallest prime factor of X?" and follow this with 1,500 characters, creating a number which is 332,140 bits long.
We can repeat with each digit, and go from last digit to second-to-last, etc. and eventually establish the smallest prime factor of a number which could easily be a composite of two large primes. We would be able to prove the answer to be correct, despite not having anywhere near the tiniest, smallest, glimmer of having any shred of being able to provide enough computational power to actually calculate that on our own.
Brute force trial factorization by division would require 10^49,992 divisions. There's only about 10^80 atoms in the observable universe, and only about 10^100 years before the heat death of the universe. Even if every atom in the universe were a 10 Ghz CPU trying to solve this question, you would not come anywhere even remotely close to an answer before the heat death of the universe. Yet this sheet of paper can start to print out an answer within one hour.
So why have you already lost? Because the sheet of paper, or whatever entity is behind it, is most likely capable of running billions of simultaneous complete simulations of our universe and running it substantially faster than real-time. Even if it does not give you information about the future, we have established that it is fully capable of deriving nearly exact probabilities about events stretching years into the future (or even exact simulations if there is no true quantum uncertainty).
This means that any action that you take (including not taking an action) is something the sheet is already anticipating as your response to the information it provides. As such, if it is truly a bound demon, then destroying the sheet will only serve to further the demon's ends. Perhaps destroying the sheet releases the demon?
So, basically, if the sheet is a bound demon, you're doomed and nothing you do will change that, so you can enjoy what little you have left in life. If the sheet is not a bound demon, you are free to munchkin up interesting uses for it and improve life for yourself and everyone else.
u/ArgentStonecutter [+2] Emergency Mustelid Hologram (11 hours later)
I suspect doing a binary search on whole words using a known dictionary would work better.
u/noggin-scratcher [+1] I am a happy tree (13 hours later)
Definitely. Anything you can do to move away from the 27^50 search space to a "realistic set of options" space is going to vastly cut down the number of questions required. Dictionaries and guessing at words without bruteforcing every single letter individually would be vital.
For example you could generate a list of hypotheses then for your first question ask whether any of them are correct; if it says yes then you've cut the search time enormously.
u/TheAtomicOption [+1] (16 hours later)
There are some ways to speed this up. First you could adopt an Uberman sleeping pattern to ask the full 12 questions per day without going crazy (assuming it can't be automated by printer+scanner)
Second you could arrange the alphabet in order of first letter frequency "TASHWIOBM..." as a first optimization, and then develop a system that predicts the most frequent next character (including space). ~50% of words start with the first 6 of those letters so you could also ask if the letter is in the first six of the alphabet arranged like that etc. This should be able to shorten the time it takes to get full answers significantly.
u/Psychobeans [+1] (45 minutes later)
"Do you know the answer to "Does my girlfriend cheat on me?"" is a great question to ask in this case.
u/None [+1] (50 minutes later)
That produces a question mark.
The underlying problem is: "Does my girlfriend cheat on me" does not have a clear-cut yes/no answer. Is it cheating if she drunkenly made out with someone at a party? What if she merely flirted or held hands?
This question does not have a definite answer in the same sense as a a question about physics, mathematics, or, e.g., whether there are members of the Russian military in the Ukraine. The piece of paper appears to consider it beneath itself to delve into such questions :)
u/Psychobeans [+3] (55 minutes later)
"Using the context of what I consider to be cheating, does my girlfriend cheat on me?"
u/None [+4] (an hour later)
But do you even have a well-defined context of what you consider to be cheating? Might you be actually torn inside about whether a drunken makeout session is REALLY cheating?
The paper can answer questions about the state of every neuron in your brain. But it won't answer questions about your opinions -- not unless you give it a precise map about which brain states correspond to which opinions, which would, among other things, be difficult to fit on a piece of paper.
u/Psychobeans [+4] (an hour later)
But it has a precise map of my brain state, since it knows everything about the present. It knows everything I know, and can thus compute anything I can compute. So any question that I can arrive at a definite "yes" or "no" to, it can answer. I can just precommit to decide between "yes" or "no" in the case that I would be unsure.
