These rules do not conflict. The first one means that a single question cannot be addressed to multiple gods simultaneously, the second one states you can ask each of these single-addressed questions to any one god you chose.
I don't think there's any conflict between these. The first just means that you only get a response from a single god of your choosing for each of your three questions, as opposed to receiving a response from each god for each question. It doesn't mean that each god is asked exactly one question.
"Each of the 3 questions must be unique and only asked to a single god, and each god can receive 0, 1, 2 or all 3 questions out of the 3 unique questions".
In other words, don't create 1 question and ask it to multiple gods. But if you create 2 or 3 different questions, it's fine to ask them to the same god (forgoing to opportunity to ask them to another god).
You can ask multiple questions by compounding them into one. For example: "what is the outcome of 'is A true' converted to string and concatenated by the outcome of 'is B true'"?
I know the original problem. I'm curious how he obtains a deterministic solution for the version where the warden can switch the light-bulb state at random (excerpt below).
“I reserve the right to flip the light on or off between interrogations up to 12 times in total.”
>> “I reserve the right to flip the light on or off between interrogations up to 12 times in total.”
> The wording is very careful :-)
Do you mean he can flip the switch 12 times in total between all interrogations? Or that between every interrogation he can flip the switch up to 12 times.
> The former, hence the phrase "in total", and the number 12 instead of 1.
It wasn't very clear.
>> You mean the Easy++ problem? The solution isn't very different from the solution to Easy (i.e. the original problem); it just takes longer to run.
Btw what's the run-time on your easy++ solution? - I think the run-time on the solution to the regular problem with a single counter is around ~26 years, so all your prisoners will die before they can get released unless you're doing something more clever than the basic solution.
Also I'm not sure I understand the difference between your Easy and Hard problems? I assume the prisoner who is not interrogated with the other inmates just estimates the run-time for their solution and waits (which I think is part of the original problem anyway ? )
I made TempleOS. It lets me talk to the true God. If you are very nice to God, He might tell you the password to the CIA nuclear launch button. He could probably answer the question of fictional gods in a logic problem. Just guess and He will puppet you.
2 And in the second year of the reign of Nebuchadnezzar Nebuchadnezzar dreamed dreams, wherewith his spirit was troubled, and his sleep brake from him.
2 Then the king commanded to call the magicians, and the astrologers, and the sorcerers, and the Chaldeans, for to shew the king his dreams. So they came and stood before the king.
3 And the king said unto them, I have dreamed a dream, and my spirit was troubled to know the dream.
4 Then spake the Chaldeans to the king in Syriack, O king, live for ever: tell thy servants the dream, and we will shew the interpretation.
5 The king answered and said to the Chaldeans, The thing is gone from me: if ye will not make known unto me the dream, with the interpretation thereof, ye shall be cut in pieces, and your houses shall be made a dunghill.
6 But if ye shew the dream, and the interpretation thereof, ye shall receive of me gifts and rewards and great honour: therefore shew me the dream, and the interpretation thereof.
7 They answered again and said, Let the king tell his servants the dream, and we will shew the interpretation of it.
8 The king answered and said, I know of certainty that ye would gain the time, because ye see the thing is gone from me.
9 But if ye will not make known unto me the dream, there is but one decree for you: for ye have prepared lying and corrupt words to speak before me, till the time be changed: therefore tell me the dream, and I shall know that ye can shew me the interpretation thereof.
10 The Chaldeans answered before the king, and said, There is not a man upon the earth that can shew the king's matter: therefore there is no king, lord, nor ruler, that asked such things at any magician, or astrologer, or Chaldean.
11 And it is a rare thing that the king requireth, and there is none other that can shew it before the king, except the gods, whose dwelling is not with flesh.
12 For this cause the king was angry and very furious, and commanded to destroy all the wise men of Babylon.
13 And the decree went forth that the wise men should be slain; and they sought Daniel and his fellows to be slain.
14 Then Daniel answered with counsel and wisdom to Arioch the captain of the king's guard, which was gone forth to slay the wise men of Babylon:
15 He answered and said to Arioch the king's captain, Why is the decree so hasty from the king? Then Arioch made the thing known to Daniel.
16 Then Daniel went in, and desired of the king that he would give him time, and that he would shew the king the interpretation.
