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### Re: Math Fun

Posted: Mon Apr 22, 2013 6:58 am
No. YOU decided to "add 50", apparently just to makeup and argument. I never said anything close to that.
And if you can't figure out how to count 50 days and deduce that no one left the island, I am not interested in your responses.

### Re: Math Fun

Posted: Mon Apr 22, 2013 7:11 am
James S Saint wrote:And if you can't figure out how to count 50 days and deduce that no one left the island, I am not interested in your responses.

Well, I guess that leaves you interested in the responses of Fixed Cross and no one else.

### Re: Math Fun

Posted: Mon Apr 22, 2013 7:25 am
Well yeah, if you are merely trying to win an online argument, not the slightest interested in the truth of the situation and perhaps learning something, then I am truly only interested in the others.

### Re: Math Fun

Posted: Mon Apr 22, 2013 7:35 am
Anyway 'deducing that no one left the island' is completely separate from 'counting 50 days'. You deduce that no one left the island by looking at them at seeing that no one left. You also just happened to have counted 50 days. Two not apparently related facts.

So, yes, I CAN count 50 days.
And I CAN look at other people and notice if no one left.

What I can't do is use those two facts to deduce my own eye color.

### Re: Math Fun

Posted: Mon Apr 22, 2013 7:42 am
Well maybe that is why you aren't a "perfect logician".

### Re: Math Fun

Posted: Mon Apr 22, 2013 8:02 am
Mm, good one.

### Re: Math Fun

Posted: Mon Apr 22, 2013 12:24 pm
Nothing has been said since my presentation of the correct solution 2 pages ago. I suggest not saying anything if you have nothing to say.

It's basically just been Carleas trying his level best to draw a more precise solution presentation from James (well, since more than just 2 pages ago), yet being met only by distraction, diversion and accusation. You can't just accuse others of being "imperfect logicians" just because they don't accept solutions that won't be presented in a detailed enough way such as to uncover their faults more clearly.

I think it's pretty safe to say that we're never going to get that from him, so there's nothing left to say. His answer will be that he's already done it, nobody excepting it on the grounds that he clearly hasn't aside - that's our fault for not understanding and not his. Whatever.
You're either one of those who protest that there "must" be a better solution than the correct one "because the islanders are perfect logicians" and everyone else is accused of not being so because we don't agree, or you've long accepted the correct solution and understood why it is the only consistent solution based on nothing but certain knowledge and deduction - as is all the puzzle asks.
And we all know who belongs to which group so...

### Re: Math Fun

Posted: Mon Apr 22, 2013 2:51 pm
If the islanders care about getting off the island as quickly as possible and if we want to complicate the simplicity of the puzzle then ...

The islanders could accelerate the process by mentally skipping the days that don't contribute 'useful' information. They know that nobody is going to leave on day 4, 5, 6, ... 96 so they deduce that they can consider night one after the guru speaks as the night when 97 blues would leave if there are 97 blues. Being 'perfect logicians', they realize that they don't need to wait.

Uncomfortable problems with the idea:
It bypasses the logical path that was open by the guru. Without that path, the browns can think exactly the same thing. Both brown and blue islanders leave on day 4, but how can any individual know their own eye color? They can't. The 'solution' is inconsistent.

It requires a leap of faith based on the concept of 'perfect' logician to start from day 9x.

### Re: Math Fun

Posted: Mon Apr 22, 2013 3:27 pm
phyllo wrote:The islanders could accelerate the process by mentally skipping the days that don't contribute 'useful' information.

There aren't any days that don't contribute useful information. Every day raises the base, and without each day's raise, the next day's isn't possible. You can't raise the base case to 97 before you raise it to 96, or to 96 before you raise it to 95, or to 95 before...

This doesn't depend on whether or not they want to get off the island, but on the common knowledge they use to deduce their eye color.

### Re: Math Fun

Posted: Mon Apr 22, 2013 3:39 pm
Carleas wrote:
phyllo wrote:The islanders could accelerate the process by mentally skipping the days that don't contribute 'useful' information.

There aren't any days that don't contribute useful information. Every day raises the base, and without each day's raise, the next day's isn't possible. You can't raise the base case to 97 before you raise it to 96, or to 96 before you raise it to 95, or to 95 before...

This doesn't depend on whether or not they want to get off the island, but on the common knowledge they use to deduce their eye color.

The problem with common knowledge is that they already have it. Everyone can already see 99 people with blue eyes. They know that nobody will leave on day 1 ... 97. That's why the problem seems so artificial. It prompts a search for 'faster' solutions.