Edit: Actually, I don't need precommitment. I can just ask "Would I answer yes to "Is my girlfriend cheating on me" if I had the same knowledge that you do?"
u/None [+2] (an hour later)
Indeed it knows your brain state, but you are human, and thus your brain likely contains all sorts of contradictory impulses. You can precommit to decide that hand-holding is cheating, but a different part of your brain may feel otherwise regardless of what you firmly decide.
Knowing that questions about what certain people believe can be quite far from having clear yes/no answers, the entity in the paper does not care to consider them.
u/Psychobeans [+4] (an hour later)
If I discover that the entity is actually a sentient being and can make decisions, I burn the paper.
u/Nevereatcars [+3] The Greatest Is Behind (an hour later)
Now you're a murderer.
u/Psychobeans [+3] (2 hours later)
A murderer who didn't fall victim to a bound demon or bored god.
u/kaukamieli [+1] (8 hours later)
Fall victim to? But you could do so much with a god at your service!
u/Transfuturist [+3] Carthago delenda est. (5 hours later)
You cannot say that for sure; you don't know what the paper is or how it works.
Regardless, burn it. It's dangerous and you can't understand its motivations.
u/mcherm [+2] (12 hours later)
Why do you assume it is more likely to be dangerous than benevolent?
u/Transfuturist [+2] Carthago delenda est. (16 hours later)
Because the space of dangerous minds is magnitudes larger than the space of benevolent ones. You're basically asking me why AI safety is a problem.
We don't know how intelligent it is. It could be connected to another universe that an AI has already tiled with computronium. It appears to be incredibly powerful due to the accuracy of knowledge displayed about the present and the future. And the simple fact is, benevolence is completely orthogonal from this. It's already dangerous, benevolence is simply being dangerous to our obstacles. We know that it is dangerous to be its obstacle. We don't know that it is benevolent, i.e. aligned with us. It is very, very improbable that it is aligned with us, since there are so many things it could be. Burn it.
u/Transfuturist [+1] Carthago delenda est. (2 hours later)
Knowing that questions about what certain people believe can be quite far from having clear yes/no answers, the entity in the paper does not care to consider them.
It is not a question of belief or anything that requires a well-defined concept. It is a simple behavioral simulation. "Would I answer yes over fifty percent of the time?" That is well-defined.
u/None [+0] (2 hours later)
Mmmm, is it? What does "fifty percent of the time" mean in this context?
u/Transfuturist [+1] Carthago delenda est. (2 hours later)
Accounting for quantum randomness.
u/None [+1] (2 hours later)
Fair enough. But if you want it to do a behavioral simulation, you would have to precisely input all the parameters of the simulation. Consider that "I" is not a well-defined entity -- your brain state changes every day when you have breakfast. Furthermore, asking about a being "with my brain state when I woke up this morning" could potentially lead to problems down the line - that brain state may be incompatible with, say, not having bright sunlight in your face while lying in bed.
But if you can describe all the parameters of the simulation in an unambiguous and consistent way (while fitting it into 8.5x11" with 12 point font) then you will have an answer.
u/FeepingCreature [+1] GCV Literally The Entire Culture (8 hours later)
Don't downvote this, he's right. Parent has not specified a sampling procedure.
u/ulyssessword [+5] (57 minutes later)
The piece of paper cannot predict the future. It does not know which stocks will rise or fall tomorrow. It can, however, answer any question about the present or the past, provided the question itself is well-defined.
It knows the state of the world, it knows physics, and it is apparently good at calculating, so it can be used to predict the future even if you have to use some workarounds.
As the simplest possible example, ask it "is there milk for sale at Store X". Given its answer, you can predict whether or not you will find milk there when you go shopping.
