There were not turtles all the way down.

Logic.

Lol, that will fit on the back of my flat phone... but can we do any better?

BTM and MDZ are trolling. They aren't this dense.

It is now common knowledge that at least one dragon has green eyes.

I am too tired to type out "Sorry. Meant to do with 5 dragons" and the whole ABCDE thing.

After the (m - 1)th midnight has passed with nothing happening, is it now common knowledge that at least m dragons have green eyes?

That's gotta be it. So if common knowledge is (paraphrased from wiki) special knowledge of p in a group of agents G when all the agents in G know p, they all know that they know p, they all know that they all know that they know p, and so on ad infinitum. Is it a true statement that before the announcement because none knows their own eye color, they don't have common knowledge because the ad infinitum is not established? That before the announcement they knew p, but all only knew they all knew they all knew... p to G-1?

Edit:
And so we can also say after the announcement they all have common knowledge that at least one dragon has green eyes. After the first night no dragon changes they all have common knowledge that at least two dragons have green eyes... after the 99th night no dragon changes they all have common knowledge that at least 100 dragons have green eyes.

Shutup brian you weren't trolling. Neither was Masque, though at least he offered an excuse

But then everyone knows it's completely impossible for anything to happen on e.g. the 37th midnight, and when nothing actually does happen their knowledge gets updated somehow.

Yeah, it's kind of a mind f*** because since they all can see 99 dragons with GE, they all know not to expect anything until day 99. But since they all don't know their own eye color, they don't know if all the other dragons expect something to happen on day 98. And since they know all others don't know their own eye color, they don't know if each of the others expect the rest to expect something to happen on day 97... so they each just gotta wait, lol.

Who said I was?

Yes, their knowledge gets updated in the same way it did when the stranger spoke. On the 37th day they all already knew nothing was going to happen on the 37th midnight, but it wasn't common knowledge. On the 38th day it is.

Yes.

Trolling or not, clearly what BTM and MDZ were saying is false, the dragons cant work out their own eye colour just by meeting each other. The interesting aspect of this situation though is that the induction relationship still holds.

In more technical language, let P_n be the proposition "If there are n dragons with green eyes, they (and only they) will turn on the midnight of day n, and this fact is common knowledge". Now if we define day one as the day they all first meet around the campfire and there is no stranger, then the induction statement "If P_m is true then P_(m+1) must be true" is still actually correct. The stranger isn't necessary for the induction process to be true, just for it to "get started".

Earlier we were trying to think of some other things that would prime them to work it out.

Can you think of anything more clever than just a stranger's announcement, like what else could give them that common knowledge? A talking parrot a stupid dragon child brought to an island show and tell? A romantic theatre rendition of Green Eyed Dragon Bitch*? A boat sails by named the "ALOOYAA Green Eyed Dragon?"

*female dragons are called bitches, fun fact

Rumor has it that the existence of chickens* can be explained by Bayesian dragons who understand Kelly betting being presented with this problem.

*male chickens do not have penises, fun fact. I am not making that part up.

It depends on how loose you are with your definitions:

http://phenomena.nationalgeographic....s-kept-theirs/

I know about chicken penises because I learned about duck penises. I learned about duck penises because I saw an article about a paper in a journal a few years ago.

O, beware, my lord, of jealousy;
It is the green-eyed monster which doth mock
The meat it feeds on….

I don't think that's true.

The new information given to them by the announcement was every dragon now knows it is a 100% fact all other 99 dragons know every dragon knows at least one dragon has green eyes.

I think I worded that correctly.

If you equate right off the bat "infallibly logical" with "they must know something is 100% before it becomes an actuality" or "they assume absolutely nothing", then this is a logic problem which you should solve in 3-5 minutes and not even need to know/use terms such as "common knowledge". It's one of those you either get it asap or it takes forever problems.

Is "infallibly logical" the best phrase to use to make most people think the above? Who knows. Worked for me back in college when I first encountered this problem.

The Boole logical puzzle is like infinitely harder than this IMO and I am about a week in trying to figure it out. Determined to not look up the answer. I'm sure someone figured that out in a few minutes like I did the dragon one.

Different minds think differently about different stuff.

In think "infallibly logical" works. Your underlined statement is incomplete, it needs to continue with the recursive: each knows that each knows that each.... That's why it's not easy to fit in the back of my phone, at least without using a term defined to mean just that, like "common knowledge."

When I read that last night, under the influence of another type of green monster, I thought you wrote something about moth dicks, and I laughed.

Well you can just think that and not write it out

a strategy insufficiently employed on 2+2

says the man with 65k posts