### Re: Math Fun

Posted: Mon Apr 22, 2013 4:08 pm
phyllo wrote:If the islanders care about getting off the island as quickly as possible and if we want to complicate the simplicity of the puzzle then ...

The islanders could accelerate the process by mentally skipping the days that don't contribute 'useful' information. They know that nobody is going to leave on day 4, 5, 6, ... 96 so they deduce that they can consider night one after the guru speaks as the night when 97 blues would leave if there are 97 blues. Being 'perfect logicians', they realize that they don't need to wait.

Uncomfortable problems with the idea:
It bypasses the logical path that was open by the guru. Without that path, the browns can think exactly the same thing. Both brown and blue islanders leave on day 4, but how can any individual know their own eye color? They can't. The 'solution' is inconsistent.

It requires a leap of faith based on the concept of 'perfect' logician to start from day 9x.

The browns and blues are in the same situation, thus it doesn't matter which is being counted; the blues or the browns.

### Re: Math Fun

Posted: Mon Apr 22, 2013 4:22 pm
phyllo wrote:If the islanders care about getting off the island as quickly as possible and if we want to complicate the simplicity of the puzzle then ...

The islanders could accelerate the process by mentally skipping the days that don't contribute 'useful' information. They know that nobody is going to leave on day 4, 5, 6, ... 96 so they deduce that they can consider night one after the guru speaks as the night when 97 blues would leave if there are 97 blues. Being 'perfect logicians', they realize that they don't need to wait.

Uncomfortable problems with the idea:
It bypasses the logical path that was open by the guru. Without that path, the browns can think exactly the same thing. Both brown and blue islanders leave on day 4, but how can any individual know their own eye color? They can't. The 'solution' is inconsistent.

It requires a leap of faith based on the concept of 'perfect' logician to start from day 9x.

Why 97? Why did you stop at 96? If I see 99, I know nobody is going to leave on day 96, 97, and 98 as well. I don't know why you stopped at 96.

### Re: Math Fun

Posted: Mon Apr 22, 2013 4:28 pm
Now you are getting close to asking the right question.

Of course if you would answer one honestly, you could get there a lot sooner (like 3-4 pages ago).

### Re: Math Fun

Posted: Mon Apr 22, 2013 4:34 pm
There's some number which makes sense. I'll take James' word that it's 97 because he's been thinking about it more than me.

### Re: Math Fun

Posted: Mon Apr 22, 2013 4:47 pm
I'm not asking 'which number makes sense' though.

Your reasoning involved knowing what days nobody is going to leave on. If that's the route, you end at 98, not 96.
If you end at 96, you must be using some criteria other than what days we know nobody is going to leave on.
What is it?

### Re: Math Fun

Posted: Mon Apr 22, 2013 4:48 pm
James S Saint wrote:Now you are getting close to asking the right question.

Of course if you would answer one honestly, you could get there a lot sooner (like 3-4 pages ago).

I don't think you're one to talk about honest questions in this thread.
"What is an eye?"

### Re: Math Fun

Posted: Mon Apr 22, 2013 4:59 pm
phyllo wrote:There's some number which makes sense. I'll take James' word that it's 97 because he's been thinking about it more than me.

My argument that I presented with a few pages back debunked the whole "If there's 100, you can start with 97" argument.
The reasoning is that, no matter what number there are, his idea is that you always start with 2 less than the person sees.
There are 2 problems with this:

1) If I see 99, then I start with 97, but I don't know that the 99 I'm seeing are starting with 97. They might only see 98, in which case they'd be starting at 96.
2) You end up using information that would be the case regardless of your eye color to deduce your eye color (namely, that nobody leaves after 3 days -- I demonstrated, and will demonstrate again if necessary, that following the plan, nobody would have left after 3 days regardless of your eye color).

### Re: Math Fun

Posted: Mon Apr 22, 2013 5:09 pm
Flannel Jesus wrote:
phyllo wrote:There's some number which makes sense. I'll take James' word that it's 97 because he's been thinking about it more than me.

My argument that I presented with a few pages back debunked the whole "If there's 100, you can start with 97" argument.
The reasoning is that, no matter what number there are, his idea is that you always start with 2 less than the person sees.
There are 2 problems with this:

1) If I see 99, then I start with 97, but I don't know that the 99 I'm seeing are starting with 97. They might only see 98, in which case they'd be starting at 96.
2) You end up using information that would be the case regardless of your eye color to deduce your eye color (namely, that nobody leaves after 3 days -- I demonstrated, and will demonstrate again if necessary, that following the plan, nobody would have left after 3 days regardless of your eye color).

