This is a bit of an old puzzle.
I actually don’t agree with the common solution.
Puzzle:“http://io9.com/can-you-solve-the-hardest-logic-puzzle-in-the-world-1642492269”
Solution
I will leave that for y’all to cogitate for a while before I post my objection.
So what’s your problem?
Specifically, I think there is a false induction because it is ignored that all dragons know for absolute certain that all other dragons can see at least 98 GED. Regardless of how many know-levels (he knows that he knows that he knows…), none of these dragons will imagine that any dragon thinks there could be less than 98 GED.
Simplify it and consider 4 dragons.
A dragon doesn’t know whether there are 3 or 4 GED.
Suppose he thinks there are 3. That means that all the other dragons see 2 GED: the other dragons might consider there are 2 or 3 GED.
That’s the end of the line: we can’t trace it further to the case where a dragon might posit another dragon posits there is only 1 GED, because we know for a gold-standard fact that every dragon knows every dragon knows there are at least 2 GED.
If you drop it to 3 dragons, then it works.
Your objection seems valid. I thought there was something fishy about the whole thing.
“And so on Thursday morning the Executioner appeared to take the condemned to the gallows and the prisoner, who had thought themself immune, was indeed surprised, just as the Judge had decreed.”
Yes, the standard solution does suspiciously seem like drawing conclusions from a hypothesis contrary to fact, which I had always been assured was a logical fallacy.
So the real solution is that each dragon would say to itself “Hmm, tell us something we don’t know,” and go about its business.
Bubblecar said:
So the real solution is that each dragon would say to itself “Hmm, tell us something we don’t know,” and go about its business.
Yes. This so-called Guru has brought nothing to the table.
I’m not a religious man, but if you’re out there, help us, Martin!
BTW Kothos was having trouble regging here.
dv said:
BTW Kothos was having trouble regging here.
Kothos is trying to come back?
At the moment the only puzzle seems to be why any reasonably intelligent person would accept the analysis given in the linked paper when it is so obviously wrong.
If I find a solution, I’ll let you know.
Done some searching on this, and now I’m even more confused.
Absolutely no-one came up with the dv solution (and I’ve looked at about 100 comments on it).
Basically the weight of opinion is so strongly against me that it is almost certain I am wrong but I can’t see how.
sibeen said:
dv said:
BTW Kothos was having trouble regging here.
Kothos is trying to come back?
Yes
email cb88, I think that’s how the more recent boat people were let in.
poikilotherm said:
email cb88, I think that’s how the more recent boat people were let in.
temporary registration visas
I will try to look at this more rigorously but I agree that there seems to be something interesting about the way ‘A thinks that B thinks’ is being construed, what it is precisely equivalent to, and what can be construed from it.
The standard solution seems to be based on showing that the number of GED that is ‘common knowledge’ – what everyone knows that everyone knows that … ad infinitum – is 0, because no one can construct A1 knows that A2 knows that … A100 knows there is a GED chains. But I don’t think that’s the issue.
I think we can all agree that the n=3 case resolves trivially (NPI). If it can be shown to work for n=4 then I’ll accept it will work for n=100.
dv said:
I think we can all agree
Fk off
The solution is probably right.
I think it’s one of those things where the maths is done first and then a story is made up and laid over the top of it.
dv said:
Basically the weight of opinion is so strongly against me that it is almost certain I am wrong but I can’t see how.
I can’t either.
dv said:
I think we can all agree that the n=3 case resolves trivially (NPI). If it can be shown to work for n=4 then I’ll accept it will work for n=100.
NPI?
dv said:
I think we can all agree that the n=3 case resolves trivially (NPI). If it can be shown to work for n=4 then I’ll accept it will work for n=100.
OK, I’ve now read the xkcd thread that goes through the objections in detail, and I’m satisfied that everyone in the world except dv actually has it right, and dv has it wrong.
The Rev Dodgson said:
dv said:
I think we can all agree that the n=3 case resolves trivially (NPI). If it can be shown to work for n=4 then I’ll accept it will work for n=100.
OK, I’ve now read the xkcd thread that goes through the objections in detail, and I’m satisfied that everyone in the world except dv actually has it right, and dv has it wrong.
I agree.
Note that the xkcd thread deals with a subtly different problem.
The Rev Dodgson said:
dv said:
Basically the weight of opinion is so strongly against me that it is almost certain I am wrong but I can’t see how.
I can’t either.
dv said:
I think we can all agree that the n=3 case resolves trivially (NPI). If it can be shown to work for n=4 then I’ll accept it will work for n=100.
NPI?
NPI = no pun intended