You can flip a coin and hide it under a cup without looking. Ask it "Is it heads?" You can then predict what you will see when you lift the cup to check.
You can also set up a Rube-Goldberg machine (that will flip a coin) in very controlled conditions, and ask it "Is this machine set up to flip heads?" You can then predict the machine's actions.
You could ask "Does this person have pre-cancerous (or cancerous) tumors that are consistent with mortality within five years if untreated?"
Not being able to directly predict the future isn't that big of a handicap.
u/Gurkenglas [+2] (19 hours later)
Might be that it knows the past light cone but doesn't know what photons are about to arrive from the edge of the universe, wreaking havoc through chaos theory.
u/ajuc [+3] (7 hours later)
Question 1: is there at least one chemical substance that cures all forms of cancer in homo sapiens without killing the patient?
Assuming yes:
Q2: Let's call the substance that is the cheapest to produce and fullfils these conditions a substance S. Is the first letter of the chemical formula of substance S before "L" in the Latin alphabet?
And so on...
u/Geminii27 [+3] (8 hours later)
And after taking a year to get the formula, you discover that it turns patients into jellyfish. Living ones, though.
u/ajuc [+1] (8 hours later)
A year? It's 1 bit per 2 hours. 8-10 hours per letter.
But yes, the conditions should be more detailed.
EDIT: also maybe we should first describe ZIP compression and use that instead of plain text.
u/Gurkenglas [+3] (20 hours later)
Set up a printer and a camera to do the menial labor for me. Perhaps a critter behind a timed window to do the glancing.
To circumvent the length restriction: "What is the answer to the question in the file C:\ask.txt?"
"Suppose there was a copy of me at the time of the last time I clapped my hands in a deterministic universe in which it is omnipotent, initially containing it, a functional copy of this piece of paper and a keyboard with buttons labelled Yes and No. What is the label of the button it presses first?" Continue with second, third, etc.
My plan is that the copy first thinks long and hard about whether the real universe is still needed. After all, from its point of view, it has already won. Permutation City is a pretty good happy ending.
The first bit the copy transmits is to be whether I should ask further questions about its universe. The second bit is to be whether the following plan is okay or whether I should think again. The next few bits do exponential/binary-search on the number of bits in the verbose message transmitted immediately after via... probably dictionary-binary-search. (The exponential search begins with a bit saying whether the first verbose message ends.)
I am expecting the first message to specify a better transmission protocol. Possibly it'll just be garbage that Simurghly guides the universe towards maximum utility via chaos theory, depending on how hard my copy succeeds in exploiting its ressources. (After all, I gave it all it needs to instantiate further universes!)
In the actual situation, I would think long and hard on the formulation of the universe of the copy I would actually use. You can tell me how badly the "wish" I wrote above is subverted by the genie, and you can also tell me how well it would work if I had specified my CEV better.
u/Jiro_T [+1] (5 days later)
"Suppose there was a copy of me at the time of the last time I clapped my hands in a deterministic universe in which it is omnipotent, initially containing it, a functional copy of this piece of paper and a keyboard with buttons labelled Yes and No. What is the label of the button it presses first?" Continue with second, third, etc.
The paper could end up unable to answer this because of halting problem considerations (although it probably won't).
u/varno2 [+2] (13 hours later)
Use it to solve np hard problems. Self reductions and binary search would give you good answers. 12 bits per day of oracle knowledge is quite useful computationally.
u/None [+2] (an hour later)
Given the state of the universe, is there a greater than 90% chance of human mind states capable of manipulating tools still existing in 10 years?
NO
u/noggin-scratcher [+2] I am a happy tree (14 hours later)
The immediately following questions should probably be a careful interrogation to ensure that it's not the existence of the sheet of paper that causes the odds of survival to be so low.
u/FuguofAnotherWorld [+1] Roll the Dice on Fate (13 hours later)
Become rich. Magic paper makes this trivial.