No you didn't (again).
What you debunked (again) was merely that a person could not just take "2 less than he sees".
As always, you rush to conclude your own success.

### Re: Math Fun

Posted: Mon Apr 22, 2013 5:19 pm
James S Saint wrote:What you debunked (again) was merely that a person could not just take "2 less than he sees".

That's what the "start with 97" argument WAS. "Take 2 less than he sees" = "start with 97". That's what I debunked. Yes. The only solution you offered which involved starting from 97 was debunked. So unless there's a new one, I don't see why we're still thinking it's a good idea to start from 97.

### Re: Math Fun

Posted: Mon Apr 22, 2013 5:24 pm
Flannel Jesus wrote:
James S Saint wrote:What you debunked (again) was merely that a person could not just take "2 less than he sees".

That's what the "start with 97" argument WAS. "Take 2 less than he sees" = "start with 97". That's what I debunked. Yes. The only solution you offered which involved starting from 97 was debunked. So unless there's a new one, I don't see why we're still thinking it's a good idea to start from 97.

No it wasn't "what the 97 argument was". Again, merely trying to claim a victory.
The argument was that IF EVERYONE STARTS WITH THE SAME NUMBER, IT WILL ALWAYS WORK.
The 97 was an example. When you started questioning it, I rushed, mistakenly, into thinking "well just take 2 less than you see". Okay, it isn't THAT simple. You can't just take 2 less than you see.

### Re: Math Fun

Posted: Mon Apr 22, 2013 6:31 pm
Urgh.
The whole reason this 97-nonsense (or 98/96/99 whatever) doesn't work has already been covered.

There are 161700 combinations of 97 blues amongst 100. Just because everyone can know that everyone can know that everyone sees 97, doesn't mean anyone has any clue about which combination is the one that everyone is hypothesising about when they are thinking "well IF there were the only those 97, they could leave on the 1st day", as in the proposed 97 "solution".

As such, nothing is gained as exhaustive knowledge when nobody leaves on the 1st day, so there is nothing firm on which to continue to deduce about 98 on the next day, and so on. It also falls foul to the transfer of the knowledge of 100 if there were only 100 onto hypotheses about the knowledge of 97 if there were only 97 (i.e. out of context). Also already covered.

When the correct solution has built up knowledge about whether 97 leave on the 97th day, the number 97 is actually founded on something definite and tested about 96, 95, 94 and so on, right down to 1, and the solid irrefutable logic that if there was 1 blue-eyed islander and he saw no blue-eyed islanders, and the Guru said her words, he would leave on the first day. If there were 2, and each saw 1, + Guru words, and it was tested that nobody left after the first day, then they both know they each have blue eyes too, and so on, with each day being absolutely necessary in order to have a firm, undeniable logical backing to what 97 would do - which is shown can ONLY be definitely and exhaustively known on the 97th day, just like what 100 would do can only be known on the 100th day when they can finally all leave with this definite and exhaustive knowledge.

### Re: Math Fun

Posted: Mon Apr 22, 2013 6:36 pm
If they had all started their count from 97, would it have worked?
If they had all started their count from 50, would it have worked?
If they had all started their count from 01, would it have worked?

### Re: Math Fun

Posted: Mon Apr 22, 2013 10:31 pm
If the guru said "I see 97 with blue eyes", it would work.
If she said "I see 50 with blue eyes" it would work.
If she said "I see 01 with blue eyes" it would work.

If everyone just picked a number out of thin air, even if they all happened to pick the same number, it would not work.

### Re: Math Fun

Posted: Mon Apr 22, 2013 11:11 pm
James S Saint wrote:If they had all started their count from 97, would it have worked?
If they had all started their count from 50, would it have worked?
If they had all started their count from 01, would it have worked?

Not without the Guru imparting information that would go against the logically deduced expected result when going only by what can be seen for definite about the eye colour of all others, and thereby revealing information about the one unknown to any one blue-eyed islander: their own eye colour. THAT is the key. They are the ONLY two possibilities.

As Carleas says, if the Guru said she can see 97 people who have blue eyes, and they can start their count from 97, if the Guru said she can see 50, they can start from 50, just like they can start from one if and only if the Guru says she can see someone who has blue eyes.

### Re: Math Fun

Posted: Mon Apr 22, 2013 11:37 pm
Really?
Is the number, the guru says, some secret code which allows them to skip days?