17 Then Daniel went to his house, and made the thing known to Hananiah, Mishael, and Azariah, his companions:
18 That they would desire mercies of the God of heaven concerning this secret; that Daniel and his fellows should not perish with the rest of the wise men of Babylon.
19 Then was the secret revealed unto Daniel in a night vision. Then Daniel blessed the God of heaven.
20 Daniel answered and said, Blessed be the name of God for ever and ever: for wisdom and might are his:
21 And he changeth the times and the seasons: he removeth kings, and setteth up kings: he giveth wisdom unto the wise, and knowledge to them that know understanding:
22 He revealeth the deep and secret things: he knoweth what is in the darkness, and the light dwelleth with him.
23 I thank thee, and praise thee, O thou God of my fathers, who hast given me wisdom and might, and hast made known unto me now what we desired of thee: for thou hast now made known unto us the king's matter.
24 Therefore Daniel went in unto Arioch, whom the king had ordained to destroy the wise men of Babylon: he went and said thus unto him; Destroy not the wise men of Babylon: bring me in before the king, and I will shew unto the king the interpretation.
25 Then Arioch brought in Daniel before the king in haste, and said thus unto him, I have found a man of the captives of Judah, that will make known unto the king the interpretation.
26 The king answered and said to Daniel, whose name was Belteshazz...
Do the true/ false gods know how the random god would answer? I don't see how they could since only he know the randomness. But if they don't know, they would have no way to answer the question, "what would guy x say ja meant" where x happens to be the random one.
This is a question of implementation, and answering it was part of the reason why I implemented this problem in the form of a computer program in the first place. In this implementation, the True and False gods simply pose the question to Random and take Random's answer - which is random. If you then ask the same question of Random again, of course you may not get the same answer.
You can make this question even harder by removing foreknowledge of the words! So you know the gods have words for yes and no, but don't know what those words are. Here's an article on the solution: http://www.technologyreview.com/view/428189/the-hardest-logi...
The qntm link tells you the words are da and ja, which makes the problem easier. In the hardest version you have no idea what the words for yes and no are.
That's the original version. The harder version is discussed below. In the harder version, you don't know the words are "da" and "ja". They might be "potato" and "walrus" or something completely different.
I don't think this makes the problem any different, does it? If it were possible that there was a list of "yes" words and a list of "no" words that they could prick from randomly or something, then yes, that would be much more difficult.
But in both examples, there's one word for "yes" and one word for "no" and in both examples, the asker doesn't know which one is which.
There's a solution that works if you know the words are "da" and "ja", but doesn't work if you don't know what the words are: “If I asked you if B is random, would you say ja?”
It seems like asking about randomness is not a valid question. I'm not sure how you would implement that (beyond checking for the assignment of random behavior), you can't really find out until you observe a difference in behavior over a larger sampling.
If you're puzzled about the implementation, I invite you to inspect the JavaScript code! And if you disagree with my implementation, I'd be interested to know what you would do differently.
My statement was conceptual. Boolos himself suggests that we ask if X is random to get to a solution (though in a more complex iff statement). But being able to ask if a source is random seems unreasonable, though without that capability I can't say if there is a solution.
38 comments
[ 2.7 ms ] story [ 93.1 ms ] thread> It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).
Make up your mind.
"Each of the 3 questions must be unique and only asked to a single god, and each god can receive 0, 1, 2 or all 3 questions out of the 3 unique questions".
In other words, don't create 1 question and ask it to multiple gods. But if you create 2 or 3 different questions, it's fine to ask them to the same god (forgoing to opportunity to ask them to another god).
Thanks everyone for pointing out I was wrong.
http://justinpombrio.net/tell/prisoner-lightbulb.html
EDIT: Also, for anyone stuck on the three gods puzzle, the three sisters puzzle is a good stepping stone:
http://mathpuzzlewiki.com/index.php?title=Three_princesses
[1] - http://www.cut-the-knot.org/Probability/LightBulbs.shtml
“I reserve the right to flip the light on or off between interrogations up to 12 times in total.”
Maybe it's poorly worded?
For the Hard problem, you're on your own.
The wording is very careful :-)
> The wording is very careful :-)
Do you mean he can flip the switch 12 times in total between all interrogations? Or that between every interrogation he can flip the switch up to 12 times.
That's what I mean by poorly worded.