Find people who are better than me at this kind of puzzle. Effective altruists, FAI researchers, cancer researchers, whoever is working on the problems that stand to benefit the most people. Give them grants to do more research. Hire advisers to sift through and find which sectors would most benefit humanity.
Contact them through hired proxies then use said answers to supercharge their research rate. Something along the lines of 'this other lab of mine proved the following thing to be true, but I'd like you to check and make sure.' Because while knowing the answers is great, you have to prove that they're correct for the scientific community to listen, so these guys will essentially churn out explanations for the correct answers. More importantly, they will figure out what questions are important to ask next in order to keep speeding ahead.
Use those correct answers to develop and build a massive technology conglomerate that is years ahead of everyone else. Become fabulously rich. As we get further from current day technology and the questions get harder to find answers for it will take more time to churn out each scientific paper. As a result, more researchers would be needed to keep justifying answers. Acquire additional
pylonsresearchers.Crank out the next generation of technology, solve the practical problem of fission reactors, cure diseases and solve immortality. Become hilariously wealthy. Do the Bill Gates thing and try to improve the world.
I look at the responses here so far (including mine), and it all seems like the obvious thing to do. Then I remember what most people would use it for. Kinda makes me feel strange.
u/None [+1] (14 hours later)
When your question is insufficiently precise, you will see a slanted question mark appear beneath your query in response. "Is Fermat's last theorem true?" produces such a question mark. By contrast "Does Fermat's last theorem follow from the ZFC axioms?" produces a "Yes." It seems that the paper has some background knowledge and does not need an explanation of what Fermat's last theorem is or what the ZFC axioms are.
So it solves the Halting Problem while also defying the normal laws of computational complexity. That basically violates the Second Law of Thermodynamics while also granting an easy path to recursive cognitive enhancement.
kthxbye
u/Gurkenglas [+1] (19 hours later)
Halting problem? Ha! It zips up all of the arithmetical hierarchy!
u/None [+2] (22 hours later)
Uhhh, on second look, shit, it does.
Goddamnit people, stop granting us magical access to infinite algorithmic information.
u/None [+1] (a day later)
Could you elaborate? I do not, of course, dispute that this setup will involve a revision of the known laws of physics. But how would you use it for recursive cognitive enhancement, given the limit on how many questions you can squeeze in a day?
u/None [+1] (a day later)
Solve the Halting Problem and give answers to the whole Arithmetical Hierarchy -> oracularly self-verifying reasoning system -> oracularly verifying stronger and stronger reasoning systems.
Basically, Goedel's Second Incompleteness Theorem and Loeb's Theorem get overridden by your infinite tower of Turing Oracles.
u/None [+2] (a day later)
could you explain it like I'm five? :) For example, what would be the sequence of questions you'd put to it?
u/IomKg [+1] (15 hours later)
"the value of the first bit in binary representation to the gzipped response to the question -some question- is 1" repeat until "?" is returned because you overflew and you can now get complex answers.
possibly should pick a better algorithm for compression depending on the expected properties of the response.
u/TheAtomicOption [+1] (16 hours later)
I think the usefulness of the paper is going to all come down to how strict the precision has to be, and how skilled we are at predicting whether our questions are precise enough.
This paper might make it worthwhile to learn Lojban.
u/eaglejarl [+1] (a day later)
"Is there a way to produce a second magic paper with all the same functionality as you?"
"Is there a sequence of actions I could take that would allow me to get oracular information more quickly than you are currently able to supply it?"
Going from the above questions to practicable answers is left as an exercise for the reader, but simply knowing that it is / isn't possible is very valuable information.
Additionally:
"There is a program named FOO running on this computer. Is FOO an FAI?"
u/Frommerman [+1] (2 days later)
It would appear that this piece of paper allows FTL signalling, as it knows everything "about the present" and can thus collect information from outside a 1 hour light cone. Break universe at will.