But they do not represent the groups to which they belong AS THEY ARE IGNORANT as to their own eye colour.
THey can count until the end of time, that will not change.
What you are asking me to believe is that counting days can inform a logician as to the colour of his own eyes; that is absurd.
As no more information is available to anyone on day 100 as day 1, why don’t they all leave on day 1?
The fact is they will remain ignorant.
Put yourself in their shoes.
Let us say that I know what your eye colour is.
Now tell me when you leave and why!
Then I will reveal why you are wrong by telling you what your eye colour is.
That is an ad hominem fallacy.
You know that were this situation duplicated no logician at the end of the time would be able to nominate his own eye colour.
That is an irrefutable fact.
It is completely obvious that I am a much better logician than you.
This little problem is designed to trap those who have a poor understanding by showing a solution that cannot work.
So if you were told that matter is made of this or that by a bunch of guys who thought they understood physics, would you believe them or tell them that you know more than they?
The puzzle works because you start by considering the case of 1 blue-eyed person and extrapolate upwards.
Consider the case of 1 brown-eyed person.
He would NEVER know what color eyes he has given what the guru said. Could be green. Could be Purple. Could be anything but blue.
You can’t extrapolate anything if your eyes aren’t blue.
In the mean while, if anybody else wants to respond to my proofs for 1 blue-eyed person or 2 blue-eyed people, please do so, whether it’s to affirm it’s a sound argument, to say you don’t get one of the logical steps or premises, or to explain why you disagree.
The logic works if you have to pass through all the stages (1 person, 2 people …). But when you start with large groups of people, that logic no longer applies. The connection to the one blue-eyed person which is the start of the logical chain is broken and can’t be rebuild with what the guru says.
Do you see that HC is right when he says that the guru is not saying anything new?
So far I’ve proved that 1 person could figure it out. I’ve also proved that 2 people could figure it out. If you think that the chain is broken, how many steps do I have to take to dissuade you? Would you like to see the proof for 3? How many will it take?
"Any islanders who have figured out the color of their own eyes then leave the island, and the rest stay. Everyone can see everyone else at all times and keeps a count of the number of people they see with each eye color "
There was nothing in the rules stating that only blue eyed people were to play.
As Hobbes pointed out, the guru didn’t really add any information, but merely inspired the game to begin amongst the blue eyes. Actually everyone should have started deducing at that point which would have caused the brown eyes to leave also.
The brown eyes would have been leaving also.
Actually everyone should leave except anyone with a unique color.
I started the proof for how it works for blue-eyed people. First you consider the case of 1 person – that works. Then you consider the case of 2 people – that works because the 1-person case works. Next I may prove the case of 3 people, which works because the 2-person case works. I can prove upwards and upwards indefinitely.
But with the brown-eyed people, the logic fails for 1 person, and I explained why. So the logic must necessarily be different for the brown-eyed people, if there is any logic at all, and I haven’t seen any for it. So…the onus is on you.
Emm… that isn’t an explanation. That was merely assertions. And seem to be incorrect.
The same logic works for all eye colors except unique colors. Everyone but those should leave the island.
How is the guru changing anything other than merely starting the game?