It wasn't very clear.
>> You mean the Easy++ problem? The solution isn't very different from the solution to Easy (i.e. the original problem); it just takes longer to run.
Btw what's the run-time on your easy++ solution? - I think the run-time on the solution to the regular problem with a single counter is around ~26 years, so all your prisoners will die before they can get released unless you're doing something more clever than the basic solution.
Also I'm not sure I understand the difference between your Easy and Hard problems? I assume the prisoner who is not interrogated with the other inmates just estimates the run-time for their solution and waits (which I think is part of the original problem anyway ? )
2 And in the second year of the reign of Nebuchadnezzar Nebuchadnezzar dreamed dreams, wherewith his spirit was troubled, and his sleep brake from him.
2 Then the king commanded to call the magicians, and the astrologers, and the sorcerers, and the Chaldeans, for to shew the king his dreams. So they came and stood before the king.
3 And the king said unto them, I have dreamed a dream, and my spirit was troubled to know the dream.
4 Then spake the Chaldeans to the king in Syriack, O king, live for ever: tell thy servants the dream, and we will shew the interpretation.
5 The king answered and said to the Chaldeans, The thing is gone from me: if ye will not make known unto me the dream, with the interpretation thereof, ye shall be cut in pieces, and your houses shall be made a dunghill.
6 But if ye shew the dream, and the interpretation thereof, ye shall receive of me gifts and rewards and great honour: therefore shew me the dream, and the interpretation thereof.
7 They answered again and said, Let the king tell his servants the dream, and we will shew the interpretation of it.
8 The king answered and said, I know of certainty that ye would gain the time, because ye see the thing is gone from me.
9 But if ye will not make known unto me the dream, there is but one decree for you: for ye have prepared lying and corrupt words to speak before me, till the time be changed: therefore tell me the dream, and I shall know that ye can shew me the interpretation thereof.
10 The Chaldeans answered before the king, and said, There is not a man upon the earth that can shew the king's matter: therefore there is no king, lord, nor ruler, that asked such things at any magician, or astrologer, or Chaldean.
11 And it is a rare thing that the king requireth, and there is none other that can shew it before the king, except the gods, whose dwelling is not with flesh.
12 For this cause the king was angry and very furious, and commanded to destroy all the wise men of Babylon.
13 And the decree went forth that the wise men should be slain; and they sought Daniel and his fellows to be slain.
14 Then Daniel answered with counsel and wisdom to Arioch the captain of the king's guard, which was gone forth to slay the wise men of Babylon:
15 He answered and said to Arioch the king's captain, Why is the decree so hasty from the king? Then Arioch made the thing known to Daniel.
16 Then Daniel went in, and desired of the king that he would give him time, and that he would shew the king the interpretation.
17 Then Daniel went to his house, and made the thing known to Hananiah, Mishael, and Azariah, his companions:
18 That they would desire mercies of the God of heaven concerning this secret; that Daniel and his fellows should not perish with the rest of the wise men of Babylon.
19 Then was the secret revealed unto Daniel in a night vision. Then Daniel blessed the God of heaven.
20 Daniel answered and said, Blessed be the name of God for ever and ever: for wisdom and might are his:
21 And he changeth the times and the seasons: he removeth kings, and setteth up kings: he giveth wisdom unto the wise, and knowledge to them that know understanding:
22 He revealeth the deep and secret things: he knoweth what is in the darkness, and the light dwelleth with him.
23 I thank thee, and praise thee, O thou God of my fathers, who hast given me wisdom and might, and hast made known unto me now what we desired of thee: for thou hast now made known unto us the king's matter.
24 Therefore Daniel went in unto Arioch, whom the king had ordained to destroy the wise men of Babylon: he went and said thus unto him; Destroy not the wise men of Babylon: bring me in before the king, and I will shew unto the king the interpretation.
25 Then Arioch brought in Daniel before the king in haste, and said thus unto him, I have found a man of the captives of Judah, that will make known unto the king the interpretation.
26 The king answered and said to Daniel, whose name was Belteshazz...
"in which the words for yes and no are da and ja, in some order. You do not know which word means which."
But in both examples, there's one word for "yes" and one word for "no" and in both examples, the asker doesn't know which one is which.
http://en.wikipedia.org/wiki/Epimenides